Laboratory work on metrology, standardization and certification. Laboratory workshop on the discipline "Metrology, standardization and certification" Practical work on metrology standardization and conformity assessment

MINISTRY OF EDUCATION AND SCIENCE OF RUSSIA

Federal State Budgetary Educational Institution of Higher Professional Education "Yugorsk State University" (SGU)

NIZHNEVARTOVSK OIL COLLEGE

(branch) of the federal state budgetary educational institution

higher professional education "Ugra State University"

(NNT (branch) FGBOU VPO "YUGU")

METROLOGY, STANDARDIZATION AND CERTIFICATION

Guidelines for performing laboratory work

for students of all forms of education of educational institutions of secondary vocational education.

Nizhnevartovsk 2015

TOPICS OF LABORATORY WORKS ON THE DISCIPLINE

"METROLOGY STANDARDIZATION AND CERTIFICATION"

Number

Number and name of the lesson

Number of classroom hours

form of control

1.

Laboratory work No. 1 "Measurement of parts with caliper tools"

2

2.

Laboratory work No. 2 “Measurement of parts with a micrometric tool

2

3.

Laboratory work No. 3 "Measuring parts with indicator devices"

2

4.

Laboratory work No. 4 "Measurement of the plug gauge"

2

5.

Laboratory work No. 5 "Surface roughness"

2

Lab #1

MEASURING PARTS WITH ROD INSTRUMENTS

Objective

To study the device, the principle of measurement and metrological characteristics of calipers.

Measure the given part with a caliper.

Draw a sketch of the part with actual dimensions.

ROD INSTRUMENTS

To measure linear dimensions by the absolute method and to reproduce dimensions when marking parts, caliper tools are used, which combine under this name a large group of measuring instruments: calipers, caliper depth gauges, caliper gauges, caliper gauges, etc.

The most common type of caliper is the caliper. There are several models of calipers (GOST 166-80).

Fig.1

Caliper ШЦ-II with bilateral arrangement of jaws (Fig. 1, b) is designed for external and internal measurements and marking work. Consists of the same main parts as ShTs-I, but has an auxiliary microfeed frame 4 for precise frame movement 1 on the bar 5 . To do this, you must first fix the auxiliary frame 4 lock screw 3 and then turning the nut 6 by microscrew 7 , move the measuring frame along the rod. As a rule, this feed is used to accurately set the size on the caliper when marking. The pointed sponges of the ShTs-II caliper are used for marking or measuring external dimensions in hard-to-reach places. The lower jaws for measuring internal dimensions have cylindrical working surfaces. The size of the jaws when flattened is usually 10 mm and defines the smallest internal dimension that can be measured with this caliper. For internal measurements, the size of the jaws indicated on their side should be added to the scale reading. Calipers type ШЦ-II have verniers with a division value of 0.1 and 0.05 mm and measurement limits of 0-160, 0-200, 0-250 mm.

Caliper ШЦ-III does not have upper pointed jaws and a device for micro-feeding of the measuring frame. It is used for external and internal measurements using the same lower jaws as those of ShTs-II. The scale division of the vernier is 0.1 and 0.05 mm, the measurement limits are from 0 to 2000 mm.

Depth gauge(Fig. 2) is used to measure depths and protrusions. It consists of a base 1 , bars 6 with basic millimeter scale, measuring frame 3 , locking screw 2 , micrometric feeders 5 , locking screw 4 , nuts and screws 7 micrometric feed and vernier 8 .

Fig.2

Fig.3

When marking vertical surfaces, the height gauge with the size set on the scale and vernier (in this case, it is recommended to use the microfeed of the frame) moves along the plate along the marked workpiece. The tip of the marking leg draws a horizontal line on the surface of the workpiece.

READING DEVICE

The design of the reading device is based on a rod (measuring ruler) with the main scale applied on it with a division interval of 1 mm. Every fifth division of the rod scale is marked with an elongated stroke, and every tenth division is marked with a longer stroke with the corresponding number of centimeters.

A measuring frame moves freely along the bar, on the bevel of which (opposite the millimeter scale of the bar) an additional scale, called a vernier, is applied. Nonius is used to count fractional millimeters.

The reading of measurements in a vernier device is based on the difference between the intervals of divisions of the main scale and, additionally, the vernier scale. Nonius has a small number of divisions n(10, 20 or 50 stroke divisions). The zero stroke of the vernier acts as an arrow and allows you to read the size in millimeters on the main scale.

Nonius division price With equal to the division value of the main scale a\u003d 1 mm divided by the number of divisions of the vernier scale n :

.

Nonius are used with a division value of 0.1; 0.05 mm and in rare cases 0.02 mm. Vernier division interval depends on the accepted modulo value , which is selected from the numbers 1; 2; 3; 4 or more. But it must be borne in mind that with an increase in the module, the length of the additional vernier scale increases and the overall dimensions of the entire reading device increase. Vernier division interval taken as a multiple of the division interval of the main scale

,

where - modulus of the vernier characterizing the extension of the vernier scale or the ratio between the values ​​of the intervals of the main scale and the vernier.

Vernier scale length

For example, let's take the price of division of the vernierWith =0.1 mm with module
, then the division interval of the vernier scale
mm. All subsequent strokes of the vernier are applied at the same interval. Due to the fact that the intervals of divisions of the vernier are smaller than on the main scale, the lag of the position of the vernier strokes from the strokes of the main scale gradually accumulates and the tenth stroke of the vernier coincides with the ninth stroke of the main scale (Fig. 4).

Fig.4

For the convenience of counting fractional millimeters, caliper tools with a vernier scale modulus equal to 2 are more often produced.

When determining the size of the part, proceed as follows. If the zero stroke of the additional vernier scale coincided with any stroke of the main scale, then the value of the measured quantity is read off only on the main scale in mm.

If the zero stroke of the vernier does not coincide with any stroke of the main scale, then the reading is obtained from two parts. An integer in millimeters is taken on the main scale to the left of the zero stroke of the vernier and a fraction of a millimeter is added to it, obtained by multiplying the division price of the vernier by the ordinal number of the stroke of the vernier scale, which coincided with the stroke of the main scale (Fig. 4, b,c).

Objective.

Caliper model and its main metrological characteristics. Method of measurement.

Control questions

Name the types of calipers.

Models of calipers, their design features and purpose.

How are integer and fractional fractions of millimeters counted during measurements? Nonius device.

For what purposes is the thickness of the jaws marked on some models of calipers?

What is a depth gauge used for?

What is the height gauge used for?

Literature

Lab #2

MEASURING PARTS WITH MICROMETRIC INSTRUMENTS

Objective

To study the device, the principle of measurement and the metrological characteristics of micrometric instruments.

Measure the part with a smooth micrometer and give a conclusion about the suitability of the part.

MICROMETRIC INSTRUMENTS

Micrometric instruments are widely used means of measuring external and internal dimensions, depths of grooves and holes. The principle of operation of these tools is based on the use of a screw-nut pair. A precise micrometer screw rotates in a fixed micronut. From this knot these instruments got their name.

In accordance with GOST 6507-78, the following types of micrometers are produced:

MK - smooth for measuring external dimensions;

ML - sheet with a dial for measuring the thickness of sheets and tapes;

MT - pipe for measuring the thickness of the walls of pipes;

МЗ - gear measuring for measuring the length of the common normal of gears;

MVM, MVT, MVP - micrometers with inserts for measuring various threads and parts made of soft materials;

MP, MRI - lever micrometers;

MV, MG, MN, MN2 - desktop micrometers.

In addition to the listed types of micrometers, micrometric inside gauges (GOST 10-75 and GOST 17215-71) and micrometric depth gauges (GOST 7470-78 and GOST 15985-70) are produced.

Almost all manufactured micrometers have a division value of 0.01 mm. The exception is lever micrometers MP, MP3 and MRI, which have a division value of 0.002 mm. The measurement ranges of smooth micrometers depend on the size of the bracket and are: 0-25, 25-50, ..., 275-300, 300-400, 400-500, 500-600 mm

In Fig.1, a, b the construction and scheme of a smooth micrometer are shown. In the holes of the bracket 1 pressed on one side fixed measuring foot 2 , and on the other - the stem 5 with a hole that guides the micrometer screw 4 . micrometer screw 4 screwed into the micronut 7 having cuts and external threads. A special adjusting nut is screwed onto this thread. 8 , which compresses the micronut 7 until the gap is completely selected in the “microscrew-micronut” connection. This device provides precise axial movement of the screw relative to the micronut depending on the angle of its rotation. For one revolution, the end of the screw moves in the axial direction by a distance equal to the thread pitch, i.e. by 0.5 mm. A drum is put on the micrometer screw 6 , fixed with an adjusting cap-nut 9 . A special safety mechanism is mounted in the cap-nut 12 , connecting the cap-nut 9 and ratchet 10 , for which it is necessary to rotate the drum 6 during measurements. The safety ratchet mechanism, consisting of a ratchet wheel, a tooth and a spring, in case of excess force between the jaws of 500-900 cN, disconnects the ratchet 10 from the mounting cap 9 and drum 6 , and it starts to turn with a characteristic click. In this case, the micrometer screw 4 does not rotate. To fix the screw 4 in the required position, the micrometer is provided with a locking screw 11 .

Fig.1

On the stem 5 micrometer marked scale 14 with divisions through 0.5 mm. For ease of reference, even strokes are drawn above, and odd strokes below the solid longitudinal line. 13 , which is used to count the drum rotation angles. A circular scale is marked on the conical end of the drum 15 , which has 50 divisions. If we take into account that for one revolution of the drum with fifty divisions, the end of the screw and the cut of the drum are moved by 0.5 mm, then turning the drum by one division will cause the movement of the end of the screw equal to 0.01 mm, i.e. the division price on the drum is 0.01 mm.

When taking a reading, use the scales on the stem and drum. The cut of the drum is an indicator of the longitudinal scale and registers readings with an accuracy of 0.5 mm. To these readings add a reading on the scale of the drum (Fig. 1, v).

Before measurement, the correct zero setting should be checked. To do this, it is necessary to rotate the microscrew with a ratchet until the measuring surfaces of the heel and the screw come into contact or these surfaces come into contact with the setting measure. 3 (fig.1, a).

Ratchet rotation 10 continue until a characteristic click. The installation is considered correct when the end of the drum coincides with the extreme left stroke of the scale on the stem and the zero stroke of the circular scale of the drum coincides with the longitudinal line on the stem. If they do not match, it is necessary to fix the microscrew with a stopper. 11 , unscrew the adjusting cap-nut by half a turn 9 , turn the drum to the position corresponding to zero, fix it with a cap-nut, release the microscrew. After that, you should once again check the correctness of the “zero setting”.

Micrometric instruments also include a micrometric depth gauge and a micrometric inside gauge.

Micrometer depth gauge(fig.2, a) consists of a micrometer head 1 , pressed into the base hole 2 . The end of the microscrew of this head has a hole where replaceable rods are inserted with split springy ends 3 with spherical measuring surface. Replacement rods have four sizes: 25; 50; 75 and 100 mm. The dimensions between the ends of the rods are very accurate. The measuring surfaces in these devices are the outer end of the replaceable rod 3 and bottom bearing surface 2 . When taking a reading, it must be remembered that the main scale located on the stem has a reverse countdown (from 25 mm to 0).

Fig.2

Measuring the depth of holes, ledges, undercuts, etc. perform as follows. The support surface of the base of the micrometric depth gauge is installed on the base surface of the part against which the size is measured. With one hand, the base is pressed against the part, and with the other hand, the drum of the micrometer head is rotated by the ratchet until the rod touches the measured surface and the ratchet clicks. Then the microscrew is fixed with a stopper and the reading is taken from the scales of the head. Micrometric depth gauges have measurement limits from 0 to 150 mm and a division value of 0.01 mm.

Micrometric inside gauges designed to measure the internal dimensions of products in the range from 50 to 6000 mm.

They consist of a micrometer head (Fig. 3, a), interchangeable extension cords (Fig. 3, b) and measuring tip (Fig. 3, v).

The micrometer head of the inside gauge is somewhat different from the head of the micrometer and depth gauge and does not have a ratchet. into the stem 6 the measuring tip is pressed on one side of the micrometer head 7 , and on the other, a microscrew is screwed 5 which is connected to the drum 4 nut 2 and locknut 1 . Protruding measuring tip of the microscrew 5 .

The gap in the screw-nut connection is selected using the adjusting nut 3 screwed onto a split micronut with an external conical thread. The set size is fixed with a locking screw 9 . To extend the measurement range in the threaded hole of the coupling 8 extensions are screwed in (Fig. 3, b) and measuring tip (Fig. 3, v).

Fig.3

The extension is a rod with spherical measuring surfaces that has an exact size in the axial direction. The rod does not protrude beyond the body, at both ends of which a thread is cut. A spring located inside the body creates a force closure between the rods when the extension cord is screwed together with a micrometer head. Another extension can be screwed onto the free end of the extension, etc., until an inside gauge with the required measurement limit is obtained. The measuring tip is screwed into the last extension. During the measurement process, the measuring tip of the microscrew and the measuring tip of the extension come into contact with the workpiece. When using the caliper with several extensions, it must be remembered that the extensions should be connected in descending order of their size and the micrometer head should be connected to the longest of them.

The micrometric caliper assembly with the measuring tip is set to zero according to the installation measure-bracket with a size of 75 mm (Fig. 3, G). If the zero setting is not satisfactory, loosen the locknut by half a turn. 1 , turn the drum until the zero risk coincides with the longitudinal line of the stem, tighten the lock nut 1 and release the screw 9 . Then check the correct installation. After setting the inside gauge to zero, it is screwed with extension cords to obtain the required size and measurements are started.

Measurements of internal dimensions with a caliper are carried out as follows. Insert the tool into the space between the measuring surfaces (for example, into a hole). One measuring tip of the inside gauge is installed on the surface and the head drum is rotated until the second measuring tip touches the opposite surface. During the measurement process, it is necessary not only to rotate the drum, but also to shake the assembled inside gauge, measuring the diameter in a plane perpendicular to the axis of the hole and in the plane of the axial section. The largest dimension in the first position and the smallest dimension in the second position must match.

Objective.

Design and metrological characteristics of a smooth micrometer. How are micrometer readings read during measurements?

Detail sketch with actual dimensions.

Assessment of the suitability of parts.

Control questions

Types of micrometric instruments.

Micrometer device.

How to take micrometer readings? Setting the micrometer to zero.

What is a ratchet used for?

Micrometric depth gauge device.

The device of a micrometric caliper.

Literature

Markov N.N., Ganevsky G.M. Design, calculation and operation of control and measuring instruments and devices. –M.: Mashinostroyeniye, 1993.

Belkin I.M. Means of linear-angular measurements. Directory. –M.: Mashinostroenie, 1987.

Vasiliev A.S. Basics of metrology and technical measurements. –M.: Mashinostroenie, 1980.

Lab #3

MEASUREMENT OF PARTS WITH INDICATOR DEVICES

Objective

To study the device, principle of operation and metrological characteristics of the dial indicator and indicator instruments.

Get the skills of independent work with devices by measuring the details with an indicator bracket and an indicator caliper.

GEAR MEASURING HEADS
OR DIAL INDICATORS

Measuring heads are called reading devices that convert small movements of the measuring rod into large movements of the pointer along the scale (clock-type indicators, lever-toothed indicators, multi-turn indicators, lever-toothed heads).

Fig.1. Dial indicator IC-10

Measuring heads are designed mainly for relative measurements. If the dimensions of the parts are less than the range of the instrument readings, then the measurements can be performed by the absolute method.

The most common geared measuring heads are dial gauges.

The principle of operation of the dial indicator is as follows (Fig. 1):

Measuring rod1 moves in precise guide bushings. A toothed rack is cut on the rod, which is engaged with the tribe4 (=16). A tribe in instrumentation is a gear wheel of a small module with the number of teeth ≤18. On the same axis with the tribe4 gear wheel installed3 (=100), which transmits rotation to the tribe2 (\u003d 10). On the same axis, the tribe2 fixed big arrow8 , which moves along the scale7 , counting tenths and hundredths of a millimeter of movement of the measuring rod with a tip12 .

When moving the measuring rod in the range of indications, the large arrow makes several turns, therefore, an additional arrow is installed in the design of the dial indicator 5 on the axis of the tribe 4 and wheels 3 . When moving the measuring rod by 1 mm, the large arrow 8 makes one revolution, and the arrow 5 moves one division of the small scale 6.

The number of divisions of the small scale determines the range of readings of dial indicators in mm.

Tribe 2 the second gear is engaged9 (=100). A spiral spring is attached to the axle of this wheel at one end.10 , the second end of which is fixed in the indicator housing. The spring ensures the operation of the gears in the mode of single-profile gearing, thereby reducing the effect of gaps in the gear pairs on the measurement error.

The dial indicator has a helical spring 11 , one end of which is fixed on the measuring rod, and the other - on the indicator body. This spring creates a measuring force on the rod R=150±60 cN.

All dial gauges have a scale interval of 0.01 mm. Most indicators have a reading range of 2 mm (IC-2), 5 mm (IC-5), 10 mm (IC-10) and indicators with a reading range of 25 mm (IC-25) and 50 mm (IC-50) are less commonly produced.

The measurement error of a dial indicator depends on the movement of the measuring rod. So in the range of readings 1÷2 mm, the measurement error is within 10÷15 µm, and in the range 5÷10mm, the error is within 18÷22 µm.

MEASURING WITH A DIAL INDICATOR

Indicator 1 mounted on an indicator stand 2 screw 3 (fig.2, a). Loosening screw 5 , lower the indicator until it touches the tip of the measuring table 4 , after which we lower it additionally by another 1 ... 2 mm (we create an “interference”). Fix this position by tightening the screw 5 . We turn the rim 6 dial of the indicator until "0" of the scale coincides with the large arrow. We write down the indicator readings (for example, 1.00 mm with an interference fit of 1 mm).

Without changing the position of the indicator housing, raise the measuring tip and place the part on the measuring table. We release the rod (Fig. 2, b) and record the indicator reading (for example, 2.15 mm) The difference between the indicator reading during measurement and during adjustment gives the value of the movement of the rod relative to the table during measurement
(b\u003d 2.15-1.00 \u003d 1.15 mm). This will be the size b. In this way, measurements are made by the absolute method.

In cases where the size of the part is greater than the range of instrument readings, the relative method is used. To do this, we determine the approximate size of the part (for example, about 42 mm), we collect a block of plane-parallel end blocks of length (also 42 mm), we set the device to "0" relative to plane-parallel end blocks of length (PKMD) (Fig. 2, v) is similar to the setting for the absolute method. We record the indicator readings (for example, 1.00 mm), remove the PKMD block and place the part. We write down the indicator readings (for example, 2.15 mm). We determine the movement of the rod when measuring relative to the PCMD ( \u003d 2.15-1.00 \u003d 1.15 mm) (Fig. 2, G). Actual part size d\u003d PKMD +  (for example, d=42+1.15=43.15 mm). When adding, it is necessary to take into account the sign of the relative displacement: if the size of the part turns out to be less than the PKMD block, then  will turn out to be negative. For example, if the indicator showed 1.00 mm when setting, and 0.42 mm when measuring, then
 \u003d 0.42-1.00 \u003d -0.58 mm.

Fig.2. Indicator measurement

The relative method is also used in cases where it is necessary to reduce the measurement error, i.e. reduce the measuring displacement in order to get rid of the accumulating instrument error.

INDICATOR BRACKET

In the body of the bracket (Fig. 3) there is a dial indicator, a movable heel 2 and replaceable adjustable heel 3 .

Movable heel 2 is constantly pressed towards the product by the measuring rod of the indicator and a special spring. Adjustable heel 3 with screw released 4 and the removed cap can move up to 50 mm. Measurement ranges of indicator brackets are: 0÷50 mm, 50÷100 mm, 100÷200 mm, …, 600÷700 mm, 700÷850 mm, 850÷1000 mm.

The main error of the device (depending on the size of the bracket) varies from 5 to 20 microns.

MEASUREMENT WITH INDICATOR CLAMP

INDICATOR BELL GAUGE

Indicator inside gauges are designed to measure the internal dimensions and diameters of holes by the relative method.

The most commonly used inside gauges of standard sizes from the following range of measurement ranges: 6-10; 10-18; 18-50; 50-100; 100-160; 160-250; 250-450; 450-700; 700-1000 mm.

We will consider the device and operation of indicator calipers using the example of an caliper of the NI-100 model (Fig. 4).

A sleeve-insert is inserted into the body of the caliper 2 , into which a replaceable fixed measuring rod is screwed on one side 3 , and on the other side there is a movable measuring rod 4 acting on the two-arm lever 5 , fixed on the axis 6 .

A rod is placed inside the body 8 pressed against the lever 5 dial indicator stylus and coil spring 10 . The latter create a measuring force ranging from 200 to 500 cN.

Fig.4.

Within the measurement range, inside gauges are supplied with a set of interchangeable measuring rods. The position of the fixed measuring rod after adjustment is fixed with a nut 7 . Movable measuring rod 4 under the influence of the measuring force is in the extreme initial position. centering bridge 12 pressed by two springs 11 to the surface of the controlled hole, ensures the alignment of the measurement line with the diameter of the hole.

The adjustment of the inside gauge to the required nominal size is carried out using the PKMD blocks with sidewalls installed in clamp holders, or according to certified rings. The error of inside gauges is usually normalized equal to 1.5 ÷ 2.5 divisions of the readout head.

MEASUREMENT WITH INDICATOR INSIDE GAUGE.

Calculate the nominal dimensions of the PMDC according to the nominal size of the hole of the measured part. Prepare an installation kit (Fig. 5) from the PMKD block, two sidewalls 2 and clamps 1 . From the set of interchangeable adjustable rods (attached to the inside gauge), select a rod with a size range in which the nominal size of the measured hole is located. Screw the replaceable adjustable rod 3 into the body of the caliper 5 .

Insert the caliper with measuring rods into the installation kit between the sidewalls and create an interference fit of 1÷2 mm for the dial indicator (Fig. 5).

Swinging the caliper from itself towards itself, turning it to the left - to the right around the vertical axis, you need to set the axis of the measuring rods (measurement axis) to a position that coincides with the smallest distance between the measuring surfaces of the sidewalls. This position will be shown by the large indicator hand when it reaches the farthest (when it moves clockwise) division of the scale and starts moving back. Having given the correct position to the indicator, it is necessary to tighten the locknut 4 interchangeable measuring rod 3 and set the zero division of the indicator scale until it coincides with the large arrow.

Fig.5. Indicator caliper when setting ( a) (centering bridge not shown)
and when measuring ( b)

After setting the inside gauge to "0", you can start measuring the deviations of the part hole size from the nominal value.

We introduce the measuring head of the caliper into the hole of the measured part. Spring-loaded centering bridge 8 orients the measuring axis of the inside gauge strictly in the diametrical plane of the measured hole (Fig. 5, b).

By swinging the caliper in a vertical plane, we determine the indicator readings at the extreme right position of the large arrow.

When determining the actual deviations of hole sizes from the nominal value, they are guided by the following rule: the deviation is accepted with a minus sign (“-”) if the large indicator needle has deviated from “0” of the scale division clockwise, and the counterclockwise deviation shows an increase in the diameter of the hole about the nominal size and the actual deviation is taken with a plus sign ("+").

The value of the actual deviation is calculated by multiplying the number of divisions of the indicator scale (indicated by a large arrow from "0") by the division value of 0.01 mm.

The actual size of the hole diameter will be equal to the nominal hole diameter plus ("+") or minus ("-") the actual deviation.

Objective.

Types of indicator instruments used in the work and their metrological characteristics. Method of measurement.

Sketches of measured parts with actual dimensions.

Assessment of the suitability of parts.

Control questions

Design of dial gauges.

Metrological characteristics of indicator instruments. Method of measurement.

How are readings read when measuring with indicator devices?

indicator bracket. Adjustment of the clamp for measurements.

What is the name of the value that the device fixes?

Indicator caliper. Setting the caliper.

Measuring with a caliper.

Literature

Belkin I.M. Means of linear-angular measurements. Directory. –M.: Mashinostroenie, 1987.

Vasiliev A.S. Basics of metrology and technical measurements. –M.: Mashinostroenie, 1980.

Lab #4

PLUG MEASUREMENT

Objective

To study the device, principle of operation and metrological characteristics of spring measuring heads IGP - microcators (GOST 6933-81).

Gain the skills to work independently with equipment for accurate measurements relative method.

Learn how to build schemes of tolerance fields for calibers.

Measure the plug gauge with the GPI installed on the C-1 or C-2 stand.

Determine the suitability of the cork gauge.

SPRING MEASURING MICROCATOR HEADS

These devices are precision measuring devices with mechanical conversion of small movements of the measuring tip into large movements of the pointer relative to the scale of the device. This group of devices is called "spring" because the sensing element is a thin bronze ribbon curled from the middle in different directions.

14

a

b

Fig.1.

Band spring 2 fixed on a corner 1 and cantilever flat spring 4 installed on a rigid ledge (Fig. 1, a). Changing the position of the spring 4 , with the help of screws adjust the tension of the tape spring. Measuring rod 7 suspended on membranes 6 and rigidly connected to the square 1 . Moving the measuring rod causes the square to rotate around the point " a» and stretching the spring 2 . The measuring force is generated by a conical spring 5 . A quartz arrow is glued to the middle part of the bronze swirling tape 3 . Spring extension 2 causes the arrow to turn 3 relative to the scale.

Spring measuring heads are used for high-precision relative measurements of the dimensions of products, as well as deviations in the shape and location of surfaces. The accuracy of controlled products can be from 2 th until 6 th quality.

For measurements, the instruments are mounted in racks (Fig. 1, b) type C-1 and C-2 or in special devices for the tube 7 28 mm in diameter. When setting to zero position on the gauge block, microfeed of the rack table is used.

During transport, the measuring rod is clamped by turning the lock into the base of the tube.

Spring measuring heads are produced in the following modifications: 01ГП; 02IGP; 05IGP; 1IGP; 2IGP; 5IGP; 10IGP and have the price of division of the scale of the device, respectively: 0.0001; 0.0002; 0.0005; 0.001; 0.002; 0.005; and 0.01 mm.

WORK PROCEDURE

1. Study the device, the principle of measurement and the metrological characteristics of the microcator on the C-1 or C-2 rack. Record in the report the main metrological characteristics of the device (scale division of the device, measurement range on the scale of the device).

2. Get a gauge-plug for measurements from the teacher.

3. By marking on the caliber, determine which hole it is intended to test (nominal hole diameter, deviation of the hole tolerance field and quality).

4. According to GOST-25347-82 ( ST SEV 144-75) determine the maximum deviations of the size of the hole, and then build a diagram of the location of the hole tolerance field (Fig. 2)

5. According to GOST-24853-81 (ST SEV 157-75) for a given plug gauge, find tolerances, limit deviations and build a diagram of the location of the tolerance field for the gauge.

7. According to the diagram, select the size with respect to which the device is set to zero using gauge blocks.

8. From a set of plane-parallel end measures of length, take a measure or several measures to compose a block, the size of which is equal to the size selected according to the scheme.

9. End measures, rinse the instrument table with gasoline, wipe with a soft cloth. Rub the wiped measures to each other and to the table.

10. Set the instrument to zero. For this (Fig. 1, b) by releasing the locking screw 2 table 3 by turning the micrometer nut 1 , the object table with the ground block of end measures is lowered to the lower position. Then, by releasing the locking screw 10 bracket 9 , by rotating the ring-nut 11 the bracket is lowered 9 with a microcator until the tip touches the surface of the gauge block or block. The moment of contact is judged by the beginning of the movement of the arrow. In this position, the bracket 9 fixed with a screw 10 .

Attention!!!

The bracket should be lowered smoothly, avoiding the impact of the tip on the end measure! Do not touch the adjusting screws 14 table, as this will disrupt the installation
table

The final setting of the device to zero is carried out using a nut 1 ; table 3 rises until the pointer of the microcutter is aligned with the zero division of the scale. In this position, the table is locked with a screw 2 and checking the zero setting by raising and lowering the probe 4 with the help of an arrester 5 .

The exact setting of the device to zero is carried out by a screw 8 , which can shift the scale relative to the pointer within ±5 divisions.

11. By pressing the arrester, raise the measuring tip and remove the end block or block (do not disassemble the end block block).

