Method for measuring any pitch deviation based on line structured light

Abstract

The invention discloses a method for measuring any pitch deviation based on linear structured light, and belongs to the field of precision testing technology and instrument and gear non-contact measurement. The method comprises the following steps: establishing a three-dimensional model of a tooth surface of a measured gear, collecting actual tooth pitch measurement points by using a line structure optical probe, reversely solving a geometric center according to the actual tooth pitch measurement points, solving tooth pitch deviation evaluation points based on a Newton interpolation principle, and solving any tooth pitch deviation according to the evaluation points. According to the method, the Newton cubic interpolation principle is innovatively adopted, the problem of measurement precision caused by uneven data acquisition points is solved, the accuracy of tooth pitch deviation calculation is improved, large sample data measured by the line structured light is fully utilized, any tooth pitch deviation of the tooth surface of the complete gear is represented in a 3D representation mode, and the accuracy of tooth pitch deviation calculation is improved. And the gear quality can be reflected more effectively.

Description

Technical Field

[0001] The invention relates to an arbitrary pitch deviation measurement method based on line structured light, and belongs to the field of precision testing technology and instruments, and gear non-contact measurement. Background Art

[0002] With the rapid development of new energy vehicles in recent years, new energy vehicles have higher and higher requirements for indicators such as noise and vibration, and the evaluation of gear performance has become more stringent. As an important indicator for gear performance evaluation, pitch deviation directly affects the performance of gear transmission, so it has become one of the must-check items for gear precision detection. According to different evaluation methods, the measurement method of pitch deviation can be divided into relative measurement method and absolute measurement method.

[0003] The relative measurement method uses any pitch of the tooth surface on the same side of the gear as the relative reference, measures the remaining pitches on the circumference of the tooth surface on the same side of the gear in sequence, and compares the measurement results with the relative reference to obtain the pitch deviation of each tooth. The absolute measurement method directly measures the pitch angle or actual arc length of two adjacent teeth on the same side of the gear at the pitch circle. The pitch angle is first converted into the actual arc length through a formula, and then subtracted from the nominal arc length to obtain the pitch deviation. Whether it is the relative measurement method or the absolute measurement method, the technology for measuring gear pitch deviation is relatively mature, but there are still shortcomings.

[0004] The current pitch deviation measurement methods have the following shortcomings: 1. The collected gear data is not fully utilized. The existing gear accuracy standards ISO 1328-1:2013 and GB 10095.1-2022 both select a point on the circumference of the same axis of the gear near the middle of the tooth height of the same side of the gear to calculate and evaluate the pitch deviation. Patent CN202010520395.3 proposes a method for evaluating pitch deviation and tooth profile deviation in visual measurement of small modulus gears, which evaluates the pitch deviation of small modulus gears according to standard ISO1328-1:2013. 2. The applicability is not high, and the accuracy of pitch deviation measurement is easily affected by the uniformity and number of collected data points. Patent CN201711007555.9 measures pitch deviation based on line structured light. When selecting the actual evaluation point, the tooth profile data of the gear coordinate system is matched with the measurement circle radius, but when the data points are uneven or the number is small, there may be no matching actual evaluation points on the measurement circle. 3. There are fewer evaluation points for pitch deviation, and the entire gear is evaluated at the points on the pitch circle, which cannot truly reflect the quality of the complete tooth surface. Patent CN201910804104.0 uses a roughness profiler to measure the gear pitch deviation, and only selects the pitch deviation angle at the pitch circle to calculate the pitch deviation. 4. The pitch measurement using line structured light does not consider the influence of eccentricity error. In actual pitch deviation measurement, eccentricity error based on line structured light is unavoidable, and related patents such as patent CN201711007555.9 do not consider the eccentricity error factor.

[0005] In order to overcome the above problems, the present invention discloses a method for measuring arbitrary pitch deviation based on line structured light. When selecting the actual evaluation point of the pitch deviation, the Newton cubic interpolation principle is innovatively adopted, and the four adjacent tooth profile data collection points closest to the measuring circle are selected on each tooth profile curve as Newton interpolation interval points, so as to more accurately calculate the evaluation point of the pitch deviation. This method can effectively reduce the problem of poor accuracy of line structured light pitch deviation evaluation caused by the fact that the collected data are not on the same measuring circle. When calculating the pitch deviation, the actual pitch geometric center is corrected according to the precise solution of the gear geometric center based on the actual measurement point of the pitch. At the same time, since the line structured light measurement of the pitch deviation has the characteristics of large samples and dense points, any measuring circle on the same side tooth profile can be calculated by Newton interpolation, which can not only realize the calculation of arbitrary gear pitch deviation, but also make full use of the collected point cloud data. Summary of the invention

[0006] In view of the problems existing in the existing gear pitch deviation measurement, the present invention provides an arbitrary pitch deviation measurement method based on line structured light, which can realize the calculation of any single pitch deviation, single pitch deviation, any pitch cumulative deviation and total pitch cumulative deviation at any measuring circle on adjacent same-side tooth profiles of different cross-sections of the gear, and innovatively uses the Newton interpolation principle to calculate the actual evaluation point of the pitch deviation, thereby improving the accuracy of the calculation of arbitrary pitch deviation.

