A wheel hub machining error compensation method and system

Abstract

The application provides a hub machining error compensation method and system, and relates to the technical field of error verification. The method comprises the following steps: selecting a plurality of observation points on a current hub end face and establishing a space coordinate system, constructing an error optimization model after obtaining the coordinate values of the observation points, and defining a residual sum of squares function; calculating the partial derivative of the residual sum of squares function with respect to the to-be-optimized parameters, iteratively adjusting the to-be-optimized parameters by using the LM algorithm until the stop condition is met, and outputting the optimal parameters; substituting the optimal parameters into the error optimization model to obtain the actual errors of the observation points, judging whether all the actual errors are less than a preset error threshold, and outputting a qualified or unqualified signal based on the judgment result. The application can capture various error factors of the hub end face, and effectively improve the evaluation accuracy of the hub product end face quality.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of error verification, in particular to a wheel hub machining error compensation method and system. BACKGROUND

[0002] As a core component of the automobile driving system, the machining precision of the wheel hub directly affects the safety, controllability and NVH (noise, vibration and harshness) performance of the vehicle. With the development of new energy vehicles and lightweight technology, aluminum alloy wheel hubs are widely used due to their high strength and low weight characteristics. However, during the manufacturing process, factors such as casting deformation and machining errors can cause the end face geometric parameters to deviate from the design values. Traditional wheel hub error detection mainly relies on manual sampling inspection or simple measurement tools, which has the problems of low efficiency and insufficient coverage. Therefore, how to achieve full inspection of wheel hub products through high-precision and automated error verification technology has become a key direction for industry technology upgrading.

[0003] A Chinese invention patent with the application publication number CN103235553A provides a numerical control machining size error automatic compensation method based on fractional order. The method measures the size of the machined workpiece to obtain actual machining size data, compares the size of the expected size data and the measured size data, solves the size error, and based on the analysis result of the error, calculates the compensation amount of the next workpiece according to the system order and the size error generated during the machining of the previous workpiece by using the iterative learning method.

[0004] The above-mentioned patent focuses on solving the size error by comparing the measured size data with the expected size data. Although this method is effective, it is not intuitive and comprehensive when dealing with the geometric error of complex-shaped workpieces, resulting in low accuracy of the quality evaluation result of the end face of the wheel hub product. SUMMARY

[0005] In order to improve the accuracy of the quality evaluation result of the end face of the wheel hub product, the application provides a wheel hub machining error compensation method and system.

[0006] In a first aspect, the application provides a wheel hub machining error compensation method, which adopts the following technical solution:

[0007] A wheel hub machining error compensation method includes the following steps:

[0008] Selecting observation points: selecting a plurality of observation points on the end face of the current wheel hub, and establishing a spatial coordinate system;

[0009] Data acquisition: acquiring the coordinate values of each observation point, constructing an error optimization model based on the coordinate values, obtaining the optimization parameters in the error optimization model, and defining a residual sum of squares function based on the error optimization model;

[0010] Calculating parameters: calculating the partial derivative of the residual sum of squares function with respect to each parameter to be optimized, adjusting the parameters to be optimized by the LM algorithm based on the partial derivative, and outputting the optimal parameters after meeting the preset stopping condition, denoted as optimal parameters;

[0011] Verification: substituting the optimal parameters into the error optimization model, obtaining the actual error of each observation point based on the error optimization model with the optimal parameters, and determining whether the actual error of all observation points is less than the preset error threshold, if yes, outputting a qualified signal; if not, outputting an unqualified signal.

[0012] The present application can comprehensively capture the geometric characteristics of the hub end face by selecting multiple observation points on the hub end face and establishing a spatial coordinate system, then obtaining the coordinate values of each observation point, and constructing an error optimization model based on the coordinate values, calculating the optimal parameters, then substituting the optimal parameters into the error optimization model, and obtaining the actual error of each observation point based on the error optimization model with the optimal parameters. The actual error directly reflects the difference between the actual shape and the ideal shape of the hub end face, and various error factors of the hub end face are captured, improving the accuracy of evaluating the quality of the hub product end face. The present application uses the residual sum of squares function as the optimization target, solves the parameter adjustment direction through the partial derivative, and iteratively optimizes the LM algorithm (Levenberg-Marquardt algorithm), thereby efficiently approaching the optimal solution and improving the calculation efficiency. The present application reconstructs the geometric model based on the optimal parameters, directly verifies the fitting effect, directly associates the production standard based on the actual error threshold, and outputs a clear qualified / unqualified signal, facilitating quality detection of the hub product.

