A large thin-walled part overall deformation sub-region compensation method based on space-time interaction

Abstract

A large thin-walled part overall deformation sub-region compensation method based on space-time interaction. The influence range of space-time interaction on deformation in the region is demarcated, and a deformation reference point is set in the region; considering the influence of initial stress release and processing stress introduction, an interaction model between regions is established; an analytical method of space-time interaction coefficient is proposed, and the offset value of the reference point is solved by using finite element analysis means; the compensation region is divided by the gradient of the offset value change, the boundary intersection points of the region are defined as characteristic reference points, the characteristic reference point positions are obtained by in-machine measurement method, and the difference between the characteristic reference point positions and the finite element calculation positions is calculated to correct the region compensation value; the processing code in the region is offset as a whole according to the compensation value, and the overall deformation compensation of the large thin-walled part is completed. The invention proposes the concept of space-time interaction coefficient, and the overall offset of the region processing track completes digital processing, which is simple in whole process operation, high in automation degree and effectively improves the machining precision, and meets the demand of overall deformation precision control of large thin-walled parts.

Description

Technical Field

[0001] This invention belongs to the field of processing deformation compensation, and relates to a method for regional compensation of overall deformation of large thin-walled parts based on spatiotemporal interaction. Background Technology

[0002] With the rapid development of aerospace and other fields in my country, large thin-walled components are widely used due to their lightweight and high structural strength. However, the processing cycle for large thin-walled components is long and the manufacturing process is complex. Due to factors such as their inherent stiffness and time deformation, they are prone to deformation during the semi-finishing and finishing stages. The processing involves material removal, leading to the release of initial stress and the introduction of processing stress. The stress rebalancing process of the component introduces deformation, and the interaction between different areas during processing can generate additional deformation. As processing time progresses, the stress state changes over time, and consequently, the overall deformation state also changes.

[0003] Currently, the machining of large thin-walled parts largely relies on worker experience, involving tool-by-tool adjustments and manual parameter modifications. This process suffers from low automation, long processing times, and high labor intensity. During the machining cycle, the interaction between the machined and unmachined areas leads to a shift in the machining reference, resulting in accumulated errors and ultimately making it difficult to guarantee machining accuracy. Therefore, a regional compensation method for the overall deformation of large thin-walled parts is proposed. This method uses a mechanistic analytical model to calculate the overall deformation value due to spatiotemporal interaction, combines on-machine measurement of feature points to correct the analytical values, and performs regional adjustments and compensation to ensure the machining accuracy of large thin-walled parts.

[0004] In 2015, Li Hongwei et al. of Beijing Xinghang Electromechanical Equipment Co., Ltd. disclosed a method for optimizing the cutting path of integral frame-type structural components in patent CN105069249B. This method establishes finite component models for both single-frame and integral frame components, performs dynamic cutting simulations, optimizes the trajectory form within single frames and the processing sequence of the integral components, thereby controlling processing deformation. This method controls deformation from the perspective of process sequence, but does not analyze the mechanism of quantitative deformation control. In 2017, Zhang Zheng et al. of Guangdong University of Technology disclosed a method for controlling deformation during the milling of integral wall panels in patent CN106826393B. This method measures residual stress by taking samples from the workpiece to be processed, analyzes the deformation value from the residual stress based on strain energy theory, and optimizes the cutting depth and material removal sequence with an objective function as a constraint. This method can control deformation to a certain extent, but it does not consider the additional deformation introduced during processing, making it difficult to accurately control the final deformation accuracy. In 2019, Yang Yinfei et al. from Nanjing University of Aeronautics and Astronautics disclosed a machining path optimization method for deformation control in the machining of large integral structural parts in patent CN 110928233B. This method solves for the influence of each region on bending deformation in the length direction by dividing the parts into regional elements, obtaining the globally optimal path while removing deformation at points of stable deflection. Although this method can reduce the final deformation, it analyzes each region as an isolated unit and does not consider the superposition effect of deformation between regions, thus limiting the solution for the deformation influence value.

