Method for equal-thickness milling of double-direction bending surface of automobile front and rear axle workpiece

Abstract

This invention discloses a method for equal-thickness milling of bidirectional curved surfaces on automotive front and rear axle workpieces, specifically relating to the field of intelligent manufacturing equipment processing. The method includes reading the axle housing inner cavity points, axle tube inner wall points, reinforcing rib back side points, workpiece milling surface point cloud, and designed wall thickness from the automotive front and rear axle blank. The axle housing inner cavity points, axle tube inner wall points, and reinforcing rib back side points are merged into an inner point set. A milling surface point set for machining surfaces curved in both directions is extracted from the workpiece milling surface point cloud, and a measurement point table is output. Based on the measurement point table, the inner point spacing, outer point spacing, outer point curvature difference, and candidate wall thickness difference are calculated, and these are used as transmission costs to perform entropy regularization Gromov-Wasserstein optimal transmission, outputting a weight table of inner and outer points. By constraining the outer surface cutting layer with the actual inner cavity thickness, the problem of acceptable shape but uncontrolled wall thickness when machining surfaces curved in both directions in the intelligent manufacturing equipment industry is relatively alleviated.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing equipment processing technology, and more specifically, to a method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces. Background Technology

[0002] In the intelligent manufacturing equipment industry, irregular curved surface milling of automotive front and rear axles is usually used to eliminate the excess material on the outer surface after casting, welding and preforming. On the production site, the outer surface of the axle housing is first scanned and aligned, and then the measured point cloud is fitted with the designed outer contour. Rough milling, semi-finish milling and finish milling toolpaths are generated according to the shape deviation to ensure that the outer dimensions of the axle housing, axle tube connection area and flange transition surface meet the assembly requirements. However, in the scenario of lightweight manufacturing of front and rear axles, the wall thickness allowance of the axle housing is compressed. The inner cavity of the axle housing, the inner wall of the shaft tube, and the back side of the reinforcing rib also have forming defects, welding shrinkage, and local deformation. The deviation of the outer surface is not synchronized with the actual position of the inner cavity. If the outer contour is still used as the cutting reference, even if the final inspection outer contour falls within the tolerance range, the remaining wall thickness of the top of the axle housing, the root of the shaft tube, and the transition of the reinforcing rib will still be too thin or the thickness will change abruptly. Online thickness measurement can only find local deviations after processing, and it is difficult to reverse the already executed toolpath depth. This results in parts that meet the external shape requirements still need to be repaired, scrapped, or downgraded for use in the same batch of workpieces. The problem is concentrated in the intersection area of ​​bidirectional bending irregular curved surfaces that are sensitive to load. The technical problem to be solved by this application is: how to make the outer surface cutting layer constrained by the actual thickness of the inner cavity during the milling process of irregular curved surfaces of automobile front and rear axles, so as to avoid the situation where the shape is qualified but the remaining wall thickness is out of control due to milling only according to the outer contour deviation. Summary of the Invention

[0003] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces. This method establishes a thickness anchoring relationship between the inner point set and the milling surface point set, divides the surface used for machining curved surfaces in both directions into milling pieces and generates a depth-limited layer, so that the outer surface cutting layer is generated according to the actual thickness of the inner cavity, the designed wall thickness, and the transition relationship between adjacent milling pieces, thereby solving the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces, comprising: S1. Read the inner cavity points of the axle housing, the inner wall points of the shaft tube, the back side points of the reinforcing rib, the milling surface point cloud of the workpiece, and the design wall thickness of the front and rear axle blanks. Merge the inner cavity points of the axle housing, the inner wall points of the shaft tube, and the back side points of the reinforcing rib into an inner point set. Extract the milling surface point set for machining the surface that bends in two directions from the milling surface point cloud of the workpiece and output the measurement point table. S2. Based on the measurement point table, calculate the spacing between inner points, the spacing between outer points, the curvature difference between outer points, and the candidate wall thickness difference, and use these as the transmission cost to perform entropy regularization Gromov-Wasserstein optimal transmission, and output the weight table of inner and outer points. S3. According to the weight table, divide the milling surface point set into bridge milling pieces, shaft tube milling pieces, rib root milling pieces and flange milling pieces, and write the inner point number, outer point number, transmission weight and design wall thickness for each milling piece, and output the milling piece set; S4. Based on the milling plate set, establish a milling plate adjacency graph, generate depth constraints according to the design wall thickness difference, transmission weight and curvature difference of adjacent milling plates, and solve the allowable cutting thickness of each milling plate and the transition reduction of adjacent milling plates through the Hodge-Laplacian graph total variation near-end ADMM, and output the depth constraint layer. S5. Convert the depth-limited layer into a milling toolpath, so that the milling cutter performs segmented milling of the curved surface in two directions along the milling plate set, and writes the remeasured wall thickness back to the weight table and the depth-limited layer to generate the equal thickness milling forming result of the irregular curved surface of the front and rear axles of automobiles.

[0005] In a preferred embodiment, S1 includes: S1-1. Read the blank number, axle housing center coordinates, axle housing radius, left axle tube end face center coordinates, right axle tube end face center coordinates, left axle tube inner diameter, right axle tube inner diameter, stiffener back side end line coordinates, and flange end face coordinates of the front and rear axle blanks. Use the line connecting the center of the left axle tube end face to the center of the right axle tube end face as the axial reference line, the perpendicular line from the center of the axle housing end face to the axial reference line as the radial reference line, and the flange end face as the end face reference plane. Output the blank coordinate system. S1-2. Based on the blank coordinate system, read the bridge package inner cavity design surface, shaft tube inner wall design surface, stiffener back side design surface and design wall thickness in the design 3D model, and write the bridge package inner cavity design surface, shaft tube inner wall design surface, stiffener back side design surface and design wall thickness into the design datum table according to the blank number. S1-3. Based on the design reference table, generate bridge package measurement positions on the inner cavity design surface of the bridge package according to the circumferential angle and radial distance of the bridge package. Generate shaft tube measurement positions on the inner wall design surface of the shaft tube according to the axial distance and inner wall circumferential angle. Generate rib back measurement positions on the back side design surface of the reinforcing rib according to the rib length and rib width. Read the measured coordinates at each measurement position using a contact probe or ultrasonic thickness gauge and output the inner cavity point of the bridge package, the inner wall point of the shaft tube, and the back side point of the reinforcing rib.

[0006] In a preferred embodiment, S1 further includes: S1-4. Based on the blank coordinate system, the measured coordinates of the outer surface are read along the outer surface of the bridge package, the outer surface of the shaft tube transition, the outer surface of the stiffener root, and the outer surface of the flange transition using a contact probe. Points in the measured coordinates of the outer surface where the axial, radial, and circumferential coordinates all change are written into the milling surface point set. S1-5. Merge the points inside the bridge cavity, the points on the inner wall of the shaft tube, and the points on the back side of the reinforcing rib into an inner point set. Write the inner point set, the milled surface point set, and the design wall thickness into the measuring point table according to the blank number, and output the measuring point table.

[0007] In a preferred embodiment, S2 includes: S2-1. Read the set of inner points, the set of milled surface points and the design wall thickness from the measuring point table. Calculate the distance between the inner points of any two inner points and the distance between the outer points of any two outer points. For each outer point, form two outer point chord vectors according to the previous outer point, the current outer point and the next outer point. Write the angle between the two outer point chord vectors as the outer point curvature difference. Output the table of inner point distance, the table of outer point distance and the table of outer point curvature difference. S2-2. Form candidate point pairs by pairing each inner point with each outer point. Calculate the absolute value of the difference between the spatial distance of the candidate point pairs and the design wall thickness as the candidate wall thickness difference. Write the candidate wall thickness difference, the curvature difference of the outer points, the spacing between the inner points and the spacing between the outer points into the transmission cost table. Write the arithmetic mean of the candidate wall thickness differences in the transmission cost table as the entropy regularization term. S2-3. Using the transmission cost table and entropy regularization term as input, and the transmission table as the iteration object, the process of updating the transmission value by combining the squared difference between the in-point spacing and the out-point spacing, the candidate wall thickness difference, the out-point curvature difference, and the entropy regularization term is the entropy regularization Gromov-Wasserstein optimal transmission. The transmission table is rewritten round by round according to cost update, exponent rewriting, row normalization, and column normalization, and the transmission table in the last round is written as the weight table of in-point and out-point.

