A method for measuring arbitrary tooth thickness deviation considering installation eccentricity

Abstract

The invention belongs to the technical field of tooth thickness deviation calculation, and discloses a method for measuring arbitrary tooth thickness deviation considering installation eccentricity, comprising the following steps: S1, establishing a three-dimensional model of a gear tooth surface: establishing a rectangular coordinate system of the gear tooth surface according to the right-hand rule; S2, solving the installation eccentricity: solving the installation eccentricity based on the geometric relationship between the actual tooth thickness measurement point and the center of the measured gear; S3, establishing a calculation model for arbitrary tooth thickness deviation: correcting the actual tooth thickness measurement point, and establishing a calculation model for the tooth thickness deviation of an arbitrary evaluation circle; S4, establishing a 3D tooth thickness deviation evaluation system: establishing a mathematical model for structured expression of tooth thickness deviation, and calculating the statistical evaluation index of the 3D tooth thickness deviation based on the mathematical model; the invention solves the problem that the existing measurement method cannot meet the measurement of arbitrary tooth thickness deviation and the influence of the installation eccentricity error on the measurement accuracy of the tooth thickness deviation.

Description

Technical Field

[0001] The invention relates to the technical field of tooth thickness deviation calculation, and in particular to a method for measuring an arbitrary tooth thickness deviation taking installation eccentricity into consideration. Background Art

[0002] Tooth thickness deviation is a mandatory inspection item stipulated by international gear standards, and its size directly affects the efficiency, accuracy, noise and service life of the transmission system. The traditional contact tooth thickness measurement method only measures a single cross section of the gear and uses the pitch circle as the evaluation circle for evaluation. This measurement and evaluation method based on local samples often results in a large difference between the gear evaluation grade and the actual performance.

[0003] Currently, tooth thickness information can be acquired efficiently and in large samples through CNC structured light non-contact methods. However, in the actual measurement process, the manufacturing error of the fixture will cause the geometric center of the gear to deviate from the rotation center of the worktable, thereby introducing installation eccentricity and reducing the tooth thickness measurement accuracy.

[0004] The current tooth thickness deviation measurement and evaluation methods still have the following deficiencies: (1) There is a lack of a calculation model suitable for large sample rapid measurement and any tooth thickness deviation from the tooth root to the tooth top area. For example, patent CN108050946B uses a binocular vision measurement system to achieve rapid measurement of gear thickness deviation. Its disadvantage is that it only selects the pitch circle to calculate the tooth thickness deviation, and only a few feature points are collected on the entire tooth surface for tooth thickness deviation calculation, ignoring most of the errors and information on the tooth surface. (2) There is a lack of a three-dimensional evaluation method for tooth thickness deviation. The current international gear accuracy standard ISO1328 does not specify a three-dimensional evaluation method for tooth thickness deviation. It only uses two-dimensional small sample data and extreme value method to calculate the evaluation index. The evaluation results often do not meet the actual performance and cannot characterize the overall quality of the gear due to insufficient tooth thickness deviation information. (3) The influence of installation eccentricity error on the measurement accuracy of tooth thickness deviation is not considered. For example, patent CN108050946B proposes the basic concept of arbitrary tooth thickness deviation. However, the disadvantage is that it cannot solve any tooth thickness measurement point, and it does not consider the installation eccentricity error and compensation problem. The measurement accuracy needs to be improved. Summary of the invention

[0005] The present invention is intended to provide a method for measuring an arbitrary tooth thickness deviation taking installation eccentricity into consideration, so as to solve the problems existing in the above-mentioned background technology.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for measuring an arbitrary tooth thickness deviation taking into account installation eccentricity comprises the following steps:

[0008] S1. Establish a three-dimensional model of the gear tooth surface

[0009] The Cartesian rectangular coordinate system of the gear tooth surface is established according to the right-hand rule, and the involute tooth surface equation of any point on the gear tooth surface is established according to the shape and position parameters of the tooth surface;

[0010] S2. Solving the installation eccentricity

[0011] Based on the geometric relationship between the actual tooth thickness measurement point and the center of the gear being measured, the installation eccentricity is iteratively solved by the Gauss-Newton method;