[0005] Currently, no method has been proposed for regional compensation of overall deformation of large thin-walled components based on spatiotemporal interaction. Summary of the Invention

[0006] The main technical problem addressed by this invention is overcoming the shortcomings of existing methods. Addressing challenges such as datum offset, deformation superposition, and low efficiency of multiple rounds of manual adjustment during the processing of large thin-walled parts, this invention proposes a regional compensation method for the overall deformation of large thin-walled parts based on spatiotemporal interaction. This method delineates the influence range of spatiotemporal interaction on deformation within a region and sets deformation datum points within that region. Based on plate and shell mechanics theory, considering the influence of initial stress release and the introduction of processing stress, a model of inter-regional interaction is established. Combining the influence of time on stress state, an analytical method for spatiotemporal interaction coefficients is proposed, and finite element analysis is used to solve for the datum point offset value. The compensation region is divided according to the gradient of the offset value change, and the boundary intersection of the regions is defined as a characteristic datum point. The position of the characteristic datum point is obtained through machine measurement and the difference between it and the finite element calculation position is calculated to correct the regional compensation value. Finally, the processing code within the region is offset overall according to the compensation value to complete the overall deformation compensation of the large thin-walled part.

[0007] The technical solution of the present invention:

[0008] A method for regional compensation of overall deformation of large thin-walled components based on spatiotemporal interaction is proposed. First, based on the surface features of the large thin-walled component, a spatiotemporal interaction influence domain is initially defined. Combined with the characteristics within the domain, a reference point representing the deformation of the feature domain is set. Second, based on the existing process sequence and the stress state of the component, a deformation interaction influence model between feature domains during processing is established. Incorporating the time factor within the processing cycle, the spatiotemporal interaction influence coefficient is calculated, thereby determining the offset of the reference point. Then, using the gradient of the reference point offset as input, the compensation area is further refined within the influence domain. Finally, the actual position of the feature point is measured, and the deviation between the actual position and the analytical position is used as a correction value to correct the offset of the compensation area. The overall processing code of the area is adjusted to complete the overall deformation compensation of the large thin-walled component. The specific steps are as follows:

[0009] The first step is to determine the influence domain of spatiotemporal interaction, and to set reference points and boundary feature points based on the surface characteristics.

[0010] For multi-frame structural components in large thin-walled parts, during the machining process, as material is removed, the residual stress in the cutting layer is gradually released, the internal stress balance is broken, and the multi-frame structural component returns to the equilibrium state after deformation; when a part of the multi-frame structural component deforms due to material removal, its adjacent areas will also deform; when the multi-frame structural component is machining one grid, it affects the surrounding n grids.

[0011] The center of the grid in a multi-frame structure is furthest from the rib, has the weakest rigidity, and experiences the most severe deformation. Therefore, the center of the grid is set as the grid reference point. When the material of a grid in a multi-frame structure is removed, its adjacent areas will deform. Since there is no external force during release, the deformation on both sides of the rib shared by adjacent grids is the same. Therefore, the intersection of the line connecting the center reference points of two adjacent grids on the curved surface and the center line of the rib width is set as the boundary feature point.

[0012] The second step is to establish a spatiotemporal interaction model between feature domains and solve for the spatiotemporal interaction coefficients.

[0013] When a new stress equilibrium state is formed, the additional stress generated at this time can be considered to act on the remaining material as an equivalent torque. The equivalent torque on the mesh rib is obtained by removing the stress from the material and is expressed as:

[0014]

[0015]

[0016] Among them, M α and M β To remove the equivalent torque generated by stress in the α and β directions in the material, H is the blank thickness of the multi-frame structural member, h is the remaining material thickness of the rib plate of the multi-frame structural member, and σα and σ β To remove stress in the α and β directions of the material;

[0017] The reference point at the center of the multi-frame structural member mesh represents the maximum deformation value inside the mesh. The deformation state of the reference point relative to the boundary feature point is expressed as:

[0018]

[0019] Among them, u i The deformation in the α direction of the line connecting the reference point and the boundary feature point, v i The deformation in the β direction of the line connecting the reference point and the boundary feature point, w i D represents the deformation of the reference point in the thickness direction. i To ensure the stiffness of the remaining material after the mesh material is removed, L i Let μ be the arc distance between two boundary feature points on the curved surface, and μ be the Poisson's ratio of the material.