12. Place a stopper gauge on the object stage and, pressing the gauge tightly against the stage with two fingers, slowly roll it under the tip and follow the movement of the arrow. The largest deviation of the arrow in "plus" or "minus" on the scale determines the actual deviation of the size of the plug in this section relative to the setting size of the end measure or block. To verify the correctness of the obtained deviation, the measurements are repeated two or three times. Each time there should be a clear repeatability of the tidy readings. Such measurements should be carried out in three sections along the length of the plug and in two planes (Fig. 3). Record the measurement results in the report table.

13. Determine the actual dimensions of the plug in the controlled sections, which are equal to the algebraic sum of the size of the end measure or block and the instrument reading. Record the result in a report table.

14. Check the zero reading of the device. To do this, by pressing the arrester, the caliber is removed from the table and the end measure or block is again installed under the measuring tip. Raising and lowering the tip two or three times, make sure that the arrow is set to zero.

The deviation of the arrow from the zero stroke should not exceed half the division of the instrument scale, if the deviation is greater, then you need to repeat the adjustment of the instrument to zero and measure the caliber.

The obtained data on the results of measurements are recorded in the report.

1. The purpose of the work.

2. The name of the measuring device and its main metrological characteristics (measurement limits on the scale of the device, scale division value).

3. The type of caliber that is controlled and its marking.

Fig. 4. Scheme of tolerance fields for the product and caliber with limiting dimensions in mm and deviations in microns (Fig. 2).

Fig.2

5. Select a gauge block or gauge block to set the instrument to zero.

6. Caliber measurement scheme (Fig. 3) and measurement results with filling in the table.

Fig.3.

Measurement results

Gauge block dimensions
or block

passing side

R-PR

impassable side

R-NOT

Sections

Sections

Indications
instrument in µm

Plane

II-II

Actual caliber dimensions in mm

Plane

II-II

7. Conclusion on the suitability of the caliber.

Control questions

Device, principle of operation and metrological characteristics of spring heads-microcators.

What is the scope of microcators.

Measuring method and microcator setting for measurements.

How are the tolerance fields of smooth limiting plug gauges and staple gauges located on the diagrams?

Why is it necessary to use measuring instruments such as microcator to assess the suitability of a cork gauge?

How is the conclusion on the suitability of the caliber formulated?

Literature

Belkin I.M. Means of linear-angular measurements. Directory. –M.: Mashinostroenie, 1987.

Vasiliev A.S. Basics of metrology and technical measurements. –M.: Mashinostroenie, 1980.

Lab #5

SURFACE ROUGHNESS

Objective

To study the main parameters of roughness and the designation of roughness in the drawings.

To get acquainted with the methods of measurement and devices for assessing the surface roughness of machine parts.

BASIC CONCEPTS

Surface roughness is a set of surface irregularities with relatively small steps, selected using the base length (GOST 25142-82).

base length - the length of the baseline used to highlight the irregularities that characterize the surface roughness.

The numerical values ​​of the surface roughness are determined from a single base, which is taken as the middle line of the profilem , i.e., a base line that has the shape of a nominal profile and is drawn so that, within the base length, the standard deviation of the profile to this line is minimal. Estimation Length - the length at which the real profile is evaluated. It may contain one or more base lengths. (Fig. 1).

Rice. 1. Profile and main parameters of surface roughness

NORMALIZED ROUGHNESS PARAMETERS

Roughness parameters in the direction of the height of the roughness. Arithmetic mean profile deviation
- arithmetic mean of the absolute values ​​of profile deviations within the base length:

or approximately
,

where - base length; - number of selected profile points on the base length;y - the distance between any point on the profile and the midline. It is normalized from 0.008 to 100 microns.

Height of profile irregularities by ten points
- the sum of the average absolute values ​​of the heights of the five largest protrusions of the profile and the depths of the five largest depressions of the profile within the base length:

,

where
- heighti -th largest protrusion of the profile;
- depthi th largest depression of the profile.

The greatest height of the profile irregularities
- the distance between the line of the protrusions of the profile and the line of the depressions of the profile within the base length . Normalized from 0.025 to 100 microns.

Roughness parameters in the direction of the profile length. Average step of profile irregularities
- arithmetic mean step of profile irregularities within the base length:

,

whereP - number of steps within base length ;
- the step of the profile irregularities is equal to the length of the segment of the middle line intersecting the profile at three adjacent points and bounded by two extreme points. It is normalized from 0.002 to 12.5 mm.

The average step of the local protrusions of the profile - arithmetic mean step of local protrusions of the profile within the base length:

,

where P - number of steps of irregularities along the vertices within the base length ; - step of profile irregularities along the tops of the protrusions. It is normalized from 0.002 to 12.5 mm.

Numerical values ​​of roughness parameters
,
,
,
and are given in GOST 2789-73, and in Appendix 1 the values ​​\u200b\u200bof the base length are indicated recommended for parameters
,
,
.

Roughness parameters related to the shape of profile irregularities. Reference profile length - the sum of the lengths of the segments cut off at a given levelR % in the profile material by a line equidistant to the midlinem - m and within the base length (Fig. 1).

- the ratio of the reference length of the profile to the base length:

.

Reference profile length determined at the level of the profile sectionR, those. at a given distance between the line of the protrusions of the profile and the line intersecting the profile equidistantly from the line of the protrusions of the profile. Profile ledge line - a line equidistant from the midline passing through the highest point of the profile within the base length. Profile section level valueR count along the line of protrusions and choose from a number of: 5; 10; 15; twenty; 25; thirty; 40; 50; 60; 70; 80; 90% off
. Relative profile reference length assigned from row 10; 15; twenty; 25; thirty; 40; 50; 60; 70; 80; 90%.

The Interstate Council for Standardization, Metrology and Certification has amended GOST 2.309-73 “Surface Roughness Designations” and set the deadline for the introduction of changes - from January 1, 2005.

The changes concern both the designation of surface roughness and the rules for applying them to the drawing.

Interstate standard GOST 2.309 fully complies with ISO 1302.

1. Designation of surface roughness

Surface roughness is indicated on the drawing for all surfaces of the product performed according to this drawing, regardless of the methods of their formation, except for surfaces whose roughness is not due to design requirements.

Fig.2.

In the designation of surface roughness, one of the signs shown in Fig. 3 is used. Height should be approximately equal to the height of the digits of the dimension numbers used in the drawing. Height
equal to (1.5…5) . The thickness of the character lines should be approximately equal to half the thickness of the solid main line used in the drawing. In the designation of surface roughness, the processing method of which is not established by the designer, the sign is used according to Fig. 3,a . In the designation of surface roughness, which should be formed only by removing a layer of material, use the sign according to Fig. 3,b . In the designation of the surface roughness, which should be formed without removing a layer of material, the sign according to Fig. 3 is used,v indicating the value of the roughness parameter.

The surfaces of a part made from a material of a certain profile and size, which are not subject to additional processing according to this drawing, must be marked with a sign according to Fig. 3, v without specifying the roughness parameters. The condition of the surface marked with such a sign must comply with the requirements established by the relevant standard or technical specifications, or another document, and this document must be referenced, for example, in the form of an indication of the material grade in column 3 of the main inscription of the drawing according to GOST 2.104-68.

Fig.3.

The value of the roughness parameter according to GOST 2789-73 is indicated in the roughness designation after the corresponding symbol, for example: 0,4;
6,3;
0,63; 70; 0,032; 50. In the example 70 indicates the relative reference length of the profile \u003d 70% at the level of the profile section =50%. . The thickness of the sign lines should be approximately equal to half the thickness of the solid main line.

The type of surface treatment is indicated in the designation of roughness only in cases where it is the only one applicable to obtain the required surface quality (Fig. 5).

It is allowed to use a simplified designation of surface roughness with an explanation of it in the technical requirements of the drawing according to the example shown in Fig.6.

2. Rules for applying roughness designations
surfaces on drawings

The designations of surface roughness in the image of the product are placed on the contour lines, extension lines (as close as possible to the dimension line) or on the shelves of leader lines. It is allowed, if there is not enough space, to place the designation of roughness on the dimension lines or on their extensions, on the shape tolerance frame, and also to break the extension line (Fig. 7).

Fig.7

Fig.8

Fig.9

The surface roughness designations, in which the sign has a shelf, are located relative to the main inscription of the drawing as shown in Figures 8 and 9. When the surface is located in the hatched zone, the designation is applied only on the leader line shelf.

When specifying the same roughness for all surfaces of the product, the roughness designation is placed in the upper right corner of the drawing and is not applied to the image (Fig. 10). The dimensions and thickness of the lines of the sign in the roughness designation placed in the upper right corner of the drawing should be approximately 1.5 times larger than in the designations printed on the image. a-c), and for globoid worms and wheels associated with them - on the line of the calculated circle (Fig. 14, G).

The designation of the surface roughness of the thread profile is applied according to the general rules when depicting the profile (Fig. 15, a), or conditionally on the extension line to indicate the size of the thread (Fig. 15, b - e), on the dimension line or on its continuation (Fig. 15, e).

If the roughness of the surfaces forming the contour must be the same, the roughness designation is applied once in accordance with Fig. 16. Auxiliary sign diameter- 4…5 mm. In the designation of the same roughness of surfaces, smoothly passing one into another, the sign

Fig.16

Fig.17

Fig.18

In this case, the letter designation of the surface is applied on the shelf of the leader line drawn from the thickened dash-dotted line, which circles the surface at a distance of 0.8 ... 1.0 mm from the contour line (Fig. 18).

SURFACE ROUGHNESS MEASUREMENT AND CONTROL

Surface roughness certification is carried out according to two types of control: qualitative and quantitative.

Quality control of surface roughness parameters is carried out by comparison with samples or exemplary parts visually or by touch. GOST 9378-75 establishes roughness samples obtained by mechanical processing, removal of positive prints by electroforming or coating of plastic prints. Sets or individual specimens have straight, arcuate, or criss-cross arcuate arrangements of surface irregularities. Parameter value is indicated on each sample
(in µm) and type of sample processing. To improve accuracy, probes and comparison microscopes are used.

Quantitative control of roughness parameters is carried out by non-contact and contact measuring instruments.

To quantify surface roughness by a non-contact method, two methods are used - increasing them using optical system or using the reflectivity of the treated surface.

Devices based on the assessment of surface irregularities when they are enlarged with the help of an optical system are "light section devices". Reflectivity-based instruments are microinterferometers.

The principle of operation of light section devices is to obtain an enlarged image of the profile of the measured surface using rays directed obliquely to this surface, and to measure the height of irregularities in the resulting image. The most common is a double microscope type MIS-11, which allows you to determine three parameters of roughness with the fact that many of the functional units they have the same. These instruments are mainly intended for use in the laboratory. Domestic industry manufactures several models of devices (201, 202, 252) based on the inductive method of converting needle vibrations into voltage fluctuations.

A profilograph is a device for recording the values ​​of surface irregularities in a section normal to it in the form of a profilogram, the processing of which determines all parameters characterizing the surface roughness and waviness.

A profilometer is a device for measuring surface irregularities in a section normal to it and presenting the measurement results on the instrument scale as a value of one of the parameters used to evaluate these irregularities. Most profilometers give an estimate of surface irregularities in terms of the parameter
and are used as workshop equipment. Roughness evaluation by parameter
associated with signal processing difficulties.

Profile drawing of surface irregularities with basic parameters.

Estimation of roughness parameters for a given profile.

Instruments for assessing surface roughness on machine parts.

An example of the designation of roughness in the detail drawing.

Control questions

What parameters are used to evaluate surface roughness?

What and how to control the surface roughness?

What roughness parameter is measured by the MIS-11 instrument?

How is roughness indicated on the drawings?

Why do they achieve low roughness on critical machine parts?

Literature

Markov N.N., Ganevsky G.M. Design, calculation and operation of control and measuring instruments and devices. –M.: Mashinostroyeniye, 1993.

Belkin I.M. Means of linear-angular measurements. Directory. –M.: Mashinostroenie, 1987.

Vasiliev A.S. Basics of metrology and technical measurements. –M.: Mashinostroenie, 1980.

Ministry of Education of the Republic of Moldova

State budgetary educational institution of the Republic of Mordovia

secondary vocational education

(secondary special educational institution)

"Ruzaevsky Polytechnic College"

Metrology, standardization and certification

guidelines and control tasks

for full-time students

specialties

151901 "Technology of mechanical engineering"

(2 course, 1 semester)

150415 "Welding production"

(2 course, 2 semester)

Compiled by Toropygina E.V.

List of laboratory works

Lab #1 " The study of the designs of smooth calibers, the control of products by calibers "

Lab #2"Control of the dimensions of parts with caliper tools"

Lab #3"Control of the dimensions of parts with micrometric tools"

Laboratory work№4 "Control of the dimensions of parts by a comparative method"

General instructions

The guidelines are intended for laboratory work in the discipline "Metrology, standardization and certification" by students of the specialties 150901 "Technology of mechanical engineering" and 150415 "Welding production".

When performing these laboratory works, students get acquainted with the methods of calculating the maximum dimensions, calibers, the choice of measuring and controlling material.

When starting practical work, students should remember the following:

Before each practical work, students carefully study the relevant sections on the recommended literature, lecture notes and these guidelines.

The report on the performed practical work should be drawn up in accordance with the requirements of GOST 7.32-91 (ISO 5966-82) and contain the following sections: title, purpose of the work, summary of the theory, assignment for practical work, list of literature used, calculations performed on the subject of practical work and answers to security questions.

A completed and signed report is presented by each student at the end of the lesson to the teacher for verification and signature, after which a note is made in the journal about the implementation of practical work.

Answer the questions of the teacher during the defense of practical work, after which the grade is given in the journal.

Lab #1

Topic: The study of the designs of smooth calibers, the control of products by calibers.

Objective : To master the choice of smooth gauges and the technique of checking dimensions.

Equipment : staple gauges, plug gauges, measuring parts.

EXERCISE:

1. Select smooth gauges for given dimensions.

2. Determine the performance dimensions of the selected calibers.

3. Check the specified dimensions.

4. Give a conclusion on the suitability of the tested parts.

Literature:

2. Guide to the selection of measuring instruments (allowance). Guide to the selection of measuring instruments (allowance).

3.M.A. Paley. ESDP / volume 2 - M.: Publishing house of standards, 2012

4. GOST 18362-73,14810-69 - M: Publishing house of standards

METHODOLOGICAL INSTRUCTIONS SMOOTH GAUGE.

In mass and large-scale production, the dimensions of smooth cylindrical surfaces with a tolerance of IT 6 before 1T17 checked by limit gauges. A set of working limit gauges consists of a through gauge PR and a non-through gauge - NOT.

With the help of limiting calibers, the suitability of the size is determined. The part is considered fit if the passing gauge (going side of the gauge) passes under the action of its own weight or a force equal to it, and the non-going gauge (non-going side)) does not pass through the controlled surface of the part. Working gauges PR and NOT are designed to control - products in the process of their manufacture. These calibers are used for control by workers and inspectors of the quality control department of the manufacturer.

Clamps are used to control the shafts. The most widespread are one-sided double-limit brackets. Adjustable brackets are also used, which can be adjusted to different sizes, but compared to rigid ones, they have less accuracy and reliability, so they are rarely used for sizes 8 quality and coarser.

Plugs are used to control holes. With a controlled diameter of up to 50 mm, double-sided plugs with inserts are used, with a diameter of 50 to 100 mm - one-sided plugs with inserts, with a diameter of more than 100 mm - one-sided incomplete plugs

The nominal size of the through-gauge-plug is performed according to the smallest, and the non-going one - according to the largest limit size of the hole being checked. The nominal size of the through gauge-bracket is performed according to the largest, and the non-through gauge - according to the smallest limit size of the shaft being checked.

Plug gauge inserts are made of grade X steel according to GOST 5950-73 or ШХ according to GOST 801-78. Cases of gauges-brackets that do not have separate jaws, and jaws of compound gauges-brackets are made of steel grades 15 or 20 according to GOST 1050-74, which are cemented, the thickness of the carburizing layer is not less than 0.5 mm

When choosing plug gauges, use GOST 14807-69 - GOST 14827-69, and GOST 18358-73 staple gauges - GOST 18369-73. .

MEASUREMENT TECHNIQUE.

before checking, the measuring surface of the gauge must be wiped with a napkin soaked in gasoline, then dry with a clean napkin.

the part to be checked must be free of dust and dirt.

do not place prepared gauges on the table with measuring surfaces.

when checking the controlled surface, if the passing gauge passes under its own weight, and the non-passing gauge does not pass, then it is considered suitable.

after finishing work, wipe the gauges with a clean cloth, grease the measuring surfaces with anti-corrosion grease and put them in a box.

Draw a sketch of the part.

Find the maximum deviations of the dimensions being checked, enter them in the table. (V.D. Myagkov "Tolerances and landings", vol. 1, table 127, p. 79)

Determine the maximum dimensions and tolerances of the surfaces to be checked and enter them in the table.

From the guide for the selection of measuring instruments for controlling the dimensions of a part, according to table No. 1, page 3, find the permissible measurement error and enter it in the table.

5. According to GOST 18362-73, select a caliber - a bracket, and according to GOST 14810-69 - a caliber-plug and enter their symbols in the table

6. For the caliber - brackets, and the caliber-plugs, find the limit deviations

(M.A. Paley ESDP reference book vol. II, table 1.9 p. 18, table 1.8, p. 11), determine the maximum dimensions of calibers and enter in the table.

7. Check the specified surfaces with gauges in 2 directions and enter the results in the table.

8. Give a conclusion on the suitability of the part for the surfaces being checked.

REPORT FORM

Job title.

Objective.

The composition of the task.

Detail sketch.

6. Determination of the limiting dimensions and tolerances of the checked surfaces of parts.

verifiable

the size

Limit deviations in mm

Limit dimensions, in mm

Tolerance in mm

Permissible measurement error, in

mm

E S,es

EI, ei

Dmax dmax

Dmin, dmin

TD,Td

d max = d + es (mm) d min = d + ei (mm) Td = es – ei (mm)

D max = D + ES (mm) D min = D + EI (mm) TD = ES - TI (mm)

7. Choice of smooth gauges to control the dimensions being checked.

verifiable

the size

Designation

caliber - staples, caliber - plugs

Limit dimensions of calibers in mm

passing side

impassable side

most

least.

most

least.

For brace:

Etc max =d +ES pr (mm);

Etc min =d +EI pr (mm);

Not max =d +Es not (mm);

Not min =d +EI not (mm).

For cork:

Etc max =D +es pr (mm);

Etc min =D +ei pr (mm);

Not max =D +es not (mm);

Not min =D +ei not (mm)

8. Measurement results:

Checked size

Validity Conclusion

Review questions:

In what types of production are limit gauges used for dimensional control?

What is the name of the limit gauges for shaft control?

What is the name of the limit gauges for hole control?

Why are gauges for controlling the dimensions of the hole and shaft called limit gauges?

Largest hole size limit? What caliber is it controlled by?

Smallest shaft size? What caliber is it controlled by?

In what qualifications are limit gauges used to control dimensions?

Lab #2

Topic: "Control of the dimensions of parts with caliper tools".

Objective: To master the measurement of dimensions with caliper tools.

Equipment: calipers, parts to be measured.

Literature:

1. V.D. Myagkov Tolerances and landings / volume 1 - M .: Mashinostroenie, 2014

Exercise:

Measure given dimensions

METHODOLOGICAL INSTRUCTIONS

ROD INSTRUMENTS

Gauge tools (SHI) are the most popular tools for measuring the linear dimensions of products, which have been used for over 100 years. Due to their simple design, easy handling and quick operation, they are the most used instruments for linear measurement. Of all (SHI), the most common is a caliper. Each machine operator, locksmith, technologist and designer has his own caliper (SC). A wide variety of forms of measuring legs, allowing you to measure a variety of surfaces (internal, external, grooves, undercuts, depth, length), make the SC universal tools. Shi are produced by many foreign companies - Tesa (Switzerland), Mitutoyo (Japan). Carl Mahr (Germany) and domestic firms - Chelyabinsk Tool Plant (CHIZ) and Kirov Tool Plant (KRIN). Also on sale are Chinese caliper tools, which should be treated with some caution.

Currently, three groups of SHI are produced:

– mechanical SHI with readings on a dashed scale, equipped with a vernier;

– SHI with countdown on the dial;

– electronic SHI with digital readout.

SHI with a dashed scale reading (calipers, caliper depth gauges, caliper height gauges, caliper gauges, etc.) have a rod (hence their name) with a matte chrome coating for glare-free reading, on which the main scale is applied, and a vernier - an auxiliary scale that serves to accurately read the shares divisions.

The device of caliper tools is determined by their purpose. The quality of modern calipers is very high. The manufacture of an accurate guide of the slider (rod) ensures its smooth movement without distortions of the jaws and backlash. The use of stainless steels and alloys and heat treatment provides anti-corrosion properties of the tool, resistance to wear and corrosion. Also produce models made of carbon fiber. Such SI are convenient for measuring magnets and have almost zero thermal conductivity, which reduces the temperature error during measurement.

Calipers (ShTs) are produced in accordance with GOST 166-89 and the international standard DIN 862 with two-sided or one-sided arrangement of jaws, for external and internal measurements and with a retractable probe for measuring depths (Figure 1).

Figure 1 - SC with a vernier from readings on a dashed scale

The main parts of the SC are: a rectangular rod, two measuring jaws, one is fixed, made integral with the rod, the other is movable, moving along the rod. Some models are equipped with a movable frame with micrometric feed for precise positioning of the sponge on the surface to be measured, or with a wheel for creating a constant measuring force. Sponges for internal measurements of ShTs have a cylindrical measuring surface with a radius of not more than half of the total thickness of the sponges. The size of the offset jaws for internal measurements (usually 10 mm) is marked on their side and determines the smallest internal dimension that can be checked by this SC. For all internal measurements, the marked size of the jaws should be added to the scale reading.

The movable jaw is equipped with a clamp, often made in the form of a screw. ShTs with a dashed scale are equipped with a vernier for accurate reading of the division of the main scale. Every fifth division of the bar and vernier must be marked with an elongated stroke, and every tenth division of the bar with a longer stroke than the fifth division and the corresponding number. The plane on which the divisions of the vernier are applied has a smooth edge overlapping the strokes of the rod by at least 0.5 mm. The length of the visible part of the short strokes of the rod and the short strokes of the vernier must be between 2 and 3 mm. The strokes of the vernier should reach the edge. The distance from the upper edge of the vernier edge to the rod scale surface in order to reduce the parallax error should not exceed 0.22 mm with a vernier reading of 0.05 mm and 0.3 mm with a reading of 0.1 mm. When shifting the jaws of the ShZ until contact, the clearance between the measuring surfaces should not exceed 0.003 mm with a vernier reading of 0.05 mm and 0.006 mm with a reading of 0.1 mm. When tightening the frame clamp, twice as large gaps are allowed. When measuring the SC, the size is determined by the reading on the rod scale, made relative to the zero stroke of the vernier. Reading on the zero stroke of the vernier allows you to determine the integer number of divisions of the scale, which consists in the measured (or set) size. The assessment of the part of the division, which is between the zero stroke of the vernier and the nearest stroke, located from the side of the beginning of the main scale, is made using the vernier scale.

Figure 2 - Nonius SC with a dashed scale

The scheme of the vernier with is shown in Figure 2. The main scale of the rod has a division value of 1.0 mm. The interval of divisions of the vernier with a reference value of 0.1 mm is usually equal to 0.9 or 1.9 mm, and the number of divisions is 10. In the zero position of the vernier, the zero strokes of the vernier and the scale coincide, and the last stroke of the vernier (tenth) coincides with the ninth or nineteenth division scales. If the vernier is shifted to the right by 0.1 mm, then its first stroke will coincide with the nearest division of the scale, with a shift of 0.2 mm, the second stroke will coincide, with a shift of 0.3 mm, the third stroke, etc. Thus, the offset of the vernier to the right within 1.0 mm is determined by the number of the vernier stroke, which coincided with the division of the scale. In the general case, the vernier offset relative to any scale stroke is determined in the same way. This offset, expressed in tenths or hundredths of a millimeter, added to the integer number of millimeters enclosed between the zero marks of the scale and the vernier, determines the size to which the chirp is set. Thus, the vernier allows you to replace the visual assessment of the division by the relative position of the scale strokes and the reference stroke with a more accurate assessment of the coincidence of the scale strokes and the vernier. Except verniers with 0.1 mm reading , elongated verniers are used with a reference value of 0.05 and in rare cases 0.02 mm .

In all cases, the value of the vernier reading, the price of the division of the rod scale, the interval and the number of divisions of the vernier are connected by a certain dependence.

They produce ShTs with a report on a dashed scale with a measurement range from 125 to 2000 mm.

Caliper with dial reading are distinguished by the absence of a vernier, which is replaced by a small dial with a diameter of 30-35 mm with an arrow. To drive the pointer, a narrow gear rack with a small pitch, for example, 0.199 mm, is installed on the rod. A gear interacts with the rack, transmitting the movement of the slider through the gear to the arrow (Figure 4).

Figure 4 - SC with a countdown on the dial

Millimeters are counted on the scale located on the bar, and fractions of a millimeter on the dial. For every millimeter traveled by the slider, the indicator needle makes a complete revolution. The measurement limit of dial calipers is up to 300 mm. The value of the reading division is 0.01 - 0.02 mm. The accuracy of the dial SC is not higher than the accuracy of the vernier one, since the main SC error caused by the violation of the Abbe principle remains, and instead of the vernier reading error, the gear transmission error is added. The main operational disadvantage of vernier and dial SCs is the inconvenient reading of measurement results on a dashed scale and vernier or dial and adding up their results, especially in poor lighting conditions. This drawback is completely eliminated in modern instruments equipped with an incremental electronic system with a digital display.

Electronic caliper. Structurally, an electronic SC differs little from a mechanical one, but instead of dashed scales and a vernier, it is equipped with an incremental, as a rule, capacitive transducer, a small converting device, and a digital display.

Figure 5 - Electronic caliper

Depth gauges designed to measure the depth of grooves, grooves, recesses and blind holes.

The simplest depth gauge is equipped with calipers with a small measuring range of 125 and 200 mm. They have a thin retractable probe connected to the movable jaw ShTs. The end of the rod serves as the measuring base. The accuracy of such a depth gauge is not high. Some SC models are equipped with a removable support, which is attached to the SC rod and slightly increases the accuracy and convenience of depth measurement.

They produce special mechanical and electronic depth gauges designed only for measuring depth. Mechanical depth gauges have a scale and vernier reading, electronic ones are equipped with an incremental capacitive transducer and a digital display with a reading resolution of 0.01 mm. Electronic depth gauges with digital readout are much more convenient to use.

They produce depth gauges with a measuring range of 200, 300, 500 and 1000 mm. The peculiarity of the depth gauge compared to other gauges is that when measuring with a depth gauge, the Abbe principle is observed. However, an error arises from the non-perpendicularity of the base plane and the movable rod.

The error of the depth gauge is 20 µm for a measuring range of 200 mm and 30 µm for a measuring range of 300 mm. The design of the depth gauge completely repeats the design of the ShTs.

Figure 6 - Electronic caliper

W tangent heights (GOST 164-90) are designed for marking work on the plate and for measuring the height of parts installed on the plate.

Height gauge is the simplest altimeter, which is more often used for marking parts on a plate. When marking, the height gauge is set to a predetermined size and, moving along the plate along the marked workpiece, a horizontal line is applied with the tip of the marking leg on the vertical surface of the workpiece.

To measure the height dimensions, instead of a marking leg, a measuring one is installed, having a lower flat and an upper measuring surface with a sharp edge. When using the upper measuring surface, the size of the stem must be added to the reference value.

Height gauges are available in mechanical version with scale and vernier and in electronic version with incremental capacitive transducer and digital readout.

Height gauges are produced with a measuring range of 200,300, 600 and 1000 mm. The price of division of the vernier is 0.02 mm. The electronic height gauge has a reading resolution of 0.01 mm. The error of the height gauge with a measurement range of 200 mm is 0.04 mm, with a measurement range of 1000 mm it is 0.08 mm.

MEASUREMENT TECHNIQUE

Before measuring, the caliper tool must be wiped with a cloth soaked in gasoline, then dry with a clean cloth (especially measuring surfaces). The measured part must be cleaned of dust and dirt, the frame and clamp must move smoothly along the rod;

Check zero setting, i.e. coincidence of the zero of the vernier with the zero of the rod scale. For calipers, by bringing the movable jaw into contact with the fixed jaw and fixing it with clamps. At caliper depth gauges by installing them with a support on the lowering plate of the frame with the rod until it comes into contact with it and fixing it with clamps. For height gages, after fixing the legs with a holder below the protrusion of the frame, by installing them with their base on the plate and lowering the frame until the legs come into contact with the plate and fixing with a clamp. Micrometric feed is used to accurately position the frame relative to the rod.

