A five-axis machining tool position adaptive compensation method for a thin-wall spherical cap part based on a measured point cloud

Abstract

A kind of five-axis machining tool position adaptive compensation method based on measuring point cloud of thin-wall spherical crown part.The profile and wall thickness of the spherical shell to be machined are obtained, and the actual machining surface point set is obtained in combination with each round target wall thickness value.Based on the equal residual height and chord height difference method, the tool position point is determined on the theoretical spherical shell inner surface with surface roughness tolerance as the constraint.The search radius is set by offsetting the theoretical tool position point and its sphere center, the surface fitting is carried out on the actual surface point set of the search domain based on the least moving square method, and the grid is dispersed on the surface with the wall thickness tolerance as the constraint.The theoretical tool position point is searched forward until the distance between it and the grid node is less than the grid length, and the grid node is taken as the compensated tool position point, and the AC axis coordinates are solved through the normal vector consistency calibration, to complete the five-axis adaptive tool position compensation.The present application realizes the five-axis compensation tool position adaptive planning of spherical shell type components, and the whole process is automatically processed, to meet the machining precision requirements of large spherical shell type components on site.

Description

Technical Field

[0001] This invention belongs to the field of digital machining technology, and specifically relates to an adaptive compensation method for tool position in five-axis machining of thin-walled spherical crown parts based on measurement point clouds. Background Technology

[0002] Large, thin-walled components, with their high strength and lightweight properties, are widely used in aerospace and other fields. Spherical shell components, due to their unique structural characteristics, are often used in the bottoms of rocket fuel tanks, the common bottoms of liquid hydrogen-liquid oxygen rocket tanks, and storage tanks in the petrochemical industry. During the machining process, these structural components are prone to significant deformation during semi-finishing and finishing stages due to their large size, complex surface shape, and the difficulty in machining the materials. If digital machining is performed according to the theoretical model of the part, the scrap rate is high due to multiple factors such as the part's inherent weak rigidity, time-varying properties during machining, and clamping forces, making it impossible to meet the required machining accuracy.

[0003] Currently, conventional milling methods for large spherical shell thin-walled parts mainly fall into two categories: the first is chemical milling, which cannot accurately control wall thickness accuracy, has a long cycle time, and causes serious environmental pollution; the second is "petal milling followed by assembly welding," which results in low overall strength due to the presence of welds, making it difficult to meet the development needs of the aerospace field. Against this backdrop, a five-axis adaptive tool position compensation method for large spherical shell components is proposed. Based on on-machine measurement data, and with tolerances as constraints, the method adaptively plans the compensation tool position points to ensure the machining accuracy of large spherical shell components.

[0004] In 2019, Huang Zhi et al. from the University of Electronic Science and Technology of China disclosed an adaptive machining trajectory planning method for free-form surfaces in patent CN106054802B. This method uses a genetic algorithm to solve for the extreme values ​​of the principal curvature of the surface, interpolates newly generated tool contacts according to step size requirements to smooth them, and then fits the tool contacts to generate the machining trajectory after the discrete points cover the entire surface. However, this method uses a 3D digital model for surface modeling, without modeling according to the actual surface configuration, ignoring the influence of surface errors introduced by multiple rounds of machining. In 2022, Wang Zhenyu et al. from Hefei University of Technology disclosed a five-axis surface machining trajectory planning method based on differential vector optimization in patent CN113341876B. This method creates a normalized optimization target model, and obtains the optimized tool posture vector from the determined tool posture differential vector that satisfies the minimum value of this model, thus achieving a smooth machining trajectory. This method plays a certain role in controlling profile tolerance and surface roughness, but it cannot control wall thickness machining errors. In 2023, Chen Mingjun et al. from Harbin Institute of Technology disclosed a method and apparatus for planning the machining trajectory of a uniformly distributed micro-pit structure on the entire surface of a thin-walled spherical shell-like micro-component in patent CN113741337B. Based on the Fibonacci principle and a uniformly distributed spherical point set iterative algorithm, this method improves the uniformity of the distribution of micro-features on the surface of spherical shells. However, this method does not consider the tool pose offset caused by tool deformation introduced during the machining process, and cannot control the surface error during the machining process.

