Methods and means for measuring angles are based on. Means and methods for measuring angles. How to use a protractor - an approximate principle of operation

The state standard GOST 10529-86 distinguishes three groups of theodolites: high-precision, precision and technical.

High-precision theodolites provide angle measurement with an error of no more than 1"; types T1, T05.

Accurate theodolites provide angle measurements with an error of 2" to 7"; types T2, T5.

Technical theodolites provide angle measurements with an error of 10" to 30"; types T15, T30.

An additional letter in the theodolite code indicates its modification or constructive solution: A - astronomical, M - mine surveyor, K - with a compensator in a vertical circle, P - direct image tube (terrestrial).

The state standard for theodolites also provides for the unification of individual components and parts of theodolites; the second modification has the number 2 in the first position of the code - 2T2, 2T5, etc., the third modification has the number 3 - 3T2, 3T5KP, etc.

Before measuring the angle, it is necessary to bring the theodolite into working position, that is, perform three operations: centering, leveling and installing the telescope.

Centering a theodolite is setting the axis of rotation of the alidade above the vertex of the angle being measured; the operation is performed using a plumb line suspended on the hook of a screw, or using an optical plummet.

Leveling a theodolite is setting the axis of rotation of the alidade to a vertical position; the operation is performed using lifting screws and a level while alidating a horizontal circle.

Installing a pipe is installing a pipe according to the eye and the subject; the operation is performed using a movable eyepiece ring (installation according to the eye - focusing the reticle) and a screw for focusing the tube on the object (pos. 15 in Fig. 4.4).

Angle measurements are performed strictly according to the methodology corresponding to the measurement method; There are several ways to measure horizontal angles: this is the way separate angle(method of techniques), method of circular techniques, method in all combinations, etc.

Single angle method. The measurement of an individual angle consists of the following steps:

pointing the pipe at the point that fixes the direction of the first side of the angle (Fig. 4.16), with the circle to the left (CL), taking reference L1;

turning the alidade clockwise and pointing the pipe at the point that fixes the direction of the second side of the angle; taking L2 sample,

calculation of the angle for CL (Fig. 4.16):

moving the dial by 1o - 2o for theodolites with one-sided reading and by 90o - for theodolites with two-sided reading,

moving the pipe through the zenith and pointing it at the point that fixes the direction of the first side of the angle, with a circle to the right (KP); taking a reading R1,

turning the alidade clockwise and pointing the pipe at the point that fixes the direction of the second side of the angle; taking a reading R2,

calculation of the angle at CP:

when the condition |vl - vp|< 1.5 * t, где t - точность теодолита, вычисление среднего значения угла:

vsr = 0.5 * (vl + vp).

Measuring the angle at one position of the circle (CL or CP) is one half step; a complete cycle of angle measurement at two positions of the circle is one step.

Recording of readings on the limb and calculation of the angle are carried out in journals of the established form.

Method of circular techniques. If more than two directions are observed from one point, then the method of circular techniques is often used. To measure angles using this method, you must perform the following operations (Fig. 4.17):

with CL, set the reading on the dial close to zero and point the pipe at the first point; take a reading on the dial.

Rotating the alidade clockwise, point the pipe sequentially at the second, third, etc. points and then again to the first point; each time take readings along the limb.

move the pipe through the zenith and, at the control point, point it at the first point; take a reading on the dial.

rotating the alidade counterclockwise, point the pipe sequentially at (n-1), ..., third, second points and again at the first point; each time take readings along the limb.

Then, for each direction, the average of the readings at CL and CP is calculated, and after that - the values ​​of the angles relative to the first (initial) direction.

The method of circular techniques allows us to weaken the influence of errors acting proportionally to time, since the average readings for all directions refer to one physical moment in time.

The influence of theodolite eccentricity on readings along the limb. Let in Fig. 4.18 let the axis of rotation of the alidade intersect horizontal plane at point B", and point B is the projection of the vertex of the measured angle onto the same plane. The distance between points B and B" will be denoted by l, the distance between points B and A by S.