[0013] Optionally, after the step of calculating parameters, before the step of verification, it further includes:

[0014] Error judgment: calculating the position error of each observation point based on the coordinate value of the observation point and the optimal parameters, calculating the standard deviation of the position error, and determining whether there is an observation point with a position error greater than twice the standard deviation, if yes, executing the step of reconstructing the function; if not, executing the step of verification;

[0015] Reconstructing the function: calculating the position weight of each observation point based on the standard deviation and the position error of each observation point, redefining the residual sum of squares function based on the position weight, and re-executing the step of calculating parameters based on the redefined residual sum of squares function.

[0016] The application can effectively identify outliers (such as measurement noise, surface defects or sampling errors) by calculating the standard deviation of the position degree error and screening out observation points with position degree error greater than twice the standard deviation, and if there are observation points with position degree error greater than twice the standard deviation, the position degree weight of each observation point is calculated based on the standard deviation and the position degree error, if there are no observation points with position degree error greater than twice the standard deviation, the step of verification is performed, the application only reconstructs the residual sum of squares function when there are observation points with position degree error greater than twice the standard deviation, which can avoid over-optimization of normal data as much as possible, while processing abnormal data.

[0017] The application calculates the position degree weight of each observation point, gives smaller position degree weight to the observation point with larger position degree error, reduces the influence of the observation point on the residual sum of squares function, redefines the residual sum of squares function based on the set position degree weight, focuses the optimization target on the reliable data, improves the fitting precision of the error optimization model, and makes the optimal parameter closer to the true value.

[0018] Optionally, the calculation model of the position degree weight is as follows:

[0019] ;

[0020] Wherein, is the position degree weight of the i th observation point; is the position degree error of the i th observation point; is the standard deviation of the position degree error.

[0021] Optionally, after outputting the unqualified signal, the method further comprises:

[0022] According to the preset detection path, a detection number is generated for each observation point, the observation point with actual error not less than the preset error threshold is recorded as an out-of-tolerance observation point, the detection number of the out-of-tolerance observation point is obtained, the turning compensation amount of the out-of-tolerance observation point is calculated, and the detection number and the turning compensation amount of the out-of-tolerance observation point are fed back.

[0023] Optionally, the method further comprises:

[0024] The error sensitivity value of each observation point is calculated respectively, the observation point with error sensitivity value greater than a first sensitivity threshold is integrated into a first observation point set, the observation point with error sensitivity value not greater than the first sensitivity threshold and greater than a second sensitivity threshold is integrated into a second observation point set, and the observation point not greater than the second sensitivity threshold is integrated into a third observation point set;

[0025] The number of error sensitivity values in the first observation point set, the second observation point set and the third observation point set is set and fed back according to the corresponding selection number.

[0026] The application divides the observation points into three levels of a high-sensitivity set (a first observation point set), a medium-sensitivity set (a second observation point set), and a low-sensitivity set (a third observation point set) by setting two sensitivity thresholds, sets the selection number corresponding to the number of error-sensitive values contained in the level of the observation point according to the level of the observation point, reduces the calculation amount of the low-sensitivity point and the redundant overhead, fully considers the high-sensitivity point, and improves the overall calculation accuracy under controllable cost.

[0027] Optionally, the method further comprises: selecting the next hub end surface observation point based on the selection number, and performing the data acquisition step.

[0028] Optionally, the error judgment step further comprises:

[0029] An error matrix is constructed using the position error of all observation points, the error matrix is centrally processed, a covariance matrix is calculated based on the centrally processed error matrix, the eigenvalue and eigenvector of the covariance matrix are calculated, the direction of the eigenvector corresponding to the maximum eigenvalue is updated as the direction of the horizontal axis of the coordinate system, a new coordinate system is obtained, and the data acquisition and parameter calculation steps are re-executed.

[0030] Optionally, after the direction of the eigenvector corresponding to the maximum eigenvalue is updated as the direction of the horizontal axis of the coordinate system, the method further comprises: determining the directions of the vertical axis and the vertical axis by orthogonal transformation.

[0031] Optionally, after the direction of the eigenvector corresponding to the maximum eigenvalue is updated as the direction of the horizontal axis of the coordinate system, the method further comprises:

[0032] Based on the updated horizontal axis direction of the coordinate system, the projection mean point of all observation points in the horizontal axis direction is calculated, and the projection mean point is set as a new coordinate origin.

[0033] The application obtains the direction of the eigenvector corresponding to the maximum eigenvalue (i.e. the direction of the maximum data variance) by calculating the eigenvalue and eigenvector of the covariance matrix, sets the direction of the eigenvector as the horizontal axis of the new coordinate system, aligns the main variation direction of the original error distribution to the coordinate axis, reduces the systematic error caused by the deviation of the coordinate system, and reduces the multi-axis coupling error superposition after aligning the main variation direction to the coordinate axis, thereby simplifying the multi-dimensional error problem into independent error analysis dominated by a single axis. Subsequently, the application sets the projection mean as a new coordinate origin, realizes the function of aligning the coordinate origin to the centroid of the main direction of the error distribution, and reduces the translation deviation. By using the above scheme, the application can also decouple the rotation error and the translation error for independent processing, thereby improving the compensation efficiency.

[0034] In a second aspect, the application provides a wheel hub machining error compensation system, which adopts the following technical scheme:

[0035] A wheel hub machining error compensation system comprises a memory and a processor,

[0036] The memory stores a computer readable storage medium;

[0037] The processor processes the computer program stored on the computer readable storage medium to implement the method of the first aspect.

[0038] In summary, the application has at least one of the following beneficial technical effects:

[0039] 1. The application can comprehensively capture the geometric characteristics of the wheel hub end face by selecting multiple observation points on the wheel hub end face and establishing a spatial coordinate system, then obtaining the coordinate values of each observation point, and constructing an error optimization model based on the coordinate values, calculating the optimal parameters, then substituting the optimal parameters into the error optimization model, and obtaining the actual error of each observation point based on the error optimization model after substituting the optimal parameters, which directly reflects the difference between the actual shape and the ideal shape of the wheel hub end face through the actual error, and further captures various error factors of the wheel hub end face, improving the accuracy of evaluating the quality of the wheel hub product end face. The application uses the sum of squared residuals function as the optimization objective, solves the parameter adjustment direction by partial derivative, and iteratively optimizes combined with the LM algorithm (Levenberg-Marquardt algorithm), thereby efficiently approaching the optimal solution and improving the calculation efficiency. The application reconstructs the geometric model based on the optimal parameters, directly verifies the fitting effect, directly associates the production standard based on the actual error threshold, and outputs clear pass / fail signals, which is convenient for quality detection of the wheel hub product.

[0040] 2. The application calculates the position degree weight of each observation point, gives smaller position degree weight to the observation point with larger position degree error, reduces the influence of the observation point on the sum of squared residuals function, redefines the sum of squared residuals function based on the set position degree weight, focuses the optimization objective on the reliable data, improves the fitting accuracy of the error optimization model, and makes the optimal parameters closer to the true value.

[0041] 3. The application divides the observation points into three levels of high sensitivity set (first observation point set), medium sensitivity set (second observation point set) and low sensitivity set (third observation point set) by setting two sensitivity thresholds, and sets the corresponding selection number according to the number of error sensitive values contained in the level of the observation point, which can reduce the calculation amount of low sensitive points and reduce redundant expenses, while fully considering high sensitive points and improving the overall calculation accuracy under controllable cost. BRIEF DESCRIPTION OF DRAWINGS

[0042] Fig. 1 is a flow chart of embodiment 1 of the present application;

[0043] Fig. 2 is a flow chart of embodiment 2 of the present application;

[0044] Fig. 3 is a flow chart of embodiment 3 of the present application. DETAILED DESCRIPTION

[0045] The following is a further detailed description of the present application. Figs. 1 to 3 The present application is further described in detail.