[0005] Currently, no adaptive compensation method for tool position in five-axis machining of thin-walled spherical crown parts based on measured point clouds has been proposed. Summary of the Invention

[0006] To overcome the shortcomings of existing methods, this invention addresses a series of challenges, including difficulty in controlling the wall thickness and profile accuracy of large spherical shell components, complex surface details, and low machining efficiency. It proposes a five-axis adaptive tool position compensation method for thin-walled spherical crown components based on measured point clouds. This method uses digital on-machine measurement to obtain the profile and wall thickness of the spherical shell to be machined. Combined with the target wall thickness value for each round, the actual machining surface point set can be obtained. Based on the equal residual height and chord height difference method, and constrained by surface roughness tolerance, the tool position point is determined on the theoretical spherical shell's inner surface. The theoretical tool position point is offset, and its center is used to set the search radius. The actual surface point set in the search domain is fitted using the least moving squares method, and a mesh is discretized on the surface with wall thickness tolerance as a constraint. The theoretical tool position point is further searched forward until its distance from the mesh node is less than the mesh edge length. This mesh node is used as the compensation tool position point, and the AC axis coordinates are solved through normal vector consistency calibration to complete the five-axis adaptive tool position compensation.

[0007] The technical solution of the present invention:

[0008] An adaptive compensation method for five-axis machining of thin-walled spherical crown parts based on measured point clouds is proposed. First, according to the theoretical surface design equation of the spherical shell, theoretical tool positions for the inner surface are generated based on the chord height difference and equal residual height method. Second, based on the measured actual outer surface and wall thickness data of the spherical shell component, and taking the wall thickness requirement as a benchmark, an actual machining surface point set is generated. The theoretical tool positions are offset outwards and used as the neighborhood center. A search domain is established within the actual outer surface point set using a neighborhood radius. Local surface fitting is performed based on the moving least squares method, with the wall thickness tolerance zone as a constraint. Grid points are discretized on the surface with the tolerance as the side length. Then, the theoretical tool positions continue to search forward with a specified step size until the distance between them and the grid nodes is less than the tolerance value, at which point the search stops. Finally, using these grid nodes as compensation tool positions, the normal vectors of all tool positions are solved, and the consistency of their normal vector directions is calibrated to obtain the five-axis coordinates of the compensation tool positions, thus completing the five-axis adaptive compensation for large thin-walled spherical shells. The specific steps are as follows:

[0009] The first step is to calculate the theoretical tool position point of the inner surface based on the theoretical inner surface equation.

[0010] For five-axis milling of large spherical shell components, the machining path adopts circumferential milling, and the circumferential path is connected by a tool lift-off method to achieve equal arc length machining. Therefore, for the internal surface equation of the theoretical design model, the equal residual height method is used to determine the machining path spacing to ensure machining quality. Since the curvature of the large spherical shell component is much greater than the residual height, the calculation formulas for machining path spacing and residual height are as follows:

[0011]

[0012] Among them, L s For processing row spacing, Δh s For residual height, R t The radius of the cutting tool;

[0013] Then, based on the chord height difference method, the circumferential dispersion length L is derived. R The formula for calculating the chord height error Δh is as follows: Given a circumferential trajectory at a specified height z0, the formula for calculating the chord height error is:

[0014]

[0015] Where a is the major axis of the bimajor axis ellipsoid and b is the minor axis of the bimajor axis ellipsoid, then the distance from the walk length L R The expression is:

[0016]

[0017] Therefore, on the bimajor axis ellipsoidal surface with the given equation, a starting point, L, is defined. s and L RBy determining the step size along the circumferential direction and the generatrix direction, and combining this with the ellipsoid equation, the theoretical tool point set P = {p1, p2, ..., p} of the inner surface can be obtained. n};

[0018] The second step involves fitting a surface to the point cloud within the neighborhood using the moving least squares method, and then discretizing the mesh with the maximum wall thickness tolerance as a constraint.