[0007] The technical solution adopted by the present invention is a method for measuring arbitrary tooth pitch deviation based on line structured light, which comprises the following steps:

[0008] Step 1: Create a 3D model of the gear tooth surface to be tested

[0009] First, according to the gear involute property, a fixed gear coordinate system ε1 = [O1, X1, Y1, Z1] is established, O1 is the origin of the gear coordinate system, Z1 is the rotation axis, and D1 (x d1 ,y d1 ,z d1 ) is any point on the gear tooth surface to be measured, then the involute equation of the left tooth surface where point D1 is located can be expressed as:

[0010]

[0011] Among them, r b is the base circle radius of the gear being measured, μ1 is the rolling angle of the left tooth surface involute, α1 is the pressure angle of the left tooth surface involute, ζ1 is the expansion angle of the left tooth surface involute, z d1 is the axial height of the tooth surface point D1 in the gear coordinate system, e x2 is the value of the geometric center of the gear on the X1 axis after eccentricity, e y2 is the value of the geometric center of the gear on the Y1 axis after eccentricity. Theoretically, when the gear three-dimensional model has no eccentricity, e x2 and e y2 The value of is 0, and the geometric center is the origin O1 of the gear coordinate system.

[0012] Similarly, establish another fixed gear coordinate system ε2 = [O2, X2, Y2, Z2], O2 is the origin of the gear coordinate system, Z2 is the rotation axis, let D2 (x d2 ,y d2 ,z d2 ) is any point on the gear tooth surface to be measured, then the involute equation of the right tooth surface where point D2 is located can be expressed as:

[0013]

[0014] Among them, μ2=α2+ζ2, μ2 is the rolling angle of the right tooth surface involute, α2 is the pressure angle of the right tooth surface involute, ζ1 is the expansion angle of the right tooth surface involute, z d2 is the axial height of the tooth surface point D2 in the gear coordinate system, e x2 is the value of the geometric center of the gear on the X2 axis after eccentricity, e y2 is the value of the geometric center of the gear on the Y2 axis after eccentricity. Theoretically, when the gear three-dimensional model has no eccentricity, e x2 and e y2 The values ​​of are all 0, and the geometric center is the origin of the gear coordinate system O2. The complete three-dimensional model of the left and right tooth surfaces of the gear can be obtained by equations (1) and (2).

[0015] Step 2: Collect actual pitch measurement points based on line structured light probe

[0016] First, reset the line structured light measurement platform and preheat the probe. In order to achieve accurate measurement of gear pitch deviation, add linear gratings on the X-axis, Y-axis and Z-axis respectively, and add circular gratings on the C-axis. Initially, reset the X-axis, Y-axis, Z-axis and C-axis to the zero position of the grating. Next, adjust the X-axis so that the light beam emitted by the line structured light probe is aligned with the center of the gear shaft; adjust the Y-axis so that the line structured light probe is within the measurable range; adjust the Z-axis so that the light beam emitted by the line structured light probe covers the tooth width and height range. Then, the gear to be measured is coaxially fixed on the rotating table, and the rotating table drives the gear to be measured to rotate, while triggering the line structured light probe to start measuring the right tooth surface of the gear. After completing the full-circle measurement, adjust the position of the line structured light probe in the X-axis direction, and repeat the above steps to measure the left tooth surface of the gear. After completing the measurement of the entire gear tooth surface, it is necessary to convert the tooth surface information of the measured gear from the line structured light probe coordinate system to the gear coordinate system. The steps of coordinate conversion are as follows:

[0017] Establish four coordinate systems: platform coordinate system ε0 = [O0, X0, Y0, Z0], line structured light probe coordinate system ε s =[O s ,X s ,Y s ,Z s ], light plane coordinate system ε of line structured light l =[O l ,X l ,Y l ,Z l ] and the gear coordinate system ε g =[O g ,X g ,Y g ,Z g ].

[0018] First, according to the measurement principle of line structured light, the tooth surface information of the gear being measured can be expressed in the light plane coordinate system of line structured light as follows:

[0019] Q l =(x l ,0,z l ) (3)

[0020] Similarly, the tooth surface information of the gear being measured can be expressed in the online structured light probe coordinate system as follows:

[0021]

[0022] Among them, Q s =(x s ,y s ,z s ), h0 is the nominal distance of the line structured light probe.

[0023] According to the mapping relationship between the line structured light probe coordinate system and the optical plane coordinate system, the tooth surface information Q l Convert to the platform coordinate system.

[0024]

[0025] in, are the rotation angles of the line structured light probe coordinate system around the X0 axis, Y0 axis and Z0 axis of the platform coordinate system, a0, b0, c0 are the offset distances between the structured light probe coordinate system and the X0 axis, Y0 axis, and Z0 axis of the platform coordinate system, respectively.

[0026] Finally, the tooth surface information Q0 of the measured gear transformed into the platform coordinate system is transformed into the gear coordinate system.

[0027]

[0028] in, Δθ is the angle that the turntable rotates when the linear structure probe is sampling. Finally, the actual tooth pitch measurement point Q is obtained. g (x g ,y g ,z g ).

[0029] Step 3: Reverse the geometric center based on the actual pitch measurement point

[0030] Due to the existence of various errors such as artificial installation error and workpiece processing error, the actual pitch measurement point will introduce the influence of eccentricity error, making the geometric center O2 (e x2 , e y2) is offset, in order to reduce the gear geometric center O2 (e x2 , e y2 ) The influence of the offset on the accuracy of the pitch deviation is established according to the relationship between the two adjacent points of the tooth profile on the same side of the measuring circle and the center of the base circle, and the following equation is established for solution:

[0031]

[0032] Where i is the number of any pitch measurement points, is the difference between the circumferential angle of the starting point of the involute where any two adjacent points of the tooth profile on the same side are located and the mean value of the circumferential angle, is the average of the circumferential angles of the starting points of the involutes of two adjacent points on the same side of the tooth profile, z is the number of teeth. It can be obtained by the following formula:

[0033]

[0034] Among them, λ i Pitch measurement point D i (x i ,y i ) corresponds to the circumferential angle, λ i+1 Pitch measurement point D i+1 (x i+1 ,y i+1 ) corresponds to the circumference angle, the specific formula is as follows:

[0035]

[0036]

[0037] Among them, r b is the base circle radius, ξ i Pitch measurement point D i (x i ,y i ) corresponds to the expansion angle, ξ i+1 Pitch measurement point D i+1 (x i+1 ,y i+1 ) corresponds to the expansion angle, α i is the tooth pitch evaluation point D i (x i ,y i ) corresponds to the pressure angle, α i+1 Pitch measurement point D i+1 (x i+1 ,y i+1 ) corresponds to the pressure angle.