[0046] Embodiment 1: The present embodiment discloses a wheel hub machining error compensation method, referring to Fig. 1 , the method comprises: S11 selecting observation points, S12 data acquisition, S13 calculating parameters, S14 verification, selecting a plurality of observation points on the current wheel hub end face and establishing a spatial coordinate system, constructing an error optimization model after obtaining the coordinate values of each observation point, and defining a residual sum of squares function; calculating the partial derivative of the residual sum of squares function with respect to the to-be-optimized parameters, iteratively adjusting the to-be-optimized parameters by the LM algorithm until the stop condition is met, and outputting the optimal parameters; substituting the optimal parameters into the error optimization model to obtain the actual errors of each observation point, judging whether all the actual errors are less than the preset error threshold, and outputting a qualified or unqualified signal based on the judgment result, the execution process of the present embodiment is as follows:

[0047] S11 selects observation points, a plurality of observation points are selected on the current wheel hub end face, at least six observation points are selected in order to improve the calculation accuracy, and then a spatial coordinate system is established by using the right-hand rule, in order to facilitate calculation, the direction of the Z axis of the spatial coordinate system in the present embodiment is the central axis direction of the center hole of the wheel hub end face, the direction of the X axis is any radial direction of the wheel hub end face, and the direction of the Y axis is perpendicular to the direction of the X axis.

[0048] S12 data acquisition, the coordinate values of each observation point are obtained by CMM (three-coordinate measuring machine) or industrial camera calibration method, wherein the coordinate values of the i-th observation point are .

[0049] The error optimization model in the present embodiment adopts quadratic surface fitting, and the calculation model is as follows:

[0050] ;

[0051] Wherein, z is the theoretical value of the vertical coordinate of the observation point, based on the above error optimization model, the to-be-optimized parameters are a, b, c, d, f and g, and all the to-be-optimized parameters are integrated into the to-be-optimized parameter vector .

[0052] In other embodiments, the error optimization model can also adopt a radial basis function, and the calculation model is as follows:

[0053] ;

[0054] ;

[0055] wherein, is an error optimization model, n is the number of observation points, is the weight coefficient of the i-th observation point, is the abscissa of the i-th observation point.

[0056] In this embodiment, the parameters to be optimized are In S13, the optimal parameters are solved by constructing a linear equation system in the calculation of the parameters.

[0057] Based on the error optimization model, a residual sum of squares function is defined, and the calculation model of the residual sum of squares function is as follows:

[0058] ;

[0059] wherein, is a theoretical value calculated based on the error optimization model, and n is the total number of selected observation points in S11.

[0060] In S13, the partial derivative of the residual sum of squares function with respect to each parameter is calculated, and all the partial derivatives are integrated into a Jacobian matrix J, wherein the element in the i-th row and the j-th column of the Jacobian matrix represents the partial derivative of the residual sum of squares function of the i-th observation point with respect to the j-th parameter to be optimized, that is:

[0061] ;

[0062] ;

[0063] Then, the parameters to be optimized are adjusted by the LM algorithm, and the update rule of the LM algorithm is as follows:

[0064] ;

[0065] wherein, is a damping factor, when the residual error of the k+1 iteration is greater than the residual error of the k iteration, the damping factor is increased , otherwise, the damping factor is decreased , is a non-negative scalar, in this embodiment, the value range of is 0.001-1000, and the initial value is 0.1.

[0066] In other embodiments, the value range of

[0067] is the to-be-optimized parameter vector after the kth iteration, is the to-be-optimized parameter vector after the kth iteration.

[0068] is a unit matrix, and the dimension is the same as that of .

[0069] is the Jacobian matrix at the kth iteration is transposed.

[0070] is the residual at the kth iteration.

[0071] After the preset number of iterations is met or each parameter change amount is less than , the optimal to-be-optimized parameter, that is, the optimal parameter, is output.

[0072] S14 verifies that the optimal parameter is substituted into the error optimization model, and actual errors of each observation point are obtained based on the error optimization model into which the optimal parameter is substituted. The calculation model of the actual error is as follows:

[0073] ;

[0074] wherein, is the actual error of the i th observation point, is the vertical coordinate of the i th observation point collected through the data collection in S12, is the theoretical value of the vertical coordinate of the i th observation point calculated through the error optimization model.

[0075] It is judged whether the actual errors of all observation points are less than the preset error threshold. If yes, a qualified signal is output; if no, an unqualified signal is output.

[0076] By adopting the above scheme, the embodiment effectively improves the accuracy of the evaluation result of the hub product end face quality.