[0019] Based on digital on-machine scanning technology, the actual surface point cloud and corresponding thickness values ​​of large spherical shell components are acquired, and combined with the target wall thickness d for the next machining cycle. t Obtain the actual processed pastry set Q j ={q1,q2,…,q m The theoretical tool point set P of the inner surface is offset outward along the normal direction, and the moving distance s is:

[0020] s < d t -δ (4)

[0021] Where δ is the estimated value of the actual surface deformation, which is guaranteed to be greater than the actual surface deformation value;

[0022] For the biased theoretical tool point set P′ i ={p′1,p′2,…,p′ n Using one of the tool points p′1 as the center of a sphere, and setting the neighborhood search range to R, search for all actual processed surface points Q′ within its neighborhood. i ={q′1,q′2,…,q′ M Based on the moving least squares method, an implicit surface is constructed for the actual processing surface point set; then, with the maximum wall thickness tolerance ε allowed in the processing as a constraint, the implicit surface is meshed based on the cubic method, and the mesh edge length is ε.

[0023] The third step involves continuing the search along the normal vector for the theoretical tool position point, using the threshold as a constraint to solve for the coordinates of the compensated tool position point.

[0024] Using the maximum wall thickness tolerance ε as the step size, the offset theoretical tool position point continues to move outward along the normal direction. When moving one step, the distance between the offset tool position point and each node is calculated. The node with the minimum distance and its corresponding mesh are selected, and the offset tool position point continues to approach forward until the minimum distance value is less than the maximum wall thickness tolerance ε, at which point the approximation process stops. According to the actual tolerance requirements, if the actual requirement is to ensure the lower wall thickness tolerance, the theoretical tool position offset point continues to be offset forward by one step; if the actual requirement is to ensure the upper wall thickness tolerance, the approximation process stops.

[0025] To determine the offset theoretical tool position coordinates at this point, first solve for the normal vector of the tool position, based on the theoretical tool position coordinates p of the inner surface. i (x i ,yi ,z i If ), then the unit normal vector of the tool position point. The calculation formula is:

[0026]

[0027] Let the offset theoretical tool point be searched for a cumulative k steps along the normal vector direction. Then the coordinates of the offset point p′ at this point are... i (x′ i ,y′ i ,z′ i The formula for calculating ) is:

[0028]

[0029] The coordinates at this point are the coordinates of the compensation tool position point; however, for digital machining on a five-axis machine tool, the coordinates of the swing axis and the rotary axis also need to be calculated.

[0030] The fourth step is to solve for the normal vector of the compensated tool position, calibrate the direction to ensure global consistency, and generate the compensated tool position trajectory.

[0031] Due to the initial stress release and the introduction of processing stress during the machining process, large spherical shell components are prone to overall surface deformation. To ensure that the tool axis adapts to the changes in the surface normal during machining, the normal of the tool position point corresponding to the actual machining surface point is assigned to the normal of the compensating tool position point. This ensures both the smoothness of the tool path and the surface machining quality and surface tolerance of the large spherical shell components. The specific steps are as follows:

[0032] First, based on principal component analysis (PCA), the normal vector of the actual machining surface is calculated; then, for the set of actual machining surface points in the neighborhood of the bias theory tool position... Regarding one point By minimizing the objective function, the dot product of the vector formed by the point and its nearest neighbors and the normal vector is equal to 0. The calculation formula is as follows:

[0033]

[0034] Where M is the number of points in the neighborhood. Let be the coordinates of the point corresponding to the normal vector to be solved. Let J be the coordinates of the neighborhood center point, J be the objective function, and the eigenvector corresponding to the minimum eigenvalue is the normal vector corresponding to that point.