[0012] S3. Establish a calculation model for arbitrary tooth thickness deviation

[0013] The installation eccentricity obtained by S2 is used to correct the actual tooth thickness measurement point to obtain an accurate tooth thickness measurement point, and a calculation model for the tooth thickness deviation of any evaluation circle is established, and any tooth thickness deviation is calculated using the calculation model;

[0014] Among them, the arbitrary evaluation of the round tooth thickness deviation e p The calculation model expression is:

[0015] e p =r p ×(θ p -ζ p )

[0016]

[0017] Among them, r p is the radius of any evaluation circle, r b is the base circle radius, r is the pitch circle radius, θ p is the polar angle value of the arbitrary evaluation round tooth thickness, θ b is the base circle tooth thickness polar angle value, ζ p is the polar angle of the tooth thickness measurement point on any evaluation circle, z is the total number of gears;

[0018] S4. Establish a 3D tooth thickness deviation evaluation system

[0019] A mathematical model is established for structured expression of tooth thickness deviation, so as to statistically analyze the tooth thickness deviation data of all tooth surfaces in radial, tooth direction and circumferential directions, and a statistical evaluation index of 3D tooth thickness deviation is calculated based on the mathematical model.

[0020] Further, in step S1, the Cartesian coordinate system of the gear tooth surface is σ g =[o g ;x g ,y g ,z g ],D:(x d ,y d ,z d ) is the three-dimensional coordinate of any point on the gear tooth surface being measured, and the involute tooth surface equation where point D is located is:

[0021]

[0022] Among them, r b is the base circle radius of the gear being measured; z d is the axial height corresponding to point D in the gear coordinate system; μ0 is the initial phase angle of the involute of the right tooth surface where point D is located; θ d is the expansion angle of the involute of the right tooth surface where point D is located; f is the tooth surface direction, when f=1, it indicates the right tooth surface, when f=-1, it indicates the left tooth surface, x0, y0 are respectively along the x g ,y g Eccentricity in the axial direction.

[0023] Further, in step S2, the steps of iteratively solving the installation eccentricity x0, y0 by Gauss-Newton method are:

[0024] S201. Establish the least squares equation based on the sum of squares of actual tooth thickness deviations on the pitch circle:

[0025]

[0026] In the formula, ψ b (x d ,y d ) is the measured value of the central angle corresponding to the base circle tooth thickness in the measured gear coordinate system, α is the known pitch circle pressure angle, m is the cylindrical gear module, t is the gear number, and z is the total number of gears;

[0027] S202, determine the iterative Jacobian matrix J calculation formula:

[0028]

[0029] S203, define Δx0 and Δy0 as iterative increments, and determine the expression of iterative increments:

[0030]

[0031] S204, perform an iterative loop based on the following expression:

[0032]

[0033] Where w is the number of iterations;

[0034] S205 . When the increments Δx0 and Δy0 are less than a specified threshold or the number of iterations exceeds a maximum value, the iteration is stopped and accurate x0 and y0 are obtained.

[0035] Furthermore, in step S3, the expression for correcting the actual tooth thickness measurement point using x0, y0 is:

[0036]

[0037] Furthermore, in step S3, the tooth thickness measurement points are converted into polar coordinates (r k , k ), calculate the interval [r k ,r k+1 ] the polar coordinates of any point P in p ,ζ p ) is:

[0038]

[0039] In the above formula:

[0040]

[0041] B=1-A,

[0042]

[0043] r p is the polar radius of point P, ζ p is the polar angle of point P, r k is the polar diameter of the accurate measurement point, ζ k To accurately measure the polar angle of a point.

[0044] Further, in step S4, the mathematical model is e(j,t)| p , where p, j, t are the evaluation circle number, section number and gear number respectively, p = {1, 2, ... h}, j = {1, 2, ... n}, t = {1, 2, ... z}, and h, n, z are the corresponding totals.

[0045] Furthermore, in step S4, the statistical evaluation index of the 3D tooth thickness deviation includes the mean value of the tooth thickness deviation μ e , tooth thickness deviation standard deviation σ e , maximum tooth thickness deviation Maxe, minimum tooth thickness deviation Mine, tooth thickness deviation range R e ;

[0046] Mean tooth thickness deviation μ e The expression is:

[0047]

[0048] Tooth thickness deviation standard deviation σ e The expression is:

[0049]

[0050] The expression of the maximum tooth thickness deviation Maxe is:

[0051] Maxe=Max[e(j,t)| p ]

[0052] The expression of the minimum tooth thickness deviation Mine is:

[0053] Mine=Min[e(j,t)| p ]

[0054] Tooth thickness deviation R e The expression is:

[0055] R e =Maxe-Mine

[0056] In the above formula, p, j, t are the evaluation circle number, section number and gear number respectively, and h, n, z are the corresponding total numbers.