[0038] Finally, the Gauss-Newton iteration method is used to solve equation (8) to obtain the geometric center O2 (ex2 , e y2 ).

[0039] Step 4: Solve the pitch deviation evaluation point based on Newton interpolation principle

[0040] Get the geometric center O2(e x2 , e y2 ), it is necessary to calculate any single pitch deviation. The usual method is to find the coordinates of the intersection between the gear measurement circle and the actual tooth profile curve. However, the tooth profile curve composed of the point cloud data obtained by actual measurement may not have an evaluation point on the measurement circle, which will lead to the problem of low pitch measurement accuracy based on line structured light.

[0041] Therefore, before solving the pitch deviation, the Newton cubic interpolation principle is used to select four adjacent tooth profile data collection points (x0, y0), (x1, y1), (x2, y2), and (x3, y3) on each tooth profile curve that are closest to the theoretical measurement circle as Newton interpolation interval points. The four selected data points are subjected to Newton cubic interpolation, and the polynomial equation obtained after interpolation is taken as the actual tooth profile curve equation, which can simplify the calculation process of the pitch deviation. The derivation process of Newton cubic interpolation method is as follows:

[0042] Newton interpolation polynomial N n (x) can be expressed as:

[0043]

[0044] Among them, f[x0,x1] is the first-order difference quotient:

[0045]

[0046] f[x0,x1,x2] is the second-order difference quotient:

[0047]

[0048] f[x0,x1,x2,x3] is the third-order difference quotient:

[0049]

[0050] Among them, f(x0)=y0, f(x1)=y1, f(x2)=y2, f(x3)=y3.

[0051] Substituting formulas (14), (15), and (16) into formula (13) can solve the cubic polynomial equation of Newton interpolation, and then obtain the actual curve equation of the tooth profile of the measuring circle N3(x):

[0052]

[0053] The equation of an arbitrary measured circle is as follows:

[0054] x i 2 +y i 2 =r t 2 (18)

[0055] Among them, r t is the radius of any measured circle.

[0056] The actual curve expression of the tooth profile on any cross section of the gear is obtained by Newton's cubic interpolation (17), and the nonlinear equation group is solved by the measurement circle equation (18) to obtain the intersection point P of the actual tooth profile curve at any measurement circle. i (x i ,y i ), intersection point P i (x i ,y i ) is the evaluation point of pitch deviation.

[0057] Step 5: Solve any pitch deviation based on the evaluation point

[0058] Substitute any two adjacent evaluation points P1(x1, y1) and P2(x2, y2) on the same side of the tooth surface into formula (19) to solve any single pitch deviation f pi :

[0059] 1) Any single pitch deviation f pi :

[0060]

[0061] Among them, the physical meaning of z is the number of teeth.

[0062] 2) Single tooth pitch deviation f p :

[0063] f p =max|f pi | (20)

[0064] Among them, f p For any single pitch deviation f pi The maximum absolute value of .

[0065] 3) Cumulative deviation of any tooth pitch F pi :

[0066]

[0067] Among them, F piIt is the algebraic difference between the arc length of n adjacent pitches and the theoretical arc length, where n ranges from 1 to z. Since the arccosine function cannot be calculated when the pitch angle is equal to π, the cumulative deviation F for any pitch is pi Perform segmented calculations.

[0068] 4) Cumulative total deviation of tooth pitch F p

[0069] F p =F pi,max -F pi,min (twenty two)

[0070] Among them, F p It is defined as the cumulative deviation F of any pitch of a given tooth surface of all teeth of the gear. pi The maximum algebraic difference of .

[0071] Similarly, any single pitch deviation f of any measuring circle of any gear section pi , single pitch deviation f p , any pitch cumulative deviation F pi Total cumulative deviation of tooth pitch F p The above methods can be used for calculation.

[0072] Step 6: Create a 3D representation of any pitch deviation

[0073] Pitch deviation can be characterized from 1D, 2D and 3D levels. When characterizing pitch deviation, existing gear accuracy standards usually characterize it at the 1D level by selecting points on the pitch circle of the gear tooth surface on the same side. Characterizing pitch deviation with only a very small part of the data will be very sensitive to random errors, resulting in inaccurate characterization results. At the 2D level, multiple sections are selected in the tooth width direction for characterization, but even on one section, there will be obvious differences in pitch deviations at different measuring circles. The method of the present invention is to characterize the pitch deviation at the 3D level. First, the actual measurement points of the pitch deviation of a large sample of the gear under test are obtained by line structured light, and then the geometric center is inversely calculated using the actual measurement points of the pitch deviation, and then the eccentricity error of the pitch measurement point is corrected, and then the tooth profile curve equation corresponding to the measurement points at different measuring circles of the gear is calculated using the Newton interpolation principle. The obtained tooth profile curve equation is combined with the equation of any measuring circle to obtain the evaluation point of any pitch deviation. Through these evaluation points, any single pitch deviation f of each gear tooth at any measuring circle can be calculated. pi Finally, any single pitch deviation f pi The results are presented in 3D. Similarly, any single pitch deviation f of any section in the tooth width direction pi The above method can also be used for 3D characterization.

