Method for determining the value of the side clearance. Backlash How to calculate backlash in gears

To eliminate possible jamming when the gear is heated, to ensure the conditions for the flow of lubricant and to limit the backlash when reversing the reference and dividing real gears, they must have a lateral clearance jn (between the non-working profiles of the teeth of the mating wheels). This gap is also necessary to compensate for errors in the manufacture and installation of the transmission and to eliminate impact on non-working profiles, which can be caused by breaking the contact of working profiles due to dynamic phenomena. Such a transmission is single-profile (the contact of the teeth of the wheels occurs along one working profiles).

The side clearance is determined in a section perpendicular to the direction of the teeth, in a plane tangent to the main cylinders (Fig. 2.52).

Regardless of the degree of accuracy in the manufacture of transmission wheels, six types of interfaces are provided. Six classes of center distance deviations have been established, designated in descending order of accuracy by Roman numerals from I to VI. Correspondence of the types of conjugation and the indicated classes given in table. 2.13, it is allowed to change.

Tolerance Tjn is set on the side clearance, which is determined by the difference between the largest and smallest gaps. As the side clearance increases, the tolerance Tjn increases. Eight types of side clearance tolerance have been established: x, y, z, a, b, c, d, h. Each type of conjugation corresponds to a certain type of tolerance (see Table 2.13). The correspondence between the types of mates and types of tolerances can be changed, using the types of tolerance x, y and z.

The side clearance jn min, necessary to compensate for thermal deformations and the placement of a lubricant, is determined by the formula

jn min = V + aw (1to1 - 2to2)2sin ,

where V is the thickness of the lubricant layer between the teeth; aw -- center distance; 1 and 2 - temperature coefficients of linear expansion of the material of the wheels and body; to1 and to2 - wheel and body temperature deviation from 20 °С; -- profile angle of the original contour.

The deformation from heating is determined along the normal to the profiles.

Lateral clearance is provided by radial displacement of the original contour of the rail (gear-cutting tool) from its nominal position into the wheel body (Fig. 2.54). The nominal position of the initial contour is understood as the position of the initial contour on the gear, devoid of errors, in which the nominal thickness of the tooth corresponds to a tight two-profile engagement.

Table 2.13

Types of mates and their corresponding types of tolerances for side clearance and deviation classes for center distance

The relationship between the displacement of the original contour and the lateral clearance jn and the thickening of the tooth thickness along the constant chord Ecs can be established, respectively, from the triangles abc and dbc (see Fig. 2.54):

jnmin = 2EHssin;

An additional displacement of the original contour EHr from its nominal position into the gear body is carried out to ensure a guaranteed lateral clearance in the transmission. The smallest additional displacement of the original contour is assigned depending on the degree of accuracy according to the standards of smoothness and the type of interface and is denoted: for gears with external teeth as - EHs, for wheels with internal teeth - through + EHi.

In table. 2.14 shows the indicators that determine the guaranteed side clearance, tolerances and deviations according to the standards of the side clearance.

Table 2.14

Side clearance

Note. The average length of the common normal is determined by the formula

Wm = (W1 + W2 + + Wz)/z ,

where W1, W2, Wz are the actual lengths of the common normal; z is the number of teeth.

The total lateral clearance must consist of a guaranteed lateral clearance jn min and clearance Kj, which compensates for errors in the manufacture of gears and gear assembly and reduces the lateral clearance:

jnmin + Kj = 2(EHs1 + EHs2)sin.

Gap Kj is measured along the normal to the teeth.

Required minimum displacement of the original contour on both gears

EHs1 + EHs2 = 0.5(jn min + Kj)/sin.

Gap Kj is designed to compensate for a number of errors in the manufacture of gear wheels and gear assembly and is determined by the formula

The largest backlash obtained between the teeth in the gear is not limited by the standard. It is the closing link of the assembly dimensional chain, in which the component dimensions with limited tolerances are the center distance and the displacement of the initial contours when cutting both wheels, etc. Therefore, the largest gap cannot exceed the value obtained with the most unfavorable combination of deviations of the component dimensions:

jn max = jn min + 2(TH1 + Tp + 2fa)sin.

M.V. Abramchuk

Scientific adviser - Doctor of Technical Sciences, Professor B.P. Timofeev

The article compares the standards ISO/TR 10064-2:1996 and GOST 1643-81 in terms of the organization of standardization and control of backlash in gears. A comparison is also made of the minimum side clearance values ​​in both of these standards.

Introduction

Consider the technical report “ISO/TR 10064-2 Spur gears. A practical guide to acceptance. Part 2: Control of total radial deviations, runout, tooth thickness and clearance. In doing so, let's start with Appendix A, which has the title "Backlash and Tooth Thickness Tolerance". We will consistently compare the provisions of the mentioned Appendix A with section 3 of the basic standard GOST 1643-81 "Side clearance standards".

Side clearance control

The ISO/TR 10064-2 standard contains recommendations for standardizing the backlash of the interface and the thickness of the teeth of the wheels. At the same time, everything stated in the standard is advisory in nature, while the norms given in the domestic standard GOST 1643-81 were mandatory.

The first paragraph of Annex A of ISO/TR 10064-2 provides a method for selecting wheel tooth thickness tolerances and minimum backlash. In addition, a method for calculating the maximum expected backlash in gearing and recommended values ​​for the minimum backlash are given. GOST 1643-81 establishes lateral clearance standards and provides tables with the values ​​​​of the corresponding standards. There are no calculation methods similar to those given in the recommendations of the ISO / TR 10064-2 standard in GOST 1643-81.

The second paragraph of ISO/TR 10064-2 defines lateral clearance and justifies the required amount. It also states that "backlash in engagement changes during transmission operation due to changes in wheel speed, temperature, load, etc." . Our standard does not contain a definition of lateral clearance and transmission operating conditions that cause it to change.

The third clause of Annex A of ISO/TR 10064-2 is called "Maximum wheel tooth thickness". It defines this concept. In GOST 1643-81 there are no explanations for maximum thickness wheel tooth is not included, only tables are given with tolerance values ​​Ecs (least deviation of tooth thickness) and Tc (tooth thickness tolerance).

The fourth paragraph of Annex A of ISO/TR 10064-2, which has the heading “Minimum side clearance”, defines the minimum side clearance and describes the need for a minimum side clearance - “this is the so-called traditional “side clearance tolerance”, which is created by the designer in order to offset:

(a) housing and bearing errors, shaft deflections;

(b) wheel axle misalignment due to housing and bearing clearance errors;

(c) axle misalignment due to housing errors and bearing clearances;

(d) mounting errors such as shaft eccentricity;

(e) runout of supports;

(f) thermal effects (a function of temperature difference between the body and wheel elements, center distance and material difference);

(g) increasing the centrifugal force of rotating elements;

(h) other factors such as lubricant contamination and enlargement of non-metallic parts of the wheel.

It also states that “the value of the minimum side clearance can be small, provided that the above factors are controlled. Each of the factors can be assessed through tolerance analysis, and then, the minimum requirements can be calculated.

The recommendations of the ISO/TR 10064-2:1996 standard oblige us to take into account the errors of non-toothed transmission elements, as well as the conditions of its operation, when calculating the side clearance tolerances, which is absolutely not taken into account in the current basic standard GOST 1643-81. Many domestic experts spoke about this shortcoming of our standard, especially B.P. Timofeev (see, for example,). It is necessary to standardize the calculation of the side clearance on the basis of extensive experimental work due to the insufficiency and inconsistency of the existing recommendations.

In general, the basic standard GOST 1643-81 normalizes the side clearance as follows. The type of gear teeth interfaces in the gear is characterized by the smallest guaranteed lateral clearance jn . Side clearance requirements are set regardless of the accuracy of gear manufacturing. The standard establishes a guaranteed (smallest) side clearance in the gear train jn min - the smallest prescribed side clearance, and a side clearance tolerance Tjn equal to the difference between the largest allowable and guaranteed (smallest) side clearances. The side clearance standards are not uniquely related to the design and operating conditions of the gears, which in some cases leads to jamming of the gear, despite the minimum side clearance "guaranteed" by the standard.

Depending on the size of the guaranteed side clearance, the GOST 1643-81 standard establishes six types of wheel tooth mates in the gear: H, E, D, C, B, A and eight types of side clearance tolerance, denoted in ascending order by the letters h, d, c, b, a, x, y, z. Mating H - with the smallest zero clearance, E - with a small one, C and D - with a reduced one, A - with an increased one. Type B coupling provides the minimum side clearance, which excludes the possibility of jamming of a steel or cast iron gear from heating at a temperature difference of gears and housing of 25 ° C.

In the absence of special requirements for gears, it is necessary to proceed from the following provisions: types of mates H and E correspond to the type of tolerance for side clearance h, types of mates D, C, B and A - types of tolerances d, c, b and a, respectively.

Correspondence between the type of pairing of gears in the transmission and the type of tolerance for side clearance can be changed; in this case, types of tolerances x, y, z can also be used.

Six classes of center distance deviations are also established, indicated in descending order of accuracy by Roman numerals from I to VI.

The manufacturing accuracy of gears and gears is set by the degree of accuracy, and the side clearance requirements are determined by the type of interface according to the side clearance standards. Guaranteed lateral clearance in each mate is provided subject to the specified classes of deviations of the center distance (for mates H and E - class II, and for mates D, C, B and A - classes III, IV, V and VI, respectively

venno). This results in a redefinition of the value of the guaranteed side clearance: on the one hand, it depends on the type of mates, on the other hand, on the class of deviation of the center distance.

It is also indicated that it is allowed to change the correspondence between the type of mate and the class of center distance deviations.

The total side clearance consists of the guaranteed side clearance, jnmin, and part of the side clearance, k, the so-called compensation for the reduction of the side clearance, which occurs due to the error in the manufacture of the gears and the installation of the transmission. The amount of compensation is determined by the formula:

k) \u003d 4 (f " 2sin a) 2 + 2fP\ + 2Fß + (sin a) 2 + (fy sin a) 2,

where fa is the maximum deviation of the center distance, fPb is the maximum deviation of the engagement pitch, Fß is the profile direction error, fx is the tolerance for parallelism of the axes, fy is the tolerance for misalignment of the axes, and is the gear engagement angle.

When determining k, the radial runout of the ring gear, Frr, is not taken into account, and with non-multiple numbers of teeth, any exhibition of wheel eccentricities does not exclude the situation when the side clearance jn in the gear will be determined by this factor.

The already mentioned fourth paragraph of Annex A of ISO/TR 10064-2 provides a table with the minimum backlash values ​​recommended for industrial drives with ferrous wheels in ferrous metal housings operating at peripheral speeds less than 15 m/s, s typical commercial (the term of the original, we have more accepted the term "economically justified") manufacturing tolerances for housings, shafts and supports.

Let's compare the values ​​of the minimum side clearance in ISO / TR 10064-2 and GOST 1643-81, taking into account the fact that in ISO / TR 10064-2 the clearance value depends on the modulus of the teeth mn and the minimum center distance ar-, while in our standard - on the type of conjugation and center distance aw. Let's take the type of conjugation B for tooth modules in the range mn=(1.5-5) mm and the type of conjugation A, for modules mn=(12-18) mm. The results obtained are summarized in a table. The values ​​of the guaranteed side clearance taken from GOST 1643-81 are highlighted in bold.

mn, mm Minimum spacing, аb mm

50 100 200 400 800 1600

1,5 90 120 110 140 - - - -

3 120 120 140 140 170 185 240 230 - -

5 - 180 140 210 185 280 230 - -

12 - - 350 290 420 360 550 500 -

18 - - - 540 360 670 500 940 780

Table. Comparison of minimum side clearance values ​​in ISO/TR 10064-2 and GOST

As can be seen from the table, with a tooth module mn = 3 mm, the minimum side clearance in ISO / TR 10064-2 and the guaranteed side clearance in GOST 1643-81

practically match. At mn<3 минимальный боковой зазор по ISO/TR 10064-2 меньше, чем в ГОСТ 1643-81, mn>3 - more.

The values ​​given in the standard table in ISO/TR 10064-2 can be calculated using the expression:

GOST 1643-81 does not contain dependencies for calculating the values ​​of the guaranteed side clearance, jnmin.

Also in the fourth paragraph of the ISO / TR 10064-2 standard, the formula for calculating the side clearance is given:

where EtsSh1 and EtsPts2 are the upper deviation of the thickness of the gear and wheel tooth, respectively, and ap is the normal profile angle.

the thinning bin and the share of the radial clearance of the gear and wheel are equal, and the value of the overlap coefficient is maximum. Unlike the ISO/TR 10064-2 standard, in GOST 1643-81 the smallest deviations of the tooth thickness of the wheel and gear cannot be equal, because they depend on the pitch diameter, the values ​​of which are different for the gear and gear wheel.

The fifth paragraph of the ISO/TR 10064-2:1996 standard deals with the normalization of tooth thickness. In particular, it gives recommendations for determining the maximum and minimum thickness of the tooth. In our standard GOST 1643-81, the topic of tooth thickness rationing, in addition to tabulating the smallest deviation of tooth thickness and tolerance for tooth thickness, is not affected.

The sixth clause of ISO/TR 10064-2 contains recommendations for the specification of maximum side clearance. The definition of this accuracy parameter is given - “the maximum backlash in the gear, jbnmax is the sum of the tooth thickness tolerance, the influence of center distance deviations and the influence of wheel tooth geometry deviations” and the condition for its occurrence: “the theoretical maximum backlash occurs when two high-quality gears wheels made in accordance with the norm of the minimum thickness of the tooth are engaged at the maximum allowable free center distance. Formulas are given for calculating the minimum actual tooth thickness and the maximum circumferential backlash, as well as the formula for converting the circumferential backlash into normal backlash. It also states that “any manufacturing deviation of the tooth will increase the maximum expected backlash. Evaluation of acceptable values ​​requires serious research work on the base a large number experiences". It is emphasized that "if you want to control the maximum backlash, then you need to conduct a thorough study of each of its components and the chosen degree of accuracy, limiting deviations in the geometry of the wheel tooth" . The normalization of the maximum side clearance in GOST 1643-81 is reduced to bringing the values ​​of the guaranteed side clearance, jnmin, and the value of the tolerance for the side clearance Г, „ is recommended to be obtained from the expression:

The provisions of the ISO / TR 10064-2 standard are advisory in nature; it does not contain specific data on standardization. As indicators of the gap, use

where TH1 and TH2 are the tolerances for the displacement of the initial contour of the gear and wheel.

Esns and Tsn values ​​are used (upper tooth thickness deviation and wheel tooth thickness tolerance). We have this Ecs (the smallest deviation in the thickness of the tooth) and Tc (tolerance for the thickness of the tooth). The Esns and Tsn values ​​in ISO/TR 10064-2 are not standardized, but only recommendations are given regarding methods for their determination. Thus, the adoption of these recommendations without the development of standard standards that provide side clearance would mean the rejection of the use of methods and means of measuring all indicators given in our standard, namely:

EHs (least additional offset of the original contour);

Ewms (smallest deviation of the average length of the common normal);

Ews (smallest deviation of the common normal length);

Ea "" s (upper limit deviation of the measuring center distance) and others.

The recommendations of the ISO/TR 10064-2 standard do not associate the clearance value and its rationing either with the type of mating, or with the type of side clearance tolerance, or with the deviation class of the center distance. However, they require mandatory consideration of the error in the manufacture and installation of non-gear parts of the transmission (housing, shafts, bearings, etc.), the operating conditions of the gear, as well as the type of lubricant, its contamination, the presence of non-metallic parts of the wheels and other elements.

Conclusion

A detailed review of the ISO / TR 10064-2: 1996 standard and its comparison with GOST 1643-81 leads us to the conclusion that it is necessary to urgently develop a domestic standard containing specific tolerances for standardized values ​​that allow full use of existing equipment for testing gears and gears . Mentioned normative document must, in contrast to the GOST 1643-81 standard, comply with the basic principles of the ISO standard recommendations. It is impossible to organize the production of gears and gears only on the basis of ISO recommendations without using the domestic standard. The existing standard GOST 1643-81 in a number of provisions directly contradicts the mentioned recommendations.

Literature

1. ISO/TR 10064-2:1996. Cylindrical gears. Code of inspection practice. Part 2. Inspection related to radial composite deviations, runout, tooth thickness and backlash.

2. Timofeev B.P., Shalobaev E.V. State and prospects of rationing the accuracy of gears and gears. // Bulletin of mechanical engineering. No. 12. 1990. S. 34-36.

3. Tishchenko O.F., Valedinsky A.S. Interchangeability, standardization and technical measurements. M.: Mashinostroenie, 1977.

4. Timofeev B.P., Shalobaev E.V. Establishment of the type of conjugation in the gear and regulation of the norms of the side clearance. // Metrological service in the USSR. M.: Publishing house of standards. 1990. Issue. 2. S. 27-31.

5. GOST 1643-81. Transmissions are gear cylindrical. Tolerances. M., Publishing house of standards, 1989.

6. Yuryev Yu.A., Murashev V.A., Shalobaev E.V. The choice of the type of conjugation and the probabilistic assessment of the backlash of the transmission. L.: LITMO., 1977. 28 p.

Measuring

linear and angular

quantities

Any linear dimension can be measured by various measuring instruments that provide different measurement accuracy. In each specific case, the measurement accuracy depends on the principle of operation, the design of the device, as well as on the conditions of adjustment and application.

The principle of choosing measuring instruments is to compare the existing maximum measurement error of a particular measuring instrument with the calculated permissible measurement error regulated by the standards. In this case, the marginal error should not exceed the permissible one, which is usually 20-35% of the size tolerance value.

In some cases, the permissible measurement error can be increased by reducing the size tolerance, for example, when dividing products into size groups during selective assembly. In this case, often the size of the group (it is conditionally taken as the tolerance of the controlled product) is taken close to or even equal to the measurement error in order to limit the difference in size of parts in groups. With selective assembly, it is not advisable to standardize more stringent requirements for measurement error.

Permissible values ​​of random measurement error (meas.), regulated by the standards ST SEV 303-76 and GOST 8.051-81, are taken at a confidence level of 0.95 (based on the assumption that the error distribution law is normal and meas. equates to a zone of ± 2 ) .

The value of the marginal randomness of the error (Lim) is equated to the distribution zone of ±3, (based on the normal distribution law), i.e., the confidence probability is 0.9973. For production measurements in mass and large-scale production, the value of the measurement error is assumed to be ±2 .

Before proceeding to the consideration of existing methods for choosing measuring instruments, let us dwell on some general concepts.

Classification of instruments for measuring linear and angular quantities

Measuring instruments - technical means intended for measurements, having normalized metrological properties (characteristics).

Measuring instruments (SI) are all kinds of measures, tools, devices and devices with which measurements are made.

The classification of measuring instruments presented in this manual refers to measuring instruments intended for measuring geometric parameters.

By type, all measuring instruments are divided into:

On measures;

Measuring tools;

Measuring instruments.

Measures- measuring instruments designed to reproduce a physical quantity of a given size.

For linear and angular measurements, there are:

plane-parallel end measures of length;

angular measures;

Special measures and standards that serve to set up instruments.

Plane gauge blocks length are sets of parallelepipeds (plates and bars) made of steel up to 1000 mm long or hard alloy up to 100 mm long with two flat mutually parallel measuring surfaces (GOST 9038-83). They are intended for direct measurement of linear dimensions, transfer of the size of a unit of length from the primary standard to end measures of lower accuracy, as well as for verification, calibration and adjustment of measuring instruments, tools, machines, etc. By the action of intermolecular forces of attraction, end measures can be assembled into blocks of the desired size, which do not fall apart when moving. Sets consist of a different number of end measures (from 2 to 112 pcs.). End measures are manufactured in the following accuracy classes: 00; 01; 0; one; 2; 3.

There are categories of tiles depending on the parallelism of the working faces: 1; 2; 3; four; 5. For 0 cells. tiles 4 are made; 5 digits; for 1 class-4; 5 digits; for grade 2 - 3; four; 5 digits; for Zkl.- 2; 3; 4 digits). Tiles of 4, 5 classes are not produced by the industry, these are worn tiles for repair production and agricultural engineering.

Table 2 of the manual shows the classes and categories of tiles recommended for setting up devices.

Angle measures are used to store and transfer a unit of a flat angle, to check and calibrate corner devices, to control corner products. They are usually made of steel in the form of three- and four-sided tiles. The measuring surfaces of the tiles are adjusted, which makes it possible to compose blocks of several measures.

In accordance with the standard, angular measures are produced in the form of several sets of 0, 1 and 2 accuracy classes, depending on the permissible deviations of the working angles. So, for the 0th class, the deviations of the working angles are within ±3...5", the first ±10" and the second ±30".

To control mutual perpendicularity, squares with a working angle of 90 ° are used. Squares are made in five types and four accuracy classes (0, 1, 2 and 3).

Measuring angles with angle measures is based on the comparison method. To read the difference in angles, a light gap is used between the sides of the measured angle and the measure (Fig. 52).

The deviation of the angle of the product from the angle of the measure is determined by the ratio of the lumen to the length of the side H. If the lumen is not more than 30 microns, then samples of the lumen are used, if more than 30 microns - special probes.

Rice. 52. Measurement of angles with a square.

Special Measures- these are boxes with plane-parallel glass plates, which are used to check micrometers for parallel heels. Gauges are scaleless instruments that are designed to control parts in mass production. More information about the classification of calibers can be found in any reference literature, incl. .

Tool is a measuring instrument having one mechanical transmission. The tools include vernier calipers and other calipers, smooth micrometers and micrometric tools (shtihmas, micrometric heads, depth gauges, all types of micrometric three-point inside gauges).

Devices- measuring instruments having two or more mechanical gears or a combination of optical and mechanical gears or a combination of one or more optical gears.

All devices and tools for their intended purpose are divided into:

Special

Universal.

Universal funds used to measure various geometric parameters either directly or in combination with object tables, plates, racks, tripods, clamps and other additional devices. Special funds allow you to measure or control the parameters of parts of a certain type.

According to the type of gear, devices and tools are divided:

1. Tools and devices with mechanical gears:

Direct transmission (bar tool);

Screw drive (micrometric tools);

Lever transmission (minimeters);

Gear (dial type indicators);

Lever-gear transmission (lever brackets, lever micrometers);

Spring transmission (microcators, micators).

2. Optical transmissions (length gauges, projectors, microscopes).

3. Optical-mechanical gears (optimeters, opticators, ultra-optimeters).

4. Electromechanical transmissions (kloglometers, profilographs-profilometers).

The following requirements apply to a device for measuring lengths and angles::

Accuracy;

Reliability;

Manufacturability;

Profitability;

Safety;

Ergonomics;

Aesthetics;

Infection;

Active influence on the technological process in order to obtain only suitable parts.

2 Gear backlash measuring instruments

To eliminate possible jamming when the gear is heated, to ensure the conditions for the flow of lubricant and to limit the backlash when reversing the reference and dividing real gears, they must have a lateral clearance j n (between non-working profiles of the teeth of the mating wheels). This gap is also necessary to compensate for errors in the manufacture and installation of the transmission. The side clearance is determined in a section perpendicular to the direction of the teeth, in a plane tangent to the main cylinders (Figure 2.1).
Figure 2.1

Measuring the backlash in engagement can be done in two ways:

1.Using indicator: install a micrometer on a special bracket so that its probe rests on the working surface of the tooth of the driven wheel in outside. With the output shaft fixed with the drive gear, turn the driven wheel all the way to the left and right. The difference in the indicator readings at the extreme points is the side clearance.

2. For side clearance measurement lead wire Two equal-length pieces of wire with a diameter of 1-3 mm are applied to the gear teeth and fixed with grease, and the distance between the wires is measured. Then, turning the wheel by hand, flatten the wire. The resulting impressions of the lateral and radial gaps will be strips with variable thickness. A smaller thickness a corresponds to the gap on the working side of the tooth, and a large one - on the non-working side. The sum of the thicknesses of both impressions, measured with a micrometer, is equal to the lateral clearance of the engagement.

Assign the degree of accuracy of the gear according to three types of standards: kinematic accuracy, smooth operation, tooth contact; Calculate guaranteed minimum side clearance:

number of teeth of the drive wheel Z 1 = 40;

number of driven wheel teeth Z 2 = 75;

circumferential speed of the wheel V okr = 5m/s;

gear module m= 3mm;

wheel width AT= 20mm;

operating temperature of the wheel and housing: t count = 60°C, t corp= 25°C;

wheel material: silumin; cases: silumin; transmission type: divides. mechanisms.

Select measuring instruments for accuracy control according to all types of accuracy standards of controlled parameters. Make an assembly drawing of the gear.

Calculation procedure

In terms of speed V env, m/s, we choose the degree of accuracy of the gear train and then adjust it according to the type of gear .

We select the degree of accuracy (according to the norms of smoothness) 8. For power transmissions, the contact norm is taken one degree lower than 9, according to the norms of kinematic accuracy 8.

Determine the center distance a w , mm, according to the formula

where a w- center distance, mm;

Z 1 - the number of teeth of the drive wheel, Z 1 = 40;

Z 2 - the number of teeth of the driven wheel, Z 2 = 75;

m- gear module, mm, m= 3 mm;

a w = mm.

Determine the temperature compensation of the gap j n 1 , mm, and the optimal thickness of the lubricant layer j n2 , µm, according to the formula

j n 1 = a sch [ b 1 (t count- 20?C) - b 2 ( t corp - 20?C)] 2sin b, (51)

where j n 1 - part of the side clearance for temperature compensation, mm;

b 1 and b 2 - temperature coefficient of linear expansion of the material of the driving and driven wheels, respectively, deg -1, b 1 = 19 10 -6 deg -1, b 2 \u003d 19 10 -6 deg -1;

t count- wheel temperature, ?С, t count= 60? FROM;

t corp- body temperature, ?С, t corp = 25? FROM;

b - driving wheel engagement angle, b = 20?;

j n 1 \u003d 172.5 2 sin 20? = 78.47 mm,

j n 2 = 30 m, (52)

j n 2 = 30 3 = 90 µm.

Determine the minimum side clearance of the transmission j n min , µm, according to the formula

j n min = j n 1 + j n 2 (53)

j n min = 78.47 + 90 = 168.47 µm.

By choosing the type of conjugation B.

Thus, the degree of transmission accuracy is 8 - 8 - 9 V GOST 1643-81.

Select the means of their measurement for the controlled parameters.

According to table 5.5, we determine the controlled parameters:

1) norms of kinematic accuracy with degree of accuracy 8:

radial runout of the ring gear,

2) smoothness standards with an accuracy degree of 8:

step deviation (angular), f pt ;

3) tooth contact rate with degree of accuracy 9:

total contact patch, ;

4) side clearance norms for interface type B:

A wme ;

T wm .

The values ​​of these parameters are determined based on the diameter of the pitch circle of the wheel and gear d 1 , d 2 mm, which are determined by the formula

d 1 = m z 1 (54)

d 1 mm

d 2 = m z 2 (55)

d 2 mm.

Table 5 - Values ​​of controlled parameters for gear and wheel

Table 6 - Measuring gears