home · On a note · Means for measuring angles and cones. Angle measures and squares. Goniometers. Methods and means for measuring angles and cones Measuring inclination angles in mechanical engineering

Means for measuring angles and cones. Angle measures and squares. Goniometers. Methods and means for measuring angles and cones Measuring inclination angles in mechanical engineering

In the polygonometric course, abutment angles, rotation angles and notches of lateral points are measured.

There are two main ways to measure angles at polygonometry points: the method of circular techniques; single angle method.

Method of circular techniques

Measuring angles in this method begins with preparing a theodolite for measuring angles, consisting of:

Centering, which is performed using an optical plumb line with an accuracy of 1 mm;

Bringing the main axis into a plumb position using a level with an alidade of a horizontal circle and three lifting screws;

Installation of the observation tube, consisting of installation of the tube by the eye, installation of the tube by the subject and elimination of parallax of the reticle;

Work at the station is performed in the following sequence:

The sighting axis of the telescope during CL is aimed at the sighting mark, which is taken as the initial direction during measurement;

Set the dial and optical micrometer to a reading close to zero (preferably slightly more than zero); To do this, first, by rotating the handle of the micrometer, set the reading on the scale of the latter, close to zero, then by rotating the handle for rearranging the dial, carefully align the image of the strokes of the opposite edges of the dial, after which the reading is made and recorded in the journal;

Using the handle of a micrometer, spread the image of the combined strokes and connect them again (second combination), make a count and write it down in a journal; the difference between two readings should not exceed 2;

Unfasten the alidade and point the sighting axis of the pipe (rotating the alidade clockwise) to the second, and then the third, etc. brands; with two combinations, readings are made and recorded in a journal;

The observations are completed by re-sighting at the point of the initial direction and, based on the initial and final readings obtained, they are convinced of the stationary position of the limb.

The described actions constitute the first half of the technique.

Re-targeting the first mark is called horizon closure. The discrepancy between the observation results for the initial direction at the beginning and end of the reception half should not exceed 8.

Move the pipe through the zenith and take measurements of the second half of the reception in the following sequence:

Point the axis of the telescope to the initial direction and, with two alignments, make readings, which are recorded in the log in the line corresponding to the observation during CP: recording is done from bottom to top;

Unfasten the alidade and turn it counterclockwise to sight the pipe axis to the third (depending on the number of directions), the second and again to the first mark. Readings are made at two combinations and recorded in a journal.

This ends the second half-reception. Two half-meals make up a full reception.

The second and subsequent methods of measuring directions are carried out in the same sequence as the first, but to weaken the influence of systematic errors in the dial divisions, the dial is rotated by an angle

G = 180\ n +10", where n is the number of techniques.

Measuring angles using the single angle method

The order of observations when measuring an angle using the method of a separate angle between two directions remains the same as in the method of techniques.

The only difference is that they do not re-point to the starting point and rotate the alidade in both the first and second half-methods, either along the clockwise or only counterclockwise.

The angle values ​​in half techniques, as well as in individual techniques, should not differ by 8”.

The final angle value is calculated as the arithmetic mean of the angles measured in separate steps.

When measuring individual corners or directions with theodolites provided for by the “Instructions for topographic surveying on scales 1: 5000, 1: 2000, 1: 1000, 1: 500. Moscow, “Nedra”, 1973”, the measurement results must be within the established tolerances.

In class 4 polygonometry for theodolites of types T2 and T1, the number of techniques is set to 4.

It is recommended to measure angles in the morning and evening hours. Times close to sunrise and sunset (about an hour before sunrise and an hour after sunset) should not be used, as these are the hours where image fluctuations are greatest. Before starting measurements, research, verification and adjustment of instruments are carried out. The angles to the left are usually measured, and observations are recorded in field journals.

In order to eliminate centering and reduction errors when laying polygonometric moves and to speed up angular measurements somewhat, it is recommended to use a three-post angle measurement system.

Currently, in geodetic work, instruments for various purposes from leading foreign companies Leica, Sokia and other geodetic instrument making companies from Switzerland, Sweden, Germany, and Japan are widely used.

The results of angular measurements in the GGS must be equally accurate, i.e. at all points have the same weight, and are obtained with the highest accuracy with the least amount of labor and time. To do this, high-precision measurements of each direction and angle are performed using strictly the same most advanced methodology during the periods of the most favorable observation time, when the influence external environment minimal. It is necessary that each direction be measured at different diameters of the dial, evenly distributed along the ring of divisions; in reception, uniformity of operations when measuring each direction and symmetry in time relative to the average observation time for reception must be ensured; It is advisable to measure all directions and angles at the point symmetrically relative to the moment of air isothermia.

Before making observations at the point, the geodetic sign is inspected, the center is dug up to the mark with the mark, the theodolite and other equipment are lifted onto the observer’s platform, and the roof of the signal is covered with a tarpaulin. As a result of the inspection, the observer must ensure that the signal table is strong and stable and that the inner pyramid does not come into contact with the floor of the observer's platform or the stairs. Any deficiencies found must be corrected.

Before observation using a theodolite, according to the geodetic network diagram, all points to be observed are found and, after pointing at them, readings are made with an accuracy of 1’ in horizontal and vertical circles. In addition, when pointing at points, the position of the alidade is fixed on the bottom of the device using strokes against the index on the alidade. The theodolite is installed on a tripod or signal table at least 40 minutes before the start of observations. Measurement of horizontal directions is started in good visibility, when the images of the sighting targets are calm or fluctuate slightly (within 2”).

Measuring a single angle. The unsecured alidade is moved to the left by 30 - 40 0 ​​and, by reverse rotation, is aimed at the sighting target of the first direction so that it is to the right of the bisector, the alidade is secured. Using the alidade's aiming screw, only by screwing it in, the bisector is aimed at the sighting target and a reading is taken using an optical micrometer (if you have an eyepiece micrometer, then its bisector is pointed at the sighting target three times and readings are taken). Unfasten the alidade and point it at the 2nd direction in the same way as at the 1st. This ends the half-reception.

The pipe is moved through the zenith, pointed clockwise to the 2nd direction, having previously moved the alidade to 30 - 40 0; Using the aiming screw, the bisector is aimed at the sighting target and a reading is taken from the optical micrometer. The alidade is turned clockwise by an angle that complements the measured one to 360 0, aimed at the sighting target of the 1st direction, and a report is taken. The reception ends.


The method of circular techniques is the Struve method. The method was proposed in 1816 by V.Ya. Struve, has been widely used in almost all countries. In our country it is used in geodetic networks of 2 - 4 classes and networks of lower accuracy.

In this method, with a stationary limb, the alidade is rotated clockwise and the bisector of the mesh of pipe threads is sequentially pointed at the first, second, ..., last and again at the first (closing the horizon) observed points, each time counting in a horizontal circle. This is the first half technique. Then the pipe is moved through the zenith and, rotating the alidade counterclockwise, the bisector is aimed at the same points, but in the reverse order: first, last, ..., second, first; finish the second half-reception and the first reception., consisting of the first and second half-receptions.

Between techniques, the dial is moved to an angle

Where m– number of receptions, i– the price of dividing the dial.

The bisector is aimed at the sighting target only by screwing in the alidade aiming screw. Before each half-reception, the alidade is rotated according to its movement in this half-reception.

Corrections for ren, inclination are introduced into the results of measured directions vertical axis theodolite (at angles of inclination of the sighting beam of 1 0 or more) and corrections for torsion of the sign - according to readings on the ocular micrometer of the calibration tube.

Control of angular measurements: by the discrepancies in the values ​​of the first direction at the beginning and end of the half-reception (non-closure of the horizon), by the fluctuation of the double collimation error determined for each direction, and by the discrepancy of the zeroed values ​​of the same directions obtained in different techniques. In triangulation of 2 – 4 classes, non-closure of the horizon and fluctuations in directions in techniques should not exceed 5, 6 and 8” for T05, T1; OT-02 and T2; 2C fluctuation is 6.8 and 12” for the same theodolites, respectively.

At points of class 2, directions are measured by 12-15 circular methods, at points of class 3 - 9, at points of class 4 - 6, and in polygonometry networks of classes 2, 3, 4 - 18, 12, 9 methods.

Adjustment at the station comes down to calculating the average value for each direction from m techniques. In this case, all previously measured directions lead to the initial one, giving it the value 0 0 00’00.00”. The weight of the adjusted direction is equal to p = m – number of measurement methods. To estimate the direction accuracy, the approximate Peters formula is usually used

Where μ – s.k.o. direction obtained from one reception (s.k.o. unit of weight); ∑‌‌[ v] – the sum of the absolute values ​​of the deviations of the measured directions from their average values, calculated in all directions; n, m– number of referrals and receptions, respectively. Values k at m= 6, 9, 12, 15 are equal to 0.23; 0.15; 0.11; 0.08. S.k.o. equalized direction (average of m techniques) are calculated using the formula

Advantages method of circular techniques: simplicity of the measurement program at the station; significant reduction in systematic errors of limb divisions; high efficiency with good visibility in all directions.