[0008] In a preferred embodiment, S3 includes: S3-1. Read the weight table, milling surface point set and measuring point table. For each outer point, read the transmission weight with the largest value and write the inner point number associated with the current transmission weight as the main inner point number. When there are parallel transmission weights with the largest values, read the candidate wall thickness difference between the parallel inner point and the current outer point, write the inner point number with the smallest candidate wall thickness difference as the main inner point number, and output the outer point master table.

[0009] In a preferred embodiment, S3 further includes: S3-2. Based on the external point master table, read the main internal point number, internal point type, axial coordinate, radial coordinate, circumferential coordinate and flange end face coordinate of each external point. Merge adjacent external points whose main internal point number belongs to the bridge package inner cavity point and whose circumferential coordinates are different into bridge package milling pieces. Merge adjacent external points whose main internal point number belongs to the shaft tube inner wall point and whose axial coordinates are different into shaft tube milling pieces. Merge adjacent external points whose main internal point number belongs to the reinforcing rib back side point and whose rib width coordinates are different into rib root milling pieces. Merge external points whose main internal point number belongs to the shaft tube inner wall point and whose axial coordinates are equal to the flange end face coordinates into flange milling pieces. S3-3. Generate milling piece numbers for bridge milling pieces, shaft tube milling pieces, rib root milling pieces, and flange milling pieces respectively, and write the milling piece number, main inner point number, outer point number, transmission weight, and design wall thickness into the milling piece set according to the blank number.

[0010] In a preferred embodiment, S4 includes: S4-1. Read the milling chip set, write each milling chip as a milling chip node, write two milling chips with a common outer point number as adjacent edges, write three milling chips enclosed by three adjacent edges and with each of the three adjacent to each other as chip rings, and write the milling chip node, adjacent edges and chip rings into the milling chip adjacency graph. S4-2. Based on the milling blade adjacency graph, read the measured wall thickness, designed wall thickness, transmission weight and curvature value of each milling blade, calculate the difference between the measured wall thickness and the designed wall thickness as the initial cutting thickness, calculate the difference in designed wall thickness, transmission weight and curvature between adjacent milling blades, and write them into the depth constraint table.

[0011] In a preferred embodiment, S4 further includes: S4-3. The allowable cutting thickness on the milling node, the transition reduction amount on the adjacent edge, the circumferential residual on the plate ring, and the Lagrange quantity are used as iteration fields. The adjacent transition reduction amount is subtracted from the initial cutting thickness according to the node field. The design wall thickness difference, transmission weight difference, and curvature difference are subtracted from the difference in allowable cutting thickness at both ends according to the edge field. The transition reduction amount of the three adjacent edges is accumulated according to the plate ring field. The residuals of the node field, edge field, and plate ring field are accumulated according to the Lagrange quantity. The above iteration fields are rewritten round by round. S4-4. The process of rewriting the allowable cutting thickness and transition reduction amount by milling nodes, adjacent edges and plate rings in S4-3 is taken as the near end ADMM of the total variation of the Hodge-Laplacian diagram. The number of iteration rounds is the sum of the number of milling nodes, the number of adjacent edges and the number of plate rings. The allowable cutting thickness of the last round is written into the milling depth limit field, and the transition reduction amount of the last round is written into the adjacent edge transition field. Then, the depth limit layer is generated according to the milling number, the milling depth limit field, the adjacent edge number and the adjacent edge transition field.

[0012] In a preferred embodiment, S5 includes: S5-1. Read the depth limit layer and milling plate set. Read the outer point number, outer point coordinates, main inner point number, milling plate depth limit field and adjacent edge transition field according to the milling plate number. Arrange the outer point coordinates in the same milling plate in the order of increasing axial coordinate, increasing circumferential coordinate, and increasing radial coordinate. Write the arranged outer point coordinates, sorting position, main inner point number and milling plate depth limit field into the trajectory point table. S5-2. Read the current trajectory point, the previous trajectory point, and the next trajectory point from the trajectory point table. Use the coordinate difference vector between the previous trajectory point and the next trajectory point as the tangent vector, and the coordinate difference vector between the current trajectory point and the current main inner point as the thickness vector. Subtract the projection of the thickness vector onto the tangent vector from the thickness vector and normalize it to the tool offset direction. Move the current trajectory point along the tool offset direction by the distance of the milling disc depth limit field to generate the tool position table.

[0013] In a preferred embodiment, S5 includes: S5-3. Read the arithmetic mean of the adjacent edge transition field, the last tool position point, the first tool position point, and the milling blade depth limit field of the adjacent milling blade. Divide the adjacent edge transition field by the arithmetic mean of the milling blade depth limit field and round up the quotient to get the number of transition points. Then, perform equal division and insertion on the coordinate difference between the last tool position point and the first tool position point according to the number of transition points, and output the milling toolpath. S5-4. Perform segmented milling according to the milling toolpath, and after milling, read the coordinates of the re-measured outer point and the re-measured inner point according to the outer point number. Write the distance between the re-measured outer point coordinates and the re-measured inner point coordinates as the re-measured wall thickness. Write the difference between the re-measured wall thickness and the design wall thickness into the weight table and the depth limit layer to generate the equal thickness milling forming result of the irregular curved surface of the front and rear axles of automobiles.