[0035] Secondly, the direction of the normal vector is corrected. The normal vector direction obtained by the above method lacks global consistency. To address this issue, the bias theory tool position normal vector correction method is adopted to ensure global consistency of the normal vector. The correction calculation formula is as follows:

[0036]

[0037] Where θ is the angle between the two normal vectors; if θ > 90°, then the normal vector... The direction remains unchanged; if θ > 90°, then the normal vector... Reverse the direction;

[0038] Finally, from the normal vector Determine the coordinates of the A-axis and C-axis, where the normal vector... These are the normal vectors in the three dimensions of x, y, and z in space. The coordinates of the A-axis and C-axis are determined based on the normal vectors in the x and z directions, i.e., by taking the inverse cosine. This yields the five-axis coordinates of the compensated tool position point in the workpiece coordinate system. By using equal arc length circumferential milling and a tool lifting feed method between adjacent layers, the five-axis adaptive compensation machining of the spherical shell component is achieved. For multi-round machining of large spherical shell components, steps two through four are repeated in each round of machining starting from the semi-finishing stage, thus achieving precise tolerance control and meeting actual machining requirements.

[0039] The beneficial effects of this invention are as follows: This invention proposes an adaptive compensation method for tool position in five-axis machining of thin-walled spherical crown parts based on measured point clouds. Based on on-machine measurement, it achieves automated measurement of the profile and wall thickness of large spherical shell components. Addressing the challenges of deformation during the machining process of spherical shell components, this invention breaks away from the traditional approach of using commercial software to reverse-engineer the measurement model and plan tool trajectories through CAM software. This method introduces significant fitting errors during surface reconstruction, and many parameter settings rely entirely on manual experience. This invention achieves adaptive generation of compensated tool trajectories from measured point cloud data with tolerance constraints, providing a new approach for five-axis digital machining of spherical shell components. It also boasts advantages such as full-process automation, simple operation, high efficiency, and high reliability, meeting actual machining accuracy requirements. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating the overall process of the five-axis adaptive tool position compensation method for tolerance-constrained spherical shell components described in this invention.

[0041] Figure 2 A schematic diagram of the tooling point generated for the theoretical internal shape surface.

[0042] Figure 3 This is a schematic diagram showing the spatial position of the theoretical tool position point after offset and the actual machining surface.

[0043] Figure 4 The diagram shows the generation of the theoretical tool position after moving least squares interpolation fitting. Among them, (a) is a schematic diagram of the offset tool position approximation process, (b) is a schematic diagram of the generation of the compensated tool position when the upper tolerance of the wall thickness is guaranteed, and (c) is a schematic diagram of the generation of the compensated tool position when the lower tolerance of the wall thickness is guaranteed.

[0044] Figure 5 This is a schematic diagram illustrating an application example of five-axis compensated toolpath planning for large spherical shell components. (a) shows the overall effect of the five-axis toolpath planning for the large spherical shell component, and (b) shows a partial toolpath diagram of the tool axis vector.

[0045] In the diagram: 1 is the distance L from the walking distance. R ;2 Processing line spacing L s 3. Tool radius R t ;4 Residual height Δh s 5. Neighborhood search for the theoretical tool position; 6. Point cloud of the actual machined surface; 7. Point cloud of the theoretical tool position; 8. The theoretical tool position; 9. Normal vector of the theoretical tool position; 10. Points of the actual machined surface; 11. Discrete mesh of the surface; 12. Compensating tool position while maintaining wall thickness tolerance; 13. Minimum distance d min ; 14 Minimum distance corresponding to mesh node; 15 Reverse normal vector; 16 Final compensation tool position normal vector; 17 Compensation tool position when maintaining wall thickness tolerance; 18 Minimum distance d min ;19 Minimum distance corresponding to mesh node;20 Reverse normal vector;21 Final compensation tool position normal vector;22 Simulated tool axis. Detailed Implementation

[0046] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0047] This invention is implemented as a large spherical shell thin-walled component. Due to the involvement of key model dimensions, only approximate values ​​are provided here. The theoretical internal surface equation is a double major axis ellipsoid equation, with a major axis of approximately 3000 mm and a minor axis of approximately 850 mm. The wall thickness requirement is 1.5 mm in the thinnest area, with a lower tolerance of 0 mm and an upper tolerance of 0.1 mm. The surface features are relatively complex. Figure 1 This is a flowchart of the five-axis adaptive tool position compensation method for tolerance-constrained spherical shell components proposed in this invention. The specific implementation steps are as follows:

[0048] The first step is to divide the theoretical tool points of the inner surface based on the theoretical inner surface equation.