[0074] In addition, other evaluation indicators of pitch deviation are single pitch deviation f p , any pitch cumulative deviation F pi Total cumulative deviation of tooth pitch F p This method can be used for assessment.

[0075] The method for measuring arbitrary tooth pitch deviation based on line structured light of the present invention has the following advantages:

[0076] 1. It is proposed to use the actual pitch measurement point to accurately solve the gear geometric center and correct the actual pitch geometric center, so as to approximately eliminate the influence of eccentricity error on the pitch measurement point.

[0077] 2. The present invention adopts Newton interpolation principle to calculate the actual evaluation point of any pitch deviation, which is not easily affected by the fact that the collected data are not in the same measuring circle and has high accuracy.

[0078] 3. Make full use of the large sample data collected by the line structured light probe, supplement it on the basis of the existing gear accuracy standards, characterize the gear error in the form of arbitrary pitch deviation, and effectively reflect the overall quality of the gear.

[0079] 4. A 3D error characterization of pitch deviation was established, which supplemented the missing three-dimensional evaluation indicators in the existing gear accuracy standards. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 Structural diagram of the line structured light measurement platform

[0081] Figure 2 3D model of the left tooth surface of the gear

[0082] Figure 3 3D model of right tooth surface of gear

[0083] Figure 4 Coordinate transformation diagram of measured tooth surface information

[0084] Figure 5 Reverse geometric center model diagram based on actual tooth pitch measurement points

[0085] Figure 6 Schematic diagram of tooth profile curve equation for the pitch deviation evaluation point based on Newton interpolation principle

[0086] Figure 7 3D representation of any single pitch deviation of any measuring circle on the left tooth surface with eccentricity error

[0087] Figure 8 3D representation of any single pitch deviation of any measuring circle on the left tooth surface after error correction

[0088] Fig. 93D representation of any single pitch deviation of any section of the left tooth surface with eccentricity error

[0089] Fig.10 3D representation of any single pitch deviation of any section on the left tooth surface after error correction

[0090] Fig.11 Flowchart of the specific measurement method of arbitrary tooth pitch deviation based on line structured light DETAILED DESCRIPTION

[0091] A method for measuring arbitrary tooth pitch deviation based on line structured light is further described below in conjunction with the accompanying drawings and specific embodiments.

[0092] According to the method of the present invention, for a tooth number z = 29, normal module m = 2mm, pressure angle α at the pitch circle = 20°, base circle radius The spur gears are measured on this line structured light measurement platform.

[0093] like Figure 1 As shown, a line structured light measurement platform is taken as an example for explanation.

[0094] The line structured light measurement platform includes a measuring unit, a rotating unit, an optical platform and a host computer, all of which are mounted on the optical platform. The measuring unit includes an X-axis moving axis, a Y-axis moving axis, a Z-axis moving axis, a linear grating and a line structured light probe. The line structured light probe is mounted on the X-axis moving axis, and linear gratings are installed on the moving axes in the three directions of X, Y and Z, so as to achieve accurate measurement of the gear. The rotating unit includes a rotating table, a gear to be measured and a circular grating. The circular grating is coaxially mounted on the outside of the rotating table to feedback the angle information of the gear to be measured, and the gear to be measured is coaxially fixed on the rotating table. During the measurement process, the host computer controls the movement of the X-axis, Y-axis and Z-axis and the rotation of the rotating table through the motion control card, and combines the linear grating and the circular grating to achieve accurate adjustment of the position of the line structured light probe and full-circle measurement of the gear to be measured. During data acquisition, the line structured light probe transmits the collected data of the measured gear back to the host computer, and the linear gratings and circular gratings of each axis feed back the position information and the angle information of the measured gear to the host computer, which finally processes the collected gear data.

[0095] Step 1: Create a 3D model of the gear tooth surface to be tested

[0096] First, according to Figure 2 Establish a fixed gear coordinate system ε1 = [O1, X1, Y1, Z1], O1 is the origin of the gear coordinate system, Z1 is the rotation axis, let D1 (x d1 ,y d1 ,z d1) is any point on the gear tooth surface to be measured, then the involute equation of the left tooth surface where point D1 is located can be expressed as:

[0097]

[0098] Among them, ζ1 is the expansion angle of the involute of the left tooth surface, z d1 is the axial height of the tooth surface point D1 in the gear coordinate system, e x2 is the value of the geometric center of the gear on the X1 axis after eccentricity, e y2 It is the value of the geometric center of the gear after eccentricity on the Y1 axis.

[0099] Similarly, according to Figure 3 Establish another fixed gear coordinate system ε2 = [O2, X2, Y2, Z2], O2 is the origin of the gear coordinate system, Z2 is the rotation axis, let D2 (x d2 ,y d2 ,z d2 ) is any point on the gear tooth surface to be measured, then the involute equation of the right tooth surface where point D2 is located can be expressed as:

[0100]

[0101] Among them, ζ1 is the expansion angle of the involute of the right tooth surface, z d2 is the axial height of the tooth surface point D2 in the gear coordinate system, e x2 is the value of the geometric center of the gear on the X2 axis after eccentricity, e y2 is the value of the gear's geometric center on the Y2 axis after eccentricity. The three-dimensional model of the complete left and right tooth surfaces of the gear can be obtained by equations (23) and (24).