The controlled size is approximately set, the micrometric feed frame is fixed, then, using the micrometer feed, the sponge, rod or leg is brought into contact with the surface to be checked, the frame is fixed, avoiding distortion and achieving a normal measuring force.

When measuring the height gauge and the product are installed on the same plate. After finishing work with a caliper tool, wipe the surfaces of the rods, frames, measuring surfaces of the jaws and legs with a clean cloth, lubricate with anti-corrosion grease and place in a case.

Draw a sketch of the part.

According to the drawing, find the unspecified limit deviations of the dimensions being checked and enter them in the table.

Select the maximum deviations of the dimensions being checked (V. D. Myagkov Tolerances and fits v. 1 table 1.43 str 140-141) and enter them in the table.

Select the permissible error for the dimensions to be checked (guide for the selection of measuring instruments, table 1, page 3) and enter them in the table.

Select measuring instruments and their characteristics for each checked size (guidance for the selection of measuring instruments) and enter them
to the table.

Take measurements in two directions and enter them in the table.

Give a conclusion on the suitability of the surfaces to be checked and on the suitability of the part.

REPORT FORM

Title of work, purpose of work.

The equipment used in the performance of the work.

Exercise.

Detail sketch.

Checked size

Limit deviations in mm

Limit dimensions in mm

Tolerance in mm

Permissible error, mm

es, es

EI, ei

D max , d max

D min , d min

D max = d + es (mm) d min = d + ei (mm) Td = es – ei (mm)

Choice of measuring instruments

Checked size

Measurement limit

Division value, mm

Measurement results:

Limit dimensions

surface to be tested

Measurement results

Conclusion

about suitability

Dmax

dmax

Dmin

dmin

Conclusion on suitability:________________

Review questions:

How are the limit size, nominal size and
marginal deviation?

Graphic representation of tolerances.

Designation of maximum deviations of incompatible dimensions in the drawings.

Types and purpose of the caliper tool.

Describe the main parts and application of a caliper.

Explain how the vernier is counted.

Laboratory work №3.

Topic: Dimensional control of parts with micrometric instruments.

Objective: To master the measurement of the dimensions of parts with micrometric instruments.

Equipment: micrometers, the part to be measured.

Literature:

1. V.D. Myagkov Tolerances and landings / volume 1 - L .: Mashinostroenie, 2014.

2. Guide to the selection of measuring instruments (manual).

Exercise:

1. Select a measuring tool to check dimensions.

Measure given dimensions

Give a conclusion on the suitability of the measured dimensions.

METHODOLOGICAL INSTRUCTIONS

Micrometer instruments

When caliper tools are not able to give the required accuracy in measuring small quantities, apply.These tools, depending on the measuring range, are available in several versions. This, among others, can be pointer counting devices for manual and desktop use.

The action of the micrometer is provided by the movement of the screw along the axis during its rotation in a fixed nut. The micrometer, depending on the design, can measure the covering and covered dimensions, the cross section of thin sheet materials and wires. Internal micrometers are used to determine slot widths and hole diameters.

For comparison with the standard of the measured part or for absolute measurements, lever micrometers are used.

In order to measure the average diameter of an external thread, special thread micrometers are made.

Micrometric instruments are called means of measuring linear dimensions, based on the use of a screw pair, called a micropair. The microcouple serves as a dimensional and conversion device in these measuring instruments. The method of measurement with micrometric instruments is direct, absolute. Micrometric instruments include: micrometers, micrometric depth gauges and inside gauges.

1. Micrometers smooth type MK are designed to measure the outer dimensions of products.

Smooth micrometers MK are made with measurement limits: 0-25 mm, 25-50 mm, 50-75 mm ... 250-275 mm. 275-300 mm. 500-400 mm, 400-500 mm, 500-600 mm 1st and 2nd accuracy class.

The design of the micrometer is shown in Figure 1. Bracket1 must be

rigid enough so that its deformation from the measuring force does not affect the accuracy of the measurement. In micrometers of small sizes (up to 300 mm) heel2 pressed into the bracket. In micrometers for sizes over 300 mm, the heels are movable (adjustable or replaceable), which makes it easier to set them to the zero position and allows you to expand the measurement limits.

M
ICROMETER - designed to measure linear dimensions. Smooth micrometers MK are made with measurement limits: 0-25 mm, 25-50 mm, 50-75 mm ... 250-275 mm. 275-300 mm. 500-400 mm, 400-500 mm, 500-600 mm 1st and 2nd accuracy class.

Smooth micrometers type MK are designed to measure

outer dimensions of products.

brace 1 must be rigid enough so that its deformation from the measuring force does not affect the accuracy of the measurement. In micrometers of small sizes (up to 300 mm) heel 2 pressed into the bracket. In micrometers for sizes over 300 mm, the heels are movable (adjustable or replaceable), which makes it easier to set them to the zero position and allows you to expand the measurement limits. Stem 5 pressed into the bracket or attached to it on the thread. In some designs, the stem is performed together with the bracket. Inside the stem, on one side, there is a micrometric thread, and on the other side, there is a smooth cylindrical hole that ensures the exact direction of the screw movement. 3 . At the end of the stem (length

micrometric thread) there are longitudinal slots, and on the outside there is a conical thread with a nut screwed onto it 10 . By turning this nut, you can change the tightness of the threaded connection of the screw with the stem, providing the necessary ease of rotation of the screw and eliminating backlash. The end surface of the screw, facing the heel, is the measuring one. End surfaces of the heel 2 and screw 3 must have a surface roughness not lower than the 12th roughness class.

The ratchet is designed to ensure the constancy of the measuring force within 7 ± 2 N. The ratchet mechanism consists of a ratchet 7 , pin 8 and springs 9 . Clockwise rotation of the ratchet head is transmitted to the micrometer screw by friction between the pin 8 , pressed by a spring 9 , and ratchet teeth. At

measuring force exceeding the allowable value, the ratchet will rotate relative to the screw. There are other designs of devices for stabilizing the measuring force (friction device with a spiral spring, with a helical spring, etc.). locking device 4 used when it is necessary to keep the micrometer screw in the set position.

The result of measuring the size with a micrometer is counted as the sum of readings on the stem and drum scale. The scale division of the stem is 0.5 mm, and the scale of the drum is 0.01 mm. Micropair thread pitch 0.5 mm. The number of divisions of the drum is 50. If you turn the drum by one division of its scale, then the end of the microscrew will move relative to the heel by 0.01 mm, because 0.5mm: 50 = 0.01mm. The readings on the micrometer scales are counted in the following order: first, on the scale of the stem, read the value of the stroke closest to the end of the bevel of the drum. Then, on the scale of the drum, the value of the stroke closest to the longitudinal stroke of the stem is read. By adding both values, the micrometer readings are obtained. To zero all m
micrometers, except for 0-25 mm, are supplied with setting measures, the size of which is equal to the lower limit of measurement. Designation: micrometer MK-50-1 GOST 6507-78.

For faster measurements, instruments are made with electronic "digital" indication, the final measurement value of which is displayed on a separate electronic display (for example, a modified micrometer MK - )

2. MICROMETRIC DEPTH GAUGE.

M micrometric depth gauges are designed to measure the depth and height of products, distances to shoulders and ledges. Micrometric design

depth gauge : 1 - micrometer screw; 2 - stem; 3 - drum; 4 - ratchet.

Depth gauge measurement range

is 0...25, 25...50, etc., up to 125...150 mm.

The numbers at the strokes of the stem and drum are applied in

in reverse order compared to micrometers, since the greater the depth, the further the microscrew is extended.

The depth gauge is set to "0" on the setting measures-sleeves on a flat, precise surface. At the end of the microscrew, a hole is made into which replaceable measuring rods are inserted.

The peculiarity of the micrometric depth gauge is that the numerical values ​​of the strokes of the stem scale are located, decreasing with the removal of the drum from the base, because the size of the depth of the measured ledge decreases accordingly. The number of stroke values ​​on the drum is also opposite to the numbers and scale of the smooth micrometer drum.

GM micrometric depth gauges are manufactured with measurement limits of 0-25 mm, 25-50 mm, 50-75 mm ... 150-175 mm, 175-200 mm of the 1st and 2nd accuracy classes. Designation: depth gauge GM - 75-1 GOST 7470-78.

3. INSIDE MICROMETRIC GAUGES.

Inside micrometers are designed to measure internal linear dimensions. They consist1 - micrometer screw;2 - drum; 3 - stopper.

The increase in the measurement limits of inside gauges is carried out using a set of extension rods of different lengths, enclosed in tubes and preloaded with springs.

To connect extension cords with one another and with a micrometric inside gauge, extension cords have an external thread at one end and an internal thread at the other.

Inside micrometers are produced in the form of sets of micrometer heads with tips and sets of extensions for them.

Setting the scales of micrometric calipers to the zero position can be

carry out by micrometers for external measurements, as well as in a special bracket.

The measurement result is calculated as the sum of: original head size + extension size + reading of the head scales.

Inside micrometers are produced with measurement limits of 50-75 mm, 75-175 mm, 75-600 mm, 150 - 1250 mm, 800-2500 mm 1250-4000 mm, 2500-6000 mm, 6000-10000 m > 1 of the first accuracy class. Designation: caliper NM-175 GOST 10-75.

MEASUREMENT TECHNIQUE

before starting work with a micrometric instrument, it is necessary to familiarize yourself with the passport and check its completeness;

remove grease from the outer surfaces of the assemblies and parts of the tool, especially carefully from the measuring surfaces with a cloth soaked in gasoline and wipe with a dry, clean cloth;

Inspect and check the quality of the tool. On the measuring surfaces, the stem and the beveled part of the drum, nicks and traces of corrosion are not allowed. Move the micrometer screw several times in both directions. The drum should move along the stem smoothly without friction against it, and the micrometer screw should not have axial play.

Check the action of the locking device, as well as the ratchet in various positions of the micrometer screw. There are no ratchets for micrometric inside gauges;

Check zero setting. Checking the micrometric tool for "0" is carried out with setting measures, with the exception of smooth micrometers and micrometric depth gauges for measuring dimensions up to 25 mm. If the zero reading is outside 0.01 mm, zero the instrument. To do this, the micrometer screw is locked, the drum is released from the clutch with the screw and rotated until the zero stroke coincides with the longitudinal stroke of the stem, and the drum is fixed again;

Take measurements with smooth micrometers and micrometric depth gauges using a ratchet. The correct measurement position is one in which the inside micrometer does not move in the transverse direction and tightly touches the generatrix of the hole in the longitudinal direction;

After completion of work, if necessary, disassemble the micrometric instrument, wash it in gasoline, lubricate with anti-corrosion grease and put it in a case.

ORDER OF PERFORMANCE OF LABORATORY WORK

1. Draw a sketch of the part.

According to the drawing, find the dimensions to be checked and enter them in the table.

Select the maximum deviations of the dimensions being checked (V.D. Myagkov Fitting tolerances vol. 1 table, 3 pp. 140-141, table 1.30 p. 99) and enter them in the table.

4. Determine the limiting dimensions and tolerances of the dimensions to be checked, write them down in the table.

5. Select the permissible error for the dimensions being checked (guide for the selection of measuring instruments table 1 page 3) and enter them in the table,

6. Select measuring instruments and their characteristics for each checked size (guidance for the selection of measuring instruments) and enter them in the table,

7 . Take measurements in two directions and enter them in the table,

8. Give a conclusion on the suitability of the tested surfaces and on the suitability of the part.

Report Form

Job title.

Objective.

The equipment used in the performance of the work.

The composition of the task.

Detail sketch.

Determination of limiting dimensions and tolerances in the checked surfaces of products

verifiable

the size

Limit deviations in mm

Limit dimensions in mm

Tolerance in

mm

TD ,Td

mm

E S,es

EI, ei

D max d max

D min , d min

D max = D + ES (mm) D min = D + EI (mm) TD = ES - EI (mm)

V selection of measuring instruments

Checked size

Measuring instrument designation

Measuring instrument error

Measurement limit

Division value, mm

Measurement results:

Limit dimensions

surface to be tested

Measurement results

Conclusion

about suitability

Dmax

dmax

Dmin

dmin

9. Conclusion on validity: _______________________

Review questions:

What measurements are called absolute?

What measurements are called relative?

What is a micrometer?

How is the scale division of a micrometer determined?

What parts does the micropair consist of, and what is its thread pitch?

What is the peculiarity of the device of a micrometric depth gauge, its scale and application?

Describe the main parts of the inside micrometer and its application.

Lab #4

Topic:"Control of the dimensions of parts by a comparative method".

Objective : To study the design of the indicator tool, plane-parallel end blocks of length. Master the technique of setting and measuring indicator instruments.

Equipment : Lever bracket, indicator bracket, indicator caliper, PPKMD with accessories, details for measurement.

Literature:

1 .V.D. Myagkov. Tolerances and landings. volume 1 - M.: Mashinostroenie, 2014

2. Guide to the selection of measuring instruments, (allowance).

Exercise:

Choose a measuring tool to check the dimensions, study their device and design.

Set up selected indicator and dimensional check tools.

Measure the specified surfaces of the part.

Provide a statement of suitability.

METHODOLOGICAL INSTRUCTIONS

INDICATOR TOOLS.

Indicator tools are equipped with measuring heads and are designed to determine the dimensions of parts using the relative method.

1. INDICATOR CLIPS

Are intended for measurement of the external linear sizes. The basis of the indicator bracket is the body-bracket 5, in the working recess of which there are a movable heel 2 located on the same measuring axis on one side, which perceives changes in the dimensions of the measured part, and on the other hand - an adjustable heel 1. On the side there is a force stop of the dial indicator 4. The indicator bracket is set to a size according to the setting measure or to a block of plane-parallel end blocks of length equal to the smallest limit size of the measured part, in this case the actual value of the size will be equal to the sum of the size of the block of end blocks of length and the reading value on the indicator scale with the corresponding sign

SI indicator brackets are manufactured with measurement limits of 0-50 mm, 50-100 mm, 100-200 mm, 200-300 mm ... accuracy class. Designation: clamp SI-300 GOST 11098-75.

2 BRACKETS LEVER.

Are intended for measurement of the external linear sizes. The bracket-body of the lever bracket has greater rigidity than that of the indicator one. Movable heel 6 and adjustable heel 1 have large measuring surfaces and their movements are much more precise. The movable heel has two recesses, one of them includes the lever of the offset, and the second is the tip of the transmission lever belonging to the measuring head, mounted in the body of the bracket. The movement of the movable heel is transmitted to the arrow 2 of the measuring head. In the rear end of the movable heel, a spring for measuring the force of the lever bracket is put on. The bracket has tolerance field indicators on the scale, which are rearranged with a key. The adjustable heel moves by turning the nut and is locked with a cap. Adjustment of the bracket to the size is made according to the block of end measures of length equal to the part. To set the arrow to zero, lock the heel by turning the cap and nut. The actual size will be equal to the sum of the dimensions of the block of end measures of length and the value of the reference on the indicator scale ( dmax + dmin ):2 with the corresponding sign. Lever staples are manufactured with measurement limits of 0-25 mm, 25-50 mm, 50-75 mm ... 125-150 mm, with a division value of 0.002 mm of the first accuracy class.

Designation: bracket СР50 GOST 11098-75

STAPLE MEASUREMENT TECHNIQUE.

Before measuring, wipe the cylindrical parts of the heels and especially carefully the measuring surfaces, wipe with a clean cloth soaked in gasoline, and finally with a dry cloth.

The parts to be measured must be dry and clean.

When using the bracket, it must not be subjected to various shocks;

After completing the measurements, the heels of the brackets are wiped with a cloth and lubricated with anti-corrosion grease, except for the measuring surfaces /, the bracket is placed in a case.

For example, to make a 27.855 mm block of tiles from the N1 set, the following tiles would be required:

tile 1.005 remains 26.85

tile 1.35 remains 25.5

tile 5.5 - "-20

tile 20 -"- 0

Check 1.005+1,35 + 5,5 + 20 = 27.855 mm

The selected measures are freed from grease and wiped with a clean soft cloth;

Tiles prepared for grinding should not be placed on the table with measuring surfaces, put on a clean sheet of paper or a clean napkin;

Lapping of tiles is carried out by their relative movement under
little pressure;

To avoid deformation of non-rigid tiles of short length

when directly measuring with a block, it is necessary to grind the tiles more rigid at the ends of the block;

5. After work, wipe the tiles and place them in the corresponding cells of the set case.

4. PLANE PARALLEL GAUGE STONES.

Plane-parallel gauge blocks are rectangular prisms.

They are designed to measure linear dimensions and are rectangular plates with two opposite measuring planes. Each tile has a specific size and is therefore a one-dimensional tool. Thanks to the careful finishing of the measuring surfaces, the tiles have a remarkable property of “grinding”, i.e., adhering to each other, which makes it possible to assemble several tiles into a block, obtaining the required size as a whole.

Measuring tiles can be measured with an accuracy of 0.001 mm. Measured tiles are made in sets.

Depending on the deviation of the average length of the measures from the nominal size and from the plane parallelism, 5 accuracy classes of the end measures are set: 00, 0.1.2, 3.

Tiles are produced in sets from 2 to 112 tiles in a set: moreover, according to GOST 9038-83, 19 sets are installed. GOST 9038-83 establishes the following series of lengths, checks and graduations of measuring instruments for accurate measurements of products and gradation: 0.001 0.005 0.01; 0.1; 1 10 5, 50; 100 mm

The most common are set. No. 1-83 measures, N 2-38 measures and sets

No. 6 and No. 7 - 11 measures each,

When compiling a set of tiles, one always strives to get it from the smallest number of tiles, since with an increase in the number of tiles in a block, the error increases.

To obtain a block from the smallest number of tiles, you must follow the following rule: first take the tile corresponding to the last character of a given size, then the penultimate one, etc. When fraction the number is ready, it is necessary to subtract from the integer part of the size the sum of whole millimeters, selected when compiling the fractional part, and take the corresponding tile in whole mm.

For example: block 71875

1st tile - 1.005

2nd tile -1.37

3rd tile - 9.5

4th tile - 60

71,875

Tiles can only measure parts with sanded surfaces. Before measuring and compiling a block, it is necessary to clean the tiles from grease with clean first-class gasoline, then wipe dry with a soft cloth and put on a clean table with a non-working surface.

So you need to consistently grind all the tiles included in this block.

1. The measurement is made at T - 20°C.

2. The measured object is cleanly wiped of dirt and washed with gasoline. The planes that are in direct contact with the tiles during measurement should not have nicks or burrs.

3. When working with tiles, it is unacceptable to touch the measuring surfaces with your hands.

4. Measuring tiles and their accessories must not be subjected to impact or fall.

5. After use, the tiles should be washed with first-class gasoline, wiped dry and lubricated with acid-free gasoline.

The nominal values ​​of the length of end measures must correspond to those indicated in table1.

Table 1

in mm

End gauge gradation

Nominal gauge block lengths

1,0005

0,001

From 0.99 to 1.01 incl.

" 1,99 " 2,0 "

" 9,99 " 10,01 "

0,005

From 0.40 to 0.41 incl.

0,01

From 0.1 to 0.7 incl.

"0.9" 1.5 incl.

" 2 " 3 "

" 9,9 " 10,1 "

From 0.1 to 3 incl.

From 0.5 to 25 incl.

From 1 to 25 incl.

From 10 to 100 incl.

From 25 to 200 incl.

From 50 to 300 incl.

From 100 to 1000 incl.

5 INDICATOR GAUGE

D For internal measurements, an indicator inside gauge is used.

It has a guide sleeve 5, in the upper part of which there is a dial indicator 1, fixed with a screw 2. Inside the sleeve there is a long rod that comes into contact with a short rod 10, which abuts against the fungus 9 of the tee 6 of the bore gauge head. In the tee there is an engine 4 and a replaceable measuring rod 8, fixed in the tee with a nut 7. On the side of the movable pin on the tee, a centering bridge 5 is mounted, which serves to install the indicator head along the diameter of the hole. When measuring holes, the engine 4 with a spiral spring 11 presses on the lever 9 and through the rod 10 transmits the movement to the long rod to the indicator.

The deviation of the size is determined by the movement of the indicator arrow.

As measures for setting indicator inside gauges to size and to zero, sets of gauge length gauges are used.

When measuring, it is necessary to shake the inside gauge in the axial plane in the longitudinal section and find the minimum position along the arrow of the measuring head, i.e. perpendicular to both generators of the hole being measured.

The inside gauge is adjusted to the nominal size of the checked size due to the replaceable tip. The indicator when set to zero should have an interference of 1-2 turns. The actual size will be equal to the sum of the nominal size and the reading on the indicator scale with the corresponding sign.

Indicator inside gauges are manufactured with measurement limits of 6-10 mm, 10-18 mm, 18-50 mm, 50-100 mm, 100-160 mm, 160-250 mm of the 1st and 2nd accuracy classes, and with measurement limits of 250 -450 mm, 450-700 mm, 700-1000 mm of the first class of accuracy with a division value of 0.01 mm. Designation: inside gauge NI-18-50-1 GOST 868-82.

MEASUREMENT TECHNIQUEINDICATOR NUTROMETERS.

before measuring, wipe the measuring surfaces with a clean cloth dampened with
gasoline and finally with a dry cloth,

the parts to be measured must be dry and clean,

when measuring a hole, the indicator caliper is inserted first by touching the hole wall with a bridge, and then the caliper is inserted further, with a slight swing in the axial direction;

after measurements, the measuring surfaces are wiped with a cloth and lubricated with anti-corrosion grease, put the inside gauge in a case.

ORDER OF PERFORMANCE OF LABORATORY WORK.

1. Draw a sketch of the part

Select the maximum deviations of the dimensions being checked (V.D. Myagkov "Tolerances and Fits", v.1, table 1. 7, p. 79, table 1.30 p. 95 and enter in the table.

Determine the maximum dimensions and tolerances of the dimensions to be checked, write them down in the table.

Select the permissible error for the dimensions being checked (guidelines for the selection of measuring instruments for controlling the dimensions of parts, Table No. 1, page 3) and enter them in the table.

For each checked size, select measuring instruments and their characteristics (guidelines for the selection of measuring instruments for controlling the dimensions of parts) and enter them in the table.

Calculate blocks of gauge blocks for setting up indicator tools.

Set up indicator tools.

Give a conclusion on the suitability of the tested surfaces and on the suitability of the part on them.

REPORT FORM:

Job title.

Objective.

The equipment used in the performance of the work.

The composition of the task.

Detail sketch.

Determination of limiting dimensions and tolerances in the checked surfaces of products

verifiable

the size

Limit deviations in mm

Limit dimensions in mm

Tolerance in mm

Permissible measurement error in

mm

E S,es

EI, ei

D max d max

D min, d min

TD ,Td

d max = d + es (mm) d min = d + ei (mm) Td = es – ei (mm)

D max = D + ES (mm) D min = D + EI (mm) TD = ES - TI (mm)

V selection of measuring instruments

Checked size

Designation

measuring instrument

Error

measuring instrument

Limit

measurements

Price

divisions, mm

Calculation of gauge block blocks for setting indicator tools

Measurement results

Conclusion on suitability _______________

Review questions:

What measuring heads do you know and how do they convert the movement of the tip into the turn of the arrow?

Describe the dial indicator, its division value and measurement.

How is the indicator caliper arranged? How is it applied?

What is an indicator bracket? How is it structured and how is it applied?

What is a lever brace? How is it arranged and what is the scale division value?

The textbook discusses the means and methods of carrying out work on various types of standardization and certification. Scientific-technical, normative-methodical and organizational bases of standardization and certification of production and services are stated. In order to harmonize work in the field of standardization and certification, the methodology and practice of certification abroad are considered in detail. A large number of examples and reference data are given in the form of tables and diagrams. After each chapter are given control questions and tasks.

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Â. n. KAKENOVA, T. n. GRAPH, Å. Â. TÅSLÅNOKO, Å. A. COMPOSITION OF METHODROLOGY, STRATEGY AND STRATEGY. ÏÐÀÊÒÈÊÓÌ Edited by B. N. Kaynova ÄÎÏÓÙÅÍÎ ÓÌÎ âóçîâ ïî îáðàçîâàíèþ â îáëàñòè àâòîìàòèçèðîâàííîãî ìàøèíîñòðîåíèÿ (ÓÌÎ ÀÌ) â êà ÷ åñòâå ó ÷ åáíîãî ïîñîáèÿ äëÿ ñòóäåíòîâ âóçîâ, îáó ÷ àþùèõñÿ ïî íàïðàâëåíèþ ïîäãîòîâêè «Êîíñòðóêòîðñêî-òåõíîëîãè ÷ åñêîå îáåñïå ÷ åíèå ìàøèíîñòðîèòåëüíûõ ïîäääääññääàÒêòòíààáááàà • • • à •à •à •à •àààààààà • • ì BBK 30.10Y73 K 12 KAYNOVA V.N., Grenelova T. N., Teslenko E. V., Kulikova E. A. K 12 Metrology, Standardization and Certification: Workshop: Textbook / Ed. V. N. Kainoy. - St. Petersburg: Publishing house "Lan", 2015. - 368 p.: ill. - (Textbooks for universities. Special literature). ISBN 9785811418329 The textbook contains theoretical and reference & methodological material on the standardization of the geometric characteristics of products, as well as on the choice of measuring instruments and processing the results of single and multiple measurements performed by direct and indirect methods. Variants of tasks used in the performance of practical classes and independent work in the discipline "Metrology, standardization and certification" have been developed. Designed for students of higher educational institutions studying in the technical areas of training bachelors & masters and graduates. It may be useful for engineering and technical services of enterprises and organizations that develop and manufacture products in the field of mechanical engineering. BBK 30.10ya73 Reviewers: F. F. REPIN - Ph.D. P. M. KOROLEV - candidate of technical sciences, deputy. chief technologist of OAO NAZ "SOKOL". Cover by EA VLASOVA Protected by the RF copyright law. Reproduction of the entire book or any part of it is prohibited without the written permission of the publisher. Any attempt to break the law will be prosecuted. © Publishing house "La; н», 2015 © Collective of authors, 2015 © Publishing house "Lan", artistic design, 2015 FOREWORD The discipline "Metrology, standardization and certification" refers to the basic part of the professional cycle of full-time and part-time education of students of higher educational institutions studying in technical areas of training bachelors, masters and graduates. This manual was developed for the first time in the form of a workshop, previous editions contained theoretical material and reference data. The authors of the manual have extensive experience in studying the issues of standardization and control of the accuracy of geometric parameters, in issues of standardization in the field of design and technological documentation. Considering that modern curricula pay considerable attention to the performance of independent and practical work by students, it became necessary to create a teaching aid in the form of a workshop. In the manual on all the topics under consideration, the theoretical part, options for tasks and examples of their solution are briefly given. The manual consists of five chapters and appendices that contain reference tables from the standards needed to complete the tasks. T. N. Grebneva prepared the first chapter, sections on keyed and splined connections from the fourth chapter. The second and third chapters, as well as the section on the choice of means 4 The preface of measurements from the fifth chapter were compiled by E. V. Teslenko. E. A. Kulikova developed a section on the rationing of metric thread parameters from the fourth chapter and a section from the fifth chapter on the calculation of measurement errors. Sections of the fifth chapter on the basics of probability theory, mathematical statistics and processing of measurement results were compiled by VN Kainova. The general edition of the manual was completed by associate professor, candidate of technical sciences Valentina Nikolaevna Kainova. The authors express their deep gratitude for valuable suggestions and comments on improving the content of the textbook to Ph.D. Exact science is unthinkable without measure. DI Mendeleev The further unreliability is found from the designer's board, the more expensive it is. AA Tupolev INTRODUCTION Design documentation determines the design quality of products. It is the main type of documents that are used to design technological processes for processing and assembly, control and measurement operations, as well as when performing certification work. When developing design documentation, it is necessary to comply with the requirements of current standards. Accuracy significantly affects the quality of products, the complexity of their manufacture, and, consequently, the cost. The purpose of this tutorial is to help students in solving these problems. The manual consists of five chapters and appendices that contain reference tables from the standards needed to complete the tasks. The first chapter gives general concepts about the system of tolerances for smooth cylindrical joints (ESDP), as well as recommendations and examples for the selection and calculation of tolerances and fits, methods for calculating dimensional chains. The second chapter is devoted to the issues of surface roughness, the accuracy of the shape and location of the surfaces of machine parts, and also contains recommendations for calculating the numerical values ​​of geometric tolerances and indicating them on the drawings. In the third chapter, joints with rolling bearings are considered, recommendations are given for choosing fits and drawing up drawings. 6 Introduction The fourth chapter contains information on feather keys, straight splines, threaded connections and spur gears. The fifth chapter covers the issues of metrological support for machine-building production: analysis of measurement errors, recommendations for choosing measuring instruments, the basics of probability theory and mathematical statistics, specific situations are considered. CHAPTER 1 REGULATION OF THE ACCURACY OF SMOOTH CYLINDRICAL JOINTS 1.1. ESDP. TOLERANCES AND FITTINGS OF SMOOTH JOINTS 1.1.1. TERMS AND DEFINITIONS ACCORDING TO GOST 25346-89 THEORETICAL PART FOR PRACTICAL LESSON 1.1 Standardization of the accuracy of linear dimensions is carried out by the standards of the Unified System of Tolerances and Fits (ESDP). The basic standard for this system is GOST 25346-89 “ONV. Unified system of tolerances and landings. General provisions, series of tolerances and basic deviations. Size - the numerical value of a linear quantity in the selected units of measurement. It is customary to divide the dimensions into free and mating, covered (shafts) and covering (holes). Hole - a term conventionally used to refer to the internal elements of parts, including non-cylindrical elements. Shaft is a term conventionally used to designate external elements of parts, including non-cylindrical elements. All shaft parameters are indicated by lowercase Latin letters, and all hole parameters are indicated by uppercase letters. The size can be actual, nominal or limit (largest or smallest). Actual size - the size of the element, set by the measurement with an allowable error. Limit dimensions - two maximum allowable dimensions of an element (largest and smallest), between which the actual size of a suitable part must be: Dmax, Dmin - the largest and smallest limit dimensions of the hole, respectively; dmax, dmin - the largest and smallest shaft dimensions, respectively. Nominal size - the size relative to which deviations are determined. The value of the nominal size is found according to the performed engineering calculations of the part for strength, rigidity, bending, etc. , taking into account the safety factor (equal to 2, 3 or more), with its further rounding in rows of normal linear dimensions according to GOST 6636-69: d - nominal shaft diameter; D is the nominal hole diameter. The nominal size serves as the starting point for deviations - actual or limit (upper and lower). All nominal sizes in the ESDP system are divided into a number of intervals,. Deviation - the algebraic difference between the size (actual, limit) and the corresponding nominal size. Limit deviation (upper or lower) - the algebraic difference between the limit and the corresponding nominal dimensions (Fig. 1.1): E, e - actual deviations of the hole and shaft, respectively; ES, es - upper limit deviations of the hole and shaft, respectively; EI, ei - lower limit deviations of the hole and shaft, respectively. ES = Dmax – D; es = dmax – d; EI = Dmin – D; (1.1) ei = dmin – d. (1.2) From here, the limiting dimensions can be determined as the algebraic sum of the nominal size and the corresponding limiting deviation according to the following formulas: Chapter 1. Rationing of the accuracy of smooth cylindrical joints 9 Fig. 1.1 Limit dimensions and deviations: a, b - shafts; in - holes. Dmax = D + ES; dmax = d + es; Dmin = D + EI; (1.3) dmin = d + ei. (1.4) The tolerance of the hole and the shaft (T) can be represented as the difference in the limiting dimensions or as the algebraic difference in the limit deviations: TD = Dmax - Dmin = ES - EI; (1.5) Td = dmax – dmin = es – ei. (1.6) The dependence of the tolerance on the nominal size is expressed in terms of the tolerance unit, which for sizes up to 500 mm is denoted by the letter i (µm), and for sizes over 500 mm - I (µm). It is a characteristic of accuracy (a function of the nominal size). Rounded values ​​​​of the tolerance unit depending on the nominal size are presented in table 1.1. In accordance with GOST 25346-89, the standard tolerance (IT) is any of the tolerances established by this system of tolerances and fits, which is specified by the quality (degree of accuracy) and is conditionally designated taking into account the quality number ITn. 10 Metrology, standardization and certification T a b l e 1.1 Dimension intervals, mm Rounded values ​​of tolerance units i, µm to 3 sv. 3 to 6 St. 6 to 10 St. 10 to 18 St. 18 to 30 St. 30 to 50 St. 50 to 80 St. 80 to 120 St. 120 to 180 St. 180 to 250 St. 250 to 315 St. 315 to 400 St. 400 to 500 i 0.6 0.8 0.9 1.1 1.3 1.6 1.9 2.2 2.5 2.9 3.2 3.6 4 Quality is a set of tolerances considered as appropriate the same level of accuracy for all nominal sizes. Size tolerances depending on the ranges of sizes and qualifications are given in Appendix B, Table B.1. The calculation was made for a normal temperature of 20°C with a probability of 0.997. Thus, quality is understood as the totality of tolerances of all nominal sizes of a given range, which are characterized by a constant relative accuracy, expressed by the coefficient a, called the number of tolerance units (Table 1.2). The range of values ​​of the coefficient a corresponds to the range R5 of preferred numbers. T a b l e 1.2 Quality Values ​​of the number of tolerance units a depending on the number of qualification 5 6 7 8 9 10 11 12 13 14 15 16 17 a 7 10 16 25 40 64 100 160 250 400 640 1000 1600 Number of tolerance units a for a given quality in the entire range of sizes is constant, and the tolerance value depends on the nominal size and quality number. Therefore, the tolerance value for grades 5 to 17, depending on the nominal size, can be determined by the formula ITn = a⋅i; (1.7) where a is the number of tolerance units; i - tolerance unit, microns. Chapter 1. Rationing the accuracy of smooth cylindrical joints 11 The tolerance unit, which is a function of the nominal size (hyperbolic dependence), is calculated by the formula i \u003d 0.453 D + 0.001D, where D \u003d Dmax Dmin, i.e. the geometric mean of the extreme dimensions of each interval (Dmax and Dmin), in mm. The standard establishes 20 qualifications: 01, 0, 1, 2, ..., 18. The qualifications from 01 to 4 are intended mainly for calibers. The executive dimensions in the drawings are given by the nominal size and the tolerance field. The tolerance field is limited by the largest and smallest limit sizes and is determined by the tolerance value and its position relative to the nominal size. With a graphical representation of tolerance fields, the position of the nominal size is depicted by a line called zero. The deviations are counted along the perpendicular to the zero line: up - with a positive sign, and down - with a negative sign. The horizontal lines limiting the tolerance field from above and below are the upper generatrices of cylindrical surfaces with the largest and smallest diameters, respectively. The position of the tolerance field is set by the main deviation, which in the ESDP is called one of the two limit deviations (upper or lower), closest to the zero line. Thus, for tolerance fields located above the zero line, the main deviation will be the lower deviation, and for tolerance fields located below the zero line, the upper deviation. The main deviations are indicated by letters of the Latin alphabet: lowercase - for shafts (a–zc), uppercase - for holes (A–ZC). For sizes up to 500 mm, 27 options are provided for the main deviations of shafts and holes (Table 1.3). The layout of the main deviations is shown in Figure 1.2. 12 Metrology, standardization and certification T a b l e 1.3 Designations of basic bore and shaft deviations Holes A B C D E EF F FG G H Js K Shafts a b c d e eff f fg g h js k m Holes N P R S T U V X Y Z ZA ZB ZC Shafts n p r s t u v x y z za zb zc M 1.2 Main deviations: a - holes; b - shafts; I - for landings with a gap; II - for transitional landings; III - for interference fit. Among the main deviations, a special place is occupied by deviations with the designation H, h, Js, js. The letters H, h Chapter 1. Rationing the accuracy of smooth cylindrical joints 13 denote the tolerance fields of the main hole and the main shaft, respectively. The main shaft (h) is a shaft whose main upper deviation is zero: es = 0. The main hole (H) is a hole whose main lower deviation is zero: EI = 0. The tolerance fields of the main hole and the main shaft are directed to the "body" details and determine the maximum size of the material. The term maximum material size refers to that of the limit sizes, which corresponds to the largest volume of the material of the part, i.e. the largest limit size of the outer (male) element (shaft) or the smallest limit size of the inner (female) element (hole). In GOST 25346, the term "material maximum limit" is used in approximately the same sense as the term "material maximum size" in accordance with GOST R 53090-2008. The designations Js, js correspond to the symmetrical (tolerance field) location of the deviations of the hole and the shaft, respectively (Fig. 1.2). The value of the basic deviation depends on the symbol and the value of the nominal size. The second deviation of the tolerance fields (Fig. 1.3) is defined as the algebraic difference or algebraic sum of the values ​​of the main deviation and the standard tolerance ITn of the hole or shaft specified by the size qualification, according to the following formulas (taking into account the sign of the main deviation and its location): ES = EI + ITn ( from A to H); (1.8) EI = ES – ITn (from K to ZC); (1.9) ei = es – ITn (from a to h); (1.10) es = ei + ITn (from k to zc). (1.11) The numerical values ​​of the main deviations are given in Appendix B, for shafts - in table B.2, for holes - in table B.3. 14 Metrology, standardization and certification Pic. 1.3 The layout of the tolerance fields: a - holes (ES and EI - positive); b - shaft (es and ei - negative). Due to the fact that the tolerance field is determined by the tolerance value and its position relative to the nominal size, its symbol in accordance with GOST 25436 should include the nominal size value, the designation of the main deviation and the quality number. For example: ∅30F7 and ∅30f6. The first dimension refers to the bore and the second dimension refers to the shaft. Tolerance fields and maximum deviations of dimensions on the drawings are indicated in accordance with ESKD according to GOST 2.307-2011 as follows: 1) the symbol of the tolerance fields (letter and number); recommended in mass production: ∅20m6, ∅50H7, ∅100f8, etc.; 2) numerical values ​​​​of limit deviations (upper and lower deviations) in mm; recommended in single production: +0.025; ∅100−0.036; ∅20++0.021 0.008; ∅50 −0.090 3) mixed method; recommended in mass production and for educational purposes: To write in a mixed way means to indicate the tolerance field twice: first with conventional signs (letter and 15 Chapter 1. Rationing the accuracy of smooth cylindrical joints with a number), and then in brackets with the values ​​\u200b\u200bof limit deviations. A parenthesis separates one way of writing a tolerance field from another. When drawing dimensions with maximum deviations on the drawings, the following rules should be observed: the upper and lower deviations are written in two lines in a font half the size of the main one, placing the upper deviation above the lower one: ∅30++0.075 0.051; the number of characters when recording the upper and lower deviations should be the same, for example, ∅30−−0.007 0.040; deviations equal to zero do not indicate, for example +0.021 ∅30; ∅30–0.033; with a symmetrical arrangement of deviations, their value is given after the “±” sign with digits equal in height to the digits of the nominal size, for example, ∅30 ± 0.026. ORDER OF PERFORMANCE OF THE PRACTICAL LESSON 1.1 To get acquainted with the theoretical part of the section. Get a task (option) of practical work. Options are given in Table 1.4. T A b l and C and 1.4 Options Options for Practical lesson 1.1 Option number Dimensions Option number Dimensions Option number Dimensions 1 30F8 30H8 10 100K7 100H6 19 80U7 80H6 2 90F8 90H9 11 120K6 120H7 20 70U6 70H7 3 45G7 45H6 12 85S7 85H6 21 50H11 50D10 4 65G6 65H7 13 75S6 75H7 22 150h10 150E9 5 112G6 112H5 14 102D8 102H7 23 12P5 12H5 6 35H6 35H4 15 135M5 135H6 24 240G7 240H6 72E7 72H6 7 16 58E8 58H9 25 20S7 20H8 8 185M6 185H7 17 10JS9 10H9 26 24K6 24H7 9 28A11 18 32C11 32H12 27 210r6 210H7 28H12 Job. Calculate tolerances and maximum deviations of given dimensions and write down the tolerance fields in a mixed way (1st level of complexity); at the 2nd level of complexity to build layouts of tolerance fields. 16 Metrology, standardization and certification Solution. 1. Find in table 1.1 the value of the tolerance unit for the given nominal dimensions. 2. Determine the number of tolerance units according to table 1.2, depending on the given qualification number. 3. Calculate the tolerance value for given dimensions using formula (1.7). 4. Round off the calculated tolerance value to the standard one according to Table B.1 of Appendix B. 5. Determine the type and value of the main deviations (Tables B.2 and B.3), as well as the second deviations of the tolerance fields for given sizes according to the formulas (1.8) , (1.9) or (1.10), (1.11). 6. Write down the given dimensions, indicating the tolerance fields in a mixed way. 7. Construct layouts of tolerance fields for given dimensions similar to Figure 1.3. EXAMPLES OF PERFORMANCE OF PRACTICAL LESSON 1.1 Example 1 (1st level of complexity) Task. Calculate the tolerances and limit deviations of the dimensions ∅30H7 and ∅30f6 and write down the tolerance fields in a mixed way. Solution. 1. For size ∅30, find the value of the tolerance unit i = 1.3 µm from Table 1.1. 2. Determine the number of tolerance units according to table 1.2: for the 7th grade -a = 16; for the 6th grade -a = 10. 3. Calculate the tolerance value for the given dimensions according to the formula (1.7): for the hole IT7 = a ⋅ i = 1.3 ⋅ 16 = 20.8 µm; for the shaft IT6 = a ⋅ i = 1.3 ⋅ 10 = 13 µm. 4. According to Table B.1, find the standard tolerance values: IT7 = 21 µm; IT6 = 13 µm. 5. Determine the type and value of the main deviations and the second deviations of the tolerance fields for the given dimensions according to the formulas (1.8), (1.9) or (1.10), (1.11). Chapter 1. Rationing the accuracy of smooth cylindrical joints 17 5.1. Size ∅30H7 has a main deviation H (Table B.3), which corresponds to a lower deviation equal to EI = 0, the second deviation is determined by formula (1.8): ES = EI + IT7 = 0 + 21 = +21 µm. 5.2. Size ∅30f6 has a basic deviation f, which corresponds to the upper deviation equal to es = –20 µm (Table B.2). Lower shaft deflection according to formula (1.10): ei = es – ITn = –20 – 13 = –33 µm. 6. Write down the specified dimensions, indicating the tolerance field in a mixed way: ∅30H7 (+0.021); ∅30f 6 (−−0.020 . 0.033) Example 2 (2nd level of difficulty) Task. Calculate limit deviations, limit dimensions ∅30H7 and ∅30f6, write down the tolerance fields in a mixed way and build tolerance fields. Solution. For size ∅30H7 determine: 1. Type and value of the main deviation H: EI = 0 (Table B.3). 2. The value of the standard tolerance IT7 = 21 (Table B.1). 3. The value of the second deviation according to formula (1.8): ES = EI + IT7 = 0 + 21 = +21 µm. 4. Record the tolerance field in a mixed way: ∅30H7(+0.021). 5. Calculate the limit dimensions of the hole using formulas (1.3): Dmax = D + ES = 30.000 + 0.021 = 30.021; Dmin = D + EI = 30.000 + 0 = 30.000. For the size ∅30f6 determine: 1. Type and value of the main deviation f: es = –20 (Table B.2). 18 Metrology, standardization and certification Pic. 1.4 Schemes for the location of tolerance fields: a - holes ∅30H7; b - shaft ∅30f6. 2. The value of the standard tolerance IT6 = 13 µm (Table B.1). 3. The value of the second deviation according to formula (1.10): ei = es – IT6 = –20 – 13 = –33 µm. 4. Write down the tolerance field in a mixed way: ∅30f 6 (−−0.020 . 0.033) 5. Calculate the maximum shaft dimensions using formulas (1.4): dmax = d + es = 30.000 - 0.020 = 29.980; dmin = d + ei = 30.000 - 0.033 = 29.967. 6. Build a layout of tolerance fields for the size ∅30H7 (Fig. 1.4a) and for the size ∅30f6 (Fig. 1.4b). 1.1.2. LANDINGS AND THEIR CHARACTERISTICS. LANDING SYSTEMS THEORETICAL PART TO PRACTICAL LESSON 1.2 Fitting is the connection of two parts, resulting in a gap or interference. The difference in dimensions Chapter 1. Rationing the accuracy of smooth cylindrical joints 19 of the hole and the shaft before assembly determines the nature of the connection of parts. Distinguish landings with a gap, landings with an interference fit and transitional landings. For the formation of landings, either the main hole H or the main shaft h is used. The main shaft is a shaft whose upper (basic) deviation is zero: es = 0 → h. Main hole - a hole whose lower (basic) deviation is zero: EI \u003d 0 → H. Nominal fit size - nominal size common to the hole and shaft that make up the connection. Fit characteristics include tightness, clearances and fit tolerance. Clearance (S) - the difference between the dimensions of the hole and the shaft before assembly, if the size of the hole is larger than the size of the shaft. Preload (N) - the difference between the dimensions of the shaft and the hole before assembly, if the size of the shaft is larger than the size of the hole. Fit tolerance - the sum of the tolerances of the hole and the shaft that make up the connection: TS (TN) = TD + Td. Rice. 1.5 Layout of tolerance fields for clearance fits (1.12) 20 Metrology, standardization and certification Clearance fit - a fit in which a gap is always formed in the connection, since the smallest limit hole size is greater than or equal to the largest limit shaft size. With a graphic representation of the fit, the hole tolerance field is located above the shaft tolerance field (Fig. 1.5). The limiting characteristics of a fit with a gap are the largest and smallest gaps and the gap tolerance: Smax = Dmax - dmin = ES - ei; (1.13) Smin = Dmin – dmax = EI – es; (1.14) TS = Smax – Smin = TD + Td. (1.15) An interference fit is a fit in which an interference is always formed in the joint, i.e., the largest limit hole size is less than or equal to the smallest limit size of the shaft. With a graphical representation, the hole tolerance field is located below the shaft tolerance field (Fig. 1.6). The limiting characteristics of an interference fit are the largest and smallest interference and interference tolerance: Fig. 1.6 Layout of tolerance fields of interference fit Chapter 1. Accuracy standardization of smooth cylindrical joints 21 Fig. 1.6. 1.7 The layout of the transition fit tolerance fields Nmax = dmax - Dmin = es - EI; (1.16) Nmin = dmin – Dmax = ei – ES; (1.17) TN = Nmax – Nmin = TD + Td. (1.18) Transitional fit - a fit in which both clearance and interference are possible in the joint, depending on the ratio of the actual dimensions of the hole and the shaft. With a graphic representation of the tolerance field, the hole and the shaft overlap completely or partially (Fig. 1.7). The limiting characteristics of the transitional fit are the largest gap, the largest interference fit and the fit tolerance: Smax = Dmax - dmin = ES - ei; (1.19) Nmax = dmax – Dmin = es – EI; (1.20) TS/N = Smax + Nmax = TD + Td. (1.21) The diagram in Figure 1.8 illustrates the calculation of clearance fit tolerance, transitional fit and interference fit through limiting characteristics. Since the gaps and tightness are of the opposite nature, it is customary to put the gaps in the positive direction from zero, and the tightness - in the negative direction. The problem, in accordance with the scheme, is solved as a geometric one, i.e., the fit tolerance is determined either as the difference between segments equal to the limiting characteristics of the fit (for landings with a gap and landings with an interference fit), or as their sum (for a transitional fit). 22 Metrology, standardization and certification Pic. 1.8 Scheme for calculating the fit tolerance according to the limiting characteristics The fit designation is indicated after the nominal size of the fit. Landing is indicated by a fraction, in the numerator of which the symbol of the hole tolerance field is indicated, and in the denominator - the symbol of the shaft tolerance field. With a mixed designation method, after the symbol for the tolerance fields of the hole and the shaft, the numerical values ​​\u200b\u200bof the maximum deviations of these tolerance fields are indicated, enclosed in brackets. For example: ∅40 H7/ k6; ∅40 H7 (+0.025) H7 ; ∅50 . k6 k6 (+0.018 +0.002) The system of tolerances and fits is a set of series of tolerances and fits, naturally built on the basis of theoretical and experimental studies. Landings can be assigned in two systems: in the hole system (СH) and in the shaft system (Сh). Landings of the hole system - landings in which the required gaps and interferences are obtained by combining shaft tolerance fields of different basic deviations with the tolerance field of the main hole H (EI \u003d 0). Thus, in order to change the nature of the connection, it is necessary to change the position of the shaft tolerance field, i.e. the main shaft deviation (Fig. 1.9), leaving the hole tolerance field (H) unchanged. Examples of landings in the hole system: ∅30N/k6; ∅30Н7/f6; ∅30Н7/р6. Landings of the shaft system - landings in which the required gaps and interferences are obtained by a combination of tolerance fields of holes that are different in terms of the main deviation with the tolerance field of the main shaft h (es \u003d 0). Chapter 1. Rationing the accuracy of smooth cylindrical joints 23 Fig.1. 1.9 Tolerance fields of the hole system Thus, in order to change the nature of the connection, it is necessary to change the main deviation of the hole, i.e. the position of the hole tolerance field (Fig. 1.10), leaving the shaft tolerance field (h) unchanged. Examples of landings in the shaft system: ∅30M7/h6; ∅30F7/h6; ∅30R7/h6. Similar landings of different systems with the same nominal size are interchangeable, since they have the same limiting characteristics. However, in some cases, the use of a shaft system is necessary. Examples of the application of the shaft system: 1) in the joints of a smooth shaft with several holes for landings of various nature; Rice. 1.10 Tolerance fields of the shaft system 24 Metrology, standardization and certification 2) in the connection of the outer ring of the bearing with the hole in the housing (the bearing is a standard product); 3) in the joints of the keys along the width with the grooves of the hole and the shaft; 4) the use of smooth cold-drawn calibrated bars as axles or shafts without additional machining in agricultural machines,. The standard allows any combination of tolerance fields for holes and shafts, but two narrower series of tolerance fields are recommended for use: the main series, in which an even narrower selection of preferred tolerance fields is highlighted (Tables 1.5 and 1.6), and an additional series of limited use. Table 1.5 Preferred tolerance fields in the hole system Main holes Shaft tolerance fields Number of fields H7 e8, f7, g6, h6, js6, k6, n6, p6, r6, s6 10 H8 d9, e8, h7, h8 4 Н9 d9, h9 2 Н11 2 d11, h11 Σ 18 Total Table 1. 6 Preferred tolerance fields in the shaft system Main shafts Hole tolerance fields h6 F8, H7, Js7, K7, N7, P7 6 h7 H8 1 h8 E9, H9 2 h11 H11 1 Total Number of fields Σ 10 Hole system (CH) is preferred, so how it allows to reduce the cost of processing parts by reducing the range of standard sizes of measuring cutting tools (drills, countersinks, reamers) and measuring tools (bore gauges for holes). Chapter 1. Rationing the accuracy of smooth cylindrical joints 25 Landings are called basic if the following conditions are met: the tolerance fields (basic deviations) of the hole and the shaft belong to the same system; the accuracy of the hole and the shaft is the same, i.e. the numbers of the hole and shaft qualifications are the same or differ by one; in rare cases, a difference in qualification numbers equal to two is allowed. If these conditions or one of them are not met, the landing will be combined on both grounds or on one of them. Examples of basic and combined landings: 1) landing ∅45Н7/k6 - basic landing: tolerance fields belong to one system - the hole system, and the difference in qualification numbers is equal to one; 2) landing ∅45Н7/h6 - combined landing on the first sign. The tolerance fields belong to different systems: the hole tolerance field belongs to the hole system, the shaft tolerance field belongs to the shaft system. 3) landing ∅45F9/k6 - combined in two ways. The hole and shaft tolerance fields belong to different systems: the hole tolerance field belongs to the shaft system, and the shaft tolerance field belongs to the hole system. The difference between the numbers of qualifications is not more than three. The hole tolerance fields recommended by the standard for nominal sizes from 1 to 500 mm for different qualifications are presented in Table B.4. The largest number of tolerance fields (10) is in the zone of 7-11 qualifications. Shaft tolerance fields recommended by the standard with nominal sizes from 1 to 500 mm for different qualifications are presented in Table B.5. The largest number of tolerance fields (16) is in the zone of 6-11 qualifications. ORDER OF PERFORMANCE OF THE PRACTICAL LESSON 1.2 Level of the first complexity - the solution of questions for one given landing, for two landings - the second level, and for three - the third level of complexity. 26 Metrology, standardization and certification Read the theoretical part of the section. Get a task (option) of practical work. Options are given in Table 1.7. T a b l e 1.7 Landings Option number Option number Options for practical exercises 1. 2 105Js7/h6 14 Landings 1 30H7/f6 62P7/h6 16H6/g5 50U8/h7 88H8/e7 2 45G7/h6 83H6/r5 58K7/h6 15 45H7/g6 76M7/h6 25H9/js9 22H7/r6/3 35h8 /x8 100M6/h5 16 30F7/h6 180K8/h7 4 22C11/h10 230H6/t5 18 K8/h7 17 25F7/h6 10Js10/h9 45H7/s6 5 40D11/h10 60H7/p6 105H7/js 7 18 32 h7 175H6/t 5 6 118F10/h9 150H7/p6 130H6/m5 19 34D9/h8 240H5/k4 102H7/s6 7 76D8/h7 205H7/u7 90H7/m6 20 72F8/h7 18H8/z8 90H7 2H7/js8 /h6 55H7/k6 21 118U8/h7 15H10/h9 20H7/n7 9 90H8/g8 110H7/t6 65N7/h6 22 27M8/h7 36H10/f9 125H7/s7 10 185H8/k7 222N8/h7 70H10/d9 H7 23 95H11 / D11 114JS9 / H6 / H9 50G7 / H6 / H6 55H7 / S6 12 80K8 / H7 122H7 / R6 / R6 / N6 / H6 / H6 140H7 / N6 40H9 / X8 26 180H10 /e9 105R7/h6 215H6/k5 50F8/h7 13 90H12/b11 When calculating the main deviations of the holes (K, M, N, as well as for P–Z up to the 7th grade), use the “Note” to Table B.3 of Appendix B. Task. Determine the maximum deviations of the tolerance fields for three given landings (with a gap, an interference fit and a transitional fit) according to a given option. 1. Determine the maximum deviations of the tolerance fields of given landings. To do this, according to tables B.1–B.3 of Appendix B, determine the tolerances and basic deviations. 2. Calculate the second deviations of the tolerance fields depending on the main deviation and tolerance, as was done during the first practical work. 3. Write down the tolerance fields for the dimensions of the parts in a mixed way. 4. Calculate the limiting characteristics of the given fits, find the fit tolerance in two ways: according to Chapter 1. Rationing the accuracy of smooth cylindrical joints 27 limit gaps or interference, and perform the check according to the tolerances of the hole and shaft according to the formula (1.12). 5. Build three layouts of tolerance fields for all three landings. EXAMPLE OF IMPLEMENTATION OF PRACTICAL LESSON 1.2 Task. Calculate the limiting characteristics of three given landings and build the layout of the tolerance fields for them: ∅40H7/f6; ∅40H7/k6; ∅40H7/r6. Solution. 1. Determine the maximum deviations of the tolerance fields of given landings. To do this, according to Table B.1 of Appendix B, determine the tolerances for the size ∅40: tolerance IT7 = 25 µm; tolerance IT6 = 16 µm. The main deviations are determined according to tables B.2, B.3 of Appendix B: for H → EI = 0; for f → es = –25 µm; for k → ei = +2 µm; for r → ei = +34 µm. 2. Calculate the second deviations of the tolerance fields depending on the main deviation and tolerance: for H → ES = EI + IT7 = 0 + 25 = +25 µm; for f → ei = es – IT6 = –25 – 16 = –41 µm; for k → es = ei + IT6 = +2 + 16 = +18 µm; for r → es = ei + IT6 = +34 + 16 = +50 µm. 3. Write down the tolerance fields for the dimensions of the parts in a mixed way: +0.018 +0.050 ∅40H7 (+0.025); ∅40f 6 (−−0.025 0.041); ∅40k6 (+0.002); ∅40r 6 (+0.034). 4. Calculate the limiting characteristics of the given landings. 4.1. Calculate the limiting characteristics by H7 (+0.025) of the cage with a gap in the hole system ∅40 by f 6 (−0.025) 0.041 formulas (1.13)–(1.15): Smax = ES – ei = +25 – (–41) = 66 µm ; 28 Metrology, standardization and certification Smin = EI – es = 0 – (–25) = 25 µm; TS = Smax – Smin = 66 – 25 = 41 µm; Check according to formula (1.12): TS = TD + Td = 25 + 16 = 41 µm. 4.2. Calculate the limiting characteristics of the transitional fit in the hole system ∅40 lam (1.12), (1.19)–(1.21): H7 (+0.025) according to form6 (++0.018 0.002) Smax = ES – ei = 25 – 2 = 23 µm; Nmax = es – EI = 18 – 0 = 18 µm; TS/N = Smax + Nmax = 23 + 18 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. Rice. 1.11 Schemes for the location of landing tolerance fields: a - with a gap; b - transitional; c - with tension. Chapter 1. Rationing the accuracy of smooth cylindrical joints 29 4.3. Calculate the limiting characteristics of an interference fit in the hole system ∅40 lam (1.12), (1.16)–(1.18): H7 (+0.025) r 6 (++0.050 0.034) according to the form - Nmin = ei – ES = 34 – 25 = 9 µm; Nmax = es – EI = 50 – 0 = 50 µm; TS/N = Nmax – Nmin = 50 – 9 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. 5. Construct the layout of the tolerance fields of the given landings (Fig. 1.11). 1.1.3. GENERAL AND SPECIAL RULES FOR THE FORMATION OF INTERCHANGEABLE SEATS THEORETICAL PART FOR PRACTICAL LESSON 1.3 GOST 25346 provides for the interchangeability of similar fits of the hole system and the shaft system with the same nominal dimensions. Such landings have the same limiting characteristics due to the use of general and special rules that establish the values ​​​​of the same basic deviations of the shaft and hole. The general rule establishes the following ratios between the same (i.e., having the same letter designation) main deviations: EI \u003d -es → from A (a) to H (h); (1.22) ES = –ei → from K (k) to ZC (zc). (1.23) In accordance with the general rule, the main deviations of the hole and the shaft of the same name are equal in magnitude and opposite in sign, i.e., they are symmetrical with respect to 30 Metrology, standardization and certification Pic. 1.12 Scheme of the location of the main deviations of the same name of the zero line. A fragment of the layout of the main deviations of the same name is shown in Figure 1.12. The general rule applies to all clearance fits, to transitional fits from grade 9 and coarser, and to interference fits from grade 8 and coarser. A special rule applies to transitional landings up to the 8th grade inclusive and interference landings up to the 7th grade. It allows you to get the same limit gaps and tightness in the same fit, specified in the hole system and in the shaft system, in which the hole of a given quality is connected to the shaft of the nearest more accurate quality. Special rule: the main deviation of the hole is equal to the main deviation of the shaft, taken with the opposite sign, with the addition of the correction ∆: ES = –ei + ∆, (1.24) where ∆ = ITq – ITq–1 is the difference between the tolerances of adjacent qualifications, i.e. the difference between the tolerance of the considered quality (hole) and the tolerance of the nearest more accurate quality (shaft). The second deviation of the tolerance field of the hole or shaft is determined through the basic deviation and tolerance ITn in accordance with the formula for calculating the tolerance. When changing the system, the accuracy (quality) of the hole and the shaft does not change. Chapter 1. Rationing the accuracy of smooth cylindrical joints 31 ORDER OF PERFORMANCE OF THE PRACTICAL LESSON 1.3 Familiarize yourself with the theoretical part of the section. Get a task (option) of practical work. Options are given in Table 1.8. T a b l e 1.8 Options for practical exercises 1.3 No. option Landing No. option Landing No. option Landing h5 12 58E9/h8 21 36G7/h6 4 25F9/h8 13 55K7/h6 22 12N9/h9 5 100F7/h6 14 60H7/p6 23 76H11/d10 6 45H7/g6 15 83R6/h5 24 210H6/t5 7 105H7/f6 25 36H7/g6 8 25H9/f8 17 55H7/k6 26 20Js9/h9 9 130H6/k5 18 27H7/r6 27 28N8/h7 For a given fit, form an interchangeable fit of the same name in another system. Calculate the limiting characteristics of both landings. Build the layout of the tolerance fields of the landings of the same name. Solution. 1. Determine the system of a given fit and assign a fit of the same name to it in another system. 2. Determine the value of the tolerance value, the type and value of the value of the main and second deviations for all tolerance fields forming similar landings (see note to Table B.3). Designate landings in a mixed way. 3. Calculate the limiting characteristics of both landings. 4. Build the layout of landing tolerance fields. 5. Make a conclusion about the interchangeability of landings. 32 Metrology, standardization and certification PRACTICAL EXAMPLES 1.3 Example 1 for the general rule (2nd level of complexity) Task. For a given fit ∅40Н7/f6, form an interchangeable fit of the same name. Calculate the limiting characteristics of both landings. Build the layout of the tolerance fields of the landings of the same name and draw a conclusion. Solution. 1. A fit with a clearance in the hole system is specified, since there is a tolerance field for the main hole. It corresponds to the fit of the same name in the shaft system ∅40F7/h6. 2. Determine the value of the tolerance value, the type and value of the main and second deviations for all tolerance fields that form similar landings. 2.1. Calculate and round up to standard values ​​according to Table B.1 the tolerance values ​​of the 6th and 7th (IT6, IT7) qualifications for a nominal size of 40 mm, which corresponds to the tolerance unit i = 1.6 µm: IT6 = a⋅i = 10 ⋅1.6 = 16 µm; IT7 = a⋅i = 16⋅1.6 = 25 µm. 2.2. Determine the type (upper or lower) and the values ​​of the main deviations of holes with ∅40 (Tables B.2 and B.3 of Appendix B): H → EI = 0; F → EI = +25 µm. 2.3. Since landings with a gap are given, based on the general rule (EI = –es), we find the values ​​of the main shaft deviations of the same name: h → es = 0; f → es = –25 µm. 2.4. Calculate the second deviations of the tolerance fields of the hole and the shaft through the main deviation and the tolerance value (in accordance with the formulas for calculating the size tolerance through deviations): TD = ES - EI; Td = es - ei. Chapter 1. Rationing the accuracy of smooth cylindrical joints 33 Calculate the second deviation of the tolerance fields: H7 → ES = EI + IT7 = 0 + 25 = +25 µm; h6 → ei = es – IT6 = 0 – 16 = –16 µm; F7 → ES = EI + IT7 = +25 + 25 = +50 µm; f6 → ei = es – IT6 = –25 – 16 = –41 µm. 2.5. Designate landings in a mixed way: 3. Calculate the limiting characteristics of both landings. 3.1. Calculate the limiting characteristics of fit with a gap in the hole system ∅40 H7 (+0.025) f 6 (−−0.025 0.041): Smax = ES – ei = +25 – (–41) = 66 µm; Smin = EI – es = 0 – (–25) = 25 µm; TS = Smax – Smin = 66 – 25 = 41 µm; TS = TD + Td = 27 + 16 = 41 µm. 3.2. Calculate the limiting characteristics of a fit with a clearance in the shaft system ∅40 F7 (++0.050 0.025) h6 (−0.016) : Smax = ES – ei = +50 – (–16) = 66 µm; Smin = EI – es = +25 – 0 = 25 µm; TS = Smax – Smin = 66 – 25 = 41 µm; TS = TD + Td = 27 + 16 = 41 µm. 4. Build the layout of the tolerance fields of the landings of the same name (Fig. 1.13). 34 Metrology, standardization and certification Pic. 1.13 The layout of the landing tolerance fields: a - in the hole system; b - in the shaft system. Conclusion. The examples considered have shown that similar landings with the same nominal dimensions, given in different systems, are interchangeable, since they have the same limiting characteristics. Thus, for landings ∅40Н7/f6 and ∅40F7/h6, the smallest and largest gaps are equal, respectively: Smin = 25 µm; Smax = 66 µm. Example 2 for a special rule (3rd level of complexity) Task. For a given fit ∅50H7/k6, form an interchangeable fit of the same name. Calculate the limiting characteristics of both landings. Build the layout of the tolerance fields of the landings of the same name. Solution. 1. A transitional fit in the hole system is set not coarser than the 8th grade: ∅50H7/k6. It corresponds to the same-name fit in the shaft system ∅50K7/h6 2. Determine the value of the tolerance value, the type and value of the main and second deviations for the tolerance fields that form the same-name fit. 2.1. Calculate the tolerance values ​​of the 6th and 7th (IT6, IT7) qualifications for a nominal size of 50 mm, which corresponds to the tolerance unit i = 1.6 µm: IT6 = a ⋅ i = 10 ⋅ 1.6 = 16 µm; Chapter 1. Rationing the accuracy of smooth cylindrical joints 35 IT7 = a ⋅ i = 16 ⋅ 1.6 = 25 µm. 2.2. Determine the type (upper or lower) and the values ​​of the main deviations of the hole and shaft tolerance fields for landing ∅50H7/k6 (Table B.2, B.3 of Appendix B): H → EI = 0; k → ei = +2 µm. 2.3. Calculate the second deviations of the tolerance fields of the hole and the shaft through the main deviation and the tolerance value (in accordance with the formulas for calculating the size tolerance through deviations): TD = ES - EI; Td = es - ei. Calculate the second deviation of the landing tolerance fields ∅50H7/k6: H7 → ES = EI + IT7 = 0 + 25 = +25 µm; k6 → es = ei + IT6 = +2 + 16 = +18 µm. 2.4. To fit in the shaft system ∅50K7/h6, determine the main deviation of the tolerance field of the hole K7 according to a special rule, since the fit is transitional, not coarser than the 8th grade: ∆ = IT7 - IT6 = 25 - 16 = 9 microns; ES = –ei + ∆ = –2 + 9 = +7 µm, where ES is the main deviation of the hole tolerance field K7; ei - the main deviation of the tolerance field of the same name of the shaft k6. 2.5. Calculate the second deviation of the hole tolerance K7: EI = ES – IT7 = +7 – 25 = –18 µm. 2.6. The main deviation of the tolerance field of the main shaft h6 is es = 0. The second deviation is: ei = es – IT6 = 0 – 16 = –16 µm. 36 Metrology, standardization and certification 3. Designate fits in a mixed way: 4. Calculate the limiting characteristics of these fits. 4.1. Calculate the limiting characteristics of the transition fit in the hole system ∅50H7/k6: Smax = Dmax – dmin = ES – ei = 25 – 2 = 23 µm; Nmax = dmax – Dmin = es – EI = 18 – 0 = 18 µm; TS/N = Smax + Nmax = 23 + 18 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. 4.2. Calculate the limiting characteristics of the transition fit in the shaft system ∅50K7/h6: Smax = Dmax – dmin = ES – ei = +7 – (–16) = 23 µm; Nmax = dmax – Dmin = es – EI = 0 – (–18) = 18 µm; ТS/N = Smax + Nmax = 23 + 18 = 41 µm; TS/N = TD + Td = 25 + 16 = 41 µm. 5. Construct the layout of the tolerance fields of the landings of the same name (Fig. 1.14). Rice. 1.14 Landing tolerance fields layout: a - ∅50H7/k6; b - ∅50K7/h6. Chapter 1. Rationing the accuracy of smooth cylindrical joints 37 Conclusion. The examples considered have shown that similar landings with equal nominal sizes, given in different systems, are interchangeable, since they have the same limiting characteristics. Thus, for landings ∅50H7/k6 and ∅50K7/h6, the largest gap and the largest interference, respectively, are equal to Smax = 23 µm; Nmax = 18 µm. 1.1.4. ASSIGNING LANDINGS BY THE METHOD OF SIMILARITY THEORETICAL PART TO PRACTICAL LESSON 1.4 Method of precedents (analogues) The method lies in the fact that the designer, designing new units and mechanisms, assigns the same landings in them that were used in the same type of previously designed and in operation product,. The similarity method It is a development of the precedent method and is based on the classification of machine parts according to their design and operational characteristics and the release of reference books with examples of the use of landings (Appendix B.6). The disadvantage of this method is a qualitative rather than quantitative description of operational features and the difficulty of their identification with the features of a newly designed structure. Recommendations for the appointment of landings by the similarity method Appointment of landings with a gap. Landings are characterized by a guaranteed minimum clearance Smin, necessary to place lubricant between mating surfaces in movable joints, to compensate for temperature deformations, shape and location errors in order to ensure the assembly of the product. Basic requirements for landings with a gap: operating temperature should not exceed 50°C; 38 Metrology, standardization and certification the ratio of the length of the conjugation to the diameter should not exceed the ratio l:d ≤ 1:2; the coefficients of linear expansion of the hole and the shaft must be close to each other; the value of the guaranteed gap should be the greater, the greater the angular velocity of rotation. Assignment of landings with an interference fit. Landings are intended for fixed one-piece connections without additional fastening with screws, pins, etc. Relative immobility is achieved due to stresses arising in the material of mating parts. The main methods of assembling parts with an interference fit are: longitudinal pressing - assembly under pressure due to axial force at normal temperature; transverse pressing - assembly with preliminary heating of the female part or cooling of the covered part to a certain temperature. Assignment of transitional landings. Transition fits are designed for fixed, but detachable connections of parts, provide good centering and are used with additional fastening. These landings differ from each other in the probability of obtaining gaps or interference (Table 1.9). T a b l e 1.9 Probability of getting gaps or tightness in transitional fit Designation of fit Name of fit Probability of gaps Probability of tightness H7/n6 blind 1% 99% H7/m6 tight 20% 80% H7/k6 tense 60% 40% H7/ js6 dense 99% 1% PROCEDURE FOR PRACTICAL LESSON 1.4 (3rd LEVEL OF Difficulty) Read the theoretical part of the section. Get a task (option) of practical work. Options are specified in Appendix A (A.1–A.12) for size D1 or D2. Chapter 1. Rationing the accuracy of smooth cylindrical joints 39 Task. Determine the fit for a given connection (options A.1–A.12); taking into account the requirements for it, calculate the limiting characteristics and landing tolerance, build a layout of the landing tolerance fields, record the landing in a mixed way. The task is presented in the form of a map of the initial data. Solution. 1. Determine which group the landing belongs to (according to the description of the nature of the connection and its purpose): with a gap, with an interference fit, or transitional. 2. Determine the fit system based on the joint design analysis. 3. Select the type of mating (combination of the main deviations of the hole and shaft tolerance fields) according to Table B.6. 4. Determine the fit accuracy: the degree of accuracy, taking into account the preference for the use of fits and tolerance fields according to tables B.4 and B.5. 5. Determine limit deviations and tolerances according to tables B.1–B.3. 6. Calculate limit characteristics and fit tolerance. 7. Build a layout of the fit tolerance fields and record the fit in a mixed way. EXAMPLE OF PERFORMING A PRACTICAL LESSON 1.4 Map of initial data Name of initial data Value of initial data Nominal size of the connection and its value D = 65 mm Name of the parts included in the connection Helical gear 4 and spindle 6 wheel 4 in D2 is well centered relative to the spindle axis and has two diametrically spaced feather keys Solution. 1. Determine the landing group. A fixed connection with additional fastening with two dowels is specified, in which it is required to ensure precise centering. These conditions correspond to the transition landing (Table B.6). 2. Assign a landing system. The connection includes a helical gear and a spindle. Since the shaft is connected to one hole along this diameter, and the inner surfaces are more difficult to machine, we choose the preferred CH hole system. Thus, we assign the tolerance field of the main hole H to the hole of the helical gear. 3. Select the type of conjugation. Using the similarity method, we assign the following type of fit H / js (Table B.6). For this species, gaps are more likely than tightness. It provides easy assembly and disassembly, precise centering and is used for interchangeable parts that require additional fastening in exact qualifications: shafts from 4th to 7th, and holes from 5th to 8th. 4. Determine the fit accuracy. Analyzing the design and operating conditions of this connection, we assign the landing H7 / js6. This fit is used in the following connections: bearing cups of the 4th, 5th accuracy classes in housings, gears connected to the shaft with two keys, tailstock quill of a lathe (Table B.6). 5. Determine the limit deviations and tolerances of the hole and shaft. According to table B.1, find the tolerances of the 6th and 7th grades in the size range from 50 to 80: IT6 = 19 microns; IT7 = 30 µm. The upper deviation for ∅65Н7 is equal to the tolerance, i.e. 30 µm. Shaft ∅65js6 has a symmetrical tolerance field, i.e. ±9.5 µm. 6. Calculate the limit characteristics and fit tolerance ∅65 H7(+0.030) . js6(±0.0095) Limit hole dimensions: Dmax = D + ES = 65 + 0.030 = 65.030 mm; Chapter 1. Rationing the accuracy of smooth cylindrical joints 41 Dmin \u003d D + EI \u003d 65 + 0 \u003d 65 mm. Maximum shaft dimensions: dmax = d + es = 65 + 0.0095 = 65.0095 mm; dmin \u003d d + ei \u003d 65 + (-0.0095) \u003d 64.9905 mm. Maximum interference: Nmax = dmax - Dmin = 65.0095 - 65 = 0.0095 mm. Maximum clearance: Smax = Dmax - dmin = 65.030 - 64.9905 = 0.0395 mm. Average probable gap: Sm = (Smax - Nmax) / 2 = (0.0395 - 0.0095) / 2 = 0.015 mm. Fit tolerance: TS/N = Smax + Nmax = 0.0095 + 0.0395 = 0.049 mm or TS/N = TD + Td = 0.030 + 0.019 = 0.049 mm. 7. Build a layout of landing tolerance fields (Fig. 1.15). Rice. 1.15 Location of landing tolerance fields 42 Metrology, standardization and certification 1.1.5. LANDING ASSIGNMENT BY CALCULATION METHOD THEORETICAL PART FOR PRACTICAL LESSON 1. 5 Calculation method - the most reasonable method of landing assignment. It is based on engineering calculations of joints for strength, stiffness, etc. However, the formulas do not always fully take into account the complex nature of the physical phenomena occurring in conjugation. The disadvantage of this method is the need to test prototypes before launching a new product into mass production and adjust the fit in the developed product. The calculation method is used when, according to the operating conditions of the mechanism, the limit values ​​of gaps or interferences are limited, , for example, for plain bearings, critical press joints, etc. For example, when calculating a fit with a gap of the form H / h, used as a centering first of all, the maximum permissible eccentricity or thermal deformation of parts, if the operating temperature differs significantly from normal. When calculating transitional fits (mainly test fits), the probability of obtaining gaps and interferences in the joint, the largest gap according to the known maximum allowable eccentricity of the parts to be joined, or the greatest assembly force with the greatest fit interference are determined, and for thin-walled bushings, a strength calculation is performed. In interference fit, the minimum allowable interference is calculated based on the largest possible forces acting on the interface, and the maximum interference is calculated from the strength condition of the parts. After calculating the limiting characteristics, it is necessary to select a standard fit with limiting characteristics close to the calculated ones. Chapter 1. Rationing the accuracy of smooth cylindrical joints 43 The selection of a standard fit is carried out in the following sequence. 1. According to the results of the analysis of the design of the node, the landing system is determined. In most cases, landings are assigned in the hole system as the preferred one. Typical cases of assigning landings in the shaft system - see clause 1.1.4. 2. The landing tolerance is calculated with a gap, with an interference fit or a transitional fit according to the specified characteristics: Tpos = TS = Smax - Smin; (1.25) Tpos = TN = Nmax – Nmin; (1.26) Tpos = TS/N = Smax + Nmax. (1.27) 3. To determine the standard landing tolerance, it is necessary to determine the relative landing accuracy apos (number of landing tolerance units), based on formulas (1.7) and (1.12): Tpos = TD + Td = aD ⋅ i + ad ⋅ i = i ⋅ (аD + ad), (1.28) where aD + ad = apos, i.e. the sum of the numbers of tolerance units of the hole and the shaft is equal to the number of landing tolerance units; i = ipos - landing tolerance unit, the value of which depends on the nominal size of the landing (Table B.1). It follows from here that apos = Tpos/i. (1.29) 4. By known number landing tolerance units, the numbers of qualifications for the hole and the shaft are determined in accordance with the second sign of the main fit: the numbers of the qualifications of the hole and the shaft are the same or differ by one (rarely by two). Thus, aD = ad = apos/2. Then, according to Table B.1, the nearest to the calculated standard value of the number of tolerance units of the hole and the shaft is determined, according to which the qualification number is determined. 5. If the value of the number of tolerance units falls between two standard values, qualifications corresponding to these standard values ​​​​are assigned to the hole and shaft (coarer - to the hole, more than 44 Metrology, standardization and certification accurate - to the shaft), while the sum is aD + ad should be close to the calculated value apos, for example apos = 35, then with aD = ad = 35/2 = 17.5 - the accuracy of the hole and shaft corresponds to ≈ IT7 (a = 16). 6. Landing can be combined according to qualifications if there is a mounting on the same diameter of the rolling bearing shaft. In this case, it is necessary to limit the accuracy of the shaft. For example, IT6 (ad = 10), then aD = 35 - 10 = 25, which corresponds to the accuracy of the hole IT8. 7. Tolerance fields for the hole and shaft are assigned depending on the selected fit system (СH or Сh) of the hole and shaft tolerances (Table B.1) and the value of one of the limiting characteristics of the fit, which is used to calculate the main deviation of the tolerance field of the non-main part ( shaft or hole) in the following sequence: first, determine the tolerances of the hole and shaft according to table B.1 and the second deviations of the main parts according to formulas (1.8) and (1.10) of practice 1.1: ES = EI + ITn (from A to H); ei = es – ITn (from a to h); for landings with a gap, with an interference fit and a transitional one, specified in the hole system, the main deviations are calculated respectively according to the following formulas: es = EI - Smin; (1.30) ei = ES + Nmin; (1.31) ei = ES – Smax; (1.32) for landings with a gap, with an interference fit and transitional, given in the shaft system, the main deviations are calculated respectively by the following formulas: EI = es + Smin; (1.33) ES = ei – Nmin; (1.34) ES = ei + Smax. (1.35) Chapter 1. Rationing the accuracy of smooth cylindrical joints 45 Based on the calculated values ​​of the main deviations of the shaft or hole in Tables B.2 and B.3, the nearest standard values ​​are selected. 8. Then the second limit deviations of the non-main shaft or hole are determined according to the formulas (1.8) - (1.10) of practical lesson 1.1, depending on the group of landings. PROCEDURE FOR PRACTICAL LESSON 1. 5 (3rd LEVEL OF Difficulty) To get acquainted with the theoretical part of the section. Get a task (option) of practical work. Variants are specified in Appendix A (A.1–A.12) in size D3. Exercise. To select, according to the given limiting characteristics, a standard fit for a given connection by the calculation method. Calculate the limiting characteristics and tolerance of a standard fit, build a layout of the fit tolerance fields and record the fit in a mixed way. The task is presented in the form of a map of the initial data. Solution. 1. Determine which group the landing belongs to (according to the description of the nature of the connection and its purpose): with a gap, with an interference fit, or transitional. 2. Determine the fit system by analyzing the connection design. 3. Determine the fit accuracy. 3.1. Calculate the landing tolerance depending on its group according to the formula (1.26), or (1.27), or (1.28). 3.2. Determine the relative landing accuracy (number of landing tolerance units apos). Calculate by formula (1.29) the number of landing tolerance units. 3.3. According to table B.1, determine the qualities of the shaft and hole. When assigning qualifications to a hole and a shaft, it is necessary to strive to ensure the fulfillment of the second sign of the main fit, i.e., assign the same qualifications to the shaft and hole or with a difference in qualification numbers equal to one. 46 Metrology, standardization and certification 3.4. Find the hole and shaft tolerances according to Table B.1. 4. Determine the main and second deviations of the hole and shaft. 4.1. The selected fit determines the main part (main hole for CH and main shaft for Ch). The main part will have a main deviation equal to 0, and the second is determined depending on the type of main deviation (ES or ei) and tolerance. 4.2. Determine the position of the tolerance field of another (not the main) part using the formulas (1.30) - (1.32) or (1.33) - (1.35) depending on the group of landings through the known values ​​of Smin; Smax or Nmin; Nmax and taking into account the accepted deviations of the main part. 4.3. Select the standard main and second deviations of the tolerance fields of the hole and shaft (Table B.2 or B.3). Record tolerance fields in mixed form. 5. Calculate the limit characteristics and landing tolerance according to the formulas of the practical lesson 1.2. 6. Build a layout of landing tolerance fields. 7. Determine the error in the selection of fit according to the fit tolerance and limiting characteristics. The allowable error of selection according to the landing characteristics can be ± 10%. The formula for determining the error (∆Тpos) has the form: ∆Tpos Tset − Тst ⋅ 100% ≤ ±10% , Тset e. the relative value of the difference between the assigned standard tolerance field and the specified one; Tzad - specified landing tolerance; Tst - tolerance of the selected standard fit. Check the correctness of the fit selection by comparing the standard values ​​​​of the limiting gaps (interferences) with the given ones: for landings with a gap Smax st ≤ Smax; Smin st ≈ Smin; for landings with interference Nmax st ≈ Nmax; Nmin st ≥ Nmin. Chapter 1. Rationing the accuracy of smooth cylindrical joints 47 EXAMPLE OF PERFORMING PRACTICAL EXERCISE 1.5 Chart of initial data to Figure A.12 Name of initial data Value of initial data Nominal size of the connection and its value Name of the parts included in the connection D = 36 mm Cutter 11 and spindle 6 Specified landing characteristics for the calculation method of landing assignment, µm: Smax= Smin= Requirements for the operation of the connection (from the description to the drawing) 42 2 Milling cutters 11 are installed at both ends of the spindle, periodically removed for sharpening or readjusting the machine Solution. 1. Determine the landing group. It is necessary to assign a standard fit with characteristics close to the specified ones. Limit clearances are set, therefore a clearance fit must be assigned. 2. Determine the landing system. Milling cutters 11 are installed at both ends of the spindle, periodically removed for sharpening or readjusting the machine. Also, along the diameter D, at the same end of the spindle, an adjusting washer and a protective ring for landings of a different nature are installed. Thus, we assign the shaft system Ch (Table B.6). 3. Determine the fit accuracy. 3.1. Calculate fit tolerance: TS = Smax - Smin = 42 - 2 = 40 µm. 3.2. Determine the relative fit accuracy (number of fit tolerance units aS). According to the nominal size, we find the tolerance unit (Table B.1) - i \u003d 1.6 microns. Calculate the number of landing tolerance units: aS = TS 40 = ≈ 25. i 1.6 48 Metrology, standardization and certification 3.3. Determine the qualities of the shaft and hole. Based on the fact that aS = aD + ad and in accordance with the principle of basic fit on the equality of the accuracy of the hole and the shaft (the hole and shaft qualification numbers are the same or differ by one), we take aD = 16, ad = 10. This corresponds to the 7th quality for the hole and 6th for the shaft. 3.4. Find bore and shaft tolerances. According to Table B.1, we determine the hole tolerance TD = IT7 = 25 µm and the shaft tolerance Td = IT6 = 16 µm. 4. Determine the main and second deviations of the hole and shaft. 4.1. Since the fit is assigned in the shaft system, we assign the tolerance field of the main shaft h6 to the shaft with the main deviation es = 0. 4.2. The second deviation of the shaft is determined taking into account the tolerance of the 6th grade according to Table B.2: ei = es – IT6 = 0 – 16 = –16 µm. Let's write the shaft tolerance field in a mixed way: 4.3. Determine the main deviation of the hole. Since a fit with a gap in the shaft system is assigned, the main deviation of the tolerance field of the hole will be the lower limit deviation, which is determined by the specified minimum gap: EI = Smin + es = 2 + 0 = +2 µm. 4.4. According to GOST 25346-89 (Table B.3), we select the standard hole tolerance field. There is no standard tolerance field for a hole with a basic deviation of EI = +2 µm. The closest to this location will be the tolerance field of the main hole H7 with a basic deviation EI = 0 µm. 4.5. The second deviation of the hole tolerance field is calculated depending on the tolerance of the 7th grade: ES = EI + IT7 = 0 + 25 = +25 microns. Chapter 1. Rationing the accuracy of smooth cylindrical joints 49 Let's write the hole tolerance field in a mixed way: ∅36Н7 (+0.025). Thus, we assign a fit to the “cutter-spindle” connection: ∅36 H7 (+0.025) . h6 (−0.016) The fit is combined by systems, since the hole is specified in the hole system, and the shaft is in the shaft system. 5. Calculate the limit characteristics and fit tolerance. The calculation of the characteristics consists in determining the maximum dimensions of the hole and the shaft and determining the values ​​of the maximum clearances and fit tolerance. Limit hole dimensions: Dmax = D + ES = 36 + 0.025 = 36.025 mm; Dmin = D + EI = 36 + 0 = 36 mm. Maximum shaft dimensions: dmax = d + es = 36 + 0 = 36 mm; dmin \u003d d + ei \u003d 36 + (-0.016) \u003d 35.984 mm. Minimum clearance: Smin = Dmin - dmax = 36 - 36 = 0 mm. Maximum clearance: Smax = Dmax - dmin = 36.025 - 35.984 = 0.041 mm. Average probable clearance: Sm = (Smax + Smin)/2 = (0.041 + 0)/2 = 0.0205 mm. Fit tolerance: TS = Smax - Smin = 0.041 - 0 = 0.041 mm = 41 µm; TS = TD + Td = 25 + 16 = 41 µm = 0.041 mm. 50 Metrology, standardization and certification 6. Build a diagram of the location of the tolerance fields of the assigned fit (Fig. 1.16). 7. Checking the correctness of the calculation and selection of landing. Determine the error ∆Тpos of the fit selection according to the tolerance: ∆Tpos = Тset − Тst ⋅ 100%; Тzad ∆Tpos = 40 − 41 ⋅ 100% = 2.5%< 10%. 40 Проверить правильность подбора посадки сравнением стандартных значений предельных зазоров (натягов) с заданными: Smaх ст = 41 ≤ Smax = 42; Smin ст = 0 ≈ Smin = 2. Следовательно, посадка назначена верно. Рис. 1.16 Схема расположения полей допусков вала и отверстия посадки Глава 1. Нормирование точности гладких цилиндрических соединений 51 1.2. ДОПУСКИ РАЗМЕРОВ, ВХОДЯЩИХ В РАЗМЕРНУЮ ЦЕПЬ 1.2.1. ОСНОВНЫЕ ПОНЯТИЯ И ОПРЕДЕЛЕНИЯ ТЕОРЕТИЧЕСКАЯ ЧАСТЬ К ПРАКТИЧЕСКОМУ ЗАНЯТИЮ 1.6 Размерная цепь - совокупность геометрических размеров (звеньев), расположенных по замкнутому контуру и определяющих взаимные положения и точность элементов деталей при изготовлении, измерении и сборке. По области применения размерные цепи можно разделить на конструкторские (сборочные), технологические (операционные, детальные) и измерительные. Звено размерной цепи - один из размеров, образующих размерную цепь. Звенья размерной цепи обозначаются заглавной буквой русского алфавита с числовым индексом, определяющим порядковый номер звена в цепи. Размерная цепь состоит из составляющих звеньев и одного замыкающего звена. Простейшей размерной цепью будет соединение вала с отверстием (рис. 1.17а). Эта размерная цепь содержит наименьшее число размеров (три), которые расположены параллельно и получены в результате обработки вала и втулки: диаметр вала d (А2), диаметр отверстия втулки D (А1). В результате сборки этих деталей получается замыкающее звено - зазор S (А∆), если размер отверстия будет больше размера вала до сборки, или натяг N (А∆), если размер вала будет больше размера отверстия до сборки. Простейшая технологическая размерная цепь двухступенчатого валика (рис. 1.17б) состоит из габаритного размера А1, ступени вала А2 и замыкающего звена, оставшейся части вала А∆, которая получается за счет обтачивания меньшего диаметра на длину А2. Схема размерной цепи - графическое изображение размерной цепи. Замыкающее звено - звено, получаемое в размерной цепи последним в результате решения поставленной задачи, 52 Метрология, стандартизация и сертификация Рис. 1.17 Виды размерных цепей: а - конструкторская (сборочная); б - технологическая (операционная). в том числе при изготовлении, сборке и измерении. В размерной цепи должно быть только одно замыкающее звено, которое получается последним в результате сборки, обработки или измерения (размер контролируемой детали). Составляющее звено - звено размерной цепи, изменение которого вызывает изменение замыкающего звена. Все составляющие звенья по характеру влияния на замыкающее звено делятся на увеличивающие и уменьшающие. Увеличивающие звенья - звенья, при увеличении которых замыкающее звено увеличивается. Уменьшающие - звенья, при увеличении которых замыкающее звено уменьшается. На рисунке 1.18 представлена схема размерной цепи, в которой звенья А1–А6 - составляющие звенья, А∆ - замыкающее звено. Для определения характера составляющего звена используют правило обхода по контуру размерной цепи. Для этого предварительно выбирают направление обхода размерной цепи (может быть любое). Оно совпадает с направлением левонаправленной стрелки (←), проставленной над замыкающим звеном. Обходя цепь в этом направлении, над Глава 1. Нормирование точности гладких цилиндрических соединений 53 составляющими звеньями расставляют стрелки в направлении обхода. Увеличивающие звенья обозначаются стрелкой над буквой, направленной вправо а уменьшающие - стрелкой, направленной влево Правило. Все составляющие звенья, имеющие такое же направление стрелок, которое имеет стрелка над замыкающим звеном, являются уменьшающими звеньями, а звенья, имеющие противоположное направление, - увеличивающими . По взаимному расположению размеров цепи делятся на плоские (звенья цепи расположены произвольно в одной или нескольких произвольных параллельных плоскостях) и пространственные (звенья цепи расположены произвольно в пространстве). В зависимости от вида звеньев цепи делятся на линейные (звенья цепи - линейные размеры, расположенные на параллельных прямых) и угловые (звенья цепи представляют собой угловые размеры, отклонения которых могут быть заданы в линейных величинах, отнесенных к условной длине, или в градусах). По месту в изделии цепи делятся на детальные (определяют точность относительного положения поверхностей или осей одной детали) и сборочные (определяют точность относительного положения поверхностей или осей деталей, образующих сборочную единицу). По характеру звеньев цепи делятся на скалярные (все звенья - скалярные величины), векторные (все Рис. 1.18 Схема размерной цепи 54 Метрология, стандартизация и сертификация звенья - векторные погрешности) и комбинированные (часть звеньев - векторные погрешности, остальные - скалярные величины). Перед тем как построить размерную цепь, следует выявить замыкающее звено. Для этого по чертежам общих видов и сборочных единиц выявляются и фиксируются все требования к точности, которым должно удовлетворять изделие или сборочная единица, например: точность взаимного расположения деталей, обеспечивающая качественную работу изделия при эксплуатации (перпендикулярность оси шпинделя станка к рабочей плоскости стола); точность взаимного расположения деталей, обеспечивающая собираемость изделия , . При выявлении замыкающих звеньев их номинальные размеры и допускаемые отклонения устанавливаются по стандартам, техническим условиям, на основании опыта эксплуатации аналогичных изделий, а также путем теоретических расчетов и специально поставленных экспериментов. Для нахождения составляющих звеньев после определения замыкающего звена следует идти от поверхностей (осей) деталей, образующих замыкающее звено, к основным базам (осям) этих деталей, от них - к основным базам деталей, образующих первые детали, и т. д. до образования замкнутого контура. В число составляющих звеньев необходимо включать размеры деталей, непосредственно влияющих на замыкающее звено, и стремиться к тому, чтобы от каждой детали в линейную цепь входил только один размер. Каждая размерная цепь должна состоять из возможно меньшего числа звеньев (принцип «кратчайшей» размерной цепи). 1.2.2. МЕТОДЫ РЕШЕНИЯ РАЗМЕРНЫХ ЦЕПЕЙ При решении размерных цепей могут быть использованы два метода расчета: метод расчета размерной цепи на max-min; вероятностный метод расчета. Глава 1. Нормирование точности гладких цилиндрических соединений 55 Метод расчета размерной цепи на max-min - метод расчета размерной цепи, при котором требуемая точность замыкающего звена размерной цепи получается при любом сочетании размеров составляющих звеньев. При этом предполагают, что в размерной цепи одновременно могут оказаться все звенья с предельными значениями, причем в любом из двух наиболее неблагоприятных сочетаний (все увеличивающие звенья имеют наибольшее предельное значение, а все уменьшающие звенья - наименьшее предельное значение или наоборот). В результате размер замыкающего звена будет максимальным или минимальным. Преимущества такого метода заключаются в простоте, наглядности, небольшой трудоемкости computational work, a full guarantee against marriage due to the inaccuracy of the closing link. The disadvantage is that the results obtained by this method often do not correspond to the actual ones. The method is economically feasible only for low-precision circuits or for precise circuits with a small number of component links. Probabilistic calculation method - a method for calculating a dimensional chain, taking into account the phenomenon of scattering and probability various combinations deviations of the constituent links. This method allows a small percentage of products in which the master link will go beyond the tolerance zone. At the same time, the tolerances of the dimensions that make up the chain are expanded, and thereby the cost of manufacturing parts is reduced. In this practical lesson, only the method of calculating the dimensional chain for max-min is used, and the probabilistic calculation method is considered in special courses. The equations of dimensional chains establish the relationship between the parameters of the closing link and the constituent links. For design (assembly) linear scalar chains, the gear ratio is taken for increasing links ξ = +1, for decreasing links - ξ = -1. Then the equations of dimensional chains when calculating for max-min can be represented in the following form. 56 Metrology, standardization and certification 1. Equation of denominations. By definition of the dimensional chain, it follows that the sum of all nominal sizes, including the closing link, is equal to zero: Based on this equality, we can find the nominal size of the closing link: where ξ = ±1 is the gear ratio; ρ is the number of constituent links. Or, taking into account the nature of the link (gear ratio), we obtain the equation of ratings for calculating the dimensional chain for max-min (the rating of the closing link is equal to the difference between the sum of the ratings of the increasing links and the sum of the ratings of the reducing links): (1.36) where n is the number of increasing links; k is the number of reducing links. 2. Equation of tolerances. The tolerance of the closing link (or the scattering field of the size of the closing link) is equal to the sum of the tolerances of the constituent links: (1.37) where p = n + k is the number of constituent links; 3. Equations of limit deviations: the upper deviation of the closing link is equal to the difference between the sum of the upper deviations of the increasing links and the sum of the lower deviations of the reducing links: (1.38) deviations of reducing links: (1.39) When calculating design dimensional chains, two problems are usually solved: direct and inverse. The direct problem lies in the fact that the tolerances and maximum deviations of the component links are determined by the limiting dimensions and tolerance of the closing link. This is the main problem solved during the design. Given: A∆; T∆; ES∆; EI∆ (closing link parameters). Find: Aj; Tj; ESj; EIj (parameters of constituent links). The inverse problem lies in the fact that the size, tolerance and maximum deviations of the closing link are determined by the dimensions, maximum deviations and tolerances of the constituent links. This task is used in verification calculations. Given: Aj; Tj; ESj; EIj (parameters of constituent links) Find: А∆; T∆; ES∆; EI∆ (closing link parameters). Finding the accuracy of the constituent links in solving the direct problem can be carried out in two ways: 1. The method of equal tolerances. This method is applicable in the case when all chain sizes are included in one size interval. Then the tolerances of the constituent links will be equal to the average tolerance Tm: TA1 = TA2 = ... = TAp = Tm. The average tolerance is determined by the formula (1.40) 58 Metrology, standardization and certification 2. One quality method. All sizes can be made according to any one quality (or two nearest qualifications), which is determined by finding the average number of tolerance units am (average relative accuracy). The tolerance values ​​in this case will be determined depending on the nominal size (Table B.1). It is known that tolerance is the product of a tolerance unit by the number of tolerance units. This is true for any link in the dimensional chain: Tj = ijaj, where ij is the tolerance unit for each link, microns; aj is the number of tolerance units for each link. Therefore, the tolerance equation of the dimensional chain can be represented in the following form, provided that the number of tolerance units a is the same for all links (i.e., the accuracy of the links is the same): Since the tolerances of the component links are unknown, based on the equation of dimensional chains (1.37), the sum of tolerances component links, we will replace the tolerance of the closing link, which is specified according to the condition of the problem. Let's determine the average number of tolerance units of the dimensional chain - am: (1.41) If standard links (bearing width) are included in the dimensional chain, it is necessary to exclude the sum of tolerances of standard links from the tolerance of the master link, since the tolerance of these links is already known and cannot be changed. In this case, the number of tolerance units is determined only for non-standard links - amnest: Chapter 1. Rationing the accuracy of smooth cylindrical joints 59 (1.42) where t is the number of standard links; p is the number of all constituent links; (ρ − t) is the number of non-standard links; Tjst - standard link tolerance; ijnest - a unit of tolerance for a non-standard link. To determine the tolerance fields for the dimensions of the constituent links, in addition to the quality, it is necessary to assign the main deviations depending on the type of dimensions: for covered - h, covering - H, the rest - js. For example, in Figure 1.17a, the size is enclosing, the size is covered; in figure 1.17b, the size is enclosing, it belongs to the group of other sizes, i.e. e. is neither covered nor inclusive. ORDER OF PERFORMANCE OF PRACTICAL LESSON 1.6 (CALCULATION OF THE DIMENSIONAL CHAIN ​​FOR MAX-MIN) (3rd LEVEL OF COMPLEXITY) Task. According to the limiting dimensions and tolerance of the closing link, determine the tolerances and maximum deviations of the component links. Check by solving the inverse problem. The limiting dimensions of the closing link and the nominal dimensions of the constituent links are given. Task options are indicated in Appendix A.13. 1. Solve the direct problem. 1.1. Present a diagram of the dimensional chain and indicate which links are covered and which are covering. 1.2. Determine the nominal size, limit deviations and tolerance of the master link. 1.3. Determine the nominal size (value) of the closing link according to the equation of the nominal values ​​of the dimensional chain (1.36). 60 Metrology, standardization and certification 1.4. Determine the limit deviations through the limit dimensions and the nominal value of the closing link. 1.5. Calculate the tolerance of the closing link according to the maximum dimensions or maximum deviations. 1.6. Determine the nature of the constituent links (increasing or decreasing links). 1.7. Determine the accuracy of the constituent links using the method of equal qualifications (formulas 1.41 and 1.42). Assign the same qualification to all links. 1.8. Determine the type and values ​​\u200b\u200bof (Table B.1) of the main deviations of the tolerance fields of the component links, depending on the type of size (for covered - h; covering - H; the rest - js). 2. Solve the inverse problem. 2.1. Perform a check according to the tolerance equation (1.37). If there is a large difference between the stray field and the tolerance of the closing link, carry out qualification matching (change the quality of one link). 2.2. Check for limit deviations (1.38), (1.39). To correct the location of the stray field of the closing link, choose the simplest matching link in design. Calculate the new limit deviations of the matching link by substituting in the left side of Table 1.10 Nominal link size, mm Tolerance unit value ij, μm Designation of the dimensions of the dimensional chain, Aj Calculation of the dimensional chain by the "maximum - minimum" method after assigning tolerance fields according to the calculated value am 55 1.9 55Js10(±0.06) 55Js10(±0.06) 3 0.6 3h10(–0.04) 3h10(–0.04) 22 1.3 22h10(–0.084) 22h11 (–0.13) 22h11(–0.13) 32 1.6 32h10(–0.10) 32h10(–0.10) 32h10(–0.10) ω∆ = 0.344 ω∆ = 0.39 ω∆ = 0.4 T∆ 0.4 A∆ 2–0.4 - Accepted values ​​of the links of the dimensional chain ω∆< T∆ после согласования значений допусков после согласования предельных отклонений 55Js10(±0,06) 2–0,4 Глава 1. Нормирование точности гладких цилиндрических соединений 61 уравнений требуемые значения предельных отклонений замыкающего звена. 2.3. Представить результаты расчета размерных цепей в виде таблицы (табл. 1.10). ПРИМЕР ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 1.6 (РАСЧЕТ РАЗМЕРНОЙ ЦЕПИ НА MAX-MIN) Задание. Необходимо обеспечить собираемость деталей с валом (Приложение А.13, табл. А.25, рис. А.13; вариант 13-1). Исходные данные: 1) предельные размеры замыкающего звена (зазор между торцами вала 13 и зубчатого колеса 3): А∆min = 1,6 мм; A∆max = 2,0 мм; 2) номинальные размеры составляющих звеньев: длина ступени вала 13 - А1 = 53 мм; буртик втулки 7 - А2 = 3 мм; длина втулки 7 - А3 = 22 мм; длина (высота) зубчатого колеса 3 - А4 = 32 мм. Решение. 1. Решить прямую задачу. 1.1. На рисунке 1.19 представлена схема размерной цепи, в которую включены размеры, влияющие на замыкающее звено, по одному от каждой детали. Размеры А2, А3, А4 - охватываемые; размер А1 не относится ни к охватываемым, ни к охватывающим (группа остальных размеров). Рис. 1.19 Схема размерной цепи 62 Метрология, стандартизация и сертификация Для обеспечения полной взаимозаменяемости сборки решение следует вести методом расчета на max-min, так как цепь невысокой точности. 1.2. Определить номинальный размер, предельные отклонения и допуск замыкающего звена. 1.3. Определить номинальный размер замыкающего звена: А∆ = (32 + 22 + 3) – 55 = 2 мм. 1.4. Определить предельные отклонения замыкающего звена через его предельные размеры и номинал: ES∆ = A∆max – А∆ = 2 – 2 = 0; EI∆ = А∆min – A∆ = 1,6 – 2 = –0,4 мм. 1.5. Определить допуск замыкающего звена: Т∆ = A∆max – А∆min = 2 – 1,6 = 0,4 мм = 400 мкм. Записать номинал и предельные отклонения замыкающего звена в виде исполнительного размера: А∆ = 2–0,4 (нулевое отклонение не обозначается). 1.6. Определить характер составляющих звеньев. Для этого обходим цепь слева направо в соответствии с левонаправленной стрелкой, указанной над замыкающим звеном. Расставляем стрелки над составляющими звеньями в направлении обхода. В соответствии с правилом обхода по контуру размерной цепи определяем характер составляющих звеньев: звено - уменьшающее; звенья - увеличивающие. 1.7. Определить точность составляющих звеньев. Так как номинальные размеры составляющих звеньев относятся к разным интервалам размеров, для определения точности составляющих звеньев используем способ одного квалитета, т. е. рассчитаем среднее число единиц допуска с учетом отсутствия в цепи стандартных звеньев по формуле (1.41): Глава 1. Нормирование точности гладких цилиндрических соединений 63 Ближайшее к рассчитанному значению аm = 74 стандартное число единиц допуска равно аm = 64, что соответствует 10-му квалитету. Поэтому принимаем для всех звеньев 10-й квалитет. 1.8. Определить вид и значения основных отклонений полей допусков составляющих звеньев в зависимости от вида размера (для охватываемых - h; охватывающих - H; остальных - js). Так как звено А1 относится к третьей группе размеров, назначим на него поле допуска js10, а для звеньев А2, А3, А4 (как на охватываемые) поле допуска h10. Составляющие звенья будут иметь следующие размеры: 2. Решить обратную задачу 2.1. Выполним проверку по допускам. Рассчитаем поле рассеяния замыкающего звена: ω∆ = 120 + 40 + 84 + 100 = 344 = 0,344 < 0,4 на 0,056 мм. Так как разница между полем рассеяния ω∆ = 0,344 мм и заданным допуском замыкающего звена T∆ = 0,4 мм получилась слишком большая, изменим 10-й квалитет звена А3 на 11-й квалитет. Тогда Это позволяет расширить поле рассеяния замыкающего звена на следующую величину: IT11 – IT10 = 0,130 – 0,084 = 0,046 мм, т. е. поле рассеяния при этом будет равно ω∆ = 0,39 мм. Примечание. Звено А3 выбрано потому, что разница между допусками 10-го и 11-го квалитетов для номинального размера этого звена наиболее близко приближает поле 64 Метрология, стандартизация и сертификация рассеяния замыкающего звена к полю допуска замыкающего звена. 2.2. Выполним проверку по предельным отклонениям: ES∆ = – [–0,060] = +0,060 мм; EI∆ = [(–0,040) + (–0,13) + (–0,10)] – [(+0,06)] = –0,33 мм. Следовательно, поле рассеяния замыкающего звена по предельным отклонениям равно: ω∆ = ES∆ – EI∆ = 0,06 – (–0,33) = 0,39 мм. Это совпадает со значением поля рассеяния, полученным по уравнению допусков: ω∆ = 0,39 мм, т. е. расчет предельных отклонений замыкающего звена выполнен правильно. Однако расположение поля рассеяния замыкающего звена, полученное по отклонениям (рис. 1.20а), не соответствует заданному положению поля допуска (рис. 1.20б). 2.3. Для обеспечения заданного расположения поля допуска замыкающего звена выберем самое простое по конструкции согласующее звено. Таким звеном будет звено А2 (высота буртика втулки). Принимаем его отклонения за неизвестные и решаем уравнения отклонений размерной цепи относительно этих неизвестных, подставив в левую часть уравнений требуемые отклонения (А∆ = 3–0,4) замыкающего звена. 0 = – [(–0,06)]; Рис. 1.20 Расположение поля допуска замыкающего звена: а - полученное по отклонениям; б - заданное. Глава 1. Нормирование точности гладких цилиндрических соединений 65 ESA2 = –0,06 мм; –0,4 = – [(+0,06)]; EIA2 = –0,11 мм. В результате для звена А2 получили новые предельные отклонения и допуск звена: TA2 = 0,05 мм. Таким образом, расширение допуска компенсирующего звена и изменение его предельных отклонений позволили получить замыкающее звено в заданных пределах (рис. 1.20б). Все расчеты внесем в таблицу 1.10. ГЛ А В А 2 НОРМИРОВАНИЕ ТРЕБОВАНИЙ К ШЕРОХОВАТОСТИ ПОВЕРХНОСТИ И ГЕОМЕТРИЧЕСКИМ ДОПУСКАМ 2.1. ШЕРОХОВАТОСТЬ ПОВЕРХНОСТИ И ЕЕ НОРМИРОВАНИЕ ТЕОРЕТИЧЕСКАЯ ЧАСТЬ К ПРАКТИЧЕСКИМ ЗАНЯТИЮ 2.1 Н а поверхности детали после обработки остаются следы от кромок режущего инструмента в виде неровностей и гребешков, близко расположенных друг от друга. Шероховатостью поверхности называется совокупность неровностей с относительно малыми шагами, выделенная на базовой длине (l). Нормирование шероховатости поверхности по ГОСТ 2789-73 выполнено с учетом рекомендаций международных стандартов. Установлены (рис. 2.1) шесть параметров: три высотных (Ra; Rz; Rmax), два шаговых (Sm; S) и параметр относительной опорной длины профиля (tp) , , . Рис. 2.1 Профилограмма шероховатости поверхности Глава 2. Нормирование требований к шероховатости поверхности 67 Характеристика параметров шероховатости: Ra - среднее арифметическое отклонение профиля, мкм: (2.1) где yi - расстояние между любой точкой профиля и средней линией m, cредняя линия имеет форму номинального профиля и проводится так, что в пределах базовой длины среднее квадратическое отклонение профиля до этой линии минимально; n - количество рассматриваемых точек профиля на базовой длине. Rz - высота неровностей профиля по 10 точкам, мкм: (2.2) где Himax; Himin - высота наибольшего выступа и глубина наибольшей впадины, мкм. Соотношение между Ra и Rz колеблется в пределах от 4 до 7 раз; Rz больше, чем Ra. Rmax - наибольшая высота профиля - расстояние между линией выступов и линией впадин, мкм; Sm - средний шаг неровностей профиля по средней линии в пределах базовой длины, мм: (2.3) где n - количество шагов в пределах базовой длины; Smi - шаг неровностей профиля по средней линии. S - средний шаг местных выступов профиля (по вершинам) в пределах базовой длины, мкм: (2.4) где n - количество шагов в пределах базовой длины; Si - шаг местных выступов профиля. tp - относительная опорная длина профиля в %: 68 Метрология, стандартизация и сертификация (2.5) где p - уровень сечения профиля в процентах - это расстояние между линией выступов и линией, пересекающей профиль эквидистантно линии выступов; за 100% принимается Rmax; bi - длина отрезка, отсекаемая на заданном уровне в материале, мм; l - базовая длина, мм. Направления неровностей обработки зависят от метода и технологии изготовления, влияют на работоспособность, износостойкость и долговечность изделия. Условные обозначения направления неровностей (табл. 2.1) указывают на чертеже при необходимости. Т а б л и ц а 2.1 Условное обозначение направлений неровностей Тип направления неровностей Обозначение Тип направления неровностей Параллельное Произвольное Перпендикулярное Кругообразное Перекрещивающееся Радиальное Обозначение Точечное Выбор параметров производится в зависимости от эксплуатационных свойств поверхности. Предпочтительным принят параметр Ra - среднее арифметическое отклонение профиля, так как он определяет шероховатость по всем точкам профиля (табл. В.1). Глава 2. Нормирование требований к шероховатости поверхности 69 Точечное направление неровностей дают поверхности, полученные методом порошковой металлургии, электроискровым методом, травлением и др. Средняя высота неровностей по 10 точкам Rz используется в тех случаях, когда нельзя измерить Ra на приборах типа профилометр путем ощупывания поверхности алмазной иглой (острые кромки, мягкий материал, особо чистая поверхность). Шаговые параметры влияют на виброустойчивость, сопротивление в волноводах и электропроводность в электротехнических деталях. Параметр tp необходимо учитывать при высоких требованиях к контактной жесткости и герметичности. В ГОСТ 2789-59 предусматривалось 14 классов шероховатости в порядке уменьшения значений параметров. В сравнительной таблице В.1 даны соотношения между классами шероховатости и другими высотными параметрами. С 1983 г. для всех классов введен ряд значений Ra предпочтительного применения по 1-му варианту. Определение значений параметров шероховатости может быть выполнено методом подобия и расчетным методом. Метод подобия (табл. В.2) ориентируется на экономическую точность, которая устанавливает зависимость шероховатости и формы поверхности от допуска размера и применяемого отделочного метода обработки. Минимальные требования к шероховатости поверхности в зависимости от допусков размера и формы даны в таблице В.3 . Примеры выбора числовых значений Ra в зависимости от вида соединения даны в таблице В.4. При расчетном методе учитывается зависимость параметров шероховатости поверхности от допуска размера, так как при обеспечении требуемой точности размера изменяется шероховатость и точность геометрической формы поверхности. Для деталей жесткой конструкции (L ≤ 2d) соотношение допусков размера (Т) и формы поверхности (Тф) установлены три уровня относительной геометрической точности (ГОСТ 24643-81): А - нормальный, используемый наиболее часто в машиностроении для поверхностей без особых требований 70 Метрология, стандартизация и сертификация к точности формы при низкой скорости вращения или перемещения; В - повышенный, используемый для поверхностей, работающих при средних нагрузках и скоростях до 1500 об/мин, при оговоренных требованиях к плавности хода и герметичности уплотнений. Поверхности, образующие соединения с натягом или по переходным посадкам при воздействии больших скоростей и нагрузок, при наличии ударов и вибраций; С - высокий, рекомендуемый для поверхностей, работающих в подвижных соединениях при высоких нагрузках и скоростях свыше 1500 об/мин, при высоких требованиях к плавности хода, герметичности уплотнения и при необходимости трения малой величины; при высоких требованиях к точности центрирования, прочности соединения в условиях воздействия больших нагрузок, ударов и вибраций. Значения коэффициентов формы (Kф) и шероховатости (Kr) приведены в таблице 2.2. Т а б л и ц а 2.2 Значения коэффициентов Kф и Kr Уровень относительной геометрической точности цилиндрические поверхности плоские поверхности Значение коэффициента Kф Значение коэффициента Kr А 0,3 0,6 0,05 В 0,2 0,4 0,025 С 0,12 0,25 0,012 Значение Ra можно рассчитать по формуле Ra = KrТ, (2.6) где Т - допуск на размер, ограничивающий данную поверхность (Td или TD); Kr - коэффициент шероховатости поверхности по таблице 2.2. Расчетное значение округлить в сторону уменьшения до величины, указанной в таблице В.1, вариант 1. Указание требований к шероховатости поверхностей производится на чертежах согласно ЕСКД по ГОСТ 2.30973 «ЕСКД. Обозначения шероховатости поверхностей». Глава 2. Нормирование требований к шероховатости поверхности 71 Рис. 2.2 Место и порядок записи параметров шероховатости Обозначение шероховатости состоит из условного значка и числовых значений . Структура обозначения шероховатости поверхности приведена на рисунке 2.2. При применении знака без указания параметра и способа обработки его изображают без полки. В обозначении шероховатости применяют один из знаков: - основной знак, когда метод обработки поверхности чертежом не регламентируется; - знак, соответствующий поверхности, полученной удалением слоя металла (точением, сверлением, фрезерованием, шлифованием и т. д.); - знак, соответствующий поверхности в состоянии поставки, без удаления слоя металла (литье, штамповка, поковка и т. д.). Согласно ГОСТ 2.309-73 с 01.01.2005 г. при задании параметров шероховатости: обязательно указывать символы (Ra, Rz, S, tp) перед их числовым значением; все параметры записывать под полочкой. Под полочкой могут быть указаны: условные обозначения неровностей, базовая длина и все параметры шероховатости по строчкам, начиная с Ra; над полочкой указывают способ обработки и другие дополнительные требования (например, полировать); 72 Метрология, стандартизация и сертификация знак «остальное» для поверхностей, обрабатываемых с одинаковыми требованиями, указывать в верхнем правом углу чертежа, например, или; обработку поверхностей сложного контура «кругом» указывать так: . Знак шероховатости может указываться на контурной линии чертежа, на размерных линиях или на их продолжениях, на рамке допуска формы, на полках линий - выносок (рис. 2.3а). При указании двух и более параметров шероховатости поверхности в обозначении шероховатости значения параметров записывают сверху вниз в следующем порядке (рис. 2.3б): параметры высоты неровностей профиля; параметры шага неровностей профиля; относительная опорная длина профиля. При нормировании требований к шероховатости поверхности параметрами Ra, Rz, Rmax базовую длину в обозначении шероховатости не приводят, если она соответствует ГОСТ 2789-73 для выбранного значения параметра шероховатости (табл. В.1). В данном примере указано (рис. 2.3б): среднеарифметическое отклонение профиля Ra не более 0,1 мкм на базовой длине l = 0,25 мм (в обозначении Рис. 2.3 Примеры обозначения шероховатости: а - возможное размещение знака шероховатости; б - указание нескольких параметров. Глава 2. Нормирование требований к шероховатости поверхности 73 Рис. 2.4 Варианты обозначения шероховатости в правом углу чертежа: а - все поверхности имеют одинаковую шероховатость; б - часть поверхностей имеет одинаковую шероховатость (остальные); в - часть поверхностей по данному чертежу не обрабатывается (полочка не рисуется, параметры не указываются. базовая длина не указана, так как соответствует значению, определенному стандартом для данной высоты неровностей); средний шаг неровностей профиля Sm должен находиться в пределах от 0,063 до 0,040 мм на базовой длине l = 0,8 мм; относительная опорная длина профиля на 50%-ном уровне сечения должна находиться в пределах 80 ± 10% на базовой длине l = 0,25 мм. Примеры задания требований к шероховатости поверхности: означает Ra ≤ 1,6 мкм, метод обработки поверх ности чертежом не регламентируется; означает Rz≤ 40 мкм, обработка резанием; означает Ra ≤ 12,5 мкм, поверхность без удале ния слоя металла (литье, штамповка, поковка и т. д.). Обозначение шероховатости поверхностей повторяющихся элементов изделия (отверстий, пазов, зубьев и т. д.), количество которых указано на чертеже, а также обозначение шероховатости одной и той же поверхности, независимо от числа изображений или поверхностей, имеющих одинаковую шероховатость и образующих контур, наносят один раз. В правом верхнем углу чертежа указывают общие требования к поверхностям детали, варианты задания таких требований указаны на рисунке 2.4. 74 Метрология, стандартизация и сертификация ПОРЯДОК ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 2.1 (1-Й УРОВЕНЬ СЛОЖНОСТИ) Ознакомиться с теоретической частью раздела. Получить задание (вариант) практической работы. Варианты заданы в таблице 2.3. Т а б л и ц а 2.3 Варианты заданий к практическому занятию 2.1 № варианта Обозначение шероховатости поверхности № варианта 1 15 2 16 3 17 4 18 5 19 6 20 Обозначение шероховатости поверхности Глава 2. Нормирование требований к шероховатости поверхности 75 П р о д о л ж е н и е т а б л. 2.3 № варианта Обозначение шероховатости поверхности № варианта 7 21 8 22 9 23 10 24 11 25 12 26 13 27 14 28 Обозначение шероховатости поверхности 76 Метрология, стандартизация и сертификация Задание. По заданному варианту расшифровать условное обозначение шероховатости. Решение. 1. Указать вид условного значка, обозначающего требования к шероховатости поверхности. 2. Определить тип направления неровностей. 3. Определить наименование параметров шероховатости, их условное обозначение и числовое значение. 4. Указать базовую длину и объяснить ее назначение. ПРИМЕР ВЫПОЛНЕНИЯ ПРАКТИЧЕСКОГО ЗАНЯТИЯ 2.1 Задание. По заданному варианту расшифровать условное обозначение шероховатости. Дано: Решение. 1. Использован знак - метод обработки поверхности чертежом не регламентируется. 2. Направление неровностей не регламентируется, т. е. соответствует методу обработки. 3. Шероховатость нормируется по: параметру Ra (среднее арифметическое отклонение профиля), значение которого не должно превышать 0,1 мкм; средний шаг неровностей профиля по средней линии Sm в пределах (0,063–0,040) мм; относительная опорная длина профиля tp, задана на уровне 50% и должна составлять 80 ± 10%; 4. Базовая длина l = 0,25 мм для Ra не указывается, так как ее числовое значение соответствует числовому значению параметра Ra (табл. В.1); базовая длина l = 0,8 мм для Sm указана, базовая длина l = 0,25 мм для tp указана, так как эти параметры на приборах профилометр - профилограф измеряются на больших базовых длинах. Глава 2. Нормирование требований к шероховатости поверхности 77 2.2. НОРМИРОВАНИЕ ОТКЛОНЕНИЙ ФОРМЫ ПОВЕРХНОСТИ 2.2.1. ТЕРМИНЫ И ОПРЕДЕЛЕНИЯ ТЕОРЕТИЧЕСКАЯ ЧАСТЬ К ПРАКТИЧЕСКИМ ЗАНЯТИЯМ 2.2, 2.3, 2.4 В ГОСТ 24642 (не действует в РФ) даны термины и определения, относящиеся к допускам формы; на территории России введен в действие с 01.01.2012 г. ГОСТ Р 53442, который устанавливает определения и правила указания на чертежах геометрических допусков (формы, ориентации, месторасположения и биения). Однако необходимо рассмотреть некоторые понятия ГОСТ 24642-81, так как аналогичных им в новом стандарте нет. Отклонением формы EF (∆ф) называется отклонение формы реального элемента от номинальной формы, оцениваемое наибольшим расстоянием от точек реального элемента по нормали к прилегающему элементу (рис. 2.5). Шероховатость поверхности в отклонение формы не включается. Номинальная поверхность - это идеальная поверхность, форма которой задана чертежом или другой технической документацией. Реальная поверхность - это поверхность, ограничивающая тело и отделяющая его от окружающей среды. Отклонения формы оцениваются по всей поверхности (по всему Рис. 2.5 Схема к определению отклонения формы поверхности 78 Метрология, стандартизация и сертификация профилю) или на нормируемом участке, если заданы площадь, длина или угол сектора, а в необходимых случаях и расположение его на поверхности. Если расположение участка не задано, то его считают любым в пределах всей поверхности или профиля. Отсчет отклонений формы поверхности производится по нормали к прилегающей поверхности как наибольшее расстояние от точек реальной поверхности до прилегающей, которая рассматривается как номинальная. Прилегающая поверхность - поверхность, имеющая форму номинальной поверхности, соприкасающаяся с реальной поверхностью и расположенная вне материала детали так, чтобы отклонение от нее наиболее удаленной точки реальной поверхности в пределах нормируемого участка имело минимальное значение. Отклонения формы профиля оцениваются аналогично - от прилегающей линии. Допуск формы TF (Тф) - это наибольшее допускаемое значение отклонения формы. Допуски формы могут быть: комплексными (плоскостность, цилиндричность, круглость, допуск формы заданного профиля); элементарными (выпуклость, вогнутость, овальность, огранка, конусообразность, седлообразность, бочкообразность). Отклонение от круглости ∆кр - наибольшее расстояние от точек реального профиля до прилегающей окружности (рис. 2.6). Основные виды частных отклонений профиля поперечного сечения цилиндрических поверхностей - овальность (рис. 2.7а) и огранка (рис. 2.7б). Частные отклонения профиля продольного сечения - конусообразность (рис. 2.8а), бочкообразность (рис. 2.8б), седлообразность (рис. 2.8в). Для всех случаев отклонение формы определяется в радиусном выражении: (2.7) Допуски формы поверхности назначаются только в том случае, если они по условиям эксплуатации изделия должны Глава 2. Нормирование требований к шероховатости поверхности Рис. 2.6 Отклонение от круглости Рис. 2.7 Частные виды отклонений от круглости: а - овальность; б - огранка. Рис. 2.8 Частные виды отклонений формы профиля продольного сечения: а - конусообразность; б - бочкообразность; в - седлообразность. 79 80 Метрология, стандартизация и сертификация быть меньше допуска размера. Виды допусков формы и другие геометрические допуски представлены в таблице В.5. Наименование геометрического допуска состоит из слова «допуск» и геометрической характеристики элемента, нормируемой им, например «допуск прямолинейности». Исключение составляет допуск позиционирования, который в сложившейся практике имеет наименование «позиционный допуск». Числовые значения допусков формы и расположения поверхностей установлены ГОСТ 24643-81 по 16 степеням точности (табл. В.6 и В.7). В таблицах рассмотрены 12 степеней, т. к. для грубых поверхностей применяется ГОСТ 30893.2 на общие допуски. Числовые значения допусков формы поверхности могут быть определены расчетным методом и методом подобия. 2.2.2. ОПРЕДЕЛЕНИЕ ЧИСЛОВЫХ ЗНАЧЕНИЙ ДОПУСКОВ ФОРМЫ ПОВЕРХНОСТИ Метод подобия применяется при известном квалитете точности размера рассматриваемой поверхности. Определяется степень точности формы поверхности по условиям экономической точности для жесткой конструкции (табл. В.2). Степень точности снижается на одну, если L/d от 2 до 5; на две степени точности грубее, если L/d >5. The calculation method is based on the ratio of dimensional tolerances to shape tolerances and surface roughness. When considering the relationship between the size tolerance and the shape tolerance for cylindrical parts, the diameter of the surface under consideration is taken, and for flat parts - the tolerance for the thickness of the part, since the largest error is equal to this tolerance, i.e. 100%. Tf max = Td. For cylindrical parts, the shape tolerance is given in terms of radius, so the largest shape error is taken equal to 50% of the diameter tolerance: Тf max = Тd/2. Chapter 2. Rationing of requirements for surface roughness 81 For level A, the shape tolerance (