[0057] The beneficial effects of the technical solution are:

[0058] 1. The present invention provides a method for measuring any tooth thickness deviation considering installation eccentricity, proposes a method for compensating tooth thickness deviation under installation eccentricity, uses the Gauss-Newton method to accurately solve the geometric center of the gear, and compensates and corrects the tooth thickness measurement point, further improving the measurement accuracy;

[0059] 2. The present invention provides a method for measuring the deviation of arbitrary tooth thickness considering installation eccentricity, and proposes an arbitrary tooth thickness calculation model based on spline difference, which can obtain tooth thickness measurement points on any evaluation circle and calculate the tooth thickness deviation, completely covering the area from tooth root to tooth top;

[0060] 3. The present invention proposes a method for measuring the deviation of any tooth thickness considering the installation eccentricity, and proposes a 3D tooth thickness deviation characterization structure, which can accurately express the detailed characteristics and 3D errors of the gear, is more comprehensive and representative, is beneficial to statistical analysis, and can quickly locate the abnormal area of ​​the tooth surface;

[0061] 4. The present invention provides a method for measuring and compensating arbitrary tooth thickness deviations taking into account installation eccentricity, and proposes statistical indicators based on a 3D tooth thickness deviation characterization structure, which is beneficial to the three-dimensional evaluation of topologically modified gears. The statistical indicators are more reliable, not affected by random errors, and can better reflect the overall quality of the gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is a schematic structural diagram of a structured light measurement device in Embodiment 1 of the present invention;

[0063] Figure 2 This is a flow chart of a method for measuring an arbitrary tooth thickness deviation taking into account installation eccentricity in Example 2 of the present invention;

[0064] Figure 3is a Cartesian rectangular coordinate system established based on the gear surface in Example 2 of the present invention;

[0065] Figure 4 This is a schematic diagram of tooth thickness measurement coordinates considering eccentric installation in Example 2 of the present invention;

[0066] Figure 5 A curve diagram showing the relationship between the serial number and the tooth thickness deviation of the pitch circle gear without considering the installation of the eccentricity in Example 2 of the present invention;

[0067] Figure 6 A curve diagram showing the relationship between the serial number and the tooth thickness deviation of the pitch circle gear with eccentric installation in Example 2 of the present invention;

[0068] Figure 7 Schematic diagram of coordinates of any tooth thickness measurement point based on spline interpolation in Embodiment 2 of the present invention;

[0069] Figure 8 This is a schematic diagram of a 3D tooth thickness deviation characterization structure in Example 2 of the present invention;

[0070] Fig. 9 3D result diagrams of tooth thickness deviation in Example 2 of the present invention, wherein (a) is a 3D result diagram of tooth thickness deviation of all evaluation circles of several gears, and (b) is a 3D result diagram of all tooth thickness deviation of a single gear;

[0071] The names of the corresponding marks in the accompanying drawings are:

[0072] 1. Host computer; 2. Rotating table; 3. Structured light probe; 31. X moving axis; 32. Y moving axis; 33. Z moving axis. DETAILED DESCRIPTION

[0073] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments:

[0074] Example 1

[0075] The content of the present invention is based on large sample data, and considers the measurement and compensation method of arbitrary tooth thickness deviation with installation eccentricity. Therefore, the structured light measurement device is briefly described as follows: Figure 1 As shown, the structured light measuring device is composed of an X-moving axis 31, a Y-moving axis 32, a Z-moving axis 33 and a rotating table 2. The structured light probe 3 is mounted on the X-moving axis 31, and the gear 4 to be measured is coaxially fixedly mounted on the rotating table 2. During the measurement process, the host computer 1 controls the movement of the XYZ moving axes and the rotation of the rotating table 2 to adjust the position of the line structured light probe 3 and measure the entire circumference of the gear 4 to be measured. During data collection, the structured light probe 3 transmits the collected data of the gear 4 to the host computer 1, and finally the host computer 1 processes the collected data of the gear 4 to be measured.