[0014] The technical effects and advantages of this invention are as follows: 1. By constraining the outer surface cutting layer with the actual thickness of the inner cavity, the problem of qualified shape but uncontrolled wall thickness when processing surfaces that are curved in two directions in the intelligent manufacturing equipment industry is relatively alleviated; 2. By linking the weights of the inner and outer points, the cutting reference in the intersection area of ​​the bridge package, shaft tube, and reinforcing ribs is changed from the outer contour deviation to the thickness relationship, which relatively reduces the risk of incorrect cutting; 3. By constraining the cutting transition of adjacent milling pieces through the milling piece adjacency diagram, the thickness jump at the curvature abrupt change is relatively suppressed when machining surfaces that are curved in two directions; 4. By re-measuring the wall thickness and writing back the weight table and the depth limit layer, the front and rear axle segment milling in the intelligent manufacturing equipment industry has a result correction link, which relatively reduces rework and downgraded use. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] Refer to the instruction manual appendix Figure 1 The present invention provides a method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces, comprising: S1. Read the inner cavity points of the axle housing, the inner wall points of the shaft tube, the back side points of the reinforcing rib, the milling surface point cloud of the workpiece, and the design wall thickness of the front and rear axle blanks. Merge the inner cavity points of the axle housing, the inner wall points of the shaft tube, and the back side points of the reinforcing rib into an inner point set. Extract the milling surface point set for machining the surface that bends in two directions from the milling surface point cloud of the workpiece and output the measurement point table. In this embodiment, S1 is used to form a measuring point table, so that the inner point set, the milled surface point set, and the design wall thickness are all generated in the blank coordinate system, and are used as inputs for S2 to calculate the inner point spacing, outer point spacing, outer point curvature difference, and candidate wall thickness difference. During execution, the blank coordinate system is first established from the bridge housing opening, the end faces of the two axle tubes on both sides, the back side of the reinforcing rib, and the flange end face of the automobile front and rear axle blank. Then, the inner cavity design surface and the design wall thickness in the design three-dimensional model are converted to the blank coordinate system. Subsequently, the inner surface measuring points and the outer surface measuring points are read respectively, and finally written into the measuring point table according to the blank number. In S1-1, the blank numbers of the front and rear axle blanks are read, and the axle opening sampling points are read along the edge of the axle opening using a contact probe. Circle fitting is performed on the axle opening sampling points to obtain the coordinates of the axle opening center and radius. End face sampling points are read along the inner circles of the left and right axle tube end faces, and circle fitting is performed on these points to obtain the coordinates of the left and right axle tube end face centers, as well as the inner diameters of the left and right axle tubes. End point coordinates are read along both ends of the back side of the reinforcing rib, and the coordinates of the two end point coordinates are connected to obtain the end line coordinates of the back side of the reinforcing rib. Three non-collinear end face sampling points are read along the flange end face. Plane fitting is performed on the end face sampling points to obtain the flange end face coordinates. The center of the left shaft tube end face is taken as the origin of the coordinate system. The direction from the center of the left shaft tube end face to the center of the right shaft tube end face is taken as the positive axial direction. The direction perpendicular from the center of the bridge port to the axial reference line is taken as the positive radial direction. The cross product of the positive axial direction and the positive radial direction is taken as the positive circumferential direction. The flange end face is taken as the end face reference plane to output the blank coordinate system. If the bridge port sampling points or shaft tube end face sampling points are missing, the missing sampling points at the circumferential position are read before performing circle fitting. If the flange end face sampling points are collinear, an end face sampling point that is not on the existing sampling point line is read before performing plane fitting. In S1-2, the design shaft tube centerline, design bridge inlet center, design flange end face, bridge inlet inner cavity design surface, shaft tube inner wall design surface, reinforcing rib back side design surface, and design wall thickness fields in the design 3D model are read based on the blank coordinate system. The design shaft tube centerline is translated and rotated to the axial reference line, the design bridge inlet center is transformed to the direction of the radial reference line, and the design flange end face is transformed to the end face reference surface, thus obtaining the rigid transformation relationship from the design 3D model to the blank coordinate system. Then, according to the rigid transformation relationship, the bridge inlet inner cavity design surface, shaft tube inner wall design surface, reinforcing rib back side design surface, and design wall thickness are transformed to the blank coordinate system and written into the design reference table according to the blank number. The design wall thickness is read according to the design surface position in the design 3D model and is not used as a single value for the entire blank. When the same measurement position falls at the intersection of two design surfaces, the design wall thickness of the design surface with the shorter projection distance of the measurement position is read and the design surface number is written into the design reference table for S2 to read when calculating the candidate wall thickness difference. In S1-3, the internal point positions are generated according to the design reference table, and the measured coordinates are read; the circumferential and radial section numbers of the inner cavity design surface of the bridge package are read, and the intersection of the circumferential and radial sections is written as the bridge package position; the axial section number and inner wall circumference line number of the inner wall design surface of the shaft tube are read, and the intersection of the axial section and inner wall circumference line is written as the shaft tube position; the rib length division line number and rib width division line number of the back side design surface of the reinforcing rib are read, and the intersection of the rib length division line and rib width division line is written as the rib back position; when using a contact probe, the contact probe is moved to the contact position of the blank inner surface corresponding to the bridge package position, shaft tube position, and rib back position, and the measured coordinates of the contact point are directly read and divided. Do not write the points as bridge cavity points, shaft tube inner wall points, and reinforcing rib back points; when using an ultrasonic thickness gauge, read the coordinates of the outer incident point, incident direction, and sound path thickness. Move the coordinates of the outer incident point in the opposite direction of the incident direction along the sound path thickness to obtain the coordinates of the inner point, and write them as bridge cavity points, shaft tube inner wall points, and reinforcing rib back points according to the measurement type; write the blank number, measurement number, inner point coordinates, inner point type, and inner point number for each bridge cavity point, shaft tube inner wall point, and reinforcing rib back point; when the measurement point cannot be contacted or the ultrasonic echo is missing, write the measurement point in the missing measurement field, and use the measured coordinates of adjacent measurement points on the same design surface and the same section line as subsequent interpolation inputs. Missing measurement points are not written as valid inner points; In S1-4, the measured coordinates of the outer surface are read based on the blank coordinate system, and the set of milling points for machining the surface curved in two directions is extracted from the measured coordinates of the outer surface. The contact probe moves in the measurement sequence of the outer surface of the bridge package, the outer surface of the shaft tube transition, the outer surface of the reinforcing rib root, and the outer surface of the flange transition, reading the measured coordinates of the outer surface point by point, and decomposing each measured coordinate of the outer surface into axial coordinates, radial coordinates, and circumferential coordinates. For the current measured coordinates of the outer surface, the measured coordinates of the previous and subsequent outer surfaces are read. There is an axial coordinate difference between the current measured coordinates of the outer surface and the previous measured coordinates of the outer surface, and the current measured coordinates of the outer surface are also different from the measured coordinates of the subsequent outer surfaces. When there is a radial or circumferential coordinate difference, the current measured coordinates of the outer surface are written into the milling surface point set. When the measured coordinates of the first outer surface are missing the measured coordinates of the previous outer surface, the reverse extension point of the measured coordinates of the second outer surface relative to the measured coordinates of the first outer surface is used as the measured coordinates of the previous outer surface. When the measured coordinates of the last outer surface are missing the measured coordinates of the next outer surface, the reverse extension point of the measured coordinates of the second to last outer surface relative to the measured coordinates of the last outer surface is used as the measured coordinates of the next outer surface. Each outer point in the milling surface point set is written with the blank number, outer point number, outer point coordinates, axial coordinates, radial coordinates, and circumferential coordinates for S2 to read when calculating the outer point spacing and outer point curvature difference. In S1-5, the points inside the bridge housing cavity, the points on the inner wall of the shaft tube, and the points on the back side of the reinforcing rib are merged into an inner point set. The inner point set, the milled surface point set, and the design wall thickness are then written into the measuring point table according to the blank number. Each inner point in the inner point set carries an inner point number, inner point type, inner point coordinates, and measurement position number. The inner point type includes points inside the bridge housing cavity, points on the inner wall of the shaft tube, and points on the back side of the reinforcing rib. Each outer point in the milled surface point set carries an outer point number, outer point coordinates, axial coordinates, radial coordinates, and circumferential coordinates. The design wall thickness... Write the design surface number, measurement position number, and external point projection position into the measurement point table; when writing into the measurement point table, first write the blank number, then write the inner point set, then write the milling surface point set, and finally write the design wall thickness field; when the same external point is projected to the intersection of two design surfaces, read the design wall thickness of the side with the shorter projection distance from the external point to the two design surfaces; after the measurement point table is output, S2 reads the inner point set according to the inner point number, reads the milling surface point set according to the outer point number, and reads the design wall thickness according to the external point projection position; Through S1 processing, the inner point set, milling surface point set, and design wall thickness of the front and rear axle blanks are written under the same blank number. Subsequently, the inner point spacing, outer point spacing, outer point curvature difference, and candidate wall thickness difference can be calculated according to the inner point number, outer point number, and design wall thickness fields, avoiding the outer surface milling depth being determined solely by shape deviation. In practical applications, for front axle blanks with eccentric axle housing openings and welding shrinkage differences on the axle tube end faces, axial reference lines are first established using the center of the left and right axle tube end faces, and then the axle housing inner cavity design surface and axle tube are... The inner wall design surface and the back side design surface of the reinforcing rib are converted to the blank coordinate system. Then, the inner cavity points of the bridge package are read at the intersection of the circumferential and radial sections of the inner cavity design surface, the inner wall points of the shaft tube are read at the intersection of the axial section of the inner wall design surface and the inner wall circumference, and the back side points of the reinforcing rib are read at the intersection of the rib length dividing line and the rib width dividing line of the back side design surface. The milled surface point set is read along the outer surface of the bridge package, the outer surface of the shaft tube transition, the outer surface of the reinforcing rib root, and the outer surface of the flange transition, and finally a measuring point table is formed for S2 to read directly.