[0077] In other embodiments, after the unqualified signal is output, the method further comprises:

[0078] According to a preset detection path, a detection number is generated for each observation point, the detection number of an out-of-tolerance observation point (that is, an observation point with an actual error not less than a preset error threshold) is obtained, and a turning compensation amount of the out-of-tolerance observation point is calculated. The calculation model of the turning compensation amount is as follows:

[0079] Turning compensation amount = compensation coefficient x actual error;

[0080] The compensation coefficient has a value range of 0.6-0.8.

[0081] Finally, feedback the detection number of the out-of-tolerance observation point and the turning compensation amount.

[0082] Embodiment 2: Reference Fig. 2 The difference between this embodiment and embodiment 1 is that, after performing S13 to calculate the parameters, before performing S14 to verify, the method further comprises:

[0083] S21 error judgment, based on the coordinate value of each observation point and the optimal parameters, calculate the position error of the observation point , the calculation model of the position error is as follows:

[0084] ;

[0085] wherein, is the theoretical horizontal coordinate of the i-th observation point; is the theoretical vertical coordinate of the i-th observation point; is the theoretical value of the vertical coordinate of the i-th observation point calculated by the error optimization model, is the coordinate value of the i-th observation point, obtained by the S12 data acquisition step.

[0086] wherein, is the theoretical horizontal coordinate of the i-th observation point and is the theoretical vertical coordinate of the i-th observation point obtained based on the design drawing of the hub.

[0087] Based on the position error of all observation points, calculate the standard deviation of the position error , the calculation model of the standard deviation is as follows:

[0088] ;

[0089] ;

[0090] wherein, is the average value of the position error.

[0091] Determine whether there is an observation point with a position error greater than twice the standard deviation, if yes, perform S22 to reconstruct the function; if not, perform S14 to verify.

[0092] S22 reconstruct the function, based on the standard deviation and the position error of each observation point calculate the position weight of each observation point, the calculation model of the position weight is as follows:

[0093] ;

[0094] wherein, is the position degree weight of the i-th observation point; is the position degree error of the i-th observation point; is the standard deviation of the position degree error.

[0095] redefine the residual sum of squares function based on the position degree weight, and re-perform the S13 calculation parameter based on the redefined residual sum of squares function, the calculation model of the redefined residual sum of squares function is as follows:

[0096] .

[0097] By adopting the above scheme, the embodiment reduces the influence degree of the observation point with the position degree error greater than twice the standard deviation on the residual sum of squares function, improves the robustness of the residual sum of squares function, separates the typical error and the abnormal error, so that the parameter adjustment is more targeted to the systematic deviation (such as workpiece thermal deformation), and reduces the invalid operation.

[0098] Embodiment 3: Referring to Fig. 3 , the difference between the embodiment and embodiment 2 is that the method further comprises:

[0099] S31 sets a selection number, and calculates an error sensitivity value of each observation point, the calculation model of the error sensitivity value of the i-th observation point is as follows:

[0100] ;

[0101] ;

[0102] ;

[0103] ;

[0104] wherein, is the error sensitivity value of the i-th observation point; n is the total number of observation points; is the sensitivity weight of the i-th observation point; is the local sensitivity value of the i-th observation point and the j-th observation point; is the actual error of the j-th observation point; is the geometric distance between the i-th observation point and the j-th observation point; is the abscissa of the i-th observation point; is the abscissa of the j-th observation point; is the ordinate of the i-th observation point; is the ordinate of the i-th observation point; is the abscissa of the j-th observation point; is the ordinate of the j-th observation point.

[0105] The observation points with error sensitivity values greater than the first sensitivity threshold value are integrated into a first observation point set, i.e., a high-sensitivity set, which contains the observation points that have the greatest impact on quality (such as the hub center hole and bolt hole positions), and the number of observation points in the first observation point set needs to be increased.

[0106] The observation points with error sensitivity values not greater than the first sensitivity threshold value and greater than the second sensitivity threshold value are integrated into a second observation point set, i.e., a medium-sensitivity set, which contains the observation points that have a moderate but non-negligible impact on quality (such as the spoke round corner and mounting surface flatness), and the number of observation points in the second observation point set is moderate.