[0076] Example 2

[0077] The tooth thickness deviation measurement method provided by the present invention is used for a tooth number z=28, module m=4mm, pitch circle pressure angle α=27°, pitch circle radius Base circle radius The tooth thickness deviation of cylindrical spur gears is measured and compensated for by taking into account the installation eccentricity on the structured light measuring device.

[0078] like Figure 2 As shown, the specific steps are as follows:

[0079] S1. Establish a three-dimensional model of the gear surface

[0080] According to the right-hand rule Figure 3 The gear coordinate system σ shown g =[o g ;x g ,y g ,z g ], the coordinate system is a Cartesian rectangular coordinate system, let D:(x d ,y d ,z d ) is the three-dimensional coordinate of any point on the gear surface to be measured. According to the shape and position parameters of the tooth surface, the equation of the involute tooth surface where point D is located is:

[0081]

[0082] Among them, z d is the axial height corresponding to point D in the gear coordinate system; μ0 is the initial phase angle of the involute of the right tooth surface where point D is located; θ d is the expansion angle of the involute of the right tooth surface where point D is located; f is the tooth surface direction, when f=1, it indicates the right tooth surface, when f=-1, it indicates the left tooth surface, x0, y0 are respectively along the x g ,y g Eccentricity in the axial direction;

[0083] Specifically, the method for obtaining the large sample tooth thickness information at point D is as follows: first, the line structured light measurement platform is reset and the structured light probe 3 is preheated, and the XYZ moving axis and the rotating table 2 are reset to the zero position; secondly, the XYZ moving axis is adjusted so that the gear 4 to be measured is in the reasonable measurement range of the structured light probe 3; then, the gear 4 to be measured is coaxially fixed on the rotating table 2, and the rotating table 2 drives the gear 4 to be measured to rotate, and at the same time, the line structured light probe 3 is triggered to start measuring the right tooth surface of the gear 4 to be measured. After completing the full-circle measurement, the position of the line structured light probe 3 in the direction of the X moving axis 31 is adjusted, and the above steps are repeated to measure the left tooth surface of the gear 4 to be measured. After completing the measurement of the entire gear surface, a large sample tooth thickness information set at point D is obtained;

[0084] S2. Solving the installation eccentricity

[0085] like Figure 4 As shown in the figure, during the tooth thickness deviation measurement process, the eccentric installation of the gear causes the actual evaluation circle of the tooth thickness deviation measurement to not coincide with the theoretical evaluation circle, which will eventually result in Figure 5 The results shown reduce the tooth thickness measurement accuracy;

[0086] For the determination of the installation eccentricity x0, y0, this method will iteratively solve it by Gauss-Newton method based on the geometric relationship between the actual tooth thickness measurement point and the center of the gear being measured; the solution steps are as follows:

[0087] S201. Ideally, the tooth thickness deviation value on any gear pitch circle should be equal to that on the theoretical pitch circle. Therefore, the least squares equation can be established based on the sum of the squares of the actual tooth thickness deviation on the pitch circle:

[0088]

[0089] In the formula, ψ b (x d ,y d ) is the measured value of the central angle corresponding to the base circle tooth thickness in the measured gear coordinate system, and t is the gear serial number;

[0090] S202, determining an iterative Jacobian matrix J calculation formula, the iterative Jacobian matrix J calculation formula is as follows:

[0091]

[0092] S203, define Δx0 and Δy0 as iterative increments, and express them as:

[0093]

[0094] S204, iterate through formula (6):

[0095]

[0096] Where w is the number of iterations;

[0097] When the increments Δx0 and Δy0 are less than 1×10 -4 Or when the number of iterations w is greater than 100, stop the iteration and get accurate x0 and y0. The results are as follows:

[0098] <![CDATA[x0(mm)]]> <![CDATA[y0(mm)]]> <![CDATA[Δx0(mm)]]> <![CDATA[Δy0(mm)]]> w -0.05 0.21 <![CDATA[0.12×10 -4 ]]> <![CDATA[0.09×10 -4 ]]> 24

[0099] S3. Establish a calculation model for arbitrary tooth thickness deviation

[0100] S301, solve any tooth thickness measurement point

[0101] Based on the installation eccentricity x0, y0 obtained by S2, the actual tooth thickness measurement point is corrected by formula (7) to obtain the accurate tooth thickness measurement point K: (x k ,y k ,z k ):