[0102] Step 2: Collect actual pitch measurement points based on line structured light probe

[0103] First, if Figure 4As shown, the line structured light measurement platform is reset and the probe is preheated. In order to achieve accurate measurement of gear pitch deviation, linear gratings are added to the X-axis, Y-axis and Z-axis respectively, and a circular grating is added to the C-axis. Initially, the X-axis, Y-axis, Z-axis and C-axis are reset to the zero position of the grating. Next, adjust the X-axis so that the light beam emitted by the line structured light probe is aligned with the center of the gear shaft; adjust the Y-axis so that the line structured light probe is within the measurable range; adjust the Z-axis so that the light beam emitted by the line structured light probe covers the tooth width height range. Then, the gear to be measured is coaxially fixed on the rotating table, and the rotating table drives the gear to be measured to rotate, while triggering the line structured light probe to start measuring the right tooth surface of the gear. After completing the full-circle measurement, adjust the position of the line structured light probe in the X-axis direction, and repeat the above steps to measure the left tooth surface of the gear. After completing the measurement of the entire gear tooth surface, it is necessary to convert the tooth surface information of the measured gear from the line structured light probe coordinate system to the gear coordinate system. The steps of coordinate conversion are as follows:

[0104] according to Figure 4 As shown, four coordinate systems are established: platform coordinate system ε0 = [O0, X0, Y0, Z0], line structured light probe coordinate system ε s =[O s ,X s ,Y s ,Z s ], light plane coordinate system ε of line structured light l =[O l ,X l ,Y l ,Z l ] and the gear coordinate system ε g =[O g ,X g ,Y g ,Z g ].

[0105] First, according to the measurement principle of line structured light, the tooth surface information of the gear being measured can be expressed in the light plane coordinate system of line structured light as follows:

[0106] Q l =(x l ,0,z l ) (25)

[0107] Similarly, the tooth surface information of the gear being measured can be expressed in the online structured light probe coordinate system as follows:

[0108]

[0109] Among them, Q s =(x s ,y s ,z s ), h0 is the nominal distance of the line structured light probe.

[0110] According to the mapping relationship between the line structured light probe coordinate system and the optical plane coordinate system, the tooth surface information Q l Convert to the platform coordinate system.

[0111]

[0112] in, are the rotation angles of the line structured light probe coordinate system around the X0 axis, Y0 axis and Z0 axis of the platform coordinate system, a0, b0, c0 are the offset distances between the structured light probe coordinate system and the X0 axis, Y0 axis, and Z0 axis of the platform coordinate system, respectively.

[0113] Finally, the tooth surface information Q0 of the measured gear transformed into the platform coordinate system is transformed into the gear coordinate system.

[0114]

[0115] in, Δθ is the angle that the turntable rotates when the linear structure probe is sampling. Finally, the actual tooth pitch measurement point Q is obtained. g (x g ,y g ,z g ).

[0116] Step 3: Reverse the geometric center based on the actual pitch measurement point

[0117] Due to the existence of various errors such as artificial installation error and workpiece processing error, the actual pitch measurement point will introduce the influence of eccentricity error, making the geometric center O2 (e x2 , e y2 ) is offset, in order to reduce the gear geometric center O2 (e x2 , e y2 ) The impact of the offset on the accuracy of the pitch deviation, such as Figure 5 As shown, according to the relationship between two adjacent points on the same side of the tooth profile on the measuring circle and the center of the base circle, the following equation is established for solution:

[0118]

[0119]

[0120] Where i is the number of any pitch measurement points, is the difference between the circumferential angle of the starting point of the involute where any two adjacent points of the tooth profile on the same side are located and the mean value of the circumferential angle, is the average of the circumferential angles of the starting points of the involutes of two adjacent points on the same side of the tooth profile, z is the number of teeth. It can be obtained by the following formula:

[0121]

[0122] Among them, λ i Pitch measurement point D i (x i ,y i ) corresponds to the circumferential angle, λ i+1 Pitch measurement point D i+1 (x i+1 ,y i+1 ) corresponds to the circumference angle, the specific formula is as follows:

[0123]

[0124] Among them, r b is the base circle radius, ξ i Pitch measurement point D i (x i ,y i ) corresponds to the expansion angle, ξ i+1 Pitch measurement point D i+1 (x i+1 ,y i+1 ) corresponds to the expansion angle, α i is the tooth pitch evaluation point D i (x i ,y i ) corresponds to the pressure angle, α i+1 Pitch measurement point D i+1 (x i+1 ,y i+1 ) corresponds to the pressure angle.

[0125] Finally, the Gauss-Newton iteration method is used to solve equation (30) to obtain the geometric center O2 (0.015, 0.018).

[0126] Step 4: Solve the pitch deviation evaluation point based on Newton interpolation principle

[0127] After obtaining the geometric center O2 (0.015, 0.018), it is necessary to calculate any single pitch deviation. The usual method is to find the coordinates of the intersection between the gear measurement circle and the actual tooth profile curve. However, the tooth profile curve composed of the point cloud data obtained by actual measurement may not have an evaluation point on the measurement circle, which will lead to the problem of low pitch measurement accuracy based on line structured light.

[0128] Therefore, before solving the pitch deviation, Figure 6As shown, using the Newton cubic interpolation principle, four adjacent tooth profile data collection points (x0, y0), (x1, y1), (x2, y2), (x3, y3) that are closest to the theoretical measurement circle are selected on each tooth profile curve as Newton interpolation interval points. For example, take any pitch deviation measurement point on the measurement circle, select the four data points before and after this pitch deviation measurement point (21.800, -20.552), (21.808, -20.573), (21.817, -20.594), (21.825, -20.615) for Newton cubic interpolation, and take the polynomial equation obtained after interpolation as the actual tooth profile curve equation, which can simplify the calculation process of the pitch deviation. The derivation process of Newton cubic interpolation method is as follows:

[0129] Newton interpolation polynomial N n (x) can be expressed as:

[0130]

[0131] Among them, f[x0,x1] is the first-order difference quotient:

[0132]

[0133] f[x0,x1,x2] is the second-order difference quotient:

[0134]

[0135] f[x0,x1,x2,x3] is the third-order difference quotient:

[0136]

[0137] Among them, f(x0)=y0=-20.552, f(x1)=y1=-20.573, f(x2)=y2=-20.594, f(x3)=y3=-20.615.