If the theodolite stood at point B, then when the pipe was pointed at point A, the reading on the limb would be equal to b. Let's move the theodolite to point B", maintaining the orientation of the limb; in this case, the reading along the limb when pointing the pipe at point A will change and become equal to b"; the difference between these readings is called the theodolite centering error and is designated by the letter c.

From triangle BB"A we have:

or by the smallness of the angle c

The quantity l is called the linear element of centering, and the angle Q is corner element alignment; angle Q is constructed by projecting the axis of rotation of the theodolite and is measured from the linear element clockwise to the direction to the observed point A.

The correct reading on the dial will be:

b = b" + c. (4.19)

The influence of the reduction of the sighting target on the readings along the limb.

If the projection of the sighting target A" onto the horizontal plane does not coincide with the projection of the center of the observed point A, then a reduction error of the sighting target occurs (Fig. 4.19). The segment AA" is called a linear reduction element and is designated l1; angle Q1 is called the angular element of reduction; it is constructed during the projection of the sighting target and is counted from the linear element clockwise to the direction to the theodolite installation point. Let's denote the correct reading on the limb - b, the actual one - b", the error in the direction BA is equal to r. From the triangle BAA" we can write:

or by the smallness of the angle r

The correct reading on the dial will be

b = b" + r. (4.21)

The largest correction values ​​c and r are reached at I = I1 = 90o (270o), when.

In this case

In the practice of measuring angles, two methods are used to take into account the eccentricity of the theodolite and the sighting target.

The first method is that centering is performed with such precision that the eccentricity error is not taken into account. For example, when working with technical theodolites, the permissible influence of centering errors of the theodolite and the sighting target can be taken as c = r = 10"; with an average distance between points S = 150 m, it turns out that l = l1 = 0.9 cm, that is, the theodolite or the sighting target it is enough to set the target above the center of the point with an error of about 1 cm. For centering with such accuracy, you can use a conventional plumb line. Centering the theodolite or sighting target with an accuracy of 1-2 mm can only be done using an optical plummet. The second method is to directly measure the elements l and. I, l1 and I1, calculating the corrections c and r using formulas (4.18) and (4.20) and correcting the measurement results using these corrections using formulas (4.19) and (4.21).

How to use a protractor yourself simple type, we have known since school, but there are many more types, areas of purpose and designs of this instrument, sometimes the principle of its operation is not even entirely clear, although the task is still the same - to measure the angle of inclination in a plane or space. We will try to eliminate the gaps as we read this article.

Goniometer - device and purpose

This tool, as you might guess, exists for measuring angles, and these can be not only planar images, as in school notebooks or production drawings, but also the inclination of parts relative to each other in any structures. It is possible to measure indicators even in distant objects, for which the optical version of the device is successfully used.

We are accustomed to the fact that for reliability it is better to touch what we are measuring, that is, the device intended for the operation is applied to the surface under study, but the contact method, although it prevails, is not the only one. The optical method allows you to calculate angles while being relatively far from the objects under study. The measurement result is always presented in degrees that are familiar to us, which we have to count independently or observe on the displays that, for example, a digital protractor has. The instruments differ in the scale from which readings should be taken.

It can be ruled, and also include an additional circular component, which is easier to navigate with the help of an arrow. The scale is represented by a vernier, this separate species We will look at devices in more detail below, and the most advanced can be considered electronic.

The device of the simplest angle meter is quite primitive: two rulers with scales that are adjusted according to the angle and give the desired value. Others are more intricate. Before work, the measurer fixes some angles of the device with known value, a kind of instrument tuning. But, for example, a carpenter's protractor is already sold with a firmly fixed and measured angle, which is convenient for quickly assessing the inclination of the surface on which the craftsman is working.

Types of Angle Measuring Tools

The most relevant one for you and me is a construction goniometer. Without him and his faithful companions (plumb and ) not a single site would exist. All equipment is installed with a clear assessment of the terrain in three dimensions, all installation work, any marking - all this requires correct orientation in space, and the human eye is far from perfect, so even the horizontality of the plane is difficult to weigh, let alone the angles.