[0020] While processing the next mesh, the previously processed mesh continues to deform; simultaneously, after processing the next mesh, the next mesh also affects the previously processed mesh. The spatiotemporal interaction coefficient characterizes the mutual influence between two meshes during processing. Considering processing time and the distance between meshes, the spatiotemporal interaction coefficient is expressed as:

[0021]

[0022] Where, ρ i+1,i ρ is the spatiotemporal interaction coefficient that represents the effect of the previous mesh processing on the subsequent mesh. i,i+1 h represents the spatiotemporal interaction coefficient that represents the influence of the subsequent mesh processing on the previous mesh. i and h i+1 t represents the wall thickness after the front and rear meshes are processed. i and t i+1 The time intervals before and after processing are given, m is the number of reference points between the two meshes before and after processing, and C is a coefficient determined by the material and structure of the multi-frame structure.

[0023] The third step is to divide the compensation area within the influence domain, using the deformation gradient of the reference point as a constraint.

[0024] After determining the spatiotemporal interaction coefficient between the two meshes, and processing all the meshes, the final processed mesh undergoes severe deformation due to the cumulative influence of the deformation of the previously processed meshes. The displacement of the reference point of the final processed mesh is expressed as:

[0025]

[0026] Where, ξ nLet ζ be the displacement along the line α connecting the reference points. n The displacement along the line β connecting the reference points. The displacement of the reference point in the thickness direction is n, and the number of grids is n.

[0027] By determining the spatiotemporal interaction coefficient, the deformation values ​​of all processed mesh feature points are obtained. The last processed mesh has the most severe cumulative deformation impact, and its reference point has the largest displacement. Using the feature point deformation values ​​calculated in the second step, the deformation values ​​of all points on the line connecting the reference point of the last processed mesh and the boundary feature point of the adjacent nth mesh can be obtained. It is assumed that the deformation value of the boundary feature point of the adjacent nth mesh is 0. The allowable tolerance Φ is used as the deformation gradient in the region. All points on the line are divided into q compensation regions. The difference in deformation values ​​in each compensation region is less than the deformation gradient.

[0028] The fourth step involves adjusting the compensation value based on the deviation between the actual and analytical positions of the feature points, thereby achieving regional compensation processing.

[0029] The compensation amount of the compensation area is determined by the deformation value of the reference point within the divided compensation area. The compensation value of the q-th compensation area is ξ. q ζ q and Use a trigger probe to measure the coordinate information P of the grid corner points. R (x R ,y R ,z R ), to obtain the measured displacement value δ of the grid corner points within the region. R , is represented as:

[0030]

[0031] Where P0(x0,y0,z0) represents the theoretical coordinates of the grid corner point;

[0032] The deformation values ​​at the corner points of the computational region in the finite element model are expressed as follows:

[0033]

[0034] Among them, P F (x F ,y F ,z F () represents the predicted coordinates of the grid corner points;

[0035] The model is corrected by obtaining the deviation value through actual measurement. The error δ between the finite element model and the actual state of the workpiece is expressed as:

[0036] δ=δ R -δ F (8)

[0037] The deformation value of the regional reference point is modified using the error value, and the compensation value of the compensation area is corrected to ξ′. q ,ζ′ q and