[0102]

[0103] The compensation of the pitch circle tooth thickness deviation is shown in the figure below: Figure 6 As shown;

[0104] The arbitrary tooth thickness deviation of cylindrical gears is calculated based on the coordinates of the intersection of an arbitrary evaluation circle and the left and right tooth profile curves. However, since the left and right tooth thickness measurement points obtained by the measuring equipment are often not on the same evaluation circle, it is impossible to accurately solve the tooth thickness deviation on any evaluation circle, and naturally it is impossible to completely cover the area from the tooth root to the tooth top. For this problem, this method uses the spline interpolation method to accurately solve any tooth thickness measurement point;

[0105] like Figure 7 As shown in the figure, first, the tooth thickness measurement point K after correction is calculated by formula (8): (x k ,y k ,z k ) is converted to polar coordinates (r k , k ) in the form of:

[0106]

[0107] In the formula, r k is the polar diameter, ζ k is the polar angle;

[0108] Secondly, in the interval [r k ,r k+1 ] Assume that any tooth thickness measurement point is P, then set any evaluation circle radius r p Substitute the following equation to find the intersection point and x g The angle between the axes p ;

[0109]

[0110] In the above formula:

[0111]

[0112] Finally, the polar coordinate form of the tooth thickness measurement point P on any evaluation circle can be obtained through equations (9) and (10) (r p ,ζ p ), where r p is the polar radius of the point, ζ p is the polar angle of the point;

[0113] S302, calculate any tooth thickness deviation

[0114] Traditional tooth thickness deviation measurement is carried out on the pitching cylindrical surface, and only taking the tooth thickness deviation on the pitching cylindrical surface as the tooth thickness deviation of the gear as a whole will increase the measurement uncertainty. To address this problem, this method uses the advantage of large sample data to extend the pitch circle tooth thickness deviation to any evaluation circle tooth thickness deviation measurement.

[0115] Arbitrary evaluation of round tooth thickness deviation e p It can be calculated by formula (11):

[0116] e p =r p ×(θ p -ζ p ) (11)

[0117]

[0118] Among them, r p is the radius of any evaluation circle, θ p is the polar angle value of the arbitrary evaluation round tooth thickness, θ b is the base circle tooth thickness polar angle value, ζ p is the polar angle value of the tooth thickness measurement point on any evaluation circle;

[0119] S4. Establish a 3D tooth thickness deviation evaluation system

[0120] S401. Establish 3D tooth thickness deviation characterization structure

[0121] This method characterizes any tooth thickness deviation from radial, tooth direction and circumferential directions. In order to statistically analyze the tooth thickness deviation data of all tooth surfaces from three directions, it is necessary to establish a mathematical model for structured expression of tooth thickness deviation. Figure 8 The UVZ special coordinate system shown, U is the direction of increasing pressure angle on the tooth profile curve, V is along the tooth width direction and parallel to the gear axis, and Z is the gear number; based on the established special coordinate system, the tooth thickness deviation of any evaluation circle, any cross section and any gear can be measured, characterized and evaluated;

[0122] 3D tooth thickness deviation can be understood as the set of tooth thickness deviations at all measuring points on the tooth surface, that is, the set of algebraic differences between the actual tooth thickness and the theoretical tooth thickness on all gear sections, all evaluation circles, and all gears. The tooth thickness deviation on the tth gear on the pth evaluation circle and the jth section is defined as e(j,t)| p, p, j, t are the evaluation circle number, section number and gear number in the U, V, Z directions respectively, p = {1, 2, ... h}, j = {1, 2, ... n}, t = {1, 2, ... z}, h = 100, n = 10, z = 28; the characterization results are shown in Fig. 9 As shown, compared with the traditional tooth thickness deviation characterization paradigm, the 3D characterization method is based on large sample data, is more complete and representative, is less susceptible to random errors, and is beneficial to statistical analysis;

[0123] S402, Calculate the statistical index of 3D tooth thickness deviation

[0124] Gear accuracy standards are the theoretical basis and foundation for gear evaluation, including many accuracy standards and evaluation parameters. For gear manufacturing quality evaluation, the inspection items should be based on single indicators such as tooth thickness deviation. However, the current international gear accuracy standard ISO1328-2013 and the domestic standard GB / T10095-2008 only point out the 1D evaluation standard for tooth thickness deviation. Therefore, in order to realize the evaluation of the overall gear tooth thickness deviation, representative evaluation indicators should be constructed based on the 3D representation of tooth thickness deviation, including the statistical results of tooth thickness deviation of a single section on the entire tooth surface, as well as the statistical results of tooth thickness deviation of all sections on the entire tooth surface. These index values ​​can be used as the basis for tooth thickness deviation control.