[0107] The observation points not greater than the second sensitivity threshold value are integrated into a third observation point set, i.e., a low-sensitivity set, which contains the observation points that have a smaller impact on quality (such as the hub outer edge chamfer and non-mating surface roughness), and the number of observation points in the third observation point set can be reduced.

[0108] The corresponding selection numbers are set and fed back based on the number of error sensitivity values in the first observation point set, the second observation point set, and the third observation point set. In this embodiment, the selection numbers are selected as follows:

[0109] If the number of observation points N1 contained in the first observation point set is N1≥3, at least observation points (i.e., high-sensitivity points are preferentially covered) in the first observation point set need to be selected in the next round of measurement.

[0110] If the number of observation points N2 contained in the second observation point set is N2≥5, observation points in the second observation point set need to be selected in the next round of measurement.

[0111] If the number of observation points N3 contained in the third observation point set is N3≥10, only observation points (i.e., non-critical measurements are reduced) in the third observation point set need to be selected in the next round of measurement.

[0112] In other embodiments, the selection numbers can also be selected as follows:

[0113] In the next round of measurement, the number of observation points selected in the first observation point set is based on the number of observation points contained in the first observation point set.

[0114] In the next round of measurement, the number of observation points selected in the second observation point set is based on the number of observation points contained in the second observation point set.

[0115] ​​​​​In the next round of measurement, based on the number of observation points contained in the third observation point set, the number of observation points selected in the third observation point set is .

[0116] S32 selects a target point, selects the next hub end surface observation point based on the selected number in S31, and performs S12 data acquisition.

[0117] By adopting the above scheme, the embodiment can adjust the selection number of the next hub observation point based on the detection situation of the last hub for the same batch of hubs, realize more accurate allocation of detection resources, and balance efficiency and quality.

[0118] Embodiment 4: The difference between this embodiment and embodiment 2 is that the S21 error judgment further includes:

[0119] The position error of each observation point is converted into a three-dimensional vector , wherein

[0120] ;

[0121] ;

[0122] ;

[0123] The three-dimensional vector represents the actual deviation of the point in the ideal coordinate system. The error vectors of all observation points are arranged in columns to form an error matrix.

[0124] Each column element in the error matrix is centrally processed to obtain a centrally processed error matrix E, and a covariance matrix of the centrally processed error matrix is calculated, and the covariance matrix F = EE T , E T is the transpose of the centrally processed error matrix.

[0125] The eigenvalues and eigenvectors of the covariance matrix are calculated, the direction of the eigenvector corresponding to the maximum eigenvalue is updated as the direction of the horizontal axis of the coordinate system, the directions of the vertical axis and the vertical axis are determined through orthogonal transformation (such as Gram-Schmidt orthogonalization), and the projection mean point of all observation points in the principal component direction is calculated based on the updated horizontal axis direction of the coordinate system. Set the projection mean point as the new coordinate origin to obtain a new coordinate system, and re-perform S12 data acquisition and S13 parameter calculation.

[0126] The traditional coordinate system may introduce systematic bias due to clamping error, equipment vibration, etc. By adopting the above scheme, the embodiment can automatically align the above systematic bias, extract the principal component of the error distribution, dynamically update the coordinate system and reacquire data, and reduce the calculation error.

[0127] Embodiment 5: This embodiment discloses a wheel hub machining error compensation system, the system comprises a memory and a processor,

[0128] The computer readable storage medium is stored in the memory;

[0129] The processor processes the computer program stored on the computer readable storage medium to implement the wheel hub machining error compensation method.

[0130] The above are preferred embodiments of the present application, not limited to the protection scope of the present application, therefore: all equivalent changes made according to the structure, shape, principle of the present application should be covered within the protection scope of the present application.