[0138] Substituting formulas (36), (37), and (38) into formula (38), the cubic polynomial equation of Newton interpolation can be solved, and then the actual curve equation of the tooth profile of the measuring circle N3(x) can be obtained:

[0139]

[0140] The equation of an arbitrary measured circle is as follows:

[0141] x i 2 +y i 2 =r t 2 (40)

[0142] Among them, r t is the radius of any measured circle.

[0143] According to Newton's cubic interpolation, the actual tooth profile curve expression (39) on different sections of the gear is obtained. By solving the nonlinear equation group in parallel with the measuring circle equation (40), the intersection point P1 (21.816, -20.615) of the actual tooth profile curve at any measuring circle can be obtained. The intersection point P1 (21.816, -20.615) is one of the evaluation points of the pitch deviation.

[0144] Step 5: Solve any pitch deviation based on the evaluation point

[0145] Similarly, according to the above pitch evaluation point calculation method, the intersection point P of the actual tooth profile curve at any measuring circle can be obtained. i (x i ,y i ), and substitute any two adjacent evaluation points P1(x1, y1) and P2(x2, y2) on the same side of the tooth surface into formula (41) to solve any single pitch deviation f pi :

[0146] 1) Any single pitch deviation f pi :

[0147]

[0148] 2) Single tooth pitch deviation f p :

[0149] f p =max|f pi | (42)

[0150] Among them, f p For any single pitch deviation f pi The maximum absolute value of .

[0151] 3) Cumulative deviation of any tooth pitch F pi :

[0152]

[0153] Among them, F pi It is the algebraic difference between the arc length of n adjacent pitches and the theoretical arc length, where n ranges from 1 to 29. Since the arccosine function cannot be calculated when the pitch angle is equal to π, the cumulative deviation F for any pitch is pi Perform segmented calculations.

[0154] 4) Cumulative total deviation of tooth pitch F p

[0155] F p =Fpi,max -F pi,min (44)

[0156] Among them, F p It is defined as the cumulative deviation F of any pitch of a given tooth surface of all teeth of the gear. pi The maximum algebraic difference of .

[0157] Step 6: Create a 3D representation of any pitch deviation

[0158] Based on the principle of this method, any pitch deviation can be calculated and the result can be expressed through 3D error representation. Taking the left tooth surface of the gear as an example, Figure 7 It shows the deviation of any single tooth pitch f at any measuring circle of the gear when there is eccentricity error. pi The tooth number (dimensionless) coordinate axis represents the distribution of any single pitch deviation value of each gear tooth, and the arbitrary measurement circle radius coordinate axis represents the distribution of any single pitch deviation value at different measurement circles, and its value range is between -6μm and 6μm. Figure 8 The single pitch deviation f of the gear at any measuring circle after inverse geometric center correction is shown. pi , after correction, any single pitch deviation f pi The values ​​range from -2.3 μm to 2.3 μm. Fig. 9 It shows the single pitch deviation f at any cross section of the gear when there is eccentricity error. pi The tooth number (dimensionless) coordinate axis represents the distribution of any single pitch deviation value of each gear tooth, and the arbitrary section number coordinate axis represents the distribution of any single pitch deviation value of any section in the tooth width direction, and its value range is between -6μm and 6μm. Fig.10 The single pitch deviation f of the gear at different cross sections after inverse geometric center correction is shown. pi , and its value ranges from -2.2μm to 2.2μm. By comparing the existence of eccentricity error and any single pitch deviation f after correction pi The characterization results show that the eccentricity error correction method of the present invention can effectively reduce the influence of eccentricity error on pitch deviation. The traditional pitch deviation calculation method only calculates the pitch deviation at the middle part of the tooth width, while the present method performs 3D characterization of any pitch deviation of any cross section of the gear, and characterizes the pitch deviation more completely and systematically. The obtained results can better reflect the overall quality of the gear.

[0159] In addition, other evaluation indicators of pitch deviation, such as single pitch deviation, cumulative deviation of any pitch and total cumulative deviation of pitch, can also be evaluated by this method.

[0160] The specific measurement process is as follows: Fig.11 shown.