[0125] By considering a series of tooth thickness deviations as a series of measured values ​​of the overall tooth thickness deviation and using basic statistical analysis methods to calculate, valuable 3D tooth thickness deviation statistical indicators can be obtained;

[0126] The constructed evaluation indicators are as follows:

[0127] Mean tooth thickness deviation μ e :

[0128]

[0129] Tooth thickness deviation standard deviation σ e :

[0130]

[0131] Maximum tooth thickness deviation Maxe:

[0132] Maxe=Max[e(j,t)| p ] (16)

[0133] Minimum tooth thickness deviation Mine:

[0134] Mine=Min[e(j,t)| p ] (17)

[0135] Tooth thickness deviation Re :

[0136] R e =Maxe-Mine (18)

[0137] Through the above formula, the statistical index results of 3D tooth thickness deviation are as follows:

[0138] <![CDATA[μ e (μm)]]> <![CDATA[σ e (μm)]]> Maxe(μm) Mine(μm) <![CDATA[R e (μm)]]> 0.41 9.97 58.50 -42.71 101.21

[0139] Combining the above statistical evaluation indicators, the overall tooth thickness deviation of the gear can be evaluated, and the large sample data based on it is significantly improved compared to contact measurement. The construction based on 3D tooth thickness deviation evaluation indicators will more comprehensively reflect the actual performance of all gears, and the final evaluation results will be more reliable;

[0140] S5. After the measurement is completed, print the 3D tooth thickness deviation result report.

[0141] In summary, the present invention provides a method for measuring arbitrary tooth thickness deviation taking installation eccentricity into consideration. First, the installation eccentricity is fully considered when calculating the tooth thickness deviation. Based on the tooth thickness data of a large sample, the Gauss-Newton method is used to accurately solve the geometric center of the gear, and the measuring point is compensated and corrected; secondly, taking advantage of the large sample, an arbitrary tooth thickness calculation model based on spline difference is proposed; then a three-dimensional tooth thickness deviation evaluation system is established, which specifically includes a three-dimensional characterization of arbitrary tooth thickness deviation and new statistical indicators; finally, the tooth thickness deviation of any cross-section and any evaluation circle of the gear is accurately measured, characterized as a whole, and statistically analyzed and evaluated; in this way, on the one hand, any tooth thickness deviation from the root to the top of the tooth can be measured, and the installation eccentricity error is compensated, thereby improving the measurement accuracy of the tooth thickness deviation; on the other hand, the evaluation result is in line with the actual performance and can fully characterize the overall quality of the gear.

[0142] The above is only an embodiment of the present invention, and the common knowledge such as the known specific technical solutions or characteristics in the solution is not described in detail here. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the technical solution of the present invention, which should also be regarded as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A method for measuring arbitrary tooth thickness deviation considering installation eccentricity, characterized in that: The following steps are involved: S1. Establish a three-dimensional model of the gear tooth surface The Cartesian rectangular coordinate system of the gear tooth surface is established according to the right-hand rule, and the involute tooth surface equation of any point on the gear tooth surface is established according to the shape and position parameters of the tooth surface; S2. Solving the installation eccentricity Based on the geometric relationship between the actual tooth thickness measurement point and the center of the gear being measured, the installation eccentricity is iteratively solved by the Gauss-Newton method; S3. Establish a calculation model for arbitrary tooth thickness deviation The installation eccentricity obtained by S2 is used to correct the actual tooth thickness measurement point to obtain an accurate tooth thickness measurement point, and a calculation model for the tooth thickness deviation of any evaluation circle is established, and any tooth thickness deviation is calculated using the calculation model; Among them, the arbitrary evaluation of the round tooth thickness deviation e p The calculation model expression is: e p =r p ×(θ p -g p ) Among them, r p is the radius of any evaluation circle, r b is the base circle radius, r is the pitch circle radius, θ p is the polar angle value of the arbitrary evaluation round tooth thickness, θ b is the base circle tooth thickness polar angle value, ζ p is the polar angle of the tooth thickness measurement point on any evaluation circle, z is the total number of gears; S4. Establish a 3D tooth thickness deviation evaluation system A mathematical model is established for structured expression of tooth thickness deviation, so as to statistically analyze the tooth thickness deviation data of all tooth surfaces in radial, tooth direction and circumferential directions, and a statistical evaluation index of 3D tooth thickness deviation is calculated based on the mathematical model.