Flaws: relatively long duration of admission, especially with a large number of directions; increased requirements for the quality of geodetic signals; the need for approximately equal visibility in all directions; dividing directions into groups if there are a large number of them at the point; higher accuracy of the initial direction.

The method for measuring angles in all directions is the Schreiber method. This method was proposed by Gauss. The technique was developed by Schreiber, who used it in the 1870s in Prussian triangulation. It began to be used in Russia in 1910 and is still used today. The essence of the method: at point c n directions measure all angles formed by combining n 2 each, i.e.

1.2 1.3 1.4 … 1.n

Number of such angles

The value of the angles can be obtained by direct measurements and by calculations. If the weight of a directly measured angle is equal to 2, then the weight of the same angle obtained from calculations will be equal to 1. Therefore. The weight of the angle obtained from the calculations is half the weight of the directly measured angle.

When adjusting at a station, for each angle its average value is calculated from all methods (with acceptable discrepancies between methods). Using these averages, the angles adjusted at the station are found as an average weight value. Considering that the sum of the weights of the measured and calculated values ​​of a given angle, we find

Where n– number of directions at the point. The angles obtained as a result of adjustment at the station are equivalent in direction.

Using the function weight formula, we find for the angle

Since, then, from where. At P = 1 , , i.e. the weights of the adjusted angles are equal to half the number of directions observed from a given point. If each angle is measured m techniques, then when n directions, the weight of each angle will be equal mn/2. For the weights of the final angles to be equal at all stations, it is necessary that the product mn for all network points was constant. Since the weight of the direction is twice the weight of the angle, then mn– direction weight.

The weight of angles measured in all combinations must be equal to the weight of angles measured using circular techniques, i.e. p = m cr = mn / 2, from where 2 m cr = mn, Where m cr– the number of techniques in the method of circular techniques. For example, if angles in class 2 triangulation are measured using 15 circular techniques ( m cr= 15), then mn= 30; with the number of directions n= 5 way in all combinations they need to be measured in 6 steps ( m = 30 / 5 = 6).

When measuring angles using this method in all combinations, the following control is performed: 1) the divergence of angles from two half-measures - 6" for a theodolite with an eyepiece micrometer and 8" - without; 2) divergence of angles from different techniques 4 and 5” for networks of 1 and 2 classes, respectively; 3) the fluctuation of the average value of the angle obtained from the results of direct measurements and found from calculations should not exceed 3 “at n up to 5 and 4” - more than 5. If the completed techniques do not meet these tolerances, then they are redone on the same wheel settings. If the second control is not performed, then the angles having the maximum and minimum values ​​are re-observed at the same circle settings. All observations are performed again if the number of repeated appointments is more than 30% of the number of appointments provided for by the program. Observations are repeated if the third control is not observed.

S.k.o. units of weight and equalized angle are determined by the formulas

Advantages method: the adjusted results are a series of equal-precision directions; angles can be measured in any order, choosing the most favorable conditions visibility and ultimately ensuring high accuracy; the short duration of one reception (2-4 minutes of angle measurement) ensures less dependence of the accuracy of the result on signal torsion; big number permutations of the horizontal circle weaken the influence of errors in the diameters of the limb.

Flaws: rapid decrease in number m methods of measuring angle with increasing number n directions at points (a small number of methods for directly measuring angles reduces the accuracy of their average and adjusted values); rapid growth in the volume of work with n > 5.

Method of incomplete techniques proposed in 1954 by Yu.A. Aladzhalov. All directions are divided into groups of three directions (without closing the horizon) so that the angles determined from them would correspond to the angles measured in all combinations, but would require less work and allow an increase in the number of methods for direct measurements of each group of directions. Consequently, this method contains the desire to get rid of the shortcomings of the Struve and Schreiber methods when observing at points with a large number of directions.

It is almost not always possible to divide directions into groups of three directions by selection. In this case, in addition to groups of three directions, individual angles are measured to complement the program. The measurement program is given in the Instructions. The method of incomplete techniques is used in class 2 triangulation at points with 7 – 9 directions.

Processing the measurement results at the station consists of determining the average direction values ​​from m techniques in each group and the average values ​​of individual angles. From these average values, all angles are calculated - three angles from each group of three directions. The final equalized angles are calculated using the formulas of the Schreiber method. S.k.o. equalized directions are determined by the formula

Where v– the difference between the measured and adjusted angle values; n– number of directions at the point; r– the number of separately measured angles in the program. Weight of adjusted directions

Where m– number of methods for measuring directions and individual angles; n, k– number of directions at the point and in the group, respectively ( k = 3, for corners k = 2).

Advantages method: the results of adjustment at the station are equally accurate; the amount of work at the point is 20–25% less than in the Schreiber method; number of techniques for direct measurements of groups at n= 7 – 9 is greater than in the Schreiber method, which allows measurement errors to be more fully mitigated; makes it possible to measure directions in which this moment there is good visibility; short reception duration (2 – 4 minutes), which reduces the dependence of measurement accuracy on signal quality.

Flaws: there are no rules for forming groups of three directions; at n= 8 it is necessary to measure a large number of individual angles, which leads to a certain violation of the equiprecision of the equalized directions; The program does not provide for the attenuation of one-way measurement errors.

A modified method of measuring angles in combinations proposed by A.F. Tomilin. Used in class 2 triangulation at points with 6 – 9 directions. In this method, at a station with n directions independently measure 2 n angles:

1.2 2.3 3.4 … n.1;

1.3 2.4 3.5 … n.2.

Each angle is measured in 5 or 6 steps. In this method, not all angles forming combinations of directions from n according to 2, so the result of the adjustment at the station is not a series of equal-precision directions, and the formulas for calculating corrections to the measured angles are quite complex.

Advantages method: with n=7 – 9 the number of methods for direct measurements of angles is greater and their accuracy is higher than in the Schreiber method; requires less measurement than the method in all combinations.

Flaws: complex formulas for calculating corrections to measured angles.

Various means are used to control angles: squares, angle measures, conical gauges, protractors, mechanical and optical dividing heads, goniometers, sine rulers, etc. Squares, gauges and angle measures are rigid control tools; they have certain angle values. Squares are divided into solid (Fig. 28, a) and composite (Fig. 28, b). Angle measures– tiles (Fig. 28, c) are produced in sets so that three to five measures can be used to make blocks ranging from 10 to 90 0; they are made in the form of 5 mm thick tiles with angular accuracy (1st class) and (2nd class). They have either one working angle or four working angles: .

Angle measures mainly used for verification and calibration various angle measuring instruments, but they can also be used directly to measure angles of machine parts.

To measure angles on parts, universal goniometers are most often used: vernier with a reading value, optical with a reading value, indicator with a reading value.


Rice. 28. Types of rigid measuring instruments:

a – solid square, b – composite, c – angular measure.

An inclinometer with a vernier (Fig. 29) consists of three main parts: rigidly fastened rulers 1 and limbo 2 , which has a semicircular shape; rigidly fastened rulers 5 with the sector 3 and an additional square 6 , which is used when measuring acute


angles (less than 90 0). Ruler 5 rotates on an axis 4 associated with the limbus. On the arc of limb 2 there is a scale with a division value of 1 0, and on the arc of the sector 3 – vernier, which makes it possible to count fractional parts of the scale.

Rice. 29. Vernier protractor.

For measuring sharp corners(less than 90 0) to the line 5 attach an additional square 6 .

The zero stroke of the vernier indicates the number of degrees, and the vernier stroke, which coincides with the stroke of the dial scale 2 , - number of minutes.

When measuring obtuse angles (more than 90 0), an additional square 6 is not needed, but in this case, 90 0 must be added to the readings taken on the scale.

Optical inclinometers are also used, having two rulers and a housing containing a glass disk with a scale divided into degrees and minutes.


Rice. 30. Scheme for measuring the angle of a cone on a sine ruler.

The report is made after the position of the protractor is fixed by the clamping lever.

Indirect methods of cone control. The most accurate and widely used are indirect measurement methods, in which they measure not directly the angles of the cones, but linear dimensions geometrically related to the angles.

After determining the values ​​of these linear dimensions, the values ​​of the angles are also found by calculation.

Measuring with a ruler. Sine bars produced by the tool industry are divided into three types: type I - without a base plate, type II - with a base plate, type III- with two base plates and double tilt.

Subject table 1 (rice. thirty) sine rule has two rollers 2 And 3 with a certain distance between them L. If you place a block under one of the rollers 4 from plane-parallel gauge blocks of size h, then the object stage will tilt at an angle and can be determined by the formula:

.

When measuring the angle of a cone, the product being tested is placed on the object stage, orienting it so that the angle being measured is in a plane perpendicular to the rollers of the sine ruler (for this, use side surfaces subject table). Having installed the product 5 on the object table 1, a block of plane-parallel gauge blocks 4 is pinned under the roller. The size of the block is determined by the formula

,

where is the nominal value of the measured angle.

If the readings of the measuring head 6 differ in two positions on the measured length, it is possible to determine the deviations of the measured angle () from the nominal value using the formula

.

The actual value of the angle can be determined by selecting a block of tiles such that the readings of the measuring head will not differ over the entire measured length.

Measuring outer cones using rollers. This indirect measurement method ( rice. 31) of the cone angle of the product 1 is carried out using a plate 2, two rollers 3 of the same size (rollers from roller bearings can be used), gauge blocks 4 and a micrometer with a division value 0.01 mm or lever with division price 0.002 mm.


Rice. 31. Schemes for measuring the cone angle using calibrated

rollers (a, b), rings (c), balls (d).

First, measure the size according to the diameters of the rollers 3 ( rice. 31,a), then blocks of end measures 4 of the same size are placed under the rollers and the size is determined ( rice. 31, b). Knowing the dimensions , , find the taper using the formula

or ,

Using the same principle, the taper of the shaft is measured using two calibrated rings ( rice. 31,v) with pre-known diameters D And d and thickness. After putting the rings on the shaft cone, measure the size H and determine the tangent of the angle using the formula

.

Measuring inner cones. The angle of the internal cone is determined using two balls, the diameters of which are known in advance, and a depth gauge ( rice. 31,g).

Bushing 1 is placed on plate 2, a small diameter ball is placed inside d and measure the size using a depth gauge (micrometric or indicator), then insert a ball of larger diameter D and measure the size. With this measurement method, the taper of the sleeve is determined by the formula:

.

Control of cones with gauges

Caliber control (Fig. 32) is based on checking deviations of the basal distance using the method of axial movement of the gauge relative to the part being tested or on a paint test.


Rice. 32. Cone gauges:

a – bushing, b – plug, c – bracket.

The gauges for checking the outer cones are bushings ( rice. 32, a) or bracket ( rice. 32, in), and for internal cones - plugs ( rice. 32, b), on the large diameter side of which marks are applied at a distance from the end of the caliber equal to the basal distance tolerance.

The end of the tested conical shaft and bushing, when mated to the gauge, should not extend beyond the boundaries of the marks or ledge on the gauge. If this condition is violated, then the cone angle goes outside the established limits (tolerance).

Cone gauges - bushings are checked against control gauges - plugs. Control gauges are manufactured with increased taper accuracy and checked using universal means.

Review questions:

1. How many degrees of accuracy are specified for angle tolerances and why does the angle tolerance decrease as the length of the shorter side of the angle increases?

2. Give examples of the use of conical joints and their advantages over cylindrical joints.

3. Draw a cone and show its main parameters.

4. What is called the basal distance and how does the change in its value depend on the tolerances on the diameters of the cone and taper?

5. How does a protractor with a vernier work and what angles can it measure?

6. Tell us about indirect methods for measuring the angle of the outer and inner cones.

7. How is the control of outer and inner cones carried out using conical gauges?

Literature:


Lecture 7. TOLERANCES, FITTS AND MEASURING MEANS

THREADED CONNECTIONS

Basic elements of metric fastening threads

and permissions for them

In mechanical engineering, various threaded connections are used: cylindrical, conical, trapezoidal, etc. These threads have a number of common features, and since the most common are cylindrical fastening threaded connections with a triangular profile, tolerances, methods and means of control will be considered in relation to them.

The profile of a metric cylindrical thread (Fig. 33, a) is an equilateral triangle with an apex angle equal to 60 0. The main thread parameters common to external thread(bolt) and internal thread (nut) are: outside diameter And , inner diameter and, average diameter and, thread pitch, profile angle, angle between the side of the thread and the perpendicular to the thread axis, theoretical height of the thread, working height of the thread. When measuring the profile angle and calculating tolerances, the angle is taken into account, since when cutting a thread, its profile can be tilted to the side so that right side will be larger or smaller than on the left side, and in general the entire profile angle can be equal to 60 0.

Rice. 33. Metric cylindrical thread:

a – thread profile, b – diagram of the location of tolerance fields.

Under average diameter understand the diameter of an imaginary cylinder, coaxial with the thread, which divides the thread profile so that the thickness of the thread, limited in Fig. 33, and in letters a – b, equal to the width of the depression bounded by the letters b – c. Thread pitch- this is the distance along the thread axis between the parallel sides of two adjacent turns.

Unified system CMEA approvals and landings for metric thread with sizes from 0,25 before 600 mm There are three standards: ST SEV 180-75 defines the thread profile; ST SEV 181-75 – diameters and pitches; ST SEV 182-75 – main dimensions. Limit deviations and tolerances threaded connections with gaps is installed by ST SEV 640-77.

The thread diameter values ​​are divided into 3 rows (1st, 2nd and 3rd). When choosing thread diameters, the first row is preferred. The second row of thread diameters is taken if the diameters of the 1st row do not satisfy the designer’s requirements; Lastly, the diameters are taken from the 3rd row. According to the numerical value of the thread pitch for diameters 1-64 mm are divided into two groups: with a large pitch and small ones, and threads with a diameter of over 64 mm, (before 600 mm) have only small steps.


Tolerances for cylindrical fastening threads ( ) are set to the following parameters: on average diameter bolt and nut in the form of values ​​and , (the tolerance range for the nut is positive, and for the bolt – negative from the nominal size); to the outer diameter of the bolt And to the inner diameter of the nut .

Tolerances for the outer diameter of the nut and the inner diameter of the bolt are not established. Thread cutting technology and the dimensions of thread-forming tools (taps, dies, etc.) ensure that the outer diameter of the nut thread will not be less than the theoretical one, and the inner diameter of the bolt thread will not be greater than the theoretical one.

There are no separate tolerances set for the thread pitch and profile angle, and possible deviations on them are allowed by changing the average thread diameter within its tolerance. Such compensation for pitch and angle errors due to tolerance , is possible because the pitch and angle are geometrically related to the average diameter.

The main parameter controlled when processing corners and cones is flat angle, the unit of which is taken to be a degree. A degree is 1/360 of a circle; it is divided into 60 minutes of arc, and minutes are divided into 60 seconds of arc.

Methods for measuring angles can be divided into 3 main types:

1. Comparison method with rigid angle measures or templates.

2. Absolute method, based on the use of measuring instruments with an angular scale.

3. Indirect method, which consists of measuring linear dimensions related to the cone angle by trigonometric relationships.

The simplest tools for checking angles are squares with an angle of 90 0, designed for marking and checking the mutual perpendicularity of individual surfaces of parts during equipment installation and for monitoring tools, instruments and machines. In accordance with the standard, there are 6 types of squares (Fig. 2.12.):


More universal tools for control and marking of angles - protractor inclinometers (simple, optical, universal). In mechanical engineering, inclinometers with a vernier type UN are widely used for measuring external and internal angles and type UM for measuring only external angles (Fig. 2.13.).


For methods of measuring angles, see Fig. 2.14.


Calibers used to control the dimensions of holes and external surfaces of parts. In manufacturing, it is not always necessary to know the actual size. Sometimes it is enough to make sure that the actual size of the part is within the limits established tolerance, i.e. between the largest and smallest size limits. In accordance with these dimensions, limit gauges are used, which have two (or two pairs) measuring surfaces of the go-through and non-go-through parts. There are smooth, threaded, conical, etc. gauges. Plug gauges, staple gauges, depending on the size of the parts being controlled, the type of production and other factors, have different structural forms(Fig. 2.15, Fig. 2.16).



The pass-through side (PR) of a plug or staple has a size equal to the smallest maximum size hole or shaft, and the non-go-through side (NOT) - the largest limiting size of the shaft and, accordingly, the hole. Methods of measuring with plug gauges and clamp gauges are shown in Fig. 2.16.

Cone gauges tools are plug gauges and bushing gauges. Control of instrumental cones is carried out using a complex method, i.e. simultaneously check the cone angle, diameters and lengths (Fig. 2.17).


Templates used to check complex part profiles and linear dimensions. Templates are made from sheet steel. Inspection is carried out by mating the template with the surface being tested. The quality of processing is judged by the size and uniformity of the lumen (Fig. 2.18., Fig. 2.19.).


Thread control Depending on the type (profile) and accuracy, it is carried out using various control and measuring equipment.

Threaded templates to determine the thread pitch and profile, they are sets of steel plates fixed in a holder with precise profiles (teeth) of metric and inch threads. Each plate is labeled with pitch values, thread diameters, or threads per inch.

Radius templates are used to measure the deviation of the dimensions of convex and concave surfaces of parts (Fig. 2.18.). To measure the depth of the grooves, the height and length of the ledges, limit gauges-templates are used that work against the light. They also have two sides and are designated B (for bigger size) and M (for smaller sizes). In Fig. 2.19. templates for checking the length, width and height of tabs and grooves are shown various methods: “through the light”, “by pushing” and “by the scratch method”.

Thread gauges(plugs and rings) are used to control internal and external threads (Fig. 2.20.).


Thread micrometers with inserts are used to measure the average diameter of a triangular external thread.

Inserts are selected in accordance with the pitch of the thread being measured from the set available in the case for the micrometer (Fig. 2.21.). Reading the micrometer is done in the same way as when measuring smooth cylindrical surfaces.


Thread control can also be carried out with a micrometer using three measuring wires (Fig. 2.22.). With this method, the distance M is measured between the protruding points of three wires placed in the recesses of the thread, then the average diameter d 2 of the thread is determined through mathematical transformations.

The wire diameter dpr is selected from the table depending on the thread pitch. Two wires are installed in the depressions on one side, and the third - in the opposite cavity (Fig. 2.22.)

Average diameter of metric thread d 2 = M – 3 d pr + 0.866 P

Average diameter of inch thread d 2 = M – 3.165 d pr + 0.9605 R

Plane-parallel gauge blocks are used to transfer the size of a unit of length onto a product (when marking), checking and adjusting measuring instruments (micrometers, staple caliber, etc. measuring instruments), direct measurement of the dimensions of products, fixtures, when setting up machines, etc.

One of the main properties of gauge blocks is adhesiveness, the ability to firmly connect to each other when one gauge is applied and pushed onto another with some pressure, which is achieved due to the very low roughness of the measuring surfaces. End gauges are supplied in a set with a quantity of 7…12 tiles (Fig. 2.23).


The most widely used sets are those consisting of 87 and 42 gauge blocks. Each tile reproduces only one size, which is marked on one of its sides. For ease of use of gauge blocks, sets of accessories are produced for them (Fig. 2.24.), which include: bases - 5, plane-parallel, radius - 2, scribers - 3, center sides - 4, holders - 1 for attaching blocks of gauge blocks with sides. The block of gauge blocks is compiled in accordance with the class or category of tiles and the sizes of the tiles available in this set.

Initially, a smaller tile is selected, the size of which includes the last decimal place, etc. Let's say you need to assemble a block of gauge blocks measuring 37.875 mm from a set consisting of 87 tiles:

1 tile 1.005 mm, remainder 36.87

2 tiles 1.37 mm, remainder 35.5

3 tiles 5.5 mm, balance 30.00

4 tiles 30 mm, remainder 0.

The block amount is 1.005+1.37+5.5+30 = 37.875.

In the same way, a block is assembled from a set of 42 tiles.

1,005+1,07+4,00+30 = 37,875.


Methods for measuring with plane-parallel gauge blocks of length and marking using accessories are shown in Fig. 2.25.

Angular prismatic measures (tiles) are intended for checking and adjusting measuring angle measuring instruments and tools, as well as for direct measurement of external and internal angles of parts with high density. Angle measures perform the same role when measuring angles,

same as gauge blocks when measuring length. The working sides of corner measures are subject to the same requirements as the end measures, i.e. ensuring adhesion (fitness).


Angle measures are produced in sets with a quantity of 7...93 tiles in each (Fig. 2.26.). Checking the corners with tiles is carried out “through the light”.

To increase the strength of a block assembled from corner tiles, they are supplied with a set of accessories, which include ties, screws, wedges and others (Fig. 2.27.). The block is strengthened through special holes in the tiles.

The rules for calculating angular measures for the formation of blocks, as well as the rules for preparing for assembly and assembling them into a block, are similar to the rules used in the preparation of end length measures.

Methods for measuring angle measures are shown in Fig. 2.28.

The main parameter controlled when processing corners and cones is the flat angle, the unit of which is taken to be a degree. A degree is 1/360 of a circle, it is divided into 60 minutes of arc, and a minute is divided into 60 seconds of arc. Peculiarity angular dimensions is that the accuracy of their manufacture and control depends on the length of the sides forming the angle. The shorter the side, the more difficult it is to make and measure the angle. Methods for measuring angles can be divided into three main types:

1) comparison method with rigid angular measures;

2) absolute method, based on the use of measuring instruments with an angular scale (the angle is measured directly from the instrument scale in angular units);

3) an indirect method, consisting in measuring linear dimensions related to the cone angle by trigonometric relationships.