[0018] S2. Based on the measurement point table, calculate the spacing between inner points, the spacing between outer points, the curvature difference between outer points, and the candidate wall thickness difference, and use these as the transmission cost to perform entropy regularization Gromov-Wasserstein optimal transmission, and output the weight table of inner and outer points. In this embodiment, S2 is used to convert the set of inner points and the set of milled surface points in the measurement point table into transmission calculation data between inner points and outer points, so that the actual position of the inner cavity, the curvature change of the outer surface, and the designed wall thickness all participate in the outer point connection; during execution, the spacing between inner points, the spacing between outer points, and the curvature difference of outer points are calculated first, then each inner point and each outer point form a candidate point pair and the candidate wall thickness difference is calculated, and then the transmission table is rewritten round by round through entropy regularization Gromov-Wasserstein optimal transmission, so that the weight table can represent the thickness anchoring relationship between inner points and outer points; this implementation process includes the following steps: In S2-1, the inner point set, milling surface point set, and design wall thickness are read from the measuring point table. First, the inner point coordinates of each inner point are read according to the inner point number. Then, the spatial distance between any two inner points is calculated and written as the inner point spacing, and written into the inner point distance table according to the two inner point numbers. Next, the outer point coordinates of each outer point are read according to the outer point number. The spatial distance between any two outer points is calculated and written into the outer point spacing table according to the two outer point numbers. When calculating the curvature difference of the outer points, the milling surface point set is first generated into an outer point sequence according to the region to which the outer point belongs, the axial coordinate increment, the circumferential coordinate increment, and the radial coordinate increment. For each current outer point, read the previous and next outer points. Use the coordinate difference vector between the previous and current outer points as the first sine vector and the coordinate difference vector between the current and next outer points as the second sine vector. Write the angle between the first and second sine vectors as the outer point curvature difference of the current outer point and write it into the outer point curvature difference table according to the outer point number. If the first outer point in the outer point sequence is missing the previous outer point, use the reverse extension point of the second outer point relative to the first outer point to make up the previous outer point. If the last outer point in the outer point sequence is missing the next outer point, use the reverse extension point of the second-to-last outer point relative to the last outer point to make up the next outer point. In S2-2, candidate point pairs are generated based on the set of interior points and the set of milled surface points, ensuring that each outer point has an interior point candidate object to participate in the transmission calculation. For each candidate point pair, the coordinates of the interior point, the coordinates of the outer point, and the design wall thickness corresponding to the current outer point are read. The spatial distance between the coordinates of the interior point and the coordinates of the outer point is calculated, and then the absolute value of the difference between the spatial distance and the design wall thickness is calculated. The absolute value of the difference is written as the candidate wall thickness difference. The design wall thickness is read according to the projection position of the current outer point in the design 3D model. When the current outer point falls at the intersection of two design surfaces, the one with the shorter projection distance is read. The design wall thickness of the side design surface is determined. Then, the inner point number, outer point number, candidate wall thickness difference, outer point curvature difference of the current outer point, inner point spacing related to the current inner point, and outer point spacing related to the current outer point are written into the transmission cost table. The arithmetic mean of all candidate wall thickness differences in the transmission cost table is calculated, and this arithmetic mean is written as the entropy regularization term. When all candidate wall thickness differences are zero, the arithmetic mean of the design wall thickness is written as the entropy regularization term. When the arithmetic mean of the design wall thickness is also zero, the sum of the arithmetic mean of the inner point spacing and the arithmetic mean of the outer point spacing is written as the entropy regularization term. In S2-3, a transmission cost table and entropy regularization are used to generate transmission weights between inliers and outliers round by round. These weights are simultaneously constrained by the spatial structure of inliers, the spatial structure of outliers, the curvature of outliers, and wall thickness deviations. First, an initial transmission table is generated, where the initial transmission value for each candidate point pair is the product of the number of inliers and the number of outliers. Then, the transmission table is used as the iteration object to perform entropy-regulated Gromov-Wasserstein optimal transmission. In each round, a cost update is performed: for the current inlier and outlier, all reference inliers and all reference outliers are read; the distance between the current inlier and the reference inlier is subtracted from the distance between the current outlier and the reference outlier, the squared result is multiplied by the distance between the reference inlier and the reference outlier from the previous round. The transmission values ​​are accumulated to obtain the structural cost of the current candidate point pair; the structural cost, candidate wall thickness difference, and outer point curvature difference are added to obtain the updated cost; then exponential rewriting is performed: the updated cost is divided by the entropy regularization term and the negative exponent is taken to obtain the positive transmission value; then row normalization is performed: each positive transmission value sent by the same inner point is divided by the sum of the positive transmission values ​​corresponding to the same inner point; then column normalization is performed: each transmission value received by the same outer point is divided by the sum of the transmission values ​​corresponding to the same outer point; one iteration includes one cost update, one exponential rewriting, one row normalization, and one column normalization. The iteration round number is the sum of the number of inner points and the number of outer points. The transmission table in the last round is written into the weight table according to the inner point number, outer point number, and transmission weight, which is read by S3 when determining the main inner point number of each outer point; Through the processing of S2, the inner and outer points are no longer directly connected based on the closest distance. Instead, the transmission weight is generated jointly by the inner point spacing structure, the outer point spacing structure, the outer point curvature difference, and the candidate wall thickness difference. This allows the inner cavity point of the bridge package, the inner wall point of the shaft tube, and the back side point of the reinforcing rib to form a thickness anchoring relationship for the bidirectional bending area of ​​the outer surface. In practical applications, when a local outer point on the outer surface of the bridge package is closer to a certain inner wall point of the shaft tube, but the outer point curvature difference and candidate wall thickness difference of the current outer point are closer to the transmission cost corresponding to the inner cavity point of the bridge package, the entropy regular Gromov-Wasserstein optimal transmission will, after multiple rounds of cost updates, exponent rewriting, row normalization, and column normalization, write a higher transmission weight to the candidate point pair between the inner cavity point of the bridge package and the current outer point. This prevents the subsequent S3 from mistakenly connecting the outer surface of the bridge package to the inner wall point of the shaft tube based solely on spatial distance.