Plumbing and carpentry goniometers accompany specialists all the time, because their products later serve in various areas human activity, and the slightest deviations in axes or angles can sometimes cost lives. To draw up reliable topographical diagrams, you also cannot use our natural optical device, in fact, how impossible it is for them to evaluate subtle medical indicators. Therefore, a topographer and orthopedist cannot work without such an instrument.

The romantic profession of astronomer is also not complete without such a device. Schoolchildren learn the first basics of geometry with such a device in their hands, most often these are ordinary squares with already fixed angles of known magnitude. Engineer, miner, sailor are professions that use almost the entire range of possible instruments for measuring angles. Each field requires such data with varying degrees of accuracy and reliability. High-tech laser inclinometers are increasingly being used, this is especially important in the military industry (sights).

If the scope of application is almost limitless, then the classification of the instrument by device is somewhat more modest: optics, mechanics, laser and electronics. Already within this classification, you can find many other parameters that influence the customer’s choice, for example, permissible errors. The price of the product is also affected by mobility, functionality, the size of the device itself, and its equipment.

Mechanical angle meter - what is it?

It is still considered common and accessible mechanical device. This protractor is universal because it allows you to attach it to almost any surface and take readings of the outer and inner angles. There are optical and vernier types. The second one is more common and convenient for contact measurement. Vernier is an auxiliary clarifying scale that is combined with the main one and increases the accuracy of the value by orders of magnitude. Its role may be familiar to you from handling calipers and other mechanical measuring instruments.

When purchasing a device, it is important to ask what regulatory document (standard) the product was manufactured according to, because accuracy will be a critical parameter, and if there is no regulatory document to check and adjust it, then your measurements may be far from the truth. That's why It’s best to avoid Chinese manufacturers, who rarely take calibration so seriously, but are cheaper than any Russian or European analogues.

Mechanical types of devices have the most intricate structure. The vernier type includes the following components: a body to which the disk is attached with a nut, a base with a main scale and a vernier, and also a ruler and a shank that moves along it in the process of fixing the angle values. Optical view consists of a housing in which there is a disk with a scale, a fixed ruler is attached to it, and a magnifying glass, a movable ruler and its lever are installed on the disk. Under the disk there is a plate with a pointer, which is visible through the eyepiece. This entire system is set in motion, then fixed in the selected location, and a reading is taken through a magnifying glass.

How to use a protractor - an approximate principle of operation

The more automated device, the less work we need to do. For example, an electronic protractor only requires you to fix the rulers in the desired position and displays the result on the display. Optics will already require installation of the instrument on flat surface to avoid vibrations relative to the horizon. And mechanics will also require a minimal understanding of the device itself in order to find a way to correctly take readings. Therefore, we will analyze the most capricious cases that can await us.

Vernier device

The device is applied to the desired angle on the plane; its ruler and body must coincide with the sides of the angle. Now we count the degrees on the main scale until we reach the zero level on the vernier, this is how the degrees are found. Now we move along the vernier scale until we find a division that coincides with the division of the main scale, as if extending it into one straight line. This is how minutes are determined. Depending on the accuracy of the device, the scale values ​​may differ; study the data sheet of your instrument.

Optical device

The movable ruler should be moved so that it and its stationary partner form the desired angle. Then the clamping ring is fixed. Now we should remember that the disk and magnifying glass of this mechanism are dependent in their position on the movable ruler, which means that they constitute a kind of indicator of the desired value. Through a magnifying glass, you can observe the markings on the disk, which are correlated with the mark on the plate, and the readings of the device are calculated.

Corner connections

In many mechanical engineering products, components and parts are used,
the quality of their work depends on their accuracy angular dimensions. Such assemblies and parts are, for example, bearings with tapered rollers, dovetail guides, ends of spindles and tools of metal-cutting machines, conical seats of precision axes, corners of optical prisms and instruments. .

Since in the production and control of angular dimensions of products, a special cutting tool and gauges, then to facilitate the production and control of the angular dimensions of parts, as well as for linear dimensions, the preferred angle values ​​are standardized general purpose.