Claims

1. A method for measuring arbitrary tooth pitch deviation based on line structured light, characterized in that: The method comprises the following steps, Step 1: Create a 3D model of the gear tooth surface to be tested First, according to the gear involute property, a fixed gear coordinate system ε1 = [O1, X1, Y1, Z1] is established, O1 is the origin of the gear coordinate system, Z1 is the rotation axis, and D1 (x d1 ,y d1 ,z d1 ) is any point on the gear tooth surface to be measured, then the involute equation of the left tooth surface where point D1 is located can be expressed as: Among them, r b is the base circle radius of the gear being measured, μ1 is the rolling angle of the left tooth surface involute, α1 is the pressure angle of the left tooth surface involute, ζ1 is the expansion angle of the left tooth surface involute, z d1 is the axial height of the tooth surface point D1 in the gear coordinate system, e x2 is the value of the geometric center of the gear on the X1 axis after eccentricity, e y2 is the value of the geometric center of the gear on the Y1 axis after eccentricity. Theoretically, when the gear three-dimensional model has no eccentricity, e x2 and e y2 The values ​​of are all 0, and the geometric center is the origin of the gear coordinate system O1; Similarly, establish another fixed gear coordinate system ε2 = [O2, X2, Y2, Z2], O2 is the origin of the gear coordinate system, Z2 is the rotation axis, let D2 (x d2 ,y d2 ,z d2 ) is any point on the gear tooth surface to be measured, then the involute equation of the right tooth surface where point D2 is located can be expressed as: Among them, μ2=α2+ζ2, μ2 is the rolling angle of the right tooth surface involute, α2 is the pressure angle of the right tooth surface involute, ζ1 is the expansion angle of the right tooth surface involute, z d2 is the axial height of the tooth surface point D2 in the gear coordinate system, e x2 is the value of the geometric center of the gear on the X2 axis after eccentricity, e y2 is the value of the geometric center of the gear on the Y2 axis after eccentricity. Theoretically, when the gear three-dimensional model has no eccentricity, e x2 and e y2 The values ​​of are all 0, and the geometric center is the origin of the gear coordinate system O2. The complete three-dimensional model of the left and right tooth surfaces of the gear can be obtained by equations (1) and (2); Step 2: Collect actual pitch measurement points based on line structured light probe First, reset the line structured light measurement platform and preheat the probe; in order to achieve accurate measurement of gear pitch deviation, add linear gratings on the X-axis, Y-axis and Z-axis respectively, and add circular gratings on the C-axis; initially, reset the X-axis, Y-axis, Z-axis and C-axis to the zero position of the grating; next, adjust the X-axis so that the light beam emitted by the line structured light probe is aligned with the center of the gear shaft; adjust the Y-axis so that the line structured light probe is within the measurable range; adjust the Z-axis so that the light beam emitted by the line structured light probe covers the tooth width and height range; then, fix the gear to be measured coaxially on the rotating table, the rotating table drives the gear to be measured to rotate, and at the same time triggers the line structured light probe to start measuring the right tooth surface of the gear; after completing the full-circle measurement, adjust the position of the line structured light probe in the X-axis direction, and repeat the above steps to measure the left tooth surface of the gear; after completing the measurement of the entire gear tooth surface, it is necessary to convert the tooth surface information of the measured gear from the line structured light probe coordinate system to the gear coordinate system. The steps of coordinate conversion are as follows: Establish four coordinate systems: platform coordinate system ε0 = [O0, X0, Y0, Z0], line structured light probe coordinate system ε s =[O s ,X s ,Y s ,Z s ], light plane coordinate system ε of line structured light l =[O l ,X l ,Y l ,Z l ] and the gear coordinate system ε g =[O g ,X g ,Y g ,Z g ]; First, according to the measurement principle of line structured light, the tooth surface information of the gear being measured can be expressed in the light plane coordinate system of line structured light as follows: Q l =(x l ,0,z l ) (3) Similarly, the tooth surface information of the gear being measured can be expressed in the online structured light probe coordinate system as follows: Q S =Q l +T l s (4) Among them, Q s =(x s ,y s ,z s ), T l s =(0,0,-h0), h0 is the nominal distance of the line structured light probe; According to the mapping relationship between the line structured light probe coordinate system and the optical plane coordinate system, the tooth surface information Q l Convert to the platform coordinate system; in, are the rotation angles of the line structured light probe coordinate system around the X0 axis, Y0 axis and Z0 axis of the platform coordinate system, T s 0 =T(a0, b0, c0), where a0, b0, c0 are the offset distances between the structured light probe coordinate system and the X0 axis, Y0 axis, and Z0 axis of the platform coordinate system respectively; Finally, the tooth surface information Q0 of the gear being measured converted to the platform coordinate system is converted to the gear coordinate system; in, Δθ is the angle that the turntable rotates when the linear structure probe is sampling; the actual tooth pitch measurement point Q is finally obtained g (x g ,y g ,z g ); Step 3: Reverse the geometric center based on the actual pitch measurement point Due to the existence of various errors such as artificial installation error and workpiece processing error, the actual pitch measurement point will introduce the influence of eccentricity error, making the geometric center O2 (e x2 , e y2 ) is offset, in order to reduce the gear geometric center O2 (e x2 , e y2 ) The influence of the offset on the accuracy of the pitch deviation is established according to the relationship between the two adjacent points of the tooth profile on the same side of the measuring circle and the center of the base circle, and the following equation is established for solution: Where i is the number of any pitch measurement points, is the difference between the circumferential angle of the starting point of the involute where any two adjacent points of the tooth profile on the same side are located and the mean value of the circumferential angle, is the average of the circumferential angles of the starting points of the involutes of two adjacent points on the same side of the tooth profile, z is the number of teeth; It can be obtained by the following formula: Among them, λ i Pitch measurement point D i (x i ,y i ) corresponds to the circumferential angle, λ i+1 Pitch measurement point D i+1 (x i+1 ,y i+1 ) corresponds to the circumference angle, the specific formula is as follows: Among them, r b is the base circle radius, ξ i Pitch measurement point D i (x i ,y i ) corresponds to the expansion angle, ξ i+1 Pitch measurement