[0049] In this example, the machining trajectory employs circumferential milling, with equal arc lengths achieved between circumferential trajectories through tool lifting. Therefore, for the internal surface equations of the theoretical design model, to ensure machining quality, the equal residual height method is used to determine the machining trajectory spacing. In this machining process, since the curvature of the large spherical shell component is much greater than the residual height, the formulas for calculating the spacing and residual height are as follows:

[0050]

[0051] Among them, L s For processing row spacing, Δh s For residual height, Rt The radius of the tool is 10mm. In this example, the tool radius is 10mm, so the calculated line spacing is 15mm.

[0052] Then, based on the chord height difference method, the circumferential dispersion length L is derived. R The formula for calculating the relationship between the chord height error Δh and the circumferential trajectory at a specified height z0 is as follows:

[0053]

[0054] Where a is the major axis and b is the minor axis (bimajor axis ellipsoid), then the distance from the walk length L R The expression is:

[0055]

[0056] Therefore, the distance L from the walk can be calculated. R The value is 1mm, thus yielding the theoretical tool point set P = {p1, p2, ..., p} for the inner surface. n The specific effects are as follows: Figure 2 As shown.

[0057] The second step involves fitting a surface to the point cloud within the neighborhood using the moving least squares method, and then discretizing the mesh with the wall thickness tolerance as a constraint.

[0058] Based on digital on-machine scanning technology, the actual surface point cloud and corresponding thickness values ​​of the spherical shell component are obtained. Combined with the target wall thickness of 2mm for the next machining cycle, the actual machining surface point set Q can be obtained. j ={q1,q2,…,q m The theoretical tool point set P of the inner surface is offset outward along the normal direction, and the moving distance s is:

[0059] s < d t -δ (4)

[0060] Where δ is the estimated value of the actual surface deformation. Based on multi-round processing experience, the maximum deformation does not exceed 0.8mm, so the moving distance s is taken as 1mm.

[0061] For the biased theoretical tool point set P′ i ={p′1,p′2,…,p′ n Using one of the tool points p′1 as the center of a sphere, and setting the neighborhood search range to 2mm, search for all actual machined surface points Q′ within its neighborhood. i ={q′1,q′2,…,q′ MBased on the moving least squares method, an implicit surface is constructed from the actual machining surface point set. Then, with the maximum allowable tolerance of 0.1mm for wall thickness during machining as a constraint, the implicit surface is meshed using the cubic method, with the mesh edge length being 0.1mm.

[0062] The third step involves continuing the search along the normal vector for the theoretical tool position point, using the threshold as a constraint to solve for the coordinates of the compensated tool position point.

[0063] Using a wall thickness tolerance of 0.1 mm as the step size, the theoretical tool position after offset continues to move outward along the normal direction. When moving one step, the distance between the offset tool position and each node is calculated. The node with the minimum distance and its corresponding mesh are selected, and the offset tool position continues to approach forward. In this example, the lower wall thickness tolerance needs to be guaranteed, so the offset tool position moves forward one more step until the minimum distance value is less than the wall thickness tolerance of 0.1 mm, at which point the approximation process stops.

[0064] To determine the offset theoretical tool position coordinates at this point, first solve for the normal vector of the tool position, based on the theoretical tool position coordinates p of the inner surface. i (x i ,y i ,z i If ), then the unit normal vector of the tool position point. The calculation formula is:

[0065]

[0066] Let the offset theoretical tool point be searched for a cumulative k steps along the normal vector direction. Then the coordinates of the offset point p′ at this point are... i (x′ i ,y′ i ,z′ i The formula for calculating ) is:

[0067]

[0068] The coordinates at this point are the coordinates of the compensation tool position point; however, for digital machining on a five-axis machine tool, the coordinates of the swing axis and the rotary axis also need to be calculated.

[0069] The fourth step is to solve for the normal vector of the compensated tool position, calibrate the direction to ensure global consistency, and generate the compensated tool position trajectory.