The tolerance values ​​for angular dimensions have also been standardized. The standard provides corner tolerances expressed in angular and linear units, with tolerance values ​​in angular units decreasing as the length of the side of the corner increases. This is due to the possibility of ensuring greater accuracy in the manufacture and control of angles with longer sides due to the possibility of their better basing, as well as due to the lesser influence of the error of the measuring device or tool when monitoring linear deviations. Note that angle tolerances are set regardless of the angle value.

Of the corner joints, conical joints are the most common. Conical connections provide high centering accuracy; with fixed fits, they provide the transmission of large torques with the possibility of repeated assembly and disassembly of the connection; with movable fits, due to the axial displacement of the connection parts, the required clearances can be obtained; a tight fit of the conical parts ensures the tightness of the connection, etc.

Normal cones for general purposes are standardized. The range of cone angles covers angles from ~1° (1:200 taper) to 120°. Special standards specify the taper for instrument cones. In particular, they contain special Morse cones with conventional numbers from 0 to 6. Their taper is close to 1:20, and the diameters vary from approximately 9 mm (No. 0) to 60 mm (No. 6). In tools and spindles of machine tools, instrumental metric tapers (taper 1:20) and Morse tapers (taper from 1:19.002 to 1: 20.047) according to GOST 25557-82 and GOST 9953-82 are widely used.

The main elements characterizing the details of conical connections are the nominal diameter of the cone, the diameters of the larger and smaller bases of the cone, the length of the cone and the angle of the cone. Instead of the cone angle, in some cases the angle of inclination of the generatrix to the axis (half the angle of the cone) and the taper (double the tangent of the inclination angle) are specified. These elements are interconnected by simple geometric relationships.

The main plane is the section of the cone in which its nominal diameter is specified. One of the characteristic sections (end, ledge), most often near the larger base, is taken as the base plane. The distance between the base and main planes is called the base distance of the cone.

Conical joints, formed by outer and inner cones with equal cone angles, are characterized by a conical fit and joint basal distance.

Tolerances of cones are established either comprehensively or element by element. With complex standardization, the values ​​of the diameters of two limiting cones that have a nominal cone angle and are located coaxially are established; all points of the real cone must lie between these limiting cones. At. In element-by-element standardization, tolerances for diameter, cone angle and shape - roundness and straightness of the generatrix - are separately established.

Angle measurement methods

The value of the angle during measurement is determined by comparing it with a known angle. A known angle can be specified by so-called rigid (with a constant angle value) measures - analogues of the shape of the elements of a part: angle measures, squares, corner templates, conical gauges, polyhedral prisms. The measured angle can also be compared with multi-valued goniometric line measures and various types circular and sector scales. Another method for obtaining a known angle is to calculate it from the values ​​of linear dimensions based on trigonometric relationships.

In accordance with this, the classification of methods for measuring angles is carried out primarily by the type of creation of a known angle: comparison with a rigid measure, comparison with a line measure (goniometric methods) and trigonometric methods (based on the values ​​of linear dimensions).

When comparing angles with a rigid measure, the deviation of the measured angle from the angle of the measure is determined by the clearance between the corresponding sides of the corners of the part and the measure, by the deviation of the readings of a linear measurement device that measures the discrepancy between these sides, or when checking “by paint”, i.e. by the nature of a thin layer of paint transferred from one surface to another.

Instruments for goniometric measurements have a dashed goniometric scale, a pointer and a device for determining the position of the sides of an angle. This device is connected to a pointer or scale, and the part being measured is connected to a scale or pointer, respectively. Determining the position of the sides of an angle can be done both by contact and non-contact (optical) methods. When the positions of the device nodes correspond to the measured angle, the angle of relative rotation of the scale and pointer is determined.

With indirect trigonometric methods, the linear dimensions of the sides of a right triangle corresponding to the measured angle are determined, and from them the sine or tangent of this angle is found (coordinate measurements). In other cases (measurement using sine or tangent rulers) reproduce right triangle with an angle nominally equal to the measured one, and setting it as lying crosswise with the measured angle, linear deviations from the parallelism of the side of the measured angle to the base of the right triangle are determined.