2. The method for measuring any tooth thickness deviation taking into account installation eccentricity according to claim 1, characterized in that: In step S1, the Cartesian coordinate system of the gear tooth surface is σ g =[o g ;x g ,y g ,z g ],D:(x d ,y d ,z d ) is the three-dimensional coordinate of any point on the gear tooth surface being measured, and the involute tooth surface equation where point D is located is: Among them, r b is the base circle radius of the gear being measured; z d is the axial height corresponding to point D in the gear coordinate system; μ0 is the initial phase angle of the involute of the right tooth surface where point D is located; θ d is the expansion angle of the involute of the right tooth surface where point D is located; f is the tooth surface direction, when f=1, it indicates the right tooth surface, when f=-1, it indicates the left tooth surface, x0, y0 are respectively along the x g ,y g Eccentricity in the axial direction.

3. The method for measuring any tooth thickness deviation taking into account installation eccentricity according to claim 1, characterized in that: In step S2, the steps of iteratively solving the installation eccentricity x0, y0 by Gauss-Newton method are: S201. Establish the least squares equation based on the sum of squares of actual tooth thickness deviations on the pitch circle: In the formula, ψ b (x d ,y d ) is the measured value of the central angle corresponding to the base circle tooth thickness in the measured gear coordinate system, α is the known pitch circle pressure angle, m is the cylindrical gear module, t is the gear number, and z is the total number of gears; S202, determine the iterative Jacobian matrix J calculation formula: S203, define Δx0 and Δy0 as iterative increments, and determine the expression of iterative increments: S204, perform an iterative loop based on the following expression: Where w is the number of iterations; S205 . When the increments Δx0 and Δy0 are less than a specified threshold or the number of iterations exceeds a maximum value, the iteration is stopped and accurate x0 and y0 are obtained.

4. The method for measuring any tooth thickness deviation taking into account installation eccentricity according to claim 2, characterized in that: In step S3, the expression for correcting the actual tooth thickness measurement point using x0, y0 is:

5. The method for measuring any tooth thickness deviation taking into account installation eccentricity according to claim 1, characterized in that: In step S3, the tooth thickness measurement points are converted into polar coordinates (r k , k ), calculate the interval [r k ,r k+1 ] the polar coordinates of any point P in p ,ζ p ) is: In the above formula: r p is the polar radius of point P, ζ p is the polar angle of point P, r k is the polar diameter of the accurate measurement point, ζ k To accurately measure the polar angle of a point.

6. The method for measuring any tooth thickness deviation taking into account installation eccentricity according to claim 1, characterized in that: In step S4, the mathematical model is e(j,t)| p , where p, j, t are the evaluation circle number, section number and gear number respectively, p = {1, 2, ... h}, j = {1, 2, ... n}, t = {1, 2, ... z}, and h, n, z are the corresponding totals.

7. The method for measuring any tooth thickness deviation taking into account installation eccentricity according to claim 6, characterized in that: In step S4, the statistical evaluation index of 3D tooth thickness deviation includes the mean value of tooth thickness deviation μ e , tooth thickness deviation standard deviation σ e , maximum tooth thickness deviation Maxe, minimum tooth thickness deviation Mine, tooth thickness deviation range R e ; Mean tooth thickness deviation μ e The expression is: Tooth thickness deviation standard deviation σ e The expression is: The expression of the maximum tooth thickness deviation Maxe is: Maxe=Max[e(j,t)| p ] The expression of the minimum tooth thickness deviation Mine is: Mine=Min[e(j,t)| p ] Tooth thickness deviation R e The expression is: R=Maxe-Mine In the above formula, p, j, t are the evaluation circle number, section number and gear number respectively, and h, n, z are the corresponding total numbers.

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