[0070] Due to the initial stress release and the introduction of machining stress during processing, spherical shell components are highly susceptible to overall surface deformation. To ensure that the tool axis adapts to the changes in the surface normal during machining, the normal of the tool position point corresponding to the actual machined surface point set is assigned to the normal of the compensating tool position point. This ensures the smoothness of the tool path, thereby guaranteeing the surface machining quality and surface tolerances of the spherical shell component. The specific steps are as follows:

[0071] First, based on principal component analysis (PCA), the normal vector of the actual machining surface is calculated; then, for the set of actual machining surface points in the neighborhood of the bias theory tool position... Regarding one point By minimizing the objective function, the dot product of the vector formed by the point and its nearest neighbors and the normal vector is equal to 0. The calculation formula is as follows:

[0072]

[0073] Where M is the number of points in the neighborhood. Let be the coordinates of the point corresponding to the normal vector to be solved. Let J be the coordinates of the neighborhood center point, J be the objective function, and the eigenvector corresponding to the minimum eigenvalue is the normal vector corresponding to that point.

[0074] Secondly, the direction of the normal vector is corrected. The normal vector direction obtained by the above method lacks global consistency. To address this issue, the bias theory tool position normal vector correction method is adopted to ensure global consistency of the normal vector. The correction calculation formula is as follows:

[0075]

[0076] Where θ is the angle between the two normal vectors; if θ > 90°, then the normal vector... The direction remains unchanged; if θ > 90°, then the normal vector... Reverse the direction;

[0077] Finally, the obtained compensated tool position points are used to generate machining trajectories through circumferential equal arc length milling. During the finishing stage, steps two through four are repeated to complete the five-axis tool position compensation machining of the large spherical shell component. This method, while controlling wall thickness accuracy, incorporates the characteristics of the actual machined surface into the tool position points, adaptively adjusting the tool axis direction to ensure profile tolerances and surface quality during machining, thus meeting actual machining requirements.

[0078] The method described in this invention is applicable to the machining of fuel tank bottoms for aerospace rockets and the manufacturing of spherical shell components in various industrial fields. It has already been applied in engineering and has achieved good results. It solves a series of problems such as uncontrollable machining accuracy and low automation in large spherical shell components, forming a new five-axis digital compensation machining process for spherical shells. This comprehensively improves machining efficiency and reliability, and can meet the ultra-precision machining requirements of various typical spherical shell workpieces.