[0038] The machining code is offset using the compensation values ​​of the corrected compensation region. Since the tool position points after offset are determined in the coordinate system of the region's reference point, the compensation values ​​of the compensation region need to be mapped to the Cartesian coordinate system R of the machining code. 3 In the region, the curve connecting the reference point and the unoffset tool position is r1(t) = (u1(t), v1(t), w1(t)). The state of the tool position on the curve is represented by a Frenet frame, and the unit tangent vector of the curve containing the unoffset tool position is r. α1 The unit normal vector is r β1 The arc length of the line connecting the regional reference point and the tool point on the surface is known, and can be expressed according to the first fundamental form of the surface as follows:

[0039]

[0040]

[0041] Where E, F, and G are the coefficients of the first basic form of the surface, α and β are the coordinate directions of the surface, and a is the parameter at the tool point with respect to t, which is obtained by solving the equation;

[0042] After determining 'a', the coordinates of the unoffset tool position point under the Frenet frame of the regional reference point are obtained. Similarly, the curve containing the line connecting the regional reference point and the offset tool position point is r2(t)=(u2(t),v2(t),w2(t)). The arc length L′ of the line connecting the regional reference point and the offset tool position point on the surface is expressed as:

[0043]

[0044] Where b is the parameter of the offset tool position point with respect to t, and the coordinates of the offset tool position point can also be obtained through the frame of the regional reference point;

[0045] By establishing a Frenet frame at the reference points on the two curves, the relationship between the compensation value and the reference point coordinate system is obtained. Furthermore, the compensation value of the tool position point in the Cartesian coordinate system of the machining code is obtained, expressed as:

[0046]

[0047] in, Let β be the angle between β and the positive x-axis of the Cartesian coordinate system, and let θ be the angle between α and the positive z-axis of the Cartesian coordinate system.

[0048] Finally, the machining is carried out according to the CNC machining program generated after the offset tool position. The work of steps two to four is repeated to complete the overall deformation and regional compensation machining of large thin-walled parts, realize the precise control of deformation, and at the same time provide support for the precise compensation of tool position for wall thickness deformation, thus meeting the actual machining requirements.

[0049] The beneficial effects of this invention are as follows: This invention proposes a regional compensation method for the overall deformation of large thin-walled parts based on spatiotemporal interaction. It determines the overall deformation influence domain of spatiotemporal interaction and divides the domain into reference points and feature points based on features within the domain. An analytical model of spatiotemporal interaction between regions is established, and the compensation domain is divided using the deformation gradient within the domain as a constraint. Considering the limitations of the analytical model, it is modified using measured feature points. Combined with Frenet's benchmark field theory, the compensation tool position points are calculated, and the final CNC machining program is generated. This solves the reference offset problem caused by deformation during the machining of large thin-walled parts, as well as the deformation problem caused by stress release under long machining cycles. The method described in this invention is convenient to operate, highly automated, and highly reliable, and can meet the overall deformation control requirements of large thin-walled parts. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method for regional compensation of overall deformation of large thin-walled parts based on spatiotemporal interaction as described in this invention.

[0051] Figure 2 This is a schematic diagram of the three-dimensional model of the large thin-walled component described in this invention.

[0052] Figure 3 A schematic diagram of setting reference points and dividing compensation domains for large thin-walled components.

[0053] Figure 4 This is a schematic diagram illustrating the principle of spatiotemporal interaction between the overall deformation regions of a large thin-walled component.

[0054] Figure 5 A schematic diagram for correcting compensation values ​​within the compensation domain.

[0055] Figure 6 A schematic diagram for solving the compensation tool position.

[0056] In the figure: 1. Large multi-frame thin-walled part; 2. Rib features of workpiece outline; 3. Spatiotemporal interaction influence domain; 4. Center reference point; 5. Boundary feature point; 6. Compensation domain boundary; 7. Spatiotemporal interaction region 1; 8. Spatiotemporal interaction region 2; 9. Measured position of correction point; 10. Calculated position of correction point in analytical model; 11. Theoretical position of correction point; 12. Regional compensation value; 13. Curve r1; 14. Curve r2; 15. Compensation pