Measure the gear tooth with a gear, along with the most common. At a certain height, the gear tooth must be a certain size.
How to measure a gear tooth with a tooth gauge.
- Set the height.
- At this height we measure the tooth.
What you need to know to correctly measure with a tooth gauge.
- First of all, the jaws of the tooth gauge should not lie very tightly, that is, they should “walk” a little. The tooth gauge must be exactly at the height. If everything is extremely tight, then there is a possibility that the gear gauge is not at the right height. therefore the measurement is incorrect! Sponges should "walk" a little - a little! It's all hard to describe, it's better to watch the video that I made for you. In the video, I measure the gear tooth of the large module, small module, spur and helical gears.
- The size of the gear gauge is tied to the diameter of the gear. Accordingly, if the diameter is not correct, it is required to change the measuring height. For example, the diameter of the gear is less than 0.5 mm. Accordingly, the height must be reduced by 0.25 mm. I recommend (necessary) to coordinate all this with technologists.
Objective
To study the principle of operation and the device of gear meters and master the method of measuring the dimensions of the elements of gears with a caliper gauge and a micrometric gear gauge.
material support
1) Caliper type ___________, No. ___________ of factory ___________, with measurement limits ____________ mm, vernier scale division value ________ mm, measurement error __________ mm.
2) Vernier caliper type ___________, No. ___________ of plant ___________, with measurement limits ____________ mm, vernier scale division value ________ mm, measurement error __________ mm.
3) Micrometric tooth gauge type ___________, No. ___________ of factory ___________, with measurement limits _____________ mm, drum scale division value ________ mm, measurement error __________ mm.
4) Gears.
1. Theoretical provisions
1.1. General information about gears and methods for their control
The gear wheel is a rather complex product. Its quality is largely determined by the accuracy of a number of parameters that depend on the technical condition of the gear-cutting equipment, the level of technology, the quality of the cutting tool and the quality of the control and measuring operations of the gear-cutting production.
The accuracy requirements for most parameters of gears are not the same and depend mainly on the specific purpose of the wheels and the transmission as a whole. For gearboxes of machine tools and for precision instruments, particularly high requirements are placed on the parameters characterizing the accuracy of motion transmission, i.e. kinematic accuracy. In high-speed transmissions, the paramount parameters are those that determine smooth operation which reduces noise, vibration and wear. For power transmissions, it is important to strictly maintain the parameters that affect the conditions tooth contact. In order to compensate for some manufacturing errors, real gears have a gap between the non-working surfaces of the profiles, which is called side clearance. The value of this gap is especially large for gears operating under conditions of large temperature fluctuations and in reversing mechanisms.
In GOST 1643 - 81 “Cylindrical gears. Tolerances” all requirements for ensuring the accuracy of gear parameters are divided into four groups, which are called accuracy standards. GOST provides norms of kinematic accuracy, norms of smoothness, norms of tooth contact and norms of side clearance. In the first three groups, tolerances for specific parameters are set depending on the degree of accuracy. There are 12 levels of accuracy in total. However, the standard specifies the values of the parameters only from the 3rd to the 12th, and the most accurate, the 1st and 2nd degrees, are left as a reserve.
In the manufacture of gears, their quality is ensured both by a high level of final (acceptance) control, and by other organizational and preventive measures - preventive, technological and active types of control.
At final control establish whether the accuracy of the manufacture of gears corresponds to the conditions of operation of the transmission.
Preventive control consists in checking the condition of technological equipment: machine tools, fixtures, cutting tools. It must be carried out before the production of gears.
Technological control consists in element-by-element control of gear wheels. It allows you to establish the accuracy of individual elements of technological equipment and, if necessary, take timely measures to eliminate defects.
Active control consists in the fact that one or more parameters are measured during processing. Using the measurement results, process control is carried out, for example, processing is interrupted when the required size is reached.
Preventive, technological and active control must precede the final (acceptance) control.
1.2. Element-by-element control of gear wheels
The devices used for element-by-element (differentiated) control are divided by design into overhead (H) and easel (C).
The first to check, as a rule, are large-sized parts that are difficult to install on machine tools. However, due to the fact that the base for overhead devices is the circumference of the wheel protrusions, and not the operational base (wheel hole or gear shaft), their error is greater than that of easel ones.
Element-by-element control consists in checking the compliance of the values of individual parameters with the requirements of the standard. The data obtained during the differentiated control of gears allows for prompt adjustment of technological equipment to prevent possible defects.
Checking the radial runout of the gear rim, which characterizes part of its kinematic error, is carried out on special devices called beaters. The schematic diagram of the measurement is shown in fig. one, a.
Rice. 1. Schemes for measuring the radial runout of gear rims:
a fundamental; b) in workshop conditions; in wheels with internal gearing
measuring tip 2 , made in the form of a truncated cone with an angle at the top of 40 °, is inserted into the cavity of the gear 7 . From measuring head 3 take a reading. Then, retracting the carriage 4 and turning the gear wheel, insert the measuring tip into each subsequent cavity. The value of the radial runout is taken equal to the difference between the largest and smallest head readings per revolution. The device also allows you to control bevel gears.
In workshop conditions, the control of the radial runout of the ring gear 7 (Fig. 1, b) can be done using control centers 5 and 9 , calibrated roller 10 , rack 11 with measuring head 8 and mandrel 6 . To do this, the gear wheel is put on the mandrel and installed in the centers using the center holes. A roller is sequentially placed in the wheel cavities and a reading is taken on the head scale. The value of the radial runout is determined in the same way as on the bienimer.
To measure the radial runout of the inner ring gear of a wheel 13 (Fig. 1, in), use the tip 12 spherical shape. Radial processing errors can be detected using spherical tips and rollers only with their most advantageous diameter.
The radial runout of the ring gear occurs due to the inconsistency of the distance between the gear and the tool that processes it. To reduce this error, it is necessary to check and eliminate the radial runout of the workpiece on the mandrel before installing it on the gear machine. Radial runout of the cutting tool is much less common.
Fluctuation in the length of the common normal W controlled by instruments having two parallel measuring surfaces and a device for measuring the distance between them.
The length of the common normal can be measured by the absolute method with micrometric tooth gauges of the MZ type (Fig. 2, a) with a division value of 0.01 mm and measurement ranges of 0...25; 25...50; 50...75 and 75...100 mm.
Rice. 2. Micrometric tooth gauge ( a), normal meter ( b), spherical tips ( in) and limit caliber ( G) to control the length of the common normal
The measurement of the length of the common normal (as well as its oscillations) by the comparison method is carried out using a normal meter (Fig. 2, b), which has two measuring jaws - the base 5 and mobile 1 . The latter is connected by a transmission mechanism to the measuring head 2 . Base jaw with split sleeve 3 fastened in the desired position on the bar 4 when setting the device to zero on the block of end measures. movable sponge 1 withdraw by arrester. Sponges cover a number of teeth, then release the measuring sponge and read from the scale the deviation of the length of the common normal from the nominal value.
Using spherical measuring tips (Fig. 2, in), you can measure the length of the common normal by direct evaluation or determine its deviation from the nominal value by comparison. In this case, universal gear measuring instruments are used as measuring instruments.
In the conditions of large-scale and mass production, the control of the length of the common normal is carried out using limit gauges (Fig. 2, G).
The measurement of the engagement pitch (basic pitch) is made by determining the distance between two parallel planes tangent to two identical working surfaces of adjacent gear teeth. In the example under consideration, measurements using a strap-on pedometer are parallel to the planes in which the measuring tips lie. 1 and 4 (Fig. 3, a).
Distance P measured along the line ah. Movable measuring tip 1 via linkage 2 connected to the measuring head 3 . Tip 4 immobile and basic. Before measurement, the device is set to zero using a special device. During the measurement, the device is shaken relative to the support tip. 5 . For the deviation of the engagement pitch value from the nominal value, the minimum reading on the head scale is taken 3 .
The step uniformity control consists in determining the deviations of the actual step from the average value. For this purpose, overhead devices are used. The gear pitch must be measured at a constant diameter. To do this, the device is equipped with special adjustable support tips. 7 and 10 (Fig. 3, b), with which it is based on the cylindrical surface of the teeth. The device has two measuring tips movable 6 and motionless 11 . Movable tip transmits pitch deviations through linkage 8 on the measuring head 9 . Before the measurement, the device is set to zero in one of the steps of the tested gear. The device allows you to measure both the difference between adjacent steps and the accumulated error of the steps of the gear. Overhead pedometer (Fig. 3, in), except for the mounting stop 13 , resting on the cylindrical surface of the teeth, is equipped with two more stops 12 , basing the device on the end surface of the gear. The pedometer has movable and fixed flat tips 14 . The measurement is carried out in the same sequence.
Rice. 3. Schemes for measuring the engagement pitch ( a) and control of its uniformity ( b) using the strap-on pedometer ( in)
The uneven pitch affects the smoothness of the wheel. Usually this error occurs due to the inaccuracy of the tool used when machining the wheels by the break-in method, or due to the inaccurate setting of the dividing chain of the machine during the division method.
Measurement of the tooth profile error is carried out by special devices - involventometers. The measurement is based on the principle of continuous comparison of the reference involute reproduced by the device with the actual profile of the measured wheel. According to the method of reproducing the exemplary involute, the devices are divided into individual disk and universal.
Individual disc involventometer (Fig. 4) has a replaceable disc 4 , the size of which is equal to the diameter of the main circle of the tested wheel.
The wheel to be checked is mounted on the same axle with the disk. 3 . The disk is pressed against the working surface of the ruler by springs 2 installed on the carriage 7 . When moving the carriage with a screw 1 a ruler that is in contact with the disk will turn it around the axis without slipping. In this case, any point of the disk moves relative to the corresponding point on the surface of the ruler along the involute. Lever measuring tip 6 is in the plane of the working surface of the ruler. If the actual tooth profile differs from the involute, then the tip is deflected and using the measuring head 8 the error of the tooth profile is fixed. Scale 9 helps to quickly return the measuring tip to its original position and set it along the diameter of the main circle; it also monitors the movement of the carriage. Using the scale 5 evaluate the angle of rotation of the tested wheel. To control the next tooth, the wheel is rotated by one angular step, and the carriage, using the scale 9 , is moved to its original position. To measure the profile on the other side of the tooth, the wheel to be checked is turned over on a mandrel. The main disadvantage of the device is the need to have its own disk for each controlled wheel, which is different from the previous one. Therefore, an individual disk involventometer is used only in conditions of large-scale and mass production.
In small-scale and single-piece production, it is more expedient to use universal devices with a permanent rolling disk, an involute cam or other devices that reproduce the theoretical involute. The use of inductive sensors instead of the measuring head makes it possible to record profile deviations on a diagram.
Rice. 4. Individual disc involventometer
Large wheels (spur and helical) are measured with overhead involventometers.
1.3. Purpose and device of a caliper gauge and
tangential gear gauge
One of the main indicators that determine the side clearance of a pair of cylindrical wheels is tooth thickness along the chord, measured by gear gauges. By design, these devices are divided into overhead and easel, and according to the principle of operation - into caliper gauges and indicator-micrometric gear gauges.
caliper(Fig. 5, a) has two scales – 5 and 1 : the first one is for thickness reading S tooth with vernier 4 , and the second - to install the jaws of the device at the required height h from the top of the teeth. Before measuring stop 3 set by vernier 2 to a size equal to the height h and fixed in this position. Then the measuring jaws are moved apart and after installing the device, focusing on the outer surface, measure the thickness of the tooth along the chord, counting its full value directly on the scale 5 and vernier 4 . The disadvantages of the vernier caliper are the low accuracy of the vernier reading, the rapid wear of the measuring jaws, and the impact on the measurement accuracy of the error of basing the device along the circumference of the protrusions.
The counting method is similar to the method of taking the result with caliper tools, but the division value of the main scale (on the rod) is 0.5 mm.
Tangential gear gauge NC type (Fig. 5, b) control the thickness of the tooth by the displacement of the original contour. The reference base for the measurement is the circumference of the protrusions. Measuring surfaces of two jaws 11 make up a double angle of engagement equal to 40. The axis of the measuring rod bisects this angle. Measuring jaws move in the housing guides 6 screw 10 having sections with both right-hand and left-hand threads. This ensures a symmetrical installation of the jaws with respect to the axis of the measuring rod of the head. 9 . Sponges are fixed with locking screws 7 . The spherical measuring tip is attached to the head shaft with a clamp 8 .
Before measurement, the device is adjusted to the size according to the reference roller, the diameter of which is 1.2036 m, where m- module of the wheel being checked. The gear gauge is applied to the roller, then, shifting with a screw 10 sponges 11 , bring the measuring tip to contact with the roller and create a preload of the tip for one or two turns of the arrow. After that carry out installation on a zero on a scale. During the control, the measuring sponges, reproducing the side profile of the cavity of the original rail, are applied to the tooth 12 and the deviation of the indicator is used to judge the displacement of the actual initial contour relative to the nominal position.
Rice. 5. Teeth gauges:
a- caliper gauge; b- tangential tooth gauge
2. Work order
1. To study the design, principle of operation of caliper gauges and a micrometric gear gauge of the MZ type.
2. Determine and record in the report the metrological characteristics of the caliper gauge and micrometric gear gauge.
3. Draw a scheme for measuring the thickness of the gear tooth and measuring the length of the overall normal of the gear.
4. Determine half the height of the tooth h according to the formula
h
=
,
where D max is the diameter of the tops of the wheel teeth; D min is the diameter of the wheel troughs.
5. Measure the thickness of ten teeth of each gear.
6. Measure the length of the common normal of the gears with a micrometric tooth gauge.
7. Record the measurement results in tables (Tables 1, 2).
Table 1. The results of measuring the thickness of the tooth along the chord
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Table 2. The results of measuring the length of the common normal
8. Define a module m gears according to the formula
where D d- diameter of the pitch circle of the gear; z- number of teeth.
The diameter of the dividing circle is calculated as
D d
=
.
9. Determine the backlash of the gearing of the wheels 1 and 2 and compare with the norms of GOST 1643 - 81.
10. Finalize the report, which should end with the conclusions on the work.
3. Contents of the Lab Report
1. Number, name, purpose, material support of laboratory work.
2. Purpose and device of the considered measuring instruments.
3. Scheme for measuring the thickness of the tooth along the chord and the length of the overall normal of the gears.
4. Table with measurement results (see Tables 1, 2).
5. Conclusion on laboratory work.
4. Instructions for the preparation of the report
The report on the laboratory work is carried out on standard sheets of A4 white paper (210 x 297 mm) with a standard frame. Requirements for drawing a frame: left margin 20 mm; top, right and bottom - 5 mm. The first page is designed as a title page. At the bottom of each subsequent sheet, a corner stamp is drawn to indicate the sheet number. When performing an explanatory note on a computer, it is allowed not to execute the frame. In this case, the Times New Roman font is used, the size is 14, the line spacing is 1.5.
test questions
1. What is the metrological characteristics of measuring instruments?
2. What methods are used in the measurement processes?
3. What are the main parts of a caliper, micrometric gear and what are they intended for?
4. What is the method of measuring with a caliper and a micrometer?
5. What are the gear accuracy standards set by the standard?
6. List the main types of control gears.
7. By what means and how are deviations and the length of the common normal measured?
8. What instruments and how can you check the indicators that determine the backlash in the gearing?
Bibliographic list
1. Makhanko A.M. Control of machine and locksmith works. - M.: Higher School, 2000. - 286 p.
2. Ganevsky G.M., Goldin V.E. Tolerances, landings and technical measurements in mechanical engineering. - M.: Higher school, 1998. - 305 p.
3. GOST 1643 - 81. Cylindrical gears. Tolerances.
- measurements Test work >>
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Rice. 78. Schematic diagram of the involventometer operation
with replaceable rolling discs
8.7. Line straightness and direction control
The control of the norms of completeness of contact lies in the fact that the gear being checked is mated with the measuring one, the side surfaces of the teeth of which are covered with a thin layer of paint (red lead, turnbull blue, Prussian blue). In the case of mutual single-profile running-in of wheels, traces of paint will remain on the side surfaces of the tested wheel, in the places where the profiles meet. These imprints are used to judge the quality of the contact line of the gear teeth and the direction of the tooth.
The straightness and direction of the contact line is controlled by a contactometer. The fit of the flank surfaces of the teeth of the mating wheels must be checked both along the height of the teeth and along their length.
The quality of contact of the mating teeth along their length for spur gears is established by controlling the straightness and parallelism of the direction of the generatrix teeth to the wheel axis. In helical gears, the fit of the mating surfaces of the teeth along their length is characterized by a helix error (deviation of the direction of the tooth from the required angle of inclination).
To control the straightness and direction of the contact line of helical gears, contactometers BV-1060 (GOST 5368-58) are used (Fig. 79). These devices are divided into overhead devices, designed to control only the straightness of the contact line without checking the direction of the tooth, and universal contactometers, designed to measure the contact line from straightness and a given direction.
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Rice. 79. Straightness control circuit
contact line
The measurement base of the device is the gear rim of the tested wheel 5, along the cavities of which the support prism 3 attached to the body of the device is installed, having the shape of a tooth of a straight-sided rack with a profile angle of 40°. The measuring tip of the device 2 with a straight measuring surface is connected to the slide 4 through a spring parallelogram. When measuring the straightness of the tooth, the sled of the device is moved by means of a rack and pinion along the controlled tooth, parallel to the reference prism, while the non-parallelism of the contact line causes the tip to shift, fixed by indicator 1.
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Rice. 80. Scheme for checking the contact line
When moving the carriage with the measuring tip along the flank of the tooth, errors in the direction of the contact line and deviations from straightness will cause the tip to vibrate in a direction perpendicular to the direction of movement of the carriage. These fluctuations are recorded by an indicator or sensor connected to the recorder.
8.8. Control of deviation of the direction of the tooth
Tooth direction error Fb cylindrical spur gears can be checked using any test fixture that provides the ability to move the measuring unit parallel to the axis of the centers.
The wheel to be checked is installed with its end face on the plane of the plate 2 (Fig. 81) with the tooth cavity resting on the tip 5, fixed on the slider 4. The slider 4 moves along the groove of the bracket 3. The measuring tip 9, which enters the same tooth cavity, is connected to the rotary lever 7 by means of two leaf springs 8. The springs create rigidity of the tip-lever system in the tangential direction and provide the possibility of some movement of the tip 9 relative to the lever in the axial plane, which reduces the measurement error. The lever 7 is placed on the axis 1 in the movable sleeve 10, which provides adjustment of the position of the lever in height. The dial indicator is fixed in the holder 6 on the sleeve 10 and is adjusted to zero using the reference wheel.
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Rice. 82. Device with a recorder to control the direction of the tooth of cylindrical gears
8.9. Monitoring deviations from parallelism and misalignment of the axes of the shafts
Deviations from parallelism and misalignment of the shaft axes are determined in linear units at a length equal to the working width of the gear wheel screw when designing the working axes of gear wheels on a plane x(non-parallelism of the axes fx) and on the plane y(axle misalignment fy) passing through one of the axes and perpendicular to the plane in which this axis lies.
8.10. Side clearance control
The side clearance is determined in a section perpendicular to the direction of the teeth, in a plane tangent to the main cylinders.
The minimum guaranteed gap is set by the standard jn min, the value of which does not depend on the degree of accuracy of the wheel, but is determined by the operating conditions of the transmission: speed, heating, lubrication.
Guaranteed lateral clearance in the gear is provided in the manufacture of gears by additional displacement of the gear-cutting tool to the center of the wheel being cut by EHS(Fig. 84 a)
8.11. Source Contour Offset Control
To determine the displacement of the initial contour of the gear rim of cylindrical spur and helical gears, tangential gear gauges are used. The principle of measuring this parameter with the help of gear gauges is based on the properties of the engagement of the gear wheel with the rack of the original contour. In this regard, the measuring planes of the tangential gear gauge are made in the form of a reference prism with an angle of 2a, that is, 40 °, formed by jaws 1 and 3 (Fig. 83).
Rice. 83. Scheme for measuring the displacement of the original
contour with a tangential gear gauge
The measurement base for tangential gear gauges is usually the circumference of the protrusions of the checked wheel, relative to which the position of the initial contour is determined.
To determine the value of the radial displacement of the original contour, the tangential gear gauge is equipped with indicator 2, the axis of which is the bisector of the angle of the prism. Since the side surfaces of the tangential gear gauge are the profile of the gear rack, then when the gear gauge is applied (after preliminary installation according to the sample) on the tooth of the wheel being checked, the contact points will be located on the engagement lines in the same way as when the rack is engaged with the wheel without backlash (Fig. 84, a, b).
Rice. 84. Tangential gear gauge GOST 4446-59:
a) measurement scheme; b) general view; c) tuning scheme
The tangential gear gauge (Fig. 84, c) consists of a body 4, to which a collet 5 is attached to install an indicator 6 with an elongated tip 8. Measuring jaws 1 and 2 of the device are driven by a common screw 3 with right and left threads. This makes it possible to move both jaws in opposite directions at the same time. The jaws are moved by turning the screw head. In the desired position, the jaws are fixed with stoppers.
The tangential gear gauge is a relative measuring device. The preliminary installation of the tangential gear gauge is carried out according to the installation pattern 7, which is usually used as calibrated rollers of a certain diameter.
When installing a tangential gear gauge on a roller, the diameter required for this dp roller is determined by the formula
, mm,
where kp- coefficient depending on .
For = 20° k= 1.2037. In this case dp = 1,2037m.
The diameter of the setting roller depends only on the module and the angle of the original contour, but does not depend on the number of teeth of the wheel being tested.
8.12. Tooth thickness control
Control of tooth thickness deviations by constant chord sc and tooth height to constant chord hc carried out by a tangential tooth gauge (Fig. 84, b). In this case, the jaws of the tangential gear gauge are adjusted to the nominal size of the tooth thickness along a constant chord, and the recording device is set to zero.
The shift of the indicator arrow during the measurement of the tooth from zero to the right (plus) indicates a decrease in thickness S the tooth to be checked DS(Fig. 85, a) and, conversely, the shift of the indicator arrow from zero to the left (to minus) indicates an increase in the thickness of the tooth (Fig. 85, b). When the indicator needle is set to zero division, the checked tooth thickness is equal to the nominal value (Fig. 85, c).
When measuring corrected gears with a tangential gear gauge, you can determine the displacement coefficient of the original contour:
where Dh- deviation of the tooth height from the constant chord;
m- module.
When measuring corrected gears with angular correction with a tangential gear meter, it is adjusted according to the installation samples (rollers or measuring wheels) intended for measuring uncorrected gears, but the gear meter readings should be corrected (the amount of reduction in the radius of the gear ledge circumference), for which the gear meter readings need to be reduced.
When measuring wheels with height correction, no correction is introduced, since for wheels with height correction, the radius of the circumference of the protrusions changes by an amount equal to the shift of the original contour of the cutting tool, since .
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Rice. 85. Indications of a tangential gear gauge:
a - when measuring thinned teeth;
b - when measuring thickened teeth;
c - when measuring normal theoretically accurate teeth
8.13. Parameter control of bevel gears
The kinematic error of bevel gears can be established using single-profile instruments, the principle of operation of which is the same as that of single-profile instruments for checking this indicator for cylindrical gears. In this case, the instantaneous gear ratios and movements of the driven link of the gear pair are continuously compared with those of the transmission with precise friction cones. The disadvantage of devices operating according to this scheme is the need to have accurate cones for each pair of controlled wheels in accordance with their gear ratio.
8.14. Accumulated circumferential pitch error control
bevel wheels
The accumulated error of the circumferential pitch of bevel wheels is the difference in circumferential pitches and the maximum deviations of this parameter can be determined using a special device (Fig. 86).
Checked gear wheel 1 is mounted on the support ring 2 and centered on it. For ease of rotation, a cage with balls is installed on top of the support ring. In the process of measurement, tips 3 and 5 are adjusted so that they do not touch the sides of the same name of two adjacent teeth of wheel 1 approximately in the middle part along the length of the tooth. The uniformity of the circumferential pitch is established when the gear wheel is rotated sequentially from one pair of teeth to another, carried out by the cam 4. The difference in any circumferential pitches is equal to the difference in the readings of the indicator associated with the movable tip 5.
The check on this device of the bevel gear shaft is carried out when fixed in the centers.
Rice. 86. Device for measuring the circumferential ball of conical
gear wheels
The circumferential pitch error control of bevel gears essentially replaces the control of the main engagement pitch, which cannot be checked for these gears due to the fact that the tooth flank of the bevel gears is not an involute.
8.15. Axial movement control of bevel gears
The axial movement of bevel gears in tight mesh can be detected using two-profile instruments (Fig. 87).
In this case, the controlled wheel is mated with the measuring one, in which the tooth thickness must be increased by the value of the average thinning provided for the wheel being tested, while a strict coincidence of the tops of the initial cones is necessary, since in this case the teeth will be in contact along their entire length, that is, there will be their full longitudinal contact is ensured.
Rice. 87. Checking the axial movement of conical
gears in a dense two-profile
engagement on the intercentromere
To be able to control the bevel wheels on two-profile devices (Fig. 87), a special bracket 5 is attached to them, which is mounted on the installation carriage of the device 6. The bracket has a vertical carriage 2 with a horizontal mandrel 1. The carriage 2 is moved by the handwheel 3. alignment of the wheels, determine the vibration of this carriage during the rotation of the wheels per revolution of the wheel and when the measured wheel is rotated by one tooth. The axial movement of one of the mating wheels in tight meshing is associated with the fluctuation of the measuring center angle by the following relationship:
,
where is the angle of the dividing cone of the gear or wheel (see Fig. 63).
8.16. Control of the radial runout of the gear
bevel wheel crown
The control of the radial runout of the gear screw of the bevel wheel is carried out by beaters (Fig. 88). The device consists of a base 6, on which a plate 8 is hinged. A mandrel 4 is fixed at the base of the device, on which the bevel wheel under test is fixed. Tip 3 is inserted into the cavities between the teeth along the average diameter of the bevel wheel (that is, in the middle of the tooth width), connected to the recording device 5. The position of the tip 3 can be adjusted by the location of the plate and the rack and pinion located in the guide 2 (having the shape of a dovetail).
As a measuring tip, to control the runout, cone and ball tips are used, similar to those used to control cylindrical gears.
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Rice. 88. Bienometer for bevel gears
To control the radial runout of the gear rim of bevel wheels, a special device is used (Fig. 89).
The device consists of a body 1 made in the form of a rectangular bar with a groove and a base prism. A movable frame 3 is installed on the rectangular bar of the body, in which the cracker 2 is fixed, which is included in the groove of the body 1. The dial indicator is fixed in the holder. fixed with screw 4.
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Rice. 89. Device for controlling the radial
ring gear beating
The device is supplied with a set of interchangeable tips 7, the dimensions of which are calculated depending on the wheel module. When checking the runout, the device is based on the diameter and the supporting end of the wheel being checked, and the measuring tip is alternately inserted into the cavity of the teeth. The bevel gear is fixed on the mandrel and mounted in the centers.
8.17. Checking the measuring side clearance of bevel wheels
The control of the measuring side clearance of the bevel wheels is carried out on control-running machines when the controlled wheel 2 is paired with the measuring wheel 1.
The measuring side clearance is determined using a dial indicator 3, mounted on the machine body. With the drive wheel stationary, the driven wheel is turned in both directions, determining the maximum deviation by the indicator (Fig. 90).
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In this lab, dependencies are given only for spur gears cut without displacement of the original contour and without modifications. The bevel gear belongs to the orthogonal gear.
Rice. 21.1. Measurement of tooth thickness along a constant chord
The thickness of the tooth is most often measured along a constant chord, which is a segment of a straight line connecting the points of contact of the ring gear with the original contour (rack) with backlash-free engagement (Fig. 21.1). The figure shows that the constant chord of the tooth = 2 BD. From DABC and DBCD follows that BD = BC cosa = AC cos 2 a, but AC = m p/4 , where m p is the gear rack pitch. Hence = 2 BD = 2AC cos 2 a = = m pcos 2 a /2.
The distance from the top of the teeth to the constant chord (measuring height) is calculated by the formula
= m– CD = m – 
.
With an engagement angle a = 20°, we obtain
1,38704m, = 0,74758m.
Therefore, the constant chord, as well as its distance to the tops of the teeth, depend only on the modulus and do not depend on the number of teeth. Because of this, the chord was called constant.
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Rice. 21.2. caliper
The caliper (Fig. 21.1) is a combination of a caliper with a caliper. To measure the thickness of the tooth along a constant chord, you must first install the support bar 5 to the calculated measuring height on the scales 1 and 2 , after which the gear gauge is installed on the tooth being checked so that the support bar rests on the top of the tooth, and the gear gauge itself is located perpendicular to the generatrix of the cylinder or cone of the wheel. In this position, measure the thickness of the tooth, counting the size on the scales 3 and 4 .
Measurement limits of the caliper in the modules of the measured teeth m= 1...35 mm, vernier reading - 0.02 mm.
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The nominal value of the tooth thickness and the measured height of the bevel gear, when measured at the outer end, is calculated by the above formulas, which use the external circumferential modulus m e
1,38704m e , = 0.74758 m e.
To measure the thickness of the tooth along the constant chord of cylindrical and bevel gears, caliper gauges or micrometric gear gauges are used.
Work order
1. Determine the gear module. To do this, measure the diameter of the tops of the teeth with a caliper. d a and counting the number of teeth z, determine the module by the formula m = d a /( z+ 2), rounding it up to the nearest standard value (Table A24 of Appendix 2).
3. Place the tooth gauge with a support bar on the top of the tooth of the wheel being measured and measure the thickness of three to five teeth in succession. Make sure that both measuring edges are in contact with the sides of the tooth; the support bar should not come off the surface.
4. Give a conclusion on the suitability of the tested gear, if it is made according to the degree of accuracy 9- FROM, 9-AT, 8-AT etc. according to GOST 1643-81. To do this, you need to find in the table. P22 and P21 of Appendix 2 smallest deviation of tooth thickness, tolerance for tooth thickness Tc and, having calculated the largest deviation of the tooth thickness 
, build a tabular tolerance field scheme.
Since when measuring the thickness of the tooth, the circle of the tops of the teeth, made with some errors, was used as a measuring base, calculate the production deviations and the tolerance for the thickness of the tooth, taking into account the tolerance for the diameter of the circle of the tops of the teeth, the upper es and lower ei its limiting deviations, as well as the tolerance for its radial runout TCR according to the formulas:
T C pr = T C – 0,73(Td a /2 + TCR)
ECS pr = ECS + 0,73(eid a /2 - TCR/2)
E CI pr = E Ci + 0,73(esd a /2 + TCR/2).
When calculating, assume that the circumference of the tops of the teeth is made as a shaft along h 8, and the radial runout of the circle of the vertices TCR- according to the 7th degree of accuracy (Table A17 of Appendix 2).
Rice. 21.3. Bevel Gear Parameters
5. Find the outer circumferential module of the bevel gear m e l Measure the diameter of the circumference of the protrusions with a vernier caliper d ae (Fig. 21.3) and, counting the number of teeth z 1 wheel to be tested and z 2 conjugated wheels, calculate the modulus by the formula
m e l = ,
where φ 1 is half the angle of the dividing cone of the tested wheel, 
. The resulting modulus is rounded up to the nearest standard value.
7. Place the gear gauge with a support bar on the protrusion cone of the wheel being checked perpendicular to its generatrix so that the measuring edges of the gear gauge touch the tooth at the intersection of the side surface of the tooth with the additional cone (largest diameter). Measure the thickness of five teeth and enter the measurement data in the table.
8. Give a conclusion on the suitability of the tested wheel, if it is performed according to the degree of accuracy 9-C, 9-B, etc. To do this, find the tabular values \u200b\u200b(Table P27 of Appendix 2) of the smallest deviation of the average constant chord of the tooth E SCS(always with a minus sign). According to the table P28 Appendix 2 find coefficient to 1 , calculate the ratio R e/R, where R e- external cone distance, calculated by the formula: 
, R– average cone distance R = R e - 0.5 b, b- the width of the bevel gear rim (must be measured with a caliper). According to the table P25 Appendix 2 to determine the tolerance for radial runout of the ring gear F r; find in the table. P26 Appendix 2 tolerance for the average permanent chord of the tooth TSC and increasing it in relation Re/R, determine the tabular tolerance for the thickness of the tooth.
Note: the above formulas refer to orthogonal bevel gears with straight teeth with the initial contour according to GOST 13754-68.
TSC pr = TSC – 0,73 ((Td e /2)cosj 1 + TCR),
E SCS pr = E SCS + 0,73 ((eid e /2)cosj 1 – TCR/2),
E SCI pr = E SCI + 0,73 ((esd e /2)cosj 1 + TCR/2).
Based on the obtained values, construct a tabular and production tolerance field, on which to plot the average value of the measured tooth thickness. Provide a statement of suitability.
9. Prepare a report on the work, according to the attached form.
Measurement protocol form
| Group No. | FULL NAME. | |||||||||||
| Job 21 | Measurement of tooth thickness with a chordal tooth gauge | |||||||||||
| Device data | Gear Data | |||||||||||
| Nonius reading, mm | Tooth tip diameter | = | ||||||||||
| Number of teeth | z= | |||||||||||
| Module | m = d a /( z + 2) = | |||||||||||
| Measurement limits, mm | Nominal tooth thickness | = 1,38704m = | ||||||||||
| measuring height | = 0,74758m = | |||||||||||
| Measurement scheme (Fig. 21.1) | For bevel wheel | |||||||||||
| Tooth tip diameter | d ae1 = | |||||||||||
| Number of teeth | z 1 = z 2 = | |||||||||||
| Module | m l = | |||||||||||
| Nominal tooth thickness | = | |||||||||||
| measuring height | = | |||||||||||
| Instrument readings, mm | ||||||||||||
| Cylindrical wheel | bevel wheel | |||||||||||
| average | average | |||||||||||
| T C = E CS= Td a = esd a = eid a = TCR = T ref = T C – 0,73 (Td a /2 + TCR) = E cs pr = E cs+0.73( eid a /2 - TCR/2) = E ci pr \u003d E ci + 0.73 ( esd a /2 + TCR/ 2) = | TSC = E SCS = Td e= esd e= eid e= TCR = TSC pr = TSC– 0,73 ((Td e /2)cosj 1 + TCR) = E SCS pr = E SCS+ 0,73 ((eid e /2)cosj 1 – TCR/2) = E SCI pr = E SCI + 0,73 ((esd e /2)cosj 1 + TCR/2)= | |||||||||||
| Layouts of the tabular and production fields of tolerances and conclusions on suitability | ||||||||||||
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