CN112254667A - Gear offset measurement method based on laser displacement sensor - Google Patents

Abstract

The invention discloses a gear offset measurement method based on a laser displacement sensor in the technical field of gear measurement. The gear to be tested drives the laser displacement sensor to move along the Z-axis guide rail to the position where the tooth profile is to be measured, sets the offset, drives the laser displacement sensor to move so that the laser beam directly hits the measured tooth profile; (3) drives the workpiece turntable along the The involute development direction of the unilateral tooth surface is reversed, and the displacement data of the projection point of the beam on the measured tooth profile relative to the central axis of the measured gear coordinate system is collected; (4) Set a new offset to make the laser displacement sensor offset to the gear. On the other side, rotate the workpiece turntable along the involute development direction of the tooth surface on the other side of the gear, and collect the displacement data of the projected point on the measured tooth profile; (5) Convert the displacement data of the two measurements into polar coordinates; use The invention has high measurement precision.

Description

A Gear Offset Measurement Method Based on Laser Displacement Sensor

technical field

The invention relates to a gear measurement method, in particular to a gear offset measurement method based on a laser displacement sensor.

Background technique

Gear measurement technology can be divided into two categories: contact measurement and non-contact measurement. At present, the contact type that records the three-dimensional coordinate position of the surface point of the shape by contacting the touch or scanning sensor probe with the surface of the geometric shape is widely used. Measurement method, this method is cumbersome to operate, has the problem of lateral resolution caused by the larger radius of the contact probe, and needs to plan the movement path of the probe in advance. Contact measurement can effectively measure spur gears, helical gears, etc., but when the contact probe probe measures the spiral gear, the contact surface is a curved surface, and the normal vector of the contact point is constantly changing, because the probe volume The existence of the contact point makes the theoretical contact point different from the actual contact point. It is difficult and expensive to compensate the position of the probe. At present, the non-contact measurement mainly uses the laser triangulation method. The measurement device includes a worktable. The worktable is provided with a workpiece turntable and a three-coordinate translation mechanism. The three-coordinate translation mechanism includes an X-axis guide fixed on the upper side of the worktable. The Y-axis guide rail is slidably connected to the Y-axis guide rail, the Z-axis guide rail is slidably connected to the Z-axis guide rail, the Z-axis guide rail is slidably connected to a carriage, and the carriage is connected to a rotatable laser displacement sensor. When the laser head and the center of the gear are always in a straight line, the distance from the measured point to the center of the gear can be obtained by measuring the distance between the laser head and the tooth surface. This method can directly measure complex gears such as spiral gears, and the operation is simple. However, in this over-center measurement method, when measuring the tooth surface, the angle between the normal vector of the tooth surface and the measuring laser beam is relatively large, and the laser beam cannot converge to a point on the tooth surface, but a large spot is formed, and the measurement result fluctuates. larger, the measurement accuracy is low.

SUMMARY OF THE INVENTION

In view of the defects in the prior art, the purpose of the present invention is to solve the technical problem of low measurement accuracy in the prior art, and to provide a gear offset measurement method based on a laser displacement sensor. The present invention can realize the measurement of complex gears. There is no fluctuation in the tooth surface data during the process, and the precision is good.

The purpose of the present invention is to achieve this: a gear offset measurement method based on a laser displacement sensor, the measurement device used in the measurement method includes a worktable, and the worktable is provided with a workpiece turntable and a three-coordinate translation mechanism, The three-coordinate translation mechanism includes an X-axis guide rail fixed on the upper side of the worktable, a Y-axis guide rail is slidably connected to the X-axis guide rail, and a Z-axis guide rail is slidably connected to the Y-axis guide rail. A lift frame is slidably connected to the Z-axis guide rail, a laser displacement sensor is connected to the lift frame, and a center positioning mandrel is vertically arranged on the workpiece turntable. The measurement method includes the following steps:

(1) Drive the laser displacement sensor to move along the X-axis, Y-axis, and Z-axis guide rails, and collect the outer circumference data of the center positioning mandrel to calibrate the position of the center axis of the measured gear;