[0019] S3. According to the weight table, divide the milling surface point set into bridge milling pieces, shaft tube milling pieces, rib root milling pieces and flange milling pieces, and write the inner point number, outer point number, transmission weight and design wall thickness for each milling piece, and output the milling piece set; In this embodiment, S3 is used to convert the weight table generated by S2 into a milling piece set, so that each external point first determines the principal internal point number, and then is grouped into bridge package milling pieces, shaft tube milling pieces, rib root milling pieces and flange milling pieces according to the internal point type and coordinate change direction corresponding to the principal internal point number, so that S4 can build the milling piece adjacency graph and calculate the depth constraint; the implementation process includes the following steps: In S3-1, the master-inner point number of each outer point is determined through a weight table, so that the thickness anchoring relationship between outer and inner points converges from a many-to-many transmission weight to a single master-inner point relationship. The weight table, milling surface point set, and measurement point table are read. All transmission weights corresponding to the current outer point are read one by one according to the outer point number. The inner point number associated with the transmission weight with the largest value is written as the master-inner point number of the current outer point. The current outer point number, master-inner point number, master-inner point coordinates, transmission weight, and candidate wall thickness difference are written into the outer point master-inner point table. When the transmission weight with the largest value is in tandem, read the candidate wall thickness difference between the in-tandem inner point and the current outer point, and write the inner point number with the lower candidate wall thickness difference value as the main inner point number; when the candidate wall thickness differences are still in tandem, read the numbering order of the in-tandem inner point numbers, and write the inner point number with the higher numbering order as the main inner point number; the inner point type is read from the measuring point table, the inner cavity point of the bridge package is written as the bridge package type, the inner wall point of the shaft tube is written as the shaft tube type, and the back side point of the reinforcing rib is written as the rib back type, for reading when dividing the milling piece in S3-2; In S3-2, the milling surface point set is divided into different milling pieces based on the external point master table, so that the outer surface of the bridge package, the outer surface of the shaft tube transition, the outer surface of the stiffener root, and the outer surface of the flange transition become the segmented objects for subsequent milling. The master internal point number, internal point type, axial coordinate, radial coordinate, circumferential coordinate, stiffener width coordinate, and flange end face axial coordinate of each external point in the external point master table are read. First, an external point sorting position is generated according to the measurement order of the external points. Then, external points with adjacent sorting positions and the same internal point type are used as a continuous external point sequence. In the continuous external point sequence, the internal point type is the bridge package type and the circumferential coordinates of adjacent external points are... Different outer points are merged into bridge milling pieces; outer points of type shaft tube and with different axial coordinates of adjacent outer points are merged into shaft tube milling pieces; outer points of type rib back and with different rib width coordinates of adjacent outer points are merged into rib root milling pieces; outer points of type shaft tube and with axial coordinates of outer points equal to the axial coordinates of flange end face are merged into flange milling pieces; the axial coordinates of flange end face are converted from the flange end face coordinates in S1; when an outer point simultaneously meets the merging conditions of shaft tube milling pieces and flange milling pieces, it is written into flange milling pieces first, and the adjacent boundary outer point numbers are retained in the shaft tube milling pieces for S4 to generate adjacent edges; In S3-3, the merged milling pieces are written with numbers and fields, enabling S4 to directly read the milling piece nodes, transmission weights, and design wall thickness. Milling piece numbers are generated for bridge milling pieces, shaft tube milling pieces, rib root milling pieces, and flange milling pieces according to blank number, milling piece type, and external point sorting position, respectively. All external point numbers within each milling piece, the corresponding master internal point number for each external point, the transmission weight from the master internal point number to the current external point, and the design wall thickness corresponding to the current external point are read. The milling piece number, milling piece type, master internal point number, external point number, transmission weight, design wall thickness, axial coordinate, radial coordinate, circumferential coordinate, and boundary external point number are written into the milling piece set according to the blank number. The transmission weight is written from the master internal point number to the current external point, and the complete transmission weight is still retained in the weight table. The design wall thickness is read according to the external point projection position of the current external point in the measurement point table. If an internal point type switch occurs in a continuous external point sequence, the milling piece is disconnected at the type switch position, and new milling piece numbers are generated respectively. Through processing in S3, the weight relationship between the inner and outer points in S2 is transformed into a set of milling pieces that can directly participate in milling. Each milling piece carries the main inner point number, outer point number, transmission weight, and design wall thickness. Subsequently, S4 can generate milling piece nodes, adjacent edges, and depth constraints based on this. In practical applications: Although an outer point on the outer surface of the bridge package is close to the inner wall point of the shaft tube, the transmission weight from the inner cavity point of the bridge package to the current outer point is higher in the weight table. S3-1 writes the inner cavity point number of the bridge package as the main inner point number of the current outer point. Then, S3-2 reads that the inner point type of the current outer point is the bridge package type, and the circumferential coordinates of the current outer point are different from those of the adjacent outer points, so the current outer point is assigned to the bridge package milling piece. S3-3 then writes the bridge package milling piece number, the current outer point number, the main inner point number, the transmission weight, and the design wall thickness into the milling piece set, so that the milling depth of the outer surface of the bridge package is constrained by the inner cavity thickness relationship in S4.

[0020] S4. Based on the milling plate set, establish a milling plate adjacency graph, generate depth constraints according to the design wall thickness difference, transmission weight and curvature difference of adjacent milling plates, and solve the allowable cutting thickness of each milling plate and the transition reduction of adjacent milling plates through the Hodge-Laplacian graph total variation near-end ADMM, and output the depth constraint layer. In this embodiment, S4 is used to convert the milling disc set into a depth-limited layer, so that the allowable cutting thickness of each milling disc is not only determined by the wall thickness difference of a single disc, but also constrained by the design wall thickness difference, transmission weight difference, and curvature difference of adjacent milling discs. During execution, the milling disc adjacency graph is first generated from the milling disc set, and then the measured wall thickness, design wall thickness, transmission weight, and curvature value are written into the depth-limited constraint table. Subsequently, through iterative rewriting between milling disc nodes, adjacent edges, and disc rings, a limited transition cutting thickness result is formed between the bridge package milling disc, shaft tube milling disc, rib root milling disc, and flange milling disc. This implementation process includes the following steps: In S4-1, a milling piece adjacency graph is established based on the milling piece set to represent the boundary relationships and transition closure relationships between milling pieces. The milling piece number, milling piece type, outer point number, and boundary outer point number are read from the milling piece set, and each milling piece is written as a milling piece node. When two milling pieces have the same boundary outer point number, the two milling pieces are written as an adjacent edge. When two milling pieces do not have the same boundary outer point number but their boundary outer point numbers are adjacent in the outer point sorting position, the two milling pieces are also written as an adjacent edge, and the adjacent boundary outer point numbers are written into the adjacent edge field. The piece ring consists of three milling piece nodes and three adjacent edges. The boundary external point sequence is connected end to end, and the three milling plate nodes are adjacent to each other in pairs; when located at the intersection of bridge package, shaft tube and rib root, the plate ring is formed by bridge package milling plate, shaft tube milling plate and rib root milling plate; when located at the intersection of shaft tube, rib root and flange, the plate ring is formed by shaft tube milling plate, rib root milling plate and flange milling plate; the milling plate node, adjacent edge, plate ring, boundary external point number and milling plate type are written into the milling plate adjacency diagram, so that S4-2 can read adjacent milling plates and calculate depth constraints; if a milling plate does not have a boundary external point number, the first and last external point numbers at both ends of the outer point sequence position of the milling plate are read as boundary external point numbers and then adjacent edges are generated; In S4-2, a depth constraint table is generated based on the milling cutter adjacency graph. This table is used to simultaneously write the machinable quantity of each milling cutter and the transition changes of adjacent milling cutters into the subsequent iteration input. The table reads the outer point number, principal inner point number, design wall thickness, transmission weight, and outer point curvature difference of each milling cutter. It reads the outer point coordinates by outer point number and the inner point coordinates by principal inner point number, and writes the spatial distance from each outer point coordinate to the corresponding principal inner point coordinate as the measured outer point wall thickness. The arithmetic mean of the measured wall thicknesses of all outer points within the same milling cutter is written as the measured wall thickness of the current milling cutter. The arithmetic mean of the design wall thicknesses of all design wall thicknesses within the same milling cutter is written as the design wall thickness of the current milling cutter. The arithmetic mean of the transmission weights of all transmission weights within the same milling cutter is written as the transmission weight of the current milling cutter. The curvature difference of all outer points within the same milling cutter is written as the measured wall thickness of the current milling cutter. The arithmetic mean of the differences is written as the curvature value of the current milling piece; the difference between the measured wall thickness and the designed wall thickness is calculated. When the difference is positive, it is written as the initial cutting thickness. When the difference is negative, the initial cutting thickness is written as zero and the negative difference is written to the thin-wall reserved field; for each adjacent edge, the designed wall thickness, transmission weight, and curvature value of the milling pieces at both ends of the adjacent edge are read, and the difference in designed wall thickness, transmission weight, and curvature at both ends are calculated respectively; the transmission weight difference is multiplied by the arithmetic mean of the designed wall thicknesses of the milling pieces at both ends to obtain the weighted thickness difference; the curvature difference is multiplied by the arithmetic mean of the distance between the outer points of the milling pieces at both ends to obtain the curvature thickness difference; the initial cutting thickness, the difference in designed wall thickness, the weighted thickness difference, and the curvature thickness difference are written into the depth constraint table for S4-3 to rewrite the allowable cutting thickness and transition reduction amount; In S4-3, the iterative fields are rewritten round by round based on the depth constraint table to jointly constrain the cutting thickness of the milling node, the transition reduction amount of adjacent edges, and the circumferential residual of the plate ring. The milling node, adjacent edges, plate ring, and depth constraint table are read. An allowable cutting thickness field is set on the milling node, a transition reduction amount field is set on the adjacent edge, and a circumferential residual field is set on the plate ring. The node Lagrangian, edge Lagrangian, and ring Lagrangian values ​​are also set respectively. In each round, the milling node field is rewritten first: all adjacent edges connecting the current milling node are read, the transition reduction amounts of these adjacent edges are summed, and then the summation result is subtracted from the initial cutting thickness of the current milling node to obtain the allowable cutting thickness for the current round. If the allowable cutting thickness is less than zero, the allowable cutting thickness for the current round is written as zero. Then, the adjacent edge field is rewritten: the allowable cutting thicknesses of the milling nodes at both ends of the adjacent edge are read, the difference in allowable cutting thickness between the two ends is calculated, and then the design wall thickness is subtracted. The difference in thickness, weight, and curvature is used to obtain the transition reduction amount for the current round. Next, the slice-ring field is rewritten: the forward and reverse edges are determined according to the circumferential reading order of the three adjacent edges in the slice-ring. The transition reduction amounts of the forward edges are summed, and the transition reduction amounts of the reverse edges are subtracted to obtain the circumferential residual. Finally, the Lagrange quantities are rewritten: the difference between the allowable cutting thickness and the node field is written as the node residual, the difference between the transition reduction amount and the edge field is written as the edge residual, and the circumferential residual obtained from the slice-ring field is written as the ring residual. The node residual, edge residual, and ring residual are then accumulated into the node Lagrange quantity, edge Lagrange quantity, and ring Lagrange quantity, respectively. The proximal term is used to limit the deviation of the current round's field from the previous round's field. The node proximal term is the square of the difference between the allowable cutting thickness of the current round and the allowable cutting thickness of the previous round, and the edge proximal term is the square of the difference between the transition reduction amount of the current round and the transition reduction amount of the previous round. These are subtracted together when the node and edge fields are rewritten in the next round. In S4-4, the process of rewriting the allowable cutting thickness and transition reduction amount by milling nodes, adjacent edges, and leaf rings in S4-3 is used as the near-end ADMM of the total variation of the Hodge-Laplacian graph. This is used to preserve the curvature abrupt changes between bridges, shafts, ribs, and flanges in the milling network of bidirectional curved irregular surfaces, while suppressing abrupt changes in the cutting thickness of adjacent milling nodes. The number of iteration rounds is the sum of the number of milling nodes, adjacent edges, and leaf rings. This number of rounds comes from the number of discrete structures in the milling adjacency graph and does not use an external stopping threshold. After completing a fixed number of iterations, the allowable cutting thickness and transition reduction of the last round are read. The allowable cutting thickness of the last milling wheel is written into the milling wheel depth limit field according to the milling wheel number, and the transition reduction amount of the last milling wheel is written into the adjacent edge transition field according to the adjacent edge number. Then, the milling wheel number, milling wheel depth limit field, adjacent edge number, adjacent edge transition field, thin wall retention field, and plate ring residual field are read to generate a depth limit layer for S5 to read when converting the milling toolpath. If the milling wheel node is not connected to the adjacent edge, the sum of the transition reduction amount of the current milling wheel node is written as zero, and the initial cutting thickness of the current milling wheel node is used as the milling wheel depth limit field. If there is no plate ring in the milling wheel adjacency diagram, the plate ring residual field is written as a null value and does not participate in the Lagrange quantity rewriting. Through S4 processing, the depth limit field of each milling cutter is simultaneously constrained by the measured wall thickness of the single cutter, the designed wall thickness, the main hanger transfer weight, and the adjacent curvature changes. The adjacent edge transition field between adjacent milling cutters can limit the single-cut jump at the junction of bridge milling cutters, shaft tube milling cutters, rib root milling cutters, and flange milling cutters. The depth limit layer output by S4 is not a simple thickness difference table, but toolpath constraint data with milling cutter node depth limit results and adjacent edge transition results. In practical applications: bridge milling cutters and shaft tube milling cutters are adjacent and When there is a curvature change between the two, S4-2 converts the curvature difference between the two ends into a curvature thickness difference and writes it into the depth constraint table. S4-3 deducts the curvature thickness difference from the adjacent edge field so that the transition reduction amount at the shaft tube transition position is written into the adjacent edge transition field. When S5 reads the depth layer to generate the tool position, the bridge package milling blade will not cut to the boundary of the shaft tube milling blade in one go according to its own thickness allowance. Instead, it will allocate the transition tool position under the constraint of the adjacent edge transition field, thereby reducing the risk of local overcutting at the intersection of the bridge package and the shaft tube.