For all methods of measuring angles, it must be ensured that the angle is measured in a plane perpendicular to the edge of the dihedral angle. Distortions lead to measurement errors.

If there is an inclination of the measurement plane in two directions, the angle measurement error can be both positive and negative. When measuring small angles, this error will not exceed 1% of the angle value at angles of inclination of the measurement plane up to 8°. The same dependence of the angle measurement error on the skew angles is also obtained in cases of inaccurate placement of parts on a sine ruler, mismatch of the direction of the edge of the measured angle or the axis of the prism with the axis of rotation on goniometric instruments (when fixing the position of the faces using an autocollimator), when measuring using levels, etc. .P.

The International System of Units (SI) uses the radian as a unit of measurement for angles - the angle between two radii of a circle cutting an arc on its circumference, the length of which is equal to the radius.

Measuring angles in radians in practice is associated with significant difficulties, since none of the modern goniometer instruments have graduations in radians.

In mechanical engineering, non-system units are mainly used for angular measurements: degrees, minutes and seconds. These units are interconnected by the following relationships:

1 rad = 57°17 ׳ 45 ״ = 206 265″;

l° = π/180 rad = 1.745329 10 -2 rad;

1 ‘ = π /10800 rad = 2.908882 ٠10 -1 rad ^

1 ” = π/648000 rad = 4.848137 10 -6 rad g

The angle of inclination of planes is usually determined by the slope, numerically equal to the tangent of the angle of inclination.

Small slope values ​​are often indicated in micrometers per 100 mm of length, in ppm or millimeters per meter of length (mm/m). For example, the price for dividing levels is indicated in mm/m. Conversion of slopes into angles is usually made using an approximate relationship: slope 0.01 mm/ m(or 1 µm/100 mm) corresponds to a tilt angle of 2″ (the error in calculating the angle from this dependence is 3%) .

As shown above, in mechanical engineering, depending on the means and methods used, there are three main ways of measuring angles:

Comparative method for measuring angles using rigid angle measures. With this measurement, the deviation of the measured angle from the angle of the measure is determined.

An absolute goniometric method for measuring angles, in which the measured angle is determined directly from the goniometric scale of the device.

Indirect trigonometric method: the angle is determined by calculation based on the results of measuring linear dimensions (legs, hypotenuse) related to the measured angle by a trigonometric function (sine or tangent).

The comparative method of measuring angles is usually combined with the indirect trigonometric method; the latter determines the difference between the compared angles in linear quantities at a certain length of the side of the angle.

Chudov V.A., Tsidulko F.V., Freidgeim N.I. Dimensional control in mechanical engineering M, Mechanical Engineering, 1982, 328 p.

Gorodetsky Yu.G. Design, calculation and operation of measuring instruments and instruments. Mechanical Engineering, 1971, 376 pp.

Product angles are measured by three main methods: comparison method with rigid control tools - angle measures, squares, cone gauges and templates; absolute goniometric method, based on the use of instruments with a goniometric scale; indirect trigonometric method, which consists in determining the linear dimensions associated with the measured angle trigonometric function.

Universal means of measuring angles include vernier, optical and indicator angle meters, as well as other instruments. The angles of inclination of product surfaces are measured with levels and optical squares.

End of work -

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Rules for certification
Rules for certification are established general recommendations, which are used in organizing and carrying out work on mandatory and voluntary certification. These rules are

Procedure for product certification
The procedure for certification in Russia was established by the Decree of the State Standard of the Russian Federation in 1994. in relation to mandatory certification (including imported products), but can also be applied

Responsibilities and main functions of the certification body
Responsibilities: 1. Conducting product certification according to the rules and within the limits of accreditation. 2. Issuance of a license to use the mark of conformity to the certificate holder. 3. Pr

Requirements for certification body personnel
1. The head of the certification body is appointed in agreement with the accrediting body. 2. The body must have permanent staff. Working conditions for personnel should completely exclude

Certification of quality assurance systems
Certification of quality assurance systems to ISO 9000 series standards is widely developed in foreign countries, in Russia they have been doing this recently. Foreign experts believe that

Service certification
The basic principles of service certification systems are the same as for product certification systems: mandatory and voluntary, third party condition, accreditation of certification bodies, issuance of certification.