(2) Install the gear to be measured on the central positioning mandrel, drive the laser displacement sensor to move along the Z-axis guide rail to the position where the tooth profile is to be measured, set the offset e, and drive the laser displacement sensor to move along the X-axis guide rail, Direct the laser beam emitted by the laser displacement sensor to the measured tooth profile;

(3) Drive the workpiece turntable to rotate at a constant speed in the opposite direction along the involute development direction of the unilateral tooth surface. The laser beam emitted by the laser displacement sensor is directed directly on the measured tooth profile in turn, and the collected beam is projected on the measured tooth profile. Relative measurement The displacement data of the central axis of the gear coordinate system;

(4) Set the offset amount 2e. By driving the laser displacement sensor to move along the X-axis guide rail, the laser displacement sensor is biased to the other side of the gear, and the workpiece turntable is rotated along the involute expansion direction of the tooth surface on the other side of the gear. The laser beam emitted by the displacement sensor is directed to the tooth profile of the measured gear in turn, and the displacement data of the projection point of the beam on the measured tooth profile relative to the central axis of the coordinate system of the measured gear is collected;

(5) Convert the displacement data of the two measurements into polar coordinates, and describe and fit the coordinate points of the tooth profile to determine the error of the measured tooth profile.

As a further improvement of the present invention, the three-coordinate translation mechanism is driven by a servo motor and the controller controls the laser displacement sensor to move along the X-axis guide rail, the Y-axis guide rail or the Z-axis guide rail, and a rotary drive device is provided at the bottom of the workpiece turntable.

In order to further realize the calibration of the coordinate system, in the step (1), the calibration method of the coordinate system is: drive the laser displacement sensor to move along the Z-axis guide rail to any suitable position on the center positioning mandrel through the servo motor, and fix the Y-axis and Z-axis Shaft guide, make the laser displacement sensor move from one side of the centering mandrel to the other side along the X-axis direction. During the recording process, the laser displacement sensor counts. When the beam approaches the center of the centering mandrel, the count first decreases. After increasing, the laser displacement sensor is driven to reciprocate along the X-axis guide rail for multiple comparisons, and the minimum number of indications just passes through the central axis of the central positioning mandrel.

In order to further realize the setting of the offset, in the step (2), the gear to be tested is installed on the central positioning mandrel, and the central positioning mandrel is fixed and rotated coaxially with the workpiece turntable through the chicken core chuck to drive the gear to be tested. Rotate coaxially with the workpiece turntable, adjust the Z height of the laser displacement sensor through the servo motor, so that the laser beam emitted by the laser displacement sensor hits the tooth surface, set the offset value e after calibration, and adjust the X-axis guide rail movement through the servo motor Make the laser displacement sensor at the offset position, and drive the servo motor through the controller to adjust the laser displacement sensor to move along the Y-axis guide rail to the surface of the gear, so that the measured tooth profile index circle is located at the standard range D of the laser displacement sensor. At this time, the laser displacement The displacement of the sensor indicates zero.

In order to further realize the collection of measurement data, in the step (3), it is stipulated that the involute unfolding direction of the measured gear is reversed to the rotation direction of the current measurement, and the rotary drive device drives the workpiece turntable to drive the measured gear to rotate, while the laser displacement sensor Project the laser beam onto the measured tooth profile, and collect the coordinate data relative to the position of the X-axis. Taking the center of the measured gear coordinate system as the pole, the collected data is the rotation of the measured gear with the pole as the center. The angle and the distance from the laser displacement sensor corresponding to the angle to the tooth surface.

In order to further set the reverse bias amount, in the step (4), the bias amount is set to be twice the unilateral bias amount in the step (2), specifically, the laser displacement sensor is driven along the X axis by the servo motor Offset in the other direction, go back to the calibration position before the offset through an offset laser beam, and reach a position with an offset relative to the X-axis of the measured gear coordinate system after two offsets. The tooth surface is the tooth surface of the other side of the gear, and it is stipulated that the involute development direction of the measured tooth surface on this side is reversed to the rotation direction of the current measurement.

以p_m为基准，p_m与X轴的夹角为arcos(e/r_m)，从p_m到p_n齿轮转过的角度为θ_n-θ_m，p_n与Y轴的夹角为arsin(e/r_n)，则p_m和p_n相对于齿轮坐标系的夹角θ＝arcos(e/r_m)+θ_n-θ_m+arsin(e/r_n)-π/2，令被测点p_m为初始点零点，p_n点为p_m点的下一个转换点，将p_m和p_n转化极坐标为p_m(r_m,0)，p_n(r_n,θ)，其中

θ＝arcos(e/r_m)+θ_n-θ_m+arsin(e/r_n)-π/2，转换下一个点时，令下一点为p_n+1，转换点p_n+1的极坐标公式为p_n+1(r_n+1,θ+θ₁)，其中，

θ₁＝arcos(e/r_n)+θ_n+1-θ_n+arsin(e/r_n+1)-π/2。In order to further realize the calculation of the coordinates of each measurement point, in the step (5), the conversion method of polar coordinates is specifically, taking any two points p _m and p _n , and the measured values of the two points are p _m (1 _{measurement m} , θ _m ), p _n (l _{measure n} , θ _n ), l _measure is the distance from the laser displacement sensor to the measured point on the tooth surface, l _{measure m} is the distance from the laser displacement sensor to the measured point p _m on the tooth surface, l _{measure n} is the distance from the laser displacement sensor to the measured point p _n on the tooth surface, θ _m is the angle reading of the point p _m corresponding to the angle encoder provided in the workpiece turntable when the laser displacement sensor measures the point p _m , and θ _n is the laser displacement sensor. When the displacement sensor measures point p _n , the angle reading of the point p _n corresponding to the angle encoder, the distance from the laser displacement sensor to the X axis is d, then the distance from the _measured point to the X axis is l=dl, and the offset value is e, the measurement results can be converted into polar coordinate formulas

Taking p _m as the benchmark, the angle between p _m and the X axis is arcos(e/r _m ), the angle that the gear rotates from p _m to p _n is θ _n -θ _m , and the angle between p _n and the Y axis is arsin(e/r _n ), then the angle between p _m and p _n relative to the gear coordinate system θ=arcos(e/r _m )+θ _n -θ _m +arsin(e/r _n )-π/2, Let the measured point p _m be the initial zero point, p _n be the next conversion point of p _m , convert p _m and p _n into polar coordinates p _m (r _m ,0), p _n (r _n ,θ ),in

θ=arcos(e/r _m )+θ _n -θ _m +arsin(e/r _n )-π/2, when converting the next point, let the next point be p _n+1 , the conversion point of p _n+1 is The polar coordinate formula is p _n+1 (r _n+1 ,θ+θ ₁ ), where,

θ ₁ =arcos(e/rn )+θ _{n +1} −θ _n +arsin(e/rn ₊₁ )−π/2.

Description of drawings

FIG. 1 is a three-dimensional structural diagram of the measuring device in the present invention.

FIG. 2 is a schematic diagram of the bias measurement in the present invention.

FIG. 3 is a schematic diagram of the reverse bias measurement in the present invention.

FIG. 4 is a schematic diagram of polar coordinate conversion in the present invention.

Among them, 1X-axis guide rail, 2 worktables, 3 rotary drive devices, 4 workpiece rotary tables, 5 lower centers, 6 core chucks, 7 center positioning mandrels, 8 tested gears, 9 fixed seats, 10 top centers, 11 laser Displacement sensor, 12Z-axis guide rail, 13 lifting frame, 14Y-axis guide rail.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings.

A gear offset measurement method based on a laser displacement sensor, the measurement device used in the measurement method comprises a worktable, and the worktable is provided with a workpiece turntable, a three-coordinate translation mechanism and a fixed seat, and the three-coordinate translation mechanism includes a fixed seat on the work table. The X-axis guide rail on the upper side of the table, the Y-axis guide rail is slidably connected to the X-axis guide rail, the Z-axis guide rail is slidably connected to the Y-axis guide rail, the Z-axis guide rail is slidably connected to a lifting frame, and the lifting frame is connected to the lifting frame. There is a laser displacement sensor, a center positioning mandrel is vertically arranged on the workpiece turntable, the three-coordinate translation mechanism is driven by a servo motor, and the laser displacement sensor is controlled by the controller to move along the X-axis guide rail, the Y-axis guide rail or the Z-axis guide rail, and the workpiece turntable The bottom is provided with a rotary drive device, the fixed seat is connected with an upper center that can be lifted up and down and protruded downward, and the upper side of the workpiece turntable is connected with a chicken core chuck and a lower center. The chicken core clamp clamps the center positioning mandrel and lowers the upper center , so that the center positioning mandrel is between the lower center and the upper center, and the upper and lower centers and the center positioning mandrel rotate with the workpiece turntable. The measurement method includes the following steps:

(1) Drive the laser displacement sensor to move along the X-axis, Y-axis, and Z-axis guide rails, and collect the outer circumference data of the center positioning mandrel to calibrate the position of the center axis of the measured gear;

(2) Install the gear to be measured on the central positioning mandrel, drive the laser displacement sensor to move along the Z-axis guide rail to the position where the tooth profile is to be measured, set the offset e, and drive the laser displacement sensor to move along the X-axis guide rail, Direct the laser beam emitted by the laser displacement sensor to the measured tooth profile;

(3) Drive the workpiece turntable to rotate at a constant speed in the opposite direction along the involute development direction of the unilateral tooth surface. The laser beam emitted by the laser displacement sensor is directed directly on the measured tooth profile in turn, and the collected beam is projected on the measured tooth profile. Relative measurement The displacement data of the central axis of the gear coordinate system;

(4) Set the offset amount 2e. By driving the laser displacement sensor to move along the X-axis guide rail, the laser displacement sensor is biased to the other side of the gear, and the workpiece turntable is rotated along the involute expansion direction of the tooth surface on the other side of the gear. The laser beam emitted by the displacement sensor is directed to the tooth profile of the measured gear in turn, and the displacement data of the projection point of the beam on the measured tooth profile relative to the central axis of the coordinate system of the measured gear is collected;

(5) Convert the displacement data of the two measurements into polar coordinates, and describe and fit the coordinate points of the tooth profile to determine the error of the measured tooth profile.

In order to further realize the calibration of the coordinate system, in step (1), the calibration method of the coordinate system is: drive the laser displacement sensor to move along the Z-axis guide rail to any suitable position on the central positioning mandrel through the servo motor, and fix the Y-axis and Z-axis guide rails. , make the laser displacement sensor move from one side of the centering mandrel to the other side along the X-axis direction. During the recording process, the laser displacement sensor counts. When the beam approaches the center of the centering mandrel, the count first decreases and then increases. Large, by driving the laser displacement sensor to reciprocate along the X-axis guide rail for multiple comparisons, the minimum number of indications just passes through the central axis of the central positioning mandrel.

In order to further realize the setting of the offset, in step (2), the gear to be tested is installed on the central positioning mandrel, and the central positioning mandrel rotates fixedly and coaxially with the workpiece turntable through the core chuck to drive the gear to be tested and the workpiece. The rotary table rotates coaxially, adjust the Z-direction height of the laser displacement sensor through the servo motor, so that the laser beam emitted by the laser displacement sensor hits the tooth surface, set the offset value e after calibration, and adjust the X-axis guide rail movement through the servo motor to make the laser The displacement sensor is located in the offset position, and the controller drives the servo motor to adjust the laser displacement sensor to move along the Y-axis guide rail to move closer to the gear surface, so that the measured tooth profile index circle is located at the standard range D of the laser displacement sensor. The displacement indicator is zero.

In order to further realize the collection of measurement data, in step (3), it is stipulated that the involute unfolding direction of the measured gear is reversed to the rotation direction of the current measurement, and the rotary drive device drives the workpiece turntable to drive the measured gear to rotate. The beam is projected onto the measured tooth profile, and the coordinate data of displacement relative to the X-axis position is collected. Taking the center of the measured gear coordinate system as the pole, the collected data is the angle and the rotation angle of the measured gear as the center. This angle corresponds to the distance from the laser displacement sensor to the tooth surface.

In order to further set the reverse bias amount, in step (4), set the bias amount to be twice the one-sided bias amount in step (2), specifically, drive the laser displacement sensor along the X-axis through the servo motor. Offset in one direction, the laser beam returns to the calibration position before the offset through an offset, and reaches a position with an offset relative to the X-axis of the measured gear coordinate system after two offsets. At this time, the measured tooth surface It is the tooth surface of the other side of the gear, and it is stipulated that the involute development direction of the measured tooth surface on this side is reversed to the rotation direction of the current measurement.

以p_m为基准，p_m与X轴的夹角为arcos(e/r_m)，从p_m到p_n齿轮转过的角度为θ_n-θ_m， p_n与Y轴的夹角为arsin(e/r_n)，则p_m和p_n相对于齿轮坐标系的夹角θ＝arcos(e/r_m)+θ_n-θ_m+arsin(e/r_n)-π/2，令被测点p_m为初始点零点，p_n点为p_m点的下一个转换点，将p_m和p_n转化极坐标为p_m(r_m,0)，p_n(r_n,θ)，其中

θ＝arcos(e/r_m)+θ_n-θ_m+arsin(e/r_n)-π/2，转换下一个点时，令下一点为p_n+1，转换点p_n+1的极坐标公式为p_n+1(r_n+1,θ+θ₁)， p_n点后的下i个转换点的极坐标公式为

其中，

θ₁＝arcos(e/r_n)+θ_n+1-θ_n+arsin(e/r_n+1)-π/2，θ_j＝arcos(e/r_n+j-1)+θ_n+j-θ_n+j-1+arsin(e/r_n+j)-π/2，j≥1且为整数；θ_n+1为激光位移传感器测量点p_n+1时角度编码器所对应的点p_n+1的角度读数。In order to further realize the calculation of the coordinates of each measurement point, in step (5), the conversion method of polar coordinates is as follows: take any two points p _m and p _n , and the measurement values of the two points are p _m (1 _{measurement m} , θ _m ) , p _n (l _{measure n} , θ _n ), l _measure is the distance from the laser displacement sensor to the measured point on the tooth surface, l _{measure m} is the distance from the laser displacement sensor to the measured point p _m on the tooth surface, l _{measure n} is the laser The distance from the displacement sensor to the measured point p _n on the tooth surface, θ _m is the angle reading of the point p _m corresponding to the angle encoder provided in the workpiece turntable when the laser displacement sensor measures the point p _m , and θ _n is the laser displacement sensor When measuring point p _n , the angle reading of the point p _n corresponding to the angle encoder, the distance from the laser displacement sensor to the X axis is d, then the distance from the _measured point to the X axis is l=dl, and the offset value is e, Measurement results can be converted into polar coordinate formulas

Taking p _m as the benchmark, the angle between p _m and the X axis is arcos(e/r _m ), the angle that the gear rotates from p _m to p _n is θ _n -θ _m , and the angle between p _n and the Y axis is arsin(e/r _n ), then the angle between p _m and p _n relative to the gear coordinate system θ=arcos(e/r _m )+θ _n -θ _m +arsin(e/r _n )-π/2, Let the measured point p _m be the initial zero point, p _n be the next conversion point of p _m , convert p _m and p _n into polar coordinates p _m (r _m ,0), p _n (r _n ,θ ),in

θ=arcos(e/r _m )+θ _n -θ _m +arsin(e/r _n )-π/2, when converting the next point, let the next point be p _n+1 , the conversion point of p _n+1 is The polar coordinate formula is p _n+1 (r _n+1 ,θ+θ ₁ ), and the polar coordinate formula of the next i conversion points after the p _n point is

in,

θ ₁ =arcos(e/r _n )+θ _n+1 -θ _n +arsin(e/r _n+1 )-π/2, θ _j =arcos(e/r _n+j-1 )+θ _{n +j} -θ _{n+j-1 +} arsin(e/r _{n +j} )-π/2, j≥1 and is an integer; The angle reading of the corresponding point p _n+1 .

In the present invention, the position of the spot image is measured by the laser displacement sensor, the angle of the chief ray is calculated, and the position parameter at the point on the surface of the object is calculated. Through the method of the present invention, the clamping between the laser beam and the normal direction of the tooth surface can be improved. The angle of the laser beam on the tooth surface converges to a point, which improves the problem that the measurement laser beam passing through the center of the gear cannot converge to a point at the steeper tooth surface, resulting in the fluctuation of the measurement data, which can realize the measurement of complex gears. , There is no fluctuation in the tooth surface data during the measurement process, and the accuracy is good; it can be used in the measurement of various gears.

The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some of the technical features according to the disclosed technical contents without creative work. Modifications, replacements and modifications are all within the protection scope of the present invention.

Claims (7)

1. A gear offset measurement method based on a laser displacement sensor is characterized in that a laser displacement sensor is connected to a lifting frame, and the measurement method comprises the following steps,

(1) driving a laser displacement sensor to move along guide rails of an X axis, a Y axis and a Z axis, and collecting peripheral data of the outer circumference of a central positioning mandrel to calibrate the position of a central shaft of a gear to be measured;

(2) mounting a gear to be measured on a central positioning mandrel, driving a laser displacement sensor to move to a position where the tooth profile is to be measured along a Z-axis guide rail, setting an offset e, and driving the laser displacement sensor to move along an X-axis guide rail to enable a laser beam emitted by the laser displacement sensor to be directly emitted to the tooth profile to be measured;

(3) driving a workpiece rotating table to rotate reversely at a constant speed along the unfolding direction of the unilateral tooth surface involute, and acquiring displacement data of a projection point of a light beam on a measured tooth profile relative to a central shaft of a measuring gear coordinate system;

(4) setting an offset 2e, driving a laser displacement sensor to move along an X-axis guide rail, so that the laser displacement sensor is offset to the other side of the gear, rotating a workpiece rotary table along the tooth surface involute unfolding direction on the other side of the gear, sequentially and directly irradiating laser beams emitted by the laser displacement sensor onto the tooth profile of the measured gear, and collecting displacement data of a projection point of the laser beams on the measured tooth profile relative to a central axis of a measuring gear coordinate system;

(5) and converting the displacement data measured twice into polar coordinates, and fitting the coordinate point description of the tooth profile to judge the error of the measured tooth profile.

2. The gear offset measurement method based on the laser displacement sensor as claimed in claim 1, wherein the three-coordinate translation mechanism is driven by a servo motor and controls the laser displacement sensor to move along an X-axis guide rail, a Y-axis guide rail or a Z-axis guide rail through a controller, and a rotary driving device is arranged at the bottom of the workpiece rotary table.

3. The gear offset measurement method based on the laser displacement sensor as claimed in claim 2, wherein in the step (1), the calibration method of the coordinate system is: the laser displacement sensor is driven by a servo motor to move to any proper position on the central positioning mandrel along the Z-axis guide rail, the Y-axis guide rail and the Z-axis guide rail are fixed, the laser displacement sensor is made to move from one side of the central positioning mandrel to the other side along the X-axis direction, the readings of the laser displacement sensor are recorded in the process, when a light beam is close to the center of the central positioning mandrel, the readings are increased after being reduced firstly, multiple comparisons are carried out by driving the laser displacement sensor to reciprocate along the X-axis guide rail, and the minimum position of the readings just passes through the central axis of the central positioning mandrel.