point D i+1 (x i+1 ,y i+1 ) corresponds to the expansion angle, α i is the tooth pitch evaluation point D i (x i ,y i ) corresponds to the pressure angle, α i+1 Pitch measurement point D i+1 (x i+1 ,y i+1 ) corresponds to the pressure angle; Finally, the Gauss-Newton iteration method is used to solve equation (8) to obtain the geometric center O2 (e x2 , e y2 ); Step 4: Solve the pitch deviation evaluation point based on Newton interpolation principle Get the geometric center O2(e x2 , e y2 ), it is necessary to calculate any single pitch deviation; the usual method is to find the coordinates of the intersection between the gear measurement circle and the actual tooth profile curve; however, the tooth profile curve composed of the point cloud data obtained by actual measurement may not have an evaluation point at the measurement circle, which will lead to the problem of low pitch measurement accuracy based on line structured light; Therefore, before solving the pitch deviation, the Newton cubic interpolation principle is used to select four adjacent tooth profile data collection points (x0, y0), (x1, y1), (x2, y2), and (x3, y3) on each tooth profile curve that are closest to the theoretical measurement circle as Newton interpolation interval points. The four selected data points are subjected to Newton cubic interpolation, and the polynomial equation obtained after interpolation is taken as the actual tooth profile curve equation, which can simplify the calculation process of the pitch deviation. The derivation process of Newton cubic interpolation method is as follows: Newton interpolation polynomial N n (x) can be expressed as: Among them, f[x0,x1] is the first-order difference quotient: f[x0,x1,x2] is the second-order difference quotient: f[x0,x1,x2,x3] is the third-order difference quotient: Among them, f(x0)=y0,f(x1)=y1,f(x2)=y2,f(x3=y3; Substituting formulas (14), (15), and (16) into formula (13) can solve the cubic polynomial equation of Newton interpolation, and then obtain the actual curve equation of the tooth profile of the measuring circle N3(x): The equation of an arbitrary measured circle is as follows: x i 2 +y i 2 =r t 2 (18) Among them, r t is the radius of any measured circle; According to Newton's cubic interpolation, the actual tooth profile curve expression (17) on any cross section of the gear is obtained, and the measurement circle equation (18) is used to solve the nonlinear equation group to obtain the intersection point P of the actual tooth profile curve at any measurement circle. i (x i ,y i ), intersection point P i (x i ,y i ) is the evaluation point of pitch deviation; Step 5: Solve any pitch deviation based on the evaluation point Substitute any two adjacent evaluation points P1(x1, y1) and P2(x2, y2) on the same side of the tooth surface into formula (19) to solve any single pitch deviation f pi : 1) Any single pitch deviation f pi : Among them, the physical meaning of z is the number of teeth; 2) Single tooth pitch deviation f p : f p =max|f pi | (20) Among them, f p For any single pitch deviation f pi The maximum absolute value of 3) Cumulative deviation of any tooth pitch F pi : Among them, F pi It is the algebraic difference between the arc length of n adjacent pitches and the theoretical arc length, where n ranges from 1 to z. Since the arccosine function cannot be calculated when the pitch angle is equal to π, the cumulative deviation F for any pitch is pi Perform segmented calculations; 4) Cumulative total deviation of tooth pitch F p F p =F pi,max -F pi,min (22) Among them, F p It is defined as the cumulative deviation F of any pitch of a given tooth surface of all teeth of the gear. pi The maximum algebraic difference of Similarly, any single pitch deviation f of any measuring circle of any gear section pi , single pitch deviation f p , any pitch cumulative deviation F pi Total cumulative deviation of tooth pitch F p The above methods can be used for calculation; Step 6: Create a 3D representation of any pitch deviation The pitch deviation can be characterized from the 1D, 2D and 3D levels. When characterizing the pitch deviation, the existing gear accuracy standards usually select points on the pitch circle of the gear on the same side for characterization at the 1D level; characterizing the pitch deviation with only a very small part of the data will be very sensitive to random errors, resulting in inaccurate characterization results; at the 2D level, multiple sections are selected in the tooth width direction for characterization, but even on one section, there will be obvious differences in the pitch deviations at different measuring circles; the method of the present invention is to characterize the pitch deviation at the 3D level. First, the actual measurement points of the pitch deviation of a large sample of the gear to be measured are obtained by line structured light, and then the geometric center is inversely calculated using the actual measurement points of the pitch deviation, and then the eccentricity error of the pitch measurement point is corrected, and then the tooth profile curve equation corresponding to the measurement points at different measuring circles of the gear is calculated using the Newton interpolation principle, and the obtained tooth profile curve equation is combined with the equation of any measuring circle to obtain the evaluation point of any pitch deviation. Through these evaluation points, any single pitch deviation f of each gear tooth at any measuring circle can be calculated. pi Finally, any single pitch deviation f pi The results are represented in 3D form; similarly, any single pitch deviation f in any section in the tooth width direction pi The above method can also be used for 3D characterization.

2. The method for measuring arbitrary tooth pitch deviation based on line structured light according to claim 1, characterized in that: In step 4, Newton's cubic interpolation principle is used to select four adjacent tooth profile data collection points that are closest to the measuring circle on each tooth profile curve as Newton's interpolation interval points to calculate the pitch deviation evaluation points.

3. The method for measuring arbitrary tooth pitch deviation based on line structured light according to claim 1, characterized in that: In step 6, the arbitrary pitch deviation of different gear sections is characterized in three dimensions on a 3D level. The gear pitch measurement points are measured by line structured light, and the tooth profile curve equations corresponding to the measurement points at different gear sections and different measurement circles are calculated using the Newton interpolation principle. The equations are then combined with the arbitrary measurement circle equations to obtain evaluation points of the arbitrary pitch deviation. Through these evaluation points, any single pitch deviation f at any measurement circle of different gear sections can be calculated. pi , single pitch deviation f p , any pitch cumulative deviation F pi Total cumulative deviation of tooth pitch F p ; Finally, any pitch deviation is fully characterized in 3D.

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