[0021] S5. Convert the depth-limited layer into a milling toolpath, so that the milling cutter performs piecewise milling of the curved surface in two directions along the milling plate set, and writes the remeasured wall thickness back to the weight table and the depth-limited layer to generate the equal thickness milling forming result of the irregular curved surface of the front and rear axles of automobiles. In this embodiment, S5 is used to convert the depth-limited layer into a milling toolpath that the machine tool can execute, and after segmented milling, write the remeasured wall thickness back to the weight table and the depth-limited layer, so that the cutting depth of the remaining milling slices continues to be constrained by the inner point thickness relationship; during execution, the trajectory points are first organized according to the milling slice number, then the tool offset direction is generated based on the current trajectory point, adjacent trajectory points and the current main inner point, then a transition tool point is inserted between adjacent milling slices, and finally the milling is machined according to the milling toolpath and the remeasurement is written back; this implementation process includes the following steps: In S5-1, the depth limit layer and milling disc set are read, and the milling disc depth limit field output from S4 is converted into a trajectory point table to determine the tool path sequence and cutting depth within each milling disc. The outer point number, outer point coordinates, master inner point number, milling disc depth limit field, and adjacent edge transition field are read according to the milling disc number. The outer point coordinates within the same milling disc are first arranged in ascending order of axial coordinates, then in ascending order of circumferential coordinates when axial coordinates are the same, and finally in ascending order of radial coordinates when circumferential coordinates are the same. The order of arrangement is written as the sorting position. Each sorting position is bound to an outer point coordinate, a master inner point number, and a milling disc depth limit field to form a trajectory point record, which is then written into the trajectory point table according to the milling disc number. If there are duplicate outer point numbers within the same milling disc, the outer point number with the earlier sorting position is retained, and the duplicate outer point number is written into the duplicate field and does not participate in tool position generation. In S5-2, the tool position point is calculated based on the trajectory point table to ensure that the milling cutter movement direction avoids interference between the tangential feed direction and the thickness direction. The coordinates of the current trajectory point, the previous trajectory point, the next trajectory point, and the current master indenter point are read. The coordinate difference vector between the previous and next trajectory points is used as the tangential vector, and the coordinate difference vector between the current trajectory point and the current master indenter point is used as the thickness vector. The projection of the thickness vector onto the tangential vector is subtracted from the thickness vector to obtain the offset vector, which is then normalized to the tool offset direction. The current trajectory point moves along the tool offset direction, corresponding to the milling disc depth limit field. The distance is used to obtain the tool position point, and the tool position point coordinates, sort position, milling disc number, and milling disc depth limit fields are written into the tool position point table; when the first trajectory point is missing a previous trajectory point, the reverse extension point of the second trajectory point relative to the first trajectory point is used as the previous trajectory point; when the last trajectory point is missing a subsequent trajectory point, the reverse extension point of the second-to-last trajectory point relative to the last trajectory point is used as the subsequent trajectory point; when the offset vector is a zero vector, the thickness vector is normalized to the tool position offset direction; when the thickness vector is also a zero vector, the cross product direction of the normal formed by two adjacent external points in the current milling disc is read as the tool position offset direction; In S5-3, transition tool positions between adjacent milling cutters are generated based on the adjacent edge transition field, enabling the changes in cutting depth between bridge milling cutters, shaft and tube milling cutters, rib milling cutters, and flange milling cutters to be completed through toolpath transitions. The arithmetic mean of the adjacent edge transition field, the last tool position of the adjacent milling cutter, the first tool position of the adjacent milling cutter, and the milling cutter depth limit field of the adjacent milling cutter is read. The adjacent edge transition field is divided by the arithmetic mean of the milling cutter depth limit field, and the quotient is rounded up to obtain the number of transition points. The coordinate difference between the last tool position and the first tool position is equally divided according to the number of transition points to obtain the transition tool positions. When the arithmetic mean of the milling cutter depth limit field is zero, the number of transition points is taken as the number of points outside the boundary of the adjacent milling cutter; when the number of points outside the boundary of the adjacent milling cutter is zero, the number of transition points is taken as one. The tool position table and transition tool positions are connected in ascending order of the milling cutter numbers (bridge milling cutter, shaft and tube milling cutter, rib milling cutter, and flange milling cutter) to output the milling toolpath. Within the same milling cutter, tool positions are connected according to the sorting position in the trajectory point table. In S5-4, segmented milling is completed according to the milling toolpath, and the thickness deviation after milling is written back to the weight table and depth limit layer, so that the machining result can inversely constrain the remaining milling pieces; the milling cutter sequentially processes the bridge package milling piece, shaft tube milling piece, rib root milling piece, and flange milling piece according to the milling toolpath; after segmented milling is completed, the coordinates of the re-measured outer points are read according to the outer point number, and the coordinates of the re-measured inner points are read according to the main inner point number; when the inner surface is allowed to be contacted for re-measurement, the coordinates of the re-measured inner points are directly read according to the measurement position corresponding to the main inner point number; when there is obstruction on the inner surface, ultrasonic thickness measurement is performed along the tool position offset direction of the re-measured outer points, and the ultrasonic thickness is read. The coordinates of the re-measured outer point are moved in the opposite direction of the tool offset to obtain the coordinates of the re-measured inner point by ultrasonic thickness; the distance between the re-measured outer point coordinates and the re-measured inner point coordinates is calculated and written as the re-measured wall thickness; the difference between the re-measured wall thickness and the design wall thickness is calculated and written into the outer point thickness residual field of the weight table according to the outer point number, and the arithmetic mean of the difference within the same milling piece is written into the milling piece thickness residual field of the depth limit layer according to the milling piece number; the milling piece depth limit field of the remaining milling pieces is obtained by subtracting the milling piece thickness residual from the original milling piece depth limit field, and finally the result of equal thickness milling of the irregular curved surface of the front and rear axles of automobiles is generated; Through the processing of S5, the milling blade depth limit field and adjacent edge transition field in the depth limit layer are converted into machine tool tool position point, transition tool position point and milling toolpath. The re-measured wall thickness after milling is written back to the weight table and depth limit layer, so that the outer surface machining result continues to be constrained by the inner point thickness relationship. In practical applications: when the bridge package milling blade transitions to the shaft tube milling blade, if the adjacent edge transition field shows a difference in cutting depth on both sides, S5-3 will insert a transition tool position point between the last tool position point of the bridge package milling blade and the first tool position point of the shaft tube milling blade. After machining is completed, S5-4 reads the re-measured outer point coordinates according to the outer point number, and calculates the re-measured inner point coordinates by re-measurement of reachable inner points or ultrasonic thickness measurement to obtain the re-measured wall thickness difference. Then, the re-measured wall thickness difference is written into the weight table and depth limit layer, so that the subsequent remaining milling blades no longer use the depth limit field before machining.