4. The gear offset measuring method based on the laser displacement sensor as claimed in claim 2, it is characterized in that in the step (2), the gear to be measured is arranged on a central positioning mandrel, the central positioning mandrel is fixed and coaxially rotates with the workpiece rotary table through a chicken heart chuck to drive the gear to be measured and the workpiece rotary table to coaxially rotate, the Z-direction height of the laser displacement sensor is adjusted through a servo motor, so that a laser beam emitted by the laser displacement sensor is irradiated on the tooth surface, a bias value e is set after calibration, the servo motor is driven to drive the servo motor to adjust the laser displacement sensor to move along the Y-axis guide rail to be close to the surface of the gear, so that the measured tooth profile reference circle is located at the standard measuring range D of the laser displacement sensor, and the displacement reading of the laser displacement sensor is zero at the moment.

5. The gear offset measurement method based on the laser displacement sensor as claimed in claim 2, wherein in the step (3), the involute expansion direction of the measured gear is defined to be opposite to the currently measured rotation direction, the rotation driving device drives the workpiece turntable to drive the measured gear to rotate, meanwhile, the laser displacement sensor projects a laser beam onto the measured tooth profile, and the data of the position displacement coordinate relative to the X axis is collected, wherein the center of the coordinate system of the measured gear is taken as a pole, and the collected data are the angle rotated by taking the measured gear as the pole as the center and the distance from the laser displacement sensor corresponding to the angle to the tooth surface.

6. The gear offset measurement method based on the laser displacement sensor as claimed in claim 2, wherein in the step (4), the offset is set to be twice of the offset of the single side in the step (2), specifically, the laser displacement sensor is driven by the servo motor to be offset along the other direction of the X axis, the laser beam returns to a calibration position before the offset through one offset, and reaches a position of one offset relative to the X axis of the measured gear coordinate system through two offsets, at this time, the measured tooth surface is the tooth surface of the other side of the gear, and it is specified that the involute expansion direction of the measured tooth surface of the side is reversed to the currently measured revolution direction.

7. The method for measuring gear offset based on the laser displacement sensor according to any one of claims 1 to 6, wherein in the step (5), the polar coordinate is converted by taking any two points p_mAnd p_nTwo points of measurement are p_m(l_{M measurement},θ_m)，p_n(l_{Measure n},θ_n)，l_MeasuringThe distance from the laser displacement sensor to the measured point of the tooth surface, l_{M measurement}For the laser displacement sensor to the measured point p of the tooth surface_mA distance of l_{Measure n}For the laser displacement sensor to the measured point p of the tooth surface_nA distance of (a), theta_mFor measuring point p of laser displacement sensor_mThe point p corresponding to the angle encoder arranged in the time workpiece rotary table_mAngle reading of theta_nFor measuring point p of laser displacement sensor_nPoint p corresponding to time angle encoder_nThe distance from the laser displacement sensor to the X axis is d, and the distance from the measured point to the X axis is d-l_MeasuringThe offset value is e, and the measurement result can be converted into a polar coordinate formula

With p_mAs a reference, p_mThe angle between the X axis and the arc cos (e/r)_m) From p_mTo p_nThe angle of rotation of the gear is theta_n-θ_m，p_nThe included angle between the Y axis and the Y axis is arsin (e/r)_n) Then p is_mAnd p_nAngle theta with respect to gear coordinate system being arccos (e/r)_m)+θ_n-θ_m+arsin(e/r_n) - π/2, let the measured point p_mAt the initial point zero point, p_nPoint is p_mNext point of conversion of point, p_mAnd p_nConversion of polar coordinate to p_m(r_m,0)，p_n(r_nθ) of which

θ＝arcos(e/r_m)+θ_n-θ_m+arsin(e/r_n) -pi/2, when converting the next point, let the next point be p_n+1Conversion point p_n+1Has the polar coordinate formula of p_n+1(r_n+1,θ+θ₁) Wherein

θ₁＝arcos(e/r_n)+θ_n+1-θ_n+arsin(e/r_n+1)-π/2。

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