Claims

1. A method for compensating for wheel hub machining errors, characterized in that, include: Select observation points: Select multiple observation points on the current hub end face and establish a spatial coordinate system; Data acquisition: Obtain the coordinates of each observation point, where the coordinates of the i-th observation point are... An error optimization model is constructed based on the coordinate values, the parameters to be optimized in the error optimization model are obtained, and a residual sum of squares function is defined based on the error optimization model. The error optimization model uses quadratic surface fitting, and the calculation model is as follows: ； Where z is the theoretical value of the vertical coordinate of the observation point, and based on the above error optimization model, the parameters to be optimized are a, b, c, d, f, and g. All the parameters to be optimized are integrated into a parameter vector. ; Based on the error optimization model, a residual sum of squares function is defined, and the calculation model of the residual sum of squares function is as follows: ； in, It is a theoretical value calculated based on the error optimization model, where n is the total number of observation points selected in the step of selecting observation points; Parameter calculation: Calculate the partial derivative of the residual sum of squares function with respect to each parameter to be optimized. Based on the partial derivatives, iteratively adjust the parameters to be optimized using the LM algorithm until the preset stopping condition is met, and then output the optimal parameters to be optimized, which are denoted as the optimal parameters. Verification: Substitute the optimal parameters into the error optimization model, obtain the actual error of each observation point based on the error optimization model with the optimal parameters, and determine whether the actual error of all observation points is less than the preset error threshold. If yes, output a qualified signal; otherwise, output a unqualified signal.

2. The wheel hub machining error compensation method according to claim 1, characterized in that, After the step of calculating the parameters and before the step of verification, the following steps are also included: Error judgment: Calculate the position error of each observation point based on its coordinates and optimal parameters, calculate the standard deviation of the position error, and determine whether there are any observation points with a position error greater than twice the standard deviation. If so, execute the reconstruction function step; otherwise, execute the verification step. Reconstruction function: Calculate the position weight of each observation point based on the standard deviation and the position error of each observation point, redefine the residual sum of squares function based on the position weight, and re-execute the parameter calculation steps based on the redefined residual sum of squares function.

3. The wheel hub machining error compensation method according to claim 2, characterized in that, The calculation model for the positional weight is as follows: ； in, The positional weight of the i-th observation point; The positional error of the i-th observation point; This represents the standard deviation of the positional error.

4. The wheel hub machining error compensation method according to claim 1, characterized in that, After outputting the non-compliance signal, the method further includes: According to the preset detection path, a detection number is generated for each observation point. Observation points with actual errors not less than the preset error threshold are recorded as out-of-tolerance observation points. The detection number of the out-of-tolerance observation points is obtained, the turning compensation amount of the out-of-tolerance observation points is calculated, and the detection number and turning compensation amount of the out-of-tolerance observation points are fed back.

5. The wheel hub machining error compensation method according to claim 2, characterized in that, The method further includes: Calculate the error sensitivity value for each observation point. Integrate the observation points with error sensitivity values ​​greater than the first sensitivity threshold into the first set of observation points. Integrate the observation points with error sensitivity values ​​no greater than the first sensitivity threshold but greater than the second sensitivity threshold into the second set of observation points. Integrate the observation points with error sensitivity values ​​no greater than the second sensitivity threshold into the third set of observation points. The system sets and feeds back the number of error-sensitive values ​​based on the first, second, and third observation point sets.

6. The wheel hub machining error compensation method according to claim 5, characterized in that, The method further includes: selecting the next observation point on the hub end face based on the number of selections, and performing data acquisition.

7. The wheel hub machining error compensation method according to claim 2, characterized in that, The error determination step also includes: An error matrix is ​​constructed using the positional errors of all observation points. The error matrix is ​​then centered. Based on the centered error matrix, the covariance matrix is ​​calculated. The eigenvalues ​​and eigenvectors of the covariance matrix are calculated. The direction of the eigenvector corresponding to the largest eigenvalue is updated to the direction of the horizontal axis of the coordinate system, thus obtaining a new coordinate system. The data acquisition and parameter calculation steps are then re-executed.

8. The wheel hub machining error compensation method according to claim 7, characterized in that, After updating the direction of the eigenvector corresponding to the maximum eigenvalue to the direction of the horizontal axis of the coordinate system, the method further includes: determining the directions of the vertical axis and the vertical axis through orthogonal transformation.

9. The wheel hub machining error compensation method according to claim 7, characterized in that, After updating the direction of the eigenvector corresponding to the maximum eigenvalue to the direction of the horizontal axis of the coordinate system, the method further includes: Based on the updated coordinate system's horizontal axis direction, calculate the mean projection point of all observation points along the horizontal axis direction, and set the mean projection point as the new coordinate origin.

10. A wheel hub machining error compensation system, characterized in that, include: Memory and processor The memory contains a computer-readable storage medium; When the processor processes a computer program stored on the computer-readable storage medium, it implements the method as described in any one of claims 1-9.

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