[0022] Working Principle: This solution addresses the scenario of irregular curved surface milling for automotive front and rear axles in the intelligent manufacturing equipment industry. First, a blank coordinate system is established on the blank. The inner cavity of the axle housing, the inner wall of the shaft tube, the back side of the reinforcing rib, and the designed wall thickness in the 3D design model are transformed to the same coordinate reference. Then, the set of inner points and the set of milling surface points are collected. Subsequently, the spacing between inner points, the spacing between outer points, the curvature difference between outer points, and the candidate wall thickness difference are calculated. Entropy regularization Gromov-Wasserstein optimal transport is used to determine which inner point primarily constrains each outer point. Then, according to the principal inner point relationship, the outer points are divided into axle housing milling pieces, shaft tube milling pieces, rib root milling pieces, and flange milling pieces. The allowable cutting thickness of each milling piece and the transition reduction amount between adjacent milling pieces are calculated using the Hodge-Laplacian total variation near-end ADMM. Finally, the depth-limited layer is converted into a milling toolpath, completing the piecewise milling and writing the remeasured wall thickness back to the weight table and the depth-limited layer, ensuring that the subsequent cutting depth continues to be constrained by the actual wall thickness result. In the front axle blank machining of the intelligent manufacturing equipment industry, even when the outer surface of the axle housing appears to have sufficient allowance, the inner cavity may still have some excess material, and the root of the shaft tube may also have shrinkage. Traditional toolpath generation based on shape deviations can easily mill the outer surface to a qualified contour, but it can cause insufficient wall thickness in some areas. This solution first reads the points in the inner cavity of the axle housing, the inner wall of the shaft tube, and the outer surface to determine whether the outer point should be constrained more by the inner cavity of the axle housing or the inner wall of the shaft tube. Then, the outer surface of the axle housing and the transition outer surface of the shaft tube are divided into different milling blades, and toolpaths are generated according to their respective allowable cutting thicknesses. After milling, the wall thickness between the outer and inner points is remeasured, and the deviation is written back to the depth limit layer, so that the remaining area is no longer cut according to the original shape allowance. This ensures that the intersection area of ​​the axle housing, shaft tube, and reinforcing ribs maintains the target wall thickness after forming.

[0023] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces, characterized in that, include: S1. Read the inner cavity points of the axle housing, the inner wall points of the shaft tube, the back side points of the reinforcing rib, the milling surface point cloud of the workpiece, and the design wall thickness of the front and rear axle blanks. Merge the inner cavity points of the axle housing, the inner wall points of the shaft tube, and the back side points of the reinforcing rib into an inner point set. Extract the milling surface point set for machining the surface that bends in two directions from the milling surface point cloud of the workpiece and output the measurement point table. S2. Based on the measurement point table, calculate the spacing between inner points, the spacing between outer points, the curvature difference between outer points, and the candidate wall thickness difference, and use these as the transmission cost to perform entropy regularization Gromov-Wasserstein optimal transmission, and output the weight table of inner and outer points. S3. According to the weight table, divide the milling surface point set into bridge milling pieces, shaft tube milling pieces, rib root milling pieces and flange milling pieces, and write the inner point number, outer point number, transmission weight and design wall thickness for each milling piece, and output the milling piece set; S4. Based on the milling plate set, establish a milling plate adjacency graph, generate depth constraints according to the design wall thickness difference, transmission weight and curvature difference of adjacent milling plates, and solve the allowable cutting thickness of each milling plate and the transition reduction of adjacent milling plates through the Hodge-Laplacian graph total variation near-end ADMM, and output the depth constraint layer. S5. Convert the depth-limited layer into a milling toolpath, so that the milling cutter performs segmented milling of the curved surface in two directions along the milling plate set, and writes the remeasured wall thickness back to the weight table and the depth-limited layer to generate the equal thickness milling forming result of the irregular curved surface of the front and rear axles of automobiles.

2. The method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces according to claim 1, characterized in that: S1 includes: S1-1. Read the blank number, axle housing center coordinates, axle housing radius, left axle tube end face center coordinates, right axle tube end face center coordinates, left axle tube inner diameter, right axle tube inner diameter, stiffener back side end line coordinates, and flange end face coordinates of the front and rear axle blanks. Use the line connecting the center of the left axle tube end face to the center of the right axle tube end face as the axial reference line, the perpendicular line from the center of the axle housing end face to the axial reference line as the radial reference line, and the flange end face as the end face reference plane. Output the blank coordinate system. S1-2. Based on the blank coordinate system, read the bridge package inner cavity design surface, shaft tube inner wall design surface, stiffener back side design surface and design wall thickness in the design 3D model, and write the bridge package inner cavity design surface, shaft tube inner wall design surface, stiffener back side design surface and design wall thickness into the design datum table according to the blank number. S1-3. Based on the design reference table, generate bridge package measurement positions on the inner cavity design surface of the bridge package according to the circumferential angle and radial distance of the bridge package. Generate shaft tube measurement positions on the inner wall design surface of the shaft tube according to the axial distance and inner wall circumferential angle. Generate rib back measurement positions on the back side design surface of the reinforcing rib according to the rib length and rib width. Read the measured coordinates at each measurement position using a contact probe or ultrasonic thickness gauge and output the inner cavity point of the bridge package, the inner wall point of the shaft tube, and the back side point of the reinforcing rib.

3. The method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces according to claim 2, characterized in that: S1 further includes: S1-4. Based on the blank coordinate system, the measured coordinates of the outer surface are read along the outer surface of the bridge package, the outer surface of the shaft tube transition, the outer surface of the stiffener root, and the outer surface of the flange transition using a contact probe. Points in the measured coordinates of the outer surface where the axial, radial, and circumferential coordinates all change are written into the milling surface point set. S1-5. Merge the points inside the bridge cavity, the points on the inner wall of the shaft tube, and the points on the back side of the reinforcing rib into an inner point set. Write the inner point set, the milled surface point set, and the design wall thickness into the measuring point table according to the blank number, and output the measuring point table.

4. The method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces according to claim 3, characterized in that: S2 includes: S2-1. Read the set of inner points, the set of milled surface points and the design wall thickness from the measuring point table. Calculate the distance between the inner points of any two inner points and the distance between the outer points of any two outer points. For each outer point, form two outer point chord vectors according to the previous outer point, the current outer point and the next outer point. Write the angle between the two outer point chord vectors as the outer point curvature difference. Output the table of inner point distance, the table of outer point distance and the table of outer point curvature difference. S2-2. Form candidate point pairs by pairing each inner point with each outer point. Calculate the absolute value of the difference between the spatial distance of the candidate point pairs and the design wall thickness as the candidate wall thickness difference. Write the candidate wall thickness difference, the curvature difference of the outer points, the spacing between the inner points and the spacing between the outer points into the transmission cost table. Write the arithmetic mean of the candidate wall thickness differences in the transmission cost table as the entropy regularization term. S2-3. Using the transmission cost table and entropy regularization term as input, and the transmission table as the iteration object, the process of updating the transmission value by combining the squared difference between the in-point spacing and the out-point spacing, the candidate wall thickness difference, the out-point curvature difference, and the entropy regularization term is the entropy regularization Gromov-Wasserstein optimal transmission. The transmission table is rewritten round by round according to cost update, exponent rewriting, row normalization, and column normalization, and the transmission table in the last round is written as the weight table of in-point and out-point.

5. The method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces according to claim 4, characterized in that: S3 includes: S3-1. Read the weight table, milling surface point set and measuring point table. For each outer point, read the transmission weight with the largest value and write the inner point number associated with the current transmission weight as the main inner point number. When there are parallel transmission weights with the largest values, read the candidate wall thickness difference between the parallel inner point and the current outer point, write the inner point number with the smallest candidate wall thickness difference as the main inner point number, and output the outer point master table.

6. The method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces according to claim 5, characterized in that: S3 further includes: S3-2. Based on the external point master table, read the main internal point number, internal point type, axial coordinate, radial coordinate, circumferential coordinate and flange end face coordinate of each external point. Merge adjacent external points whose main internal point number belongs to the bridge package inner cavity point and whose circumferential coordinates are different into bridge package milling pieces. Merge adjacent external points whose main internal point number belongs to the shaft tube inner wall point and whose axial coordinates are different into shaft tube milling pieces. Merge adjacent external points whose main internal point number belongs to the reinforcing rib back side point and whose rib width coordinates are different into rib root milling pieces. Merge external points whose main internal point number belongs to the shaft tube inner wall point and whose axial coordinates are equal to the flange end face coordinates into flange milling pieces. S3-3. Generate milling piece numbers for bridge milling pieces, shaft tube milling pieces, rib root milling pieces, and flange milling pieces respectively, and write the milling piece number, main inner point number, outer point number, transmission weight, and design wall thickness into the milling piece set according to the blank number.

7. The method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces according to claim 6, characterized in that: S4 includes: S4-1. Read the milling chip set, write each milling chip as a milling chip node, write two milling chips with a common outer point number as adjacent edges, write three milling chips enclosed by three adjacent edges and with each of the three adjacent to each other as chip rings, and write the milling chip node, adjacent edges and chip rings into the milling chip adjacency graph. S4-2. Based on the milling blade adjacency graph, read the measured wall thickness, designed wall thickness, transmission weight and curvature value of each milling blade, calculate the difference between the measured wall thickness and the designed wall thickness as the initial cutting thickness, calculate the difference in designed wall thickness, transmission weight and curvature between adjacent milling blades, and write them into the depth constraint table.

8. The method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces according to claim 7, characterized in that: S4 further includes: S4-3. The allowable cutting thickness on the milling node, the transition reduction amount on the adjacent edge, the circumferential residual on the plate ring, and the Lagrange quantity are used as iteration fields. The adjacent transition reduction amount is subtracted from the initial cutting thickness according to the node field. The design wall thickness difference, transmission weight difference, and curvature difference are subtracted from the difference in allowable cutting thickness at both ends according to the edge field. The transition reduction amount of the three adjacent edges is accumulated according to the plate ring field. The residuals of the node field, edge field, and plate ring field are accumulated according to the Lagrange quantity. The iteration fields are rewritten round by round. S4-4. The process of rewriting the allowable cutting thickness and transition reduction amount by milling nodes, adjacent edges and plate rings in S4-3 is taken as the near end ADMM of the total variation of the Hodge-Laplacian diagram. The number of iteration rounds is the sum of the number of milling nodes, the number of adjacent edges and the number of plate rings. The allowable cutting thickness of the last round is written into the milling depth limit field, and the transition reduction amount of the last round is written into the adjacent edge transition field. Then, the depth limit layer is generated according to the milling number, the milling depth limit field, the adjacent edge number and the adjacent edge transition field.

9. The method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces according to claim 8, characterized in that: S5 includes: S5-1. Read the depth limit layer and milling plate set. Read the outer point number, outer point coordinates, main inner point number, milling plate depth limit field and adjacent edge transition field according to the milling plate number. Arrange the outer point coordinates in the same milling plate in the order of increasing axial coordinate, increasing circumferential coordinate, and increasing radial coordinate. Write the arranged outer point coordinates, sorting position, main inner point number and milling plate depth limit field into the trajectory point table. S5-2. Read the current trajectory point, the previous trajectory point, and the next trajectory point from the trajectory point table. Use the coordinate difference vector between the previous trajectory point and the next trajectory point as the tangent vector, and the coordinate difference vector between the current trajectory point and the current main inner point as the thickness vector. Subtract the projection of the thickness vector onto the tangent vector from the thickness vector and normalize it to the tool offset direction. Move the current trajectory point along the tool offset direction by the distance of the milling disc depth limit field to generate the tool position table.

10. The method for equal-thickness milling of bidirectional curved surfaces of automotive front and rear axle workpieces according to claim 9, characterized in that: S5 includes: S5-3. Read the arithmetic mean of the adjacent edge transition field, the last tool position point, the first tool position point, and the milling blade depth limit field of the adjacent milling blade. Divide the adjacent edge transition field by the arithmetic mean of the milling blade depth limit field and round up the quotient to get the number of transition points. Then, perform equal division and insertion on the coordinate difference between the last tool position point and the first tool position point according to the number of transition points, and output the milling toolpath. S5-4. Perform segmented milling according to the milling toolpath, and after milling, read the coordinates of the re-measured outer point and the re-measured inner point according to the outer point number. Write the distance between the re-measured outer point coordinates and the re-measured inner point coordinates as the re-measured wall thickness. Write the difference between the re-measured wall thickness and the design wall thickness into the weight table and the depth limit layer to generate the equal thickness milling forming result of the irregular curved surface of the front and rear axles of automobiles.

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