Angle measures and squares

Angle measures (Fig. 1.19, a) are made in the form of straight prisms and are used to control angles and calibrate angle measuring tools and angle templates. Angle measures are similar to the previously discussed plane-parallel end measures of length. Angle measures are produced in the form of sets with gradation of angles through 2°, 1°, 15′ and various nominal angle values. Angular measures are manufactured in four accuracy classes (00, 0, 1, 2) and certified for grades. Angle measures can rub against each other, but their adhesion is less reliable than that of plane-parallel end length measures, therefore blocks of angle measures are connected to each other using special devices. Tiles are connected into blocks using holders (Fig. 1.19, b-d), screws and conical pins. Holders (see Fig. 1.19, b, c) allow you to assemble blocks of two and three angular measures. To obtain additional angles, holders with special pattern rulers are used (see Fig. 1.19, d). Control of angles using angular measures is usually carried out in the light. In the absence of an angular measure with necessary values angle or in the case where the product does not allow the use of an angle measure, a special angle template is made.

To control and mark right angles (90 °), test squares are intended (Fig. 1.20), which are also used for control relative position surfaces of parts during assembly. Making squares following types UL, ULP, ULSH, ULTS, UP, USH.

Squares of the UL, ULP and ULSh types are intended for precise patterning work; they have two sharp working edges.

Squares such as UP and USh are used in metalwork assembly, processing and repair.

Angles of the ULC type are a section of a shaft with ends perpendicular to the generatrix of the cylindrical surface. These squares are used to test other squares, as they allow you to get exact value angle 90°.

Goniometers

To control angles by direct assessment in mechanical engineering, they are widely used. Vernier protractors. These protractors are produced in two types: UN - for measuring external and internal angles (Fig. 1.21, a) and UM - for measuring only external angles (Fig. 1.21, b).

Goniometer type UN consists of a base 2 with a degree scale printed around the circumference, which is rigidly connected to a ruler 3. The ruler has an externally adjusted measuring surface. Sector 5 with vernier 1 and stopper 4 moves along base 2. Square 6 is attached to the sector using holder 9. Removable ruler 7 is attached to square 6 using holder 8. Measurement options are shown in Fig. 1.22. The goniometer allows you to measure angles in the range from 0 to 50° (Fig. 1.22, a). To measure angles in the range from 50 to 140°, remove the square from the protractor, and install rulers in its place (Fig. 1.22, b). To measure external angles in the range from 140 to 230°, it is necessary to remove the ruler; in this case, measurements are carried out using a square. If you remove the square, ruler and holders from the protractor, you can use it to control the size of the angles in the range from 240 to 320°. Therefore, the general measurement range of the UN protractor is from 0 to 320 ° for external angles.

When measuring the angles of parts of complex contours, it is necessary to set the protractor to a given length of the straight contour. This installation is carried out using a block of length gauges 2, which is installed on a removable ruler 3, and the base of the protractor is moved along the square 1 so that the measuring ruler is installed on the block of gauges. A diagram of such an installation is shown in Fig. 1.22, c.

If you remove the square and ruler from the protractor, you can use it to measure internal corners in the range from 40 to 180° (Fig. 1.22, d).

Measuring angles in hard-to-reach places is carried out according to the scheme shown in Fig. 1.22, d.

Goniometer type UM(see Fig. 1.21, b) is widely used in training plumbing. It consists of a base 4 with a scale graduated in degrees. A ruler 3 is fixed to the base. The movable ruler 10 with a sector 9 and a vernier 7 can be rotated on axis A, the ruler is fixed at the time of measurement by a locking screw 5. The goniometer has a screw 6 for the micrometric feed of the measuring movable ruler 10 with a sector 9. On Square 2 is attached to the movable ruler using holder 1. The goniometer provides angle measurements in the range from 0 to 180°. To measure angles over 90°, square 2 must be removed; in this case, to obtain the angle value, 90° is added to the readings on the protractor scales.

When working with a UM type goniometer, you must:

Determine the method of measuring the angle (with or without a square);

Make sure that the protractor sector moves smoothly;

Make sure that the inclinometer is set to zero accurately;

When measuring, hold the protractor firmly by the body;

The measuring surface must fit tightly to the surface of the part (without gaps or distortion);

Pay attention to the achieved measurement accuracy, which is stamped on the vernier.