Problems solved when ensuring the accuracy of dimensional chains
Task 1. Determining the maximum dimensions of the closing link of a dimensional chain (the accuracy of this link), when the maximum dimensions of the remaining component links are known

Results of calculation of the closing link
Nominal size, mm Tolerance, mm Upper deviation, mm Lower deviation, mm

For design calculation
Link Nominal size, mm Size tolerance, mm Type of link Аδ

Results of calculation of component links
Link Nominal diameter, mm Tolerance, mm Bottom deviation, mm Top deviation, mm

Educational materials
Main literature 1. Krylova G.D. Fundamentals of standardization, certification, metrology: Textbook for universities. – M.: Audit-UNITY.1998. 2. Lifits I.M. Basics of standardization, metrolo

The following methods exist for measuring and controlling angles and cones:

- comparison method with rigid control tools - angle measures, squares, cone gauges and templates;

- absolute goniometric method , based on the use of instruments with a goniometer scale (vernier, indicator and optical goniometers);

- indirect trigonometric method , based on the determination of linear dimensions associated with the measured angle by a trigonometric function (sine rulers, cone meters).

A brief description of the measuring instruments and control of angles and cones is presented in table. 2.14. Let's look at some of them.

Angle measures and squares.

Angular prismatic measures are designed to transfer a unit of flat corner from standards to the product. They are most often used for pattern work, as well as for checking and calibrating measuring and control instruments. Angular measures (Fig. 2.51) can be single-valued and multi-valued; they represent geometric figure in the form of a straight prism with adjusted surfaces, which are the sides of the working angle.

In accordance with GOST 2875 - 88, prismatic angle measures are manufactured in five types: I, II, III, IV, V with working angles α, β, γ, δ.

Tiles of type I have the following nominal dimensions of angle a: from 1 to 29" with gradation in 2" and from 1 to 9° with gradation in G. Tiles of type II have the following nominal dimensions of angle α: from 10 to 75°50" with gradation angle values ​​15", T, 10", 1°, 15°10". The corresponding GOST establishes the nominal dimensions of the working angles α, β, γ, δ for type III tiles, type IV prisms and type V prisms.

Based on manufacturing accuracy, angle measures are distinguished into three classes: 0, 1,2. Permissible deviations of working angles, as well as permissible deviations from flatness and location of measuring surfaces are regulated depending on the type of measures and accuracy class. Thus, the permissible deviations of working angles are in the range from +3 to +5" for measures of class 0 and within ±30" for measures of class 2. Permissible deviations from flatness are set in the range from 0.10 to 0.30 µm.

Angle measures are supplied in sets and can be supplied as individual measures of all classes.

The working surfaces of corner measures have the property of being lapped, i.e. blocks can be created from them. For this purpose, as well as for obtaining internal corners, special accessories and pattern rulers are provided, which are included in the accessory set. When compiling blocks of angle measures, it is necessary to follow the same rules as when compiling blocks of plane-parallel end measures of length (see subsection 2.2.1).

This is an angle measure with a working angle of 90°. When testing using squares, the amount of clearance between the square and the part being inspected is assessed. The clearance is determined by eye or by comparison with the clearance created using gauge blocks and a measuring ruler, as well as a set of feeler gauges.

Rice. 2.51.

In accordance with GOST 3749 - 77, squares differ: according to design features - six types (Fig. 2.52), according to accuracy - three classes (0, 1, 2). Pattern angles (types UL, ULP, ULSh, ULC) are made of hardened classes 0 and 1 and are used for patterning and instrumental work (Fig. 2.52, a, b). Bench squares of the UP and USH types (Fig. 2.52, c, d) are used for normal work in mechanical engineering and instrument making.

Rice. 2.52. :

a and b - pattern squares; c and d - bench squares

Permissible deviations of squares are established depending on their class and height H. Thus, for a 1st class square with a height of 160 mm, the deviation from the perpendicularity of the measuring surfaces to the supports should not exceed 7 microns, the deviation from the flatness and straightness of the measuring surfaces should be within 3 µm. For a square with a height of 400 mm, these values ​​are 12 and 5 microns, respectively, and for similar squares of the 2nd class, 30 and 10 microns.

Rice. 2.53. :

a and b - UN type goniometers; c - the order of counting according to the vernier; guide-inclinometers type UM; 1 - half-disc; 2 - axis; 3 - square clamp screw; 4 - additional square; 5 - movable ruler; 6 - fixed ruler; 7 and 8 - devices for micrometric feed; 9 - locking screw; 10 - vernier

Rice. 2.54. :

a - type I; b - type II; V - type III: 7 - table; 2 - roller bearings; 3 - side bars; 4 - threaded holes; 5 - front bar

Goniometer devices.

These devices are based on direct measurement of angles using a goniometer scale. Most by known means measurements from this series are atlometers with vernier, optical dividing heads (see subsection 2.2.4), optical atlometers, levels, goniometers, etc.

(GOST 5378 - 88) are intended for measuring angular dimensions and marking parts. Protractors are available in two types. Goniometers of the UN type (Fig. 2.53, a, b) are designed for measuring external angles from 0 to 180°, internal angles from 40 to 180° and have a vernier reading of 2 and 5". The goniometer consists of the following main parts: half-disk ( sector) 1, fixed ruler 6, movable ruler 5, clamping screw of the square 3, vernier 10, locking screw 9, devices for micrometric feed 7 and 8, additional square 4, clamping screw of the additional square 3. For measuring angles from zero to 90° an additional square 4 is installed on the fixed ruler 6. Angles from 90 to 180° are measured without an additional square 4. The order of reading on the angular vernier of the protractor is similar to the reading on the linear vernier of a caliper (Fig. 2.53, c).

Protractors of the UM type are designed for measuring external angles from 0 to 180° and have a vernier reading value of 2 and 5" (Fig. 2.53, d) and 15" (Fig. 2.53, e). Limit of permissible error of the goniometer equal to the value vernier counting.

Rice. 2.55. :

1 - measured cone; 2 - indicator; 3- table; 4 - block of gauge blocks; 5 - calibration plate

For indirect measurements of angles during inspection and measurement work, as well as during machining use sine bars. The rulers are produced in three types:

Type I (Fig. 2.54, a) without a base plate with one slope;

Type II (Fig. 2.54, b) with a base plate with one slope;

Type III (Fig. 2.54, c) with two base plates with double slope.

The sine ruler of type I is a table 1 mounted on two roller supports 2. The side strips 3 and the front strip 5 serve as stops for parts that are attached to the table surface with clamps using threaded holes 4.

Sine rulers are available in accuracy classes 1 and 2. The distance L between the roller axes can be 100, 200, 300 and 500 mm.

The measurement of cone angles on a sine ruler is shown in Fig. 2.55. Table 3, on which the measured cone 1 is fixed, is set at the required nominal angle a to the plane surface plate 5 using a block of length gauges 4. The size of the block of gauges is determined by the formula

where h is the size of the installation block of gauge blocks, mm; L - distance between the axes of the ruler rollers, mm; α is the angle of rotation of the ruler.

Indicator 2 mounted on a tripod determines the position difference δh of the cone surface over length 1. The deviation of the angle, ", at the apex of the cone is calculated by the formula

δα = 2*10 5 δh/l.

The actual angle of the tested cone ak is determined by the formula

αк = α ± δα ± Δл,

where Δл is the measurement error with a sine ruler, which depends on the angle α, the error of the block of gauge blocks and the error of the distance between the axes of the rollers L.

Thus, the errors in measuring angles using sine rulers with a distance between the roller axes of 200 mm for measured angles up to 15° are 3", when measuring angles up to 45° - 10", when measuring angles up to 600 - 17", when measuring angles up to 80° - 52".

The limits of permissible error of rulers when installing them at angles up to 45 ° should not exceed ±10" for the 1st class, and ±15" for the 2nd class.