[0079] The specific implementation examples described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific implementation examples of the present invention and are 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 five-axis machining tool position adaptive compensation method for thin-walled spherical cap parts based on measured point cloud, characterized in that, The steps are as follows: Firstly, the theoretical tool position of inner surface is calculated based on the theoretical inner surface equation For the five-axis milling of large spherical shell components, the machining trajectory adopts the circumferential milling method, and the equal arc length machining is realized by lifting the tool between circumferential trajectories. Therefore, for the inner surface equation of the theoretical design model, the equal residual height method is used to determine the machining track pitch to ensure the machining quality. Since the curvature of large spherical shell components is much larger than the residual height, the calculation formula of the machining pitch and the residual height is: where L s is the processing line distance, Δh s is the residual height, R t is the tool radius; Then, the circumferential discrete step L is derived based on the chord height difference method R The circumferential trajectory of the specified height z0 is set, and the calculation formula of the chord height error is as follows: Wherein a is the long axis of the double long axis ellipsoid, b is the short axis of the double long axis ellipsoid, and L is the discrete step length R The expression is: Thus, on the double long axis ellipsoid surface of the given equation, a starting point L s and L R Determine the step length in the circumferential direction and the generatrix direction, combined with the ellipsoid equation, that is, the inner surface theoretical tool position point set P = {p1, p2, …, p n} is solved. Secondly, the point cloud in the neighborhood is fitted to a surface based on the moving least squares method with the maximum wall thickness tolerance as the constraint discrete grid Based on digital on-machine scanning technology, the actual outer surface point cloud and the corresponding thickness value of the large spherical shell component are obtained, and the target wall thickness d of the next machining is combined t , the actual machining surface point set Q j ={q1, q2, …, q m} is obtained; the inner surface theoretical tool position point set P is offset outward along the normal direction, and the moving distance s is: s < d t - delta (4) Where δ is the estimated value of the actual surface deformation, which is greater than the actual surface deformation value; P′ i = {p′1, p′2, …, p′ n}, and taking one of the tool position points p′1 as the center of a sphere, a neighborhood search range R is set, and all actual machining surface points set Q′ i = {q′1, q′2, …, q′ M} in the neighborhood is searched; based on the moving least square method, an implicit surface is constructed based on the actual machining surface points set; then, based on the cubic method, the implicit surface is meshed with a maximum wall thickness tolerance ε allowed in the machining process as a constraint, and the length of the meshed grid is ε; Thirdly, the theoretical tool position continues to search along the normal vector, and the compensation tool position coordinates are solved with the threshold as the constraint With the maximum wall thickness tolerance ε as the step, the offset theoretical tool position continues to move outward along the normal vector direction. When moving one step, the distance between the offset tool position and each node is calculated. The minimum distance node and its corresponding grid are taken, and the offset tool position continues to approach forward until the minimum distance value is less than the maximum wall thickness tolerance ε, and the approaching process is stopped. According to the actual tolerance requirement, if the actual requirement is to ensure the lower wall thickness tolerance, the theoretical tool offset point continues to offset one step forward. If the actual requirement is to ensure the upper wall thickness tolerance, the approaching process is stopped. Solving the bias theory cutter location point coordinates at this time, first solve the normal vector of the cutter location point, according to the inner surface theory cutter location point coordinates p i (x i ,y i ,z i ), the unit normal vector of the cutter location point The calculation formula is: If the offset theory tool position is accumulated along the normal direction for k steps, the coordinate of the offset point p' i (x' i ,y' i ,z' i ) is calculated as follows: The coordinate value at this time is the compensation tool position coordinate. However, for digital machining of five-axis machine tools, the coordinates of the swing axis and the rotary axis also need to be calculated. Fourthly, the normal vector of the compensation tool position is solved, the direction is corrected to ensure global consistency, and the compensation tool path is generated Due to the initial stress release and the introduction of machining stress in the machining process, large spherical shell components are prone to overall surface deformation. To ensure that the tool axis adapts to the change of the surface normal vector during the machining process, the actual machining surface point corresponding to the tool position is assigned to the normal vector of the compensation tool position. In this way, the smoothness of the tool path is ensured, and the surface machining quality and surface tolerance of large spherical shell components are also ensured. The specific steps are as follows: Firstly, the actual machining surface normal vector is calculated based on the PCA principal component analysis method. The actual machining surface point set in the neighborhood of the offset theoretical tool position is calculated For one of them The point product of the vector composed of the point and its near points and the normal vector is 0 by minimizing the objective function, and the calculation formula is: Wherein, M is the number of points in the neighborhood, is the coordinate of the point corresponding to the normal vector to be solved, is the coordinate of the center point of the neighborhood, J is the optimization objective function, and the characteristic normal vector corresponding to the minimum eigenvalue is the normal vector corresponding to the point Secondly, the normal vector direction is corrected. The normal vector direction solved by the above method does not have global consistency. To solve this problem, the offset theoretical tool position normal vector correction method is used, which ensures that the normal vector has global consistency. The correction calculation formula is: where θ is the angle between the two normals; if θ > 90°, the normal direction remains unchanged; if θ > 90°, the normal direction is reversed. Finally, the normal vector is determined, and the coordinates of the A-axis and the C-axis are determined, wherein the normal vector is a normal vector in three dimensions of x, y, and z in space, and the coordinates of the A-axis and the C-axis are determined according to the normal vector in the x and z directions, that is, the inverse cosine is taken; thus, the five-axis coordinates of the compensation tool position in the workpiece coordinate system are obtained, and the five-axis adaptive compensation machining of the spherical shell component is implemented according to the equal-arc-length circumferential milling and the lifting feed mode between adjacent layers; for multi-round machining of a large spherical shell component, the second step to the fourth step are repeatedly executed from the semi-finishing stage, that is, the precise control of the tolerance is implemented, and the actual machining requirements are met.

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