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1 MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State Autonomous Educational Institution of Higher Education "NATIONAL RESEARCH TOMSK POLYTECHNICAL UNIVERSITY" A.S. Spiridonova, N.M. Natalinova WORKSHOP ON METROLOGY, STANDARDIZATION AND CERTIFICATION Recommended as a teaching aid by the Editorial and Publishing Council of Tomsk Polytechnic University Publishing house of Tomsk Polytechnic University 2014

2 UDC (076.5) LBC ya73 С72 С72 Spiridonova A.S. Workshop on metrology, standardization and certification: textbook / A.S. Spiridonova, N.M. Natalinova; Tomsk Polytechnic University. Tomsk: Publishing House of the Tomsk Polytechnic University, p. The manual contains six laboratory works and four practical exercises, which include the necessary theoretical materials and control questions to prepare for the defense of the work performed. Designed for students of all directions to consolidate theoretical foundations metrology, measurement methods, the procedure for measuring the values ​​of physical quantities and the rules for processing measurement results, estimating the uncertainty of measurements, the regulatory framework of metrology, as well as the theoretical provisions of standardization activities, the principles of construction and rules for using standards, sets of standards and other regulatory documentation. UDC (076.5) LBC Ya73 Reviewers Candidate of Technical Sciences, Associate Professor of TSUAE A.A. Alekseev Candidate of Chemical Sciences, Associate Professor of TSU N.A. Gavrilenko FGAOU VO NR TPU, 2014 Spiridonova A.S., Natalinova N.M., 2014 Design. Publishing house of Tomsk Polytechnic University, 2014

3 INTRODUCTION Metrology and standardization are tools for ensuring the quality and safety of products, works and services, an important aspect of a multifaceted activity. Quality and safety are the main factors in the sale of goods. The purpose of teaching the discipline "Metrology, standardization and certification" is the presentation of concepts, the formation of students' knowledge, skills and abilities in the areas of standardization, metrology and conformity assessment to ensure the efficiency of production and other activities. As a result of studying the discipline, the student must have the following competencies: to know the goals, principles, areas of application, objects, subjects, means, methods, the regulatory framework for standardization, metrology, conformity assessment activities; be able to apply technical and metrological legislation; work with regulatory documents; recognize conformity confirmation forms; distinguish between international and national units of measurement; have experience in working with current federal laws, regulatory and technical documents necessary for the implementation of professional activities. The work complies with the requirements of the State Educational Standard of Higher Professional Education (FSES HPE and TPU OOP standards) in the discipline "Metrology, standardization and certification" for students of all specialties. This manual is intended to consolidate the theoretical foundations of metrology, measurement methods, the procedure for measuring the values ​​of physical quantities and the rules for processing measurement results, the legal framework of metrology, as well as the theoretical provisions of standardization and certification activities, the principles of construction and rules for using standards, sets of standards and other regulatory documentation. 3

4 SECTION 1. METROLOGY LABORATORY WORK 1 CLASSIFICATION OF MEASURING INSTRUMENTS AND RATED METROLOGICAL CHARACTERISTICS 1.1. Basic concepts and definitions In accordance with the RMG, a measuring instrument is a technical instrument intended for measurements, having normalized metrological characteristics, reproducing and (or) storing a unit of physical quantity, the size of which is taken unchanged (within a specified error) for a known time interval. Measuring instruments (SI) used in various fields of science and technology are extremely diverse. However, for this set, it is possible to single out some common features inherent in all SI, regardless of the field of application. These features form the basis of various SI classifications, some of which are given below. Classification of measuring instruments By technical purpose: A measure of a physical quantity is a measuring instrument designed to reproduce and (or) store a physical quantity of one or more given dimensions, the values ​​of which are expressed in established units and are known with the required accuracy; The following types of measures are distinguished: a single-valued measure is a measure that reproduces a physical quantity of the same size (for example, a 1 kg weight, a capacitor of constant capacitance); multi-valued measure - a measure that reproduces a physical quantity of different sizes (for example, a dashed measure of length, a capacitor of variable capacitance); a set of measures a set of measures of different sizes of the same physical size, intended for practical use both individually and in various combinations (for example, a set of gauge blocks); store of measures a set of measures structurally combined into a single device, in which there are devices for connecting them in various combinations (for example, a store electrical resistance). 4

5 Measuring device is a measuring instrument designed to obtain the values ​​of the measured physical quantity in the specified range. The measuring device, as a rule, contains a device for converting the measured value into a signal of measuring information and indexing it in the most accessible form for perception. In many cases, the display device has a scale with an arrow or other device, a chart with a pen or a digital display, thanks to which a reading or registration of the values ​​of a physical quantity can be made. Depending on the type of output value, analog and digital measuring instruments are distinguished. An analog measuring instrument is a measuring instrument whose readings (or output signal) are a continuous function of the measured quantity (eg pointer voltmeter, mercury-in-glass thermometer). A digital meter is a meter whose readings are presented in digital form. In a digital device, the input analog signal of the measuring information is converted into a digital code, and the measurement result is displayed on a digital display. According to the form of presentation of the output value (according to the method of indicating the values ​​of the measured value), measuring instruments are divided into indicating and recording measuring instruments. indicating measuring instrument a measuring instrument that allows only the reading of indications of the values ​​of the measured quantity (micrometer, analog or digital voltmeter). recording measuring device measuring device in which the recording of readings is provided. The registration of the values ​​of the measured value can be carried out in analog or digital form, in the form of a diagram, by printing on paper or magnetic tape (thermograph or, for example, a measuring device associated with a computer, display and device for printing readings). By action, measuring instruments are divided into integrating and summing. There are also direct action devices and comparison devices. A measuring transducer is a technical tool with normative metrological characteristics that serves to convert a measured value into another value or a measuring signal that is convenient for processing, storage, further transformations, indication or transmission. The resulting value 5

6 or the measuring signal are not directly accessible to the observer, they are determined through the conversion factor. A measuring transducer is either part of a measuring device (measuring setup, measuring system), or is used together with any measuring instrument. According to the nature of the conversion, analog, digital-to-analog, analog-to-digital converters are distinguished. According to the place in the measuring circuit, primary and intermediate converters are distinguished. There are also scale and transmitting converters. Examples: thermocouple in a thermoelectric thermometer, measuring current transformer, electro-pneumatic converter. Measuring installation is a set of functionally combined measures, measuring instruments, measuring transducers and other devices, designed to measure one or more physical quantities and located in one place. The measuring setup used for verification is called a calibration setup. The measuring setup that is part of the standard is called the reference setup. Some large measuring installations are called measuring machines, designed to accurately measure the physical quantities that characterize the product. Examples: installation for measuring the resistivity of electrical materials, installation for testing magnetic materials. Measuring system is a set of functionally combined measures, measuring instruments, measuring transducers, computers and other technical means located at different points of a controlled object, etc., with the aim of measuring one or more physical quantities inherent in this object, and generating measuring signals for different purposes . Depending on the purpose, measuring systems are divided into measuring information, measuring control, measuring control systems, etc. A measuring system that is reconfigured depending on a change in the measuring task is called a flexible measuring system (GIS). Examples: measuring system of a thermal power plant, which allows obtaining measuring information about a number of physical quantities in different power units. It can contain hundreds of measurement channels; a radio navigation system for determining the location of various objects, consisting of a number of measuring and computing complexes spaced apart in space at a considerable distance from each other. 6

7 Measuring and computing complex is a functionally integrated set of measuring instruments, computers and auxiliary devices designed to perform a specific measuring task as part of a measuring system. Comparator means of comparison intended for comparison of measures of homogeneous quantities (lever balance, comparator for comparison of normal elements). According to the metrological purpose, all SI are divided into standards, working standards and working SI. The standard of a physical quantity unit (standard) is a measuring instrument (or a set of measuring instruments) intended for reproduction and (or) storage of a unit and transfer of its size to measuring instruments lower in the verification scheme and approved as a standard in the prescribed manner. The design of the standard, its properties and the method of reproducing the unit are determined by the nature of the given physical quantity and the level of development of measuring technology in this area of ​​measurement. The standard must have at least three essential features of immutability, reproducibility and comparability that are closely related to each other. Working standard A standard designed to transfer the size of a unit to working measuring instruments. If necessary, working standards are divided into categories (1st, 2nd, ..., nth). In this case, the transfer of the size of the unit is carried out through a chain of working standards subordinate in terms of digits. At the same time, from the last working standard in this chain, the size of the unit is transferred to the working measuring instrument. A working measuring instrument is a measuring instrument intended for measurements not related to the transfer of the size of a unit to other measuring instruments. According to the significance of the measured physical quantity, all measuring instruments are divided into main and auxiliary measuring instruments. The main means of measuring SI of that physical quantity, the value of which must be obtained in accordance with the measurement task. Auxiliary measuring instruments SI of that physical quantity, the influence of which on the main measuring instrument or object of measurement must be taken into account in order to obtain measurement results of the required accuracy (a thermometer for measuring gas temperature in the process of measuring the volume flow of this gas). 7

8 The classification of measuring instruments according to their technical purpose is the main one and is shown in Fig. 1.1 Metrological characteristic of a measuring instrument (MX SI): Characteristic of one of the properties of a measuring instrument that affects the measurement result and its error. For each type of measuring instruments, their metrological characteristics are established. The metrological characteristics established by normative and technical documents are called standardized metrological characteristics, and those determined experimentally are called valid metrological characteristics. The nomenclature of metrological characteristics and methods for their normalization are established by GOST. All metrological characteristics of MI can be divided into two groups: characteristics that affect the result of measurements (determining the scope of MI); characteristics affecting the accuracy (quality) of the measurement. The main metrological characteristics that affect the result of measurements include: measurement range of measuring instruments; eight

9 the value of a one-to-one or multi-valued measure; conversion function measuring transducer; the value of division of the scale of a measuring instrument or a multi-valued measure; type of output code, number of digits of the code, price of the unit of the smallest digit of the code of measuring instruments intended for issuing results in a digital code. Measuring range of a measuring instrument (measurement range) is the range of values ​​within which the permissible error limits of a measuring instrument are normalized (for transducers, this is the conversion range). The values ​​of the quantity that limit the measurement range from below and above (left and right) are called the lower measurement limit or the upper measurement limit, respectively. For measures, the limits of reproduction of values. Single digit measures have nominal and actual reproducible values. The nominal value of a measure is the quantity value assigned to a measure or batch of measures during manufacture. Example: resistors with a nominal value of 1 ohm, a weight with a nominal value of 1 kg. Often the nominal value is indicated on the measure. The actual value of a measure is the value of a quantity assigned to a measure based on its calibration or verification. Example: the composition of the state standard of the unit of mass includes a platinum-iridium weight with a nominal mass value of 1 kg, while the actual value of its mass is 1 kg, obtained as a result of comparisons with the international standard of the kilogram stored at the International Bureau of Weights and Measures (BIPM) (in in this case it is the calibration). The range of indications of a measuring instrument (range of indications) is the range of values ​​of the instrument scale, limited by the initial and final values ​​of the scale. Measuring range of a measuring instrument (range of measurements) is the range of values ​​within which the permissible error limits of a measuring instrument are normalized. The values ​​of the quantity that limit the measurement range from below and above (left and right) are called the lower measurement limit or the upper measurement limit, respectively. The scale division price (division price) is the difference between the values ​​of the quantities corresponding to two adjacent marks on the scale of the measuring instrument. The metrological characteristics that determine the accuracy of measurement include the error of the measuring instrument and the accuracy class of the measuring instrument. 9

10 Measuring instrument error is the difference between the indication of the measuring instrument (x) and the true (real) value (x d) of the measured physical quantity. x x x d. (1.1) As x d is either a nominal value (for example, measures), or the value of a quantity measured more accurate (at least an order of magnitude, i.e., 10 times) SI. The smaller the error, the more accurate the measuring instrument. MI errors can be classified according to a number of features, in particular: in relation to the measurement conditions, basic, additional; according to the method of expression (by the method of normalization of MX) absolute, relative, reduced. The basic error of a measuring instrument (basic error) is the error of a measuring instrument used under normal conditions. As a rule, normal operating conditions are: temperature (293 5) K or (20 5) ºС; relative air humidity (65 15)% at 20 ºС; mains voltage 220 V 10% with a frequency of 50 Hz 1%; atmospheric pressure from 97.4 to 104 kPa. Additional error of a measuring instrument (additional error) is a component of the error of a measuring instrument that occurs in addition to the main error due to the deviation of any of the influencing quantities from its normal value or due to its going beyond the normal range of values. When normalizing the characteristics of the errors of measuring instruments, the limits of permissible errors (positive and negative) are established. The limits of permissible basic and additional errors are expressed in the form of absolute, reduced or relative errors, depending on the nature of the change in errors within the measurement range. The limits of the permissible additional error can be expressed in a form different from the form of expression of the limits of the permissible basic error. The absolute error of the measuring instrument (absolute error, expressed in unity of error) is the error of the measuring instrument in the values ​​of the measured physical quantity. The absolute error is determined by formula (1.1). 10

11 The limits of the permissible basic absolute error can be specified as: a (1.2) or a bx, (1.3) where the limits of the permissible absolute error, expressed in units of the measured value at the input (output) or conventionally in scale divisions; x the value of the measured value at the input (output) of measuring instruments or the number of divisions counted on the scale; ab, positive numbers independent of x. The reduced error of the measuring instrument (reduced error) is the relative error expressed as the ratio of the absolute error of the measuring instrument to the conditionally accepted value of the quantity (normalizing value), which is constant over the entire measurement range or in part of the range. The reduced error of the measuring instrument is determined by the formula: 100%, (1.4) x N where the limits of the allowable reduced basic error, %; limits of permissible absolute basic error, established by formula (1.2); x N normalizing value expressed in the same units as. The limits of the allowable reduced basic error should be set in the form: p, (1.5) where p is an abstract positive number chosen from the series 1 10 n ; 1.5 10n; (1.6 10n); 2 10n; 2.5 10n; (3 10 n); 4 10n; 5 10n; 6 10 n (n = 1, 0, 1, 2, etc.). The normalizing value x N is taken equal to: the final value of the working part of the scale (x k), if the zero mark is on the edge or outside the working part of the scale (uniform or exponential); the sum of the final values ​​of the scale (excluding the sign), if the zero mark is inside the scale; the modulus of the difference in measurement limits for SI, the scale of which has a conditional zero; the length of the scale or its part corresponding to the measurement range, if it is significantly non-uniform. In this case, the absolute error, like the length of the scale, must be expressed in millimeters. eleven

12 Relative error of the measuring instrument (relative error) error of the measuring instrument, expressed as the ratio of the absolute error of the measuring instrument to the measurement result or to the actual value of the measured physical quantity. The relative error of the measuring instrument is calculated by the formula: 100%, (1.6) x where the limits of the permissible relative basic error, %; limits of permissible absolute error, expressed in units of the measured value at the input (output) or conventionally in scale divisions; x value of the measured quantity at the input (output) of measuring instruments or the number of divisions counted on the scale. If bx, then the limits of the permissible relative basic error are set in the form: q, (1.7) where q is an abstract positive number selected from the series given a bx, then in the form: given above; or if x cd k 1, (1.8) x where x k is greater (in absolute value) from the measurement limits; cd, positive numbers chosen from the series above. In justified cases, the limits of the permissible relative basic error are determined by more than complex formulas either in the form of a graph or a table. The characteristics introduced by GOST 8.009 most fully describe the metrological properties of SI. However, there are currently quite a few a large number of SI, the metrological characteristics of which are normalized in a slightly different way, namely on the basis of accuracy classes. The accuracy class of measuring instruments (accuracy class) is a generalized characteristic of this type of measuring instruments, as a rule, reflecting the level of their accuracy, expressed by the limits of permissible basic and additional errors, as well as other characteristics that affect accuracy. The accuracy class makes it possible to judge the limits of the measurement error of this class. This is important when choosing measuring instruments depending on the given measurement accuracy. 12

13 The designation of accuracy classes of SI is assigned in accordance with GOST. The construction rules and examples of designation of accuracy classes in the documentation and on measuring instruments are given in Appendix B. The designation of the accuracy class is applied to dials, shields and SI cases, and is given in normative documentation on SI. The range of standardized metrological characteristics of measuring instruments is determined by the purpose, operating conditions, and many other factors. The norms for the main metrological characteristics are given in the standards, in the technical specifications (TS) and operational documentation for SI The purpose of the work is to familiarize yourself with the technical documentation for SI and determine the main classification features and normalized metrological characteristics of the measuring instruments used; acquisition of skills in determining the main classification features, the measuring instruments used and their standardized metrological characteristics directly on the measuring instruments; consolidation of theoretical knowledge in the section "Classification of measuring instruments" of the studied discipline "Metrology, standardization and certification" Used equipment and instruments 1) oscilloscope; 2) digital voltmeter; 3) analog voltmeter; 4) generator; 5) amplifier; 6) power supply; 7) the element is normal temperature-controlled; 8) programmable source of calibrated voltages Work program Determine the classification features indicated in Table. 1.2 from the number of measuring instruments (SI) at the workplace Familiarize yourself with the technical documentation for the SI (operating manual, technical description with operating instructions or passport). thirteen

14 Determine the normalized metrological characteristics of MI directly by measuring instruments and technical documentation for them and fill in the table for each measuring instrument Compile a report on the work done (see Appendix A for an example of a title page). Table 1.2 Classification features Measuring instrument (indicate the type of MI) By type (by technical purpose) By type of output value By the form of information presentation (only for measuring instruments) By purpose By metrological purpose Normalized metrological characteristics 1.5. Control questions 1. Name the types of measuring instruments. 2. According to what classification criteria are SI subdivided. 3. Describe each type of SI. 4. What groups are the metrological characteristics of SI divided into. 5. What are metrological characteristics? 6. What are normalized and valid metrological characteristics and how do they differ from metrological characteristics? 7. Name the metrological characteristics that determine: the scope of the SI; measurement quality. 8. Name the types of errors. 9. What characteristic determines the accuracy of SI? 10. What is the function of standards? 11. What is the difference in the appointment of working SI and working standards? 1.6. Literature 1. RMG GSI. Metrology. Basic terms and definitions. Recommendations for interstate standardization. 2. GOST GSI. Normalized metrological characteristics of measuring instruments. 3. GOST GSI. Accuracy classes of measuring instruments. 4. Sergeev A.G., Teregerya V.V. Metrology, standardization and certification. M.: Yurayt Publishing House: ID Yurayt,

15 LABORATORY WORK 2 INDIRECT SINGLE MEASUREMENTS 2.1. Basic concepts and definitions Measurement is a set of operations for the use of a technical means that stores a unit of a physical quantity, providing a ratio (in an explicit or implicit form) of the measured quantity with its unit and obtaining the value of this quantity. Measurements are the main source of information about the compliance of products with the requirements of regulatory documents. Only the reliability and accuracy of measurement information ensure the correctness of decision-making about the quality of products, at all levels of production when testing products, in scientific experiments, etc. Measurements are classified: a) by the number of observations: a single measurement a measurement performed once. The disadvantage of these measurements is the possibility of a gross miss error; multiple measurement measurement of a physical quantity of the same size, the result of which is obtained from several successive measurements, i.e., consisting of a number of single measurements. Usually their number is n 3. Multiple measurements are carried out in order to reduce the influence of random factors on the measurement result; b) by the nature of accuracy (according to the conditions of measurement): equal-precision measurements of a series of measurements of any quantity, made with the same accuracy of measuring instruments in the same conditions with the same care; unequal measurements - a series of measurements of some quantity, performed by several measuring instruments differing in accuracy and (or) under different conditions; c) by the expression of the measurement result: an absolute measurement a measurement based on direct measurements of one or more basic quantities and (or) the use of physical constant values ​​(for example, the measurement of force F mg is based on the measurement of the basic quantity of mass m and the use of the physical constant of gravitational acceleration g (at the point of measurement of mass); relative measurement is the measurement of the ratio of a quantity to the quantity of the same name, which plays the role of a unit, or the measurement of a change

16 values ​​in relation to the value of the same name, taken as the original; d) according to the method of obtaining the measurement result: direct measurement is a measurement in which the desired value of a physical quantity is obtained directly (for example, measuring the mass on a scale, measuring the length of a part with a micrometer); indirect measurement is the determination of the desired value of a physical quantity based on the results of direct measurements of other physical quantities that are functionally related to the sought value; cumulative measurements are simultaneous measurements of several quantities of the same name, in which the desired values ​​\u200b\u200bof the quantities are determined by solving a system of equations obtained by measuring these quantities in various combinations (for example, the mass value of individual weights of the set is determined from the known value of the mass of one of the weights and from the measurement results ( comparisons) masses of various combinations of weights); joint measurements are simultaneous measurements of two or more dissimilar quantities to determine the relationship between them; e) by the nature of the change in the measured physical quantity: static measurement is the measurement of a physical quantity taken in accordance with a specific measurement task as unchanged throughout the measurement time. They are carried out with the practical constancy of the measured value; dynamic measurement measurement of a physical quantity that changes in size; f) according to the metrological purpose of the measuring instruments used: technical measurements measurements using working measuring instruments; metrological measurements measurements with the help of reference measuring instruments in order to reproduce units of physical quantities in order to transfer their size to working measuring instruments. The measurement results are approximate estimates of the values ​​of quantities found by measurements, since even the most accurate instruments cannot show the actual value of the measured quantity. There is necessarily a measurement error, the causes of which can be various factors. They depend on the method of measurement, on the technical means by which measurements are taken, and on the perception of the observer making the measurements. sixteen

17 The accuracy of the measurement result is one of the characteristics of the quality of measurement, reflecting the closeness to zero of the error of the measurement result. The smaller the measurement error, the greater its accuracy. Measurement error x deviation of the measurement result x from the true or actual value (x i or x d) of the measured quantity: xx x id. (2.1) The true value of a physical quantity is the value of a physical quantity that ideally characterizes the corresponding physical quantity qualitatively and quantitatively. It does not depend on the means of our knowledge and is an absolute truth. It can only be obtained as a result of an endless process of measurements with endless improvement of methods and measuring instruments. The actual value of a physical quantity is the value of a physical quantity obtained experimentally and so close to the true value that it can be used instead of it in the given measurement problem. Measurement errors can also be classified according to a number of criteria, in particular: a) according to the method of numerical expression; b) by the nature of the manifestation; c) according to the type of source of occurrence (causes of occurrence). According to the method of numerical expression, the measurement error can be: The absolute measurement error (x) is the difference between the measured value and the actual value of this value, i.e. x x x d. (2.2) Relative measurement error () is the ratio of the absolute measurement error to the actual value of the measured quantity. The relative error can be expressed in relative units (in fractions) or as a percentage: x or x 100%. (2.3) x x The relative error shows the accuracy of the measurement. 17

18 Depending on the nature of the manifestation, there are systematic (s) and random (0) components of measurement errors, as well as gross errors (misses). A systematic measurement error (s) is a component of the measurement result error that remains constant or regularly changes during repeated measurements of the same physical quantity. Random measurement error (0) is a component of the measurement result error, which changes randomly (in sign and value) during repeated measurements, carried out with the same care, of the same physical quantity. Gross errors (misses) occur due to erroneous actions of the operator, a malfunction of the measuring instrument, or sudden changes in measurement conditions (for example, a sudden drop in voltage in the power supply network). The following components of the total measurement error are considered depending on the type of source of error: allowed simplifications in measurements. The instrumental components of the error are errors that depend on the errors of the measuring instruments used. The study of instrumental errors is the subject of a special discipline of the theory of accuracy of measuring devices. The subjective components of the error are errors due to the individual characteristics of the observer. Errors of this kind are caused, for example, by a delay or advance in signal registration, incorrect reading of tenths of a division of the scale, asymmetry that occurs when a stroke is set in the middle between two risks, etc. Approximate estimation of the error Single measurements. The vast majority of technical measurements are single. The performance of single measurements is substantiated by the following factors: production necessity (destruction of the sample, impossibility of repeating the measurement, economic feasibility, etc.); eighteen

19 the possibility of neglecting random errors; random errors are significant, but the confidence limit of the measurement result error does not exceed the permissible measurement error. For the result of a single measurement, a single reading value of the instrument reading is taken. Being essentially random, a single reading x includes instrumental, methodological and personal components of the measurement error, in each of which systematic and random components of the error can be distinguished. The components of the error of the result of a single measurement are the errors of the measuring instrument, the method, the operator, as well as the errors due to changes in the measurement conditions. The error of the result of a single measurement is most often represented by systematic and random errors. The error of MI is determined on the basis of their metrological characteristics, which must be specified in regulatory and technical documents, and in accordance with the RD Method and operator errors must be determined during the development and certification of a specific MIM. Personal errors in single measurements are usually assumed to be small and are not taken into account. indirect measurements. With indirect measurements, the desired value of the quantity is found by calculation based on direct measurements of other physical quantities that are functionally related to the desired quantity by the known dependence yf x1, x2,..., xn, (2.4) where x1, x2,..., xn are subject to direct measurements function arguments y. The result of indirect measurement is an estimate of the value of y, which is found by substituting the measured values ​​of the arguments x i into formula (4). Since each of the arguments x i is measured with some error, the problem of estimating the error of the result is reduced to summing the errors in the measurement of the arguments. However, a feature of indirect measurements is that the contribution of individual errors in the measurement of arguments to the error of the result depends on the type of function (4). nineteen

20 For estimation of errors, it is essential to divide indirect measurements into linear and non-linear indirect measurements. For linear indirect measurements, the measurement equation has the form: y n bi xi, (2.5) i1 where b i are constant coefficients at the arguments x i. The result of a linear indirect measurement is calculated by formula (2.5), substituting the measured values ​​of the arguments into it. The measurement errors of the arguments x i can be set by their boundaries xi. With a small number of arguments (less than five), a simple estimate of the error of the result y is obtained by simply summing the marginal errors (ignoring the sign), i.e., substituting the boundaries x 1, x 2, x n into the expression: y x1x2 ... xn. (2.6) However, this estimate is overestimated, since such summation actually means that the measurement errors of all arguments simultaneously have a maximum value and coincide in sign. The probability of such a coincidence is practically zero. To find a more realistic estimate, we proceed to the static summation of the error of the arguments according to the formula: n 2 2 ii, (2.7) i1 yk bx where k is the coefficient determined by the accepted confidence probability (at P = 0.9 at k = 1.0; .95 at k = 1.1, P = 0.99 at k = 1.4). Nonlinear indirect measurements any other functional dependencies other than (2.5). With a complex function (2.4) and, in particular, if it is a function of several arguments, the determination of the law of distribution of the result error is associated with significant mathematical difficulties. Therefore, the approximate estimation of the error of nonlinear indirect measurements is based on the linearization of function (2.4) and further processing of the results, as in linear measurements. Let us write the expression for the total differential of the function y in terms of partial derivatives with respect to the arguments x i: y y y dy dx1 dx2... dxn. (2.8) x x x 1 2 n 20

21 By definition, the total differential of a function is the increment of a function caused by small increments of its arguments. Considering that the measurement errors of the arguments are always small compared to the nominal values ​​of the arguments, we can replace in formula (2.8) the differentials of the arguments dx n with the measurement error xn, and the function differential dy with the error of the measurement result y: y y y y x x... xn. (2.9) x x x If we analyze formula (2.9), we can obtain a simple rule for estimating the error of the result of a non-linear indirect measurement . Errors in works and private. If the measured values ​​x1, x2,..., x n are used to calculate y x... 1x2 xn or y 1, x2 then the relative errors y x1x2... xn are summed, where y y. y 2.3. Recording (rounding) error of a number The recording (rounding) error of a number is defined as the ratio of half of the unit of the least significant digit of the number to the value of the number. For example, for the normal acceleration of falling bodies g \u003d 9.81 m / s 2, the unit of the least significant digit is 0.01, therefore, the error in writing the number 9.81 will be equal to 0.01 5, \u003d 0.05%. 29, Purpose of work n x development of methods for conducting single direct and indirect measurements; mastering the rules for processing, presenting (recording) and interpreting the results of measurements; acquisition of practical skills in the use of measuring instruments of different accuracy, as well as analysis and comparison of the accuracy of the results of indirect measurements with the accuracy of the measuring instruments used in direct measurements; identification of possible sources and causes of methodological errors; 21

22 consolidation of theoretical material in the section "Metrology" of the discipline under study "Metrology, standardization and certification" Equipment used vernier caliper (hereinafter SC); micrometer; ruler. When recording the measuring instruments used, indicate their normalized metrological characteristics using the measuring instruments Work program Perform single measurements of the diameter and height of the cylinder with measuring instruments of various accuracy: caliper, micrometer and ruler. Record the measurement results in the table. As cylinder 1, select a cylinder of lower height. Record the results of direct measurements of the diameter and height of the cylinders in a table with the accuracy with which the measuring instrument allows you to measure. Table 2.1 Measurement results Measured Cylinder 1 (small) Cylinder 2 (large) parameter Diameter d, mm Height h, mm Volume V, mm Rel. V Abs. error V, mm 3 micrometer ШЦ ШЦ ruler Determine the volume of the cylinder using the ratio: 2 V d h, mm 3, (2.10) 4 where = 3.14 is a numerical coefficient; d cylinder diameter, mm; h cylinder height, mm Determine the relative measurement error, expressed in relative units V V. (2.11) V 22

23 To determine the relative measurement error V, it is necessary to transform formula (2.11) into a convenient one for calculation using formula (2.9) (see section 2.2). In the resulting formula, d, h are the errors of the measuring instruments used in the measurements. In indirect measurements of physical quantities, tabular data or irrational constants are very often used. Because of this, the value of the constant used in the calculations, rounded up to a certain sign, is an approximate number that contributes its share to the measurement error. This fraction of the error is defined as the error in recording (rounding off) the constant (see clause 2.3) Determine the error in calculating the volume using the formula VV, mm 3. (2.12) V Round off the measurement errors and record the result of measuring the cylinder volumes VVV mm 3. (2.13) in order to record the final result of indirect measurements, it is necessary to round off the measurement error V in accordance with MI 1317, to agree on the numerical values ​​​​of the result and the measurement errors (see clause 2.4) for each of the cylinders. An example is shown in Figure 2.1. V 2 ΔV 2 V 2 V 1 ΔV 1 V 1 V 1 + ΔV 1 V 2 + ΔV 2 Then you need to select the scale and put down all the other points. Show the error of the method in the figure. 23

24 2.6.7 Prepare a report and draw a conclusion (see Appendix A for an example of a title page). In the conclusion, evaluate the results of measurements, identify possible sources and causes of methodological errors. Control questions 1. Name the main types of measurements. 2. By what criteria are measurement errors classified? 3. Name and describe the main types of measurement errors. 4. How to determine the error in writing a number? 5. How to determine the error of the result of indirect measurement? 2.8. Literature used 1. RMG Recommendations on interstate standardization. GSI. Metrology. Basic terms and definitions. 2. R Recommendations on metrology. GSI. Direct single measurements. Estimation of errors and uncertainty of the measurement result. M., Publishing house of standards, Borisov Yu.I., Sigov A.S., Nefedov V.I. Metrology, standardization and certification: textbook. Moscow: FORUM: INFRA-M, MI Guidelines. GSI. Results and characteristics of measurement errors. Submission Forms. Methods of use in testing product samples and monitoring their parameters. 24

25 LABORATORY WORK 3 PROCESSING THE RESULTS OF DIRECT MULTIPLE MEASUREMENTS 3.1. Introduction The need to perform direct multiple measurements is established in specific measurement procedures. During statistical processing of a group of results of direct multiple independent measurements, the following operations are performed: known systematic errors are excluded from the measurement results; calculating an estimate of the measurand; calculate the standard deviation of the measurement results; check for gross errors and, if necessary, exclude them; checking the hypothesis that the measurement results belong to a normal distribution; calculate the confidence limits of the random error (confidence random error) estimates of the measured value; calculate the confidence limits (boundaries) of the non-excluded systematic error in the estimate of the measured value; calculate the confidence limits of the error in estimating the measured value. The hypothesis that the measurement results belong to a normal distribution is tested with a significance level q from 10% to 2%. Specific values ​​of significance levels should be specified in a specific measurement procedure. To determine the confidence limits of the error in estimating the measured value, the confidence probability P is taken equal to 0. Basic concepts and definitions Depending on the nature of the manifestation, systematic (C) and random (0) components of the measurement error are distinguished, as well as gross errors (misses). Gross errors (misses) arise due to erroneous actions of the operator, a malfunction of the measuring instrument, or sudden changes in measurement conditions, for example, a sudden drop in voltage in the power supply network. Closely adjoining them are the errors that depend on 25

26 observers and related to improper handling of measuring instruments. The systematic measurement error (systematic error C) is the component of the measurement result error that remains constant or regularly changes during repeated measurements of the same physical quantity. It is believed that systematic errors can be detected and eliminated. However, in real conditions It is impossible to completely eliminate the systematic component of the measurement error. There are always some factors that need to be taken into account, and which will constitute a non-excluded systematic error. Non-excluded systematic error (NSE) is a component of the error of the measurement result, due to errors in the calculation and introduction of corrections for the influence of systematic errors or a systematic error, the correction for which was not introduced due to its smallness. Non-excluded systematic error is characterized by its boundaries. The boundaries of the non-excluded systematic error Θ with the number of terms N 3 are calculated by the formula: N i, (3.1) i1 where the boundary of the i-th component of the non-excluded systematic i error. With the number of non-excluded systematic errors N 4, the calculation is carried out according to the formula k N 2 i, (3.2) i1 ; at P = 0.99, k = 1.4). Here Θ is considered as a confidence quasi-random error. Random measurement error (0) is a component of the measurement result error, which changes randomly (in sign and value) during repeated measurements, carried out with the same care, of the same physical quantity. 26

27 To reduce the random component of the error, multiple measurements are carried out. Random error is estimated by the confidence interval tp Sx, (3.3) where t P is the Student's coefficient for a given level of confidence Р d and sample size n (number of measurements). Confidence limits of the error of the measurement result of the boundary of the interval within which the desired (true) error value of the measurement result is located with a given probability. Sample a series of x measurement results (x i ), i = 1,..., n (n > 20), from which known systematic errors are excluded. The sample size is determined by the requirements of measurement accuracy and the possibility of repeated measurements. A variational series is a selection sorted in ascending order. Histogram of the dependence of the relative frequencies of the measurement results falling into the grouping intervals on their values, presented in graphical form. Estimation of the distribution law Estimation of the correspondence between the experimental distribution law and the theoretical distribution. It is carried out using special statistical criteria. When p< 15 не проводится. Точечные оценки закона распределения оценки закона распределения, полученные в виде одного числа, например оценка дисперсии результатов измерений или оценка математического ожидания и т. д. Средняя квадратическая погрешность результатов единичных измерений в ряду измерений (средняя квадратическая погрешность результата измерений) оценка S рассеяния единичных результатов x измерений в ряду равноточных измерений одной и той же физической величины около среднего их значения, вычисляемая по формуле: 1 n S 2 x x 1 i x n, (3.4) i1 где i x результат i-го единичного измерения; x среднее арифметическое значение измеряемой величины из n единичных результатов. Примечание. На практике широко распространен термин среднее квадратическое отклонение (СКО). Под отклонением в соответствии с приведенной выше формулой понимают отклонение единичных результатов в ряду измерений от их среднего арифметического значения. В метрологии это отклонение называется погрешностью измерений. 27

28 The mean square error of the measurement result of the arithmetic mean estimate S x of the random error of the arithmetic mean of the measurement result of the same value in a given series of measurements, calculated by the formula 2 i S Sx 1 xxxn nn1, (3.5) measurements obtained from a series of equally accurate measurements; n number of single measurements in a series Exclusion of gross errors To exclude gross errors, Grubbs' statistical test is used, which is based on the assumption that a group of measurement results belongs to a normal distribution. For this, the Grubbs G 1 and G 2 criteria are calculated, assuming that the largest x max or the smallest x min measurement result is caused by gross errors: xmax xxx G1, min S G. (3.6) x 2 Sx Compare G 1 and G 2 with the theoretical value GT of the Grubbs test at the chosen significance level q. A table of critical values ​​of the Grubbs criterion is given in Appendix B. If G 1 > G T, then x max is excluded as an unlikely value. If G 2 > G T, then x min is excluded as an unlikely value. Next, the arithmetic mean and standard deviation of a number of measurement results are calculated again, and the procedure for checking for the presence of gross errors is repeated. If G1 G T, then x max is not considered a miss and is stored in the measurement series. If G 2 G T, then x min is not considered a miss and it is stored in a series of measurement results. The error limits for estimating the measured value (without taking into account the sign) are calculated by the formula 28

29 K S, (3.7) where K is a coefficient depending on the ratio of the random component of the error and the NSP. The total standard deviation S of the estimate of the measured value is calculated by the formula S S2 S2 x, (3.8) from formulas (3.1), or PS, (3.10) k 3 where P are the confidence limits of the NSP, which are determined by one of the formulas (3.2); k is a coefficient determined by the accepted confidence probability P, the number of NSP components and their relationship to each other. The coefficient K for substitution into formula (3.7), depending on the number of NSPs, is determined by the empirical formulas, respectively, K, P K. (3.11) S S S x x S 3.5. Algorithm for processing the results of observations Processing of the results of observations is carried out in accordance with GOST “GSI. Measurements are direct with multiple. Methods for processing measurement results. Basic Provisions» Determination of point estimates of the distribution law x 1 n x i ; 1 n S 2 x x 1 i x n ; S S x x. n n i Construction of the experimental law of distribution of the results of multiple observations a) in Table 3.2, write the variational series of the results of multiple observations x ; i i1 29




PRACTICAL LESSON 6 "Processing the results of equal-precision measurements, free from systematic errors" The lesson is devoted to solving problems of calculating the errors of equal-precision measurements

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Measurements of physical quantities Measurement of a physical quantity is a set of operations on the use of a technical means that stores a unit of a physical quantity, providing a ratio (in explicit

MSIIK Basic concepts Physical quantity (PV) True value of PV Real value of PV Unit of PV basic units of the SI system, decibel, testing, control, measuring instruments, classification

Metrological characteristics Metrological characteristics (MC) are characteristics that allow determining the suitability of SI for measurements in a known range with a known accuracy. Specifications,

Laboratory work 1. Calculation of voltage measurement error using a potentiometer and a voltage divider. Theoretical information. Classification of measurement errors Error of measuring instruments

MINISTRY OF HEALTH OF THE RUSSIAN FEDERATION VOLGOGRAD STATE MEDICAL UNIVERSITY DEPARTMENT OF BIOTECHNICAL SYSTEMS AND TECHNOLOGY

FOUNDATIONS OF THE THEORY OF ERRORS OF PHYSICAL MEASUREMENTS Introduction Measurements of physical quantities are an integral part of experimental research, including those conducted in a physical workshop. measurements

MEASUREMENT ERRORS. SYSTEMATIC ERRORS Measurement The measurement of a physical quantity consists in comparing this quantity with a homogeneous quantity taken as a unit. In the law of the Republic of Belarus On security

“Errors in measurements, tests and control. The main characteristics of measuring instruments" Purpose: 1. To form students' knowledge on the topic, to achieve an understanding of the issues, to ensure the assimilation and consolidation

Control tasks in metrology 1. When measuring the active resistance of the resistor, ten equal measurements were made, the results of which are shown in the table. Assess absolute and relative

MEASUREMENT ERRORS The measurement error (measurement error for short) is represented by the deviation of the measurement result from the true value of the quantity. Main sources of result error

MEASUREMENT OF PHYSICAL QUANTITIES. TYPES AND METHODS OF MEASUREMENTS. Measurements and their types Physical quantity as an object of measurement A physical quantity is a property that is qualitatively common to many physical objects

1 Processing the results of the experiment Definitions Measurement Finding the value of a physical quantity empirically using specially designed technical means Measurement consists of

Theory of errors When analyzing measurements, two concepts should be clearly distinguished: the true values ​​of physical quantities and their empirical manifestations - the results of measurements. True values ​​of physical

Lecture 3 MEASUREMENT ERRORS. SYSTEMATIC ERRORS 3.1 Postulates of metrology. Classification of errors It is customary to characterize the quality of means and measurement results by indicating their errors.

MEASUREMENT OF PHYSICAL QUANTITIES Measurement is the process of determining the quantitative value of a physical quantity empirically using special technical means (instruments) and expressing this value in

1 OPTION 1 (The choice provides for the rationale for the correct answer) 1) When determining the hardness of a material, a scale is used 2) An ordered set of values ​​of a physical quantity, adopted by agreement

1 Metrology is ... TESTS a) the theory of transferring the dimensions of units of physical quantities; b) the theory of initial measuring instruments (standards); c) the science of measurements, methods and means of ensuring them

GOST R 8.736-2011 State system for ensuring the uniformity of measurements. Multiple direct measurements. Methods for processing measurement results. Main provisions NATIONAL STANDARD OF THE RUSSIAN FEDERATION

Lecture 4 METROLOGICAL CHARACTERISTICS OF SI 4.1 Metrological characteristics of SI and their normalization Metrological characteristics (MX) are those characteristics of MI that allow one to judge their suitability

Digital laboratories "Archimedes" - a powerful mobile measuring laboratory for conducting natural science experiments. Multiple sensors, measurement interface converting continuous signals

LECTURE 4 Metrological characteristics of measuring instruments All measuring instruments, regardless of their specific design, have a number of common properties necessary for them to perform their functional

Measurement of physical quantities GN Andreev The exact natural sciences are based on measurements. In measurements, the values ​​​​of quantities are expressed as numbers that indicate how many times the measured value is greater

Metrology, standardization and certification Chapter 1 Metrology 1 Object and subject of metrology Metrology (from the Greek “metron” measure, “logos” teaching) is the science of measurements, methods and means of ensuring unity

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION KAZAN STATE UNIVERSITY OF ARCHITECTURE AND CONSTRUCTION

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

Ministry of Education and Science of the Russian Federation Federal State Budgetary Educational Institution of Higher Education “Russian University of Economics named after G.V. Plekhanov» THEORETICAL

Lecture 9 CREATION OF NON-STANDARDIZED MEASURING INSTRUMENTS 9. Metrological work related to the creation and application of reference data

I. Measurement of physical quantities. Brief theory of measurement errors direct measurements, which are indirect measurements, which are comparisons of the value of a physical calculation

Work 3 Standard processing of the results of direct measurements with multiple observations 1. PURPOSE OF THE WORK Acquaintance with the technique of performing direct measurements with multiple observations. Getting in this

Measurement error From Wikipedia, the free encyclopedia Measurement error is an estimate of the deviation of the measured value of a quantity from its true value. The measurement error is

APPROVED by order of the Federal Agency for Technical Regulation and Metrology dated December 27, 2018 2768 STATE VERIFICATION SCHEME FOR MEASURING INSTRUMENTS

1 GENERAL PROVISIONS FOR CONDUCT OF ENTRANCE TESTS FOR ADMISSION TO MASTER'S STUDIES IN THE DIRECTION 27.04.01 "Standardization and Metrology" 3 1.1 This Program, drawn up in accordance with the federal

Ministry of Education of the Republic of Belarus BELARUSIAN NATIONAL TECHNICAL UNIVERSITY E.V. Zhuravkevich PROCESSING OF THE RESULTS OF MEASUREMENTS IN THE PHYSICAL WORKSHOP Guidelines for laboratory

Federal Agency of Railway Transport Ural State University of Railway Transport L. S. Gorelova T. A. Antropova Measurement errors Processing of multiple measurements Ekaterinburg

Ministry of Agriculture of the Russian Federation Federal State Budgetary Educational Institution of Higher Professional Education "Samara State Agricultural

Lecture 2 Classification of measurements. Measurement of physical quantities. Types and methods of measurements 2.1 Measurement Measurement of physical quantities consists in comparing a quantity with a homogeneous quantity,

Work 1. Determination of linear dimensions and volumes of bodies. Processing of measurement results Equipment: caliper, micrometer, test bodies. Introduction Errors in any measurement are made up of errors

Nizhny Novgorod State Technical University named after R.E. Alekseeva Department of FTOS Statistical processing of measurement results in a laboratory workshop Popov E.A., Uspenskaya G.I. Nizhny Novgorod

Appendix EVALUATION OF EXPERIMENTAL ERRORS IN PROCESSING MEASUREMENT RESULTS Basic concepts. All experimental studies carried out in the laboratory of strength of materials are accompanied by measurements

UDC 373.167.1:3 BBC 22.3ya72 K28 K28 Kasyanov, V. A. Physics. Grade 10. Basic and advanced levels: a notebook for laboratory work / V. A. Kasyanov, V. A. Korovin. 3rd ed., stereotype. M. : Drofa, 2017.

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State Budgetary Educational Institution of Higher Professional Education "UFA STATE AVIATION TECHNICAL

Laboratory work 1.01 DETERMINATION OF THE DENSITY OF A SOLID BODY E.V. Kosis, E.V. Zhdanova The purpose of the work: to study the methodology for conducting the simplest physical measurements, as well as the main methods for estimating errors

REQUIRED INFORMATION ON MATHEMATICAL PROCESSING OF MEASUREMENT RESULTS In the laboratory practice, you will constantly deal with measurements of physical quantities. Must be able to properly handle

Section 1 MECHANICS Operation 1.1 Measurement of ball impact time. Statistical method for estimating random errors Equipment: tripod, balls, electronic counter-stopwatch. Introduction Measure physical

MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION

MINISTRY OF EDUCATION OF THE RUSSIAN FEDERATION State educational institution of higher professional education Orenburg State University L.N. TRETIAK RESULTS PROCESSING

Annotation to the work program of the discipline "Metrology, standardization and certification in infocommunications" The work program is intended for teaching the discipline "Metrology, standardization and certification

TASK 1 (Code 04) VERIFICATION OF TECHNICAL DEVICES BASIC METROLOGIST The technical ammeter of the magnetoelectric system with a rated current of 5 with a number of nominal divisions of 100 has digitized divisions from zero to

MOSCOW ENERGY INSTITUTE (TECHNICAL UNIVERSITY)

Determination of the density of a wooden block. The purpose of the work: to get acquainted with the theory of errors, learn how to make the simplest measurements, find measurement errors, process and analyze the obtained

LECTURE 3 Types, methods and means of measurement Measurement of a physical quantity is a set of operations for the use of a technical means that stores a unit of a physical quantity, consisting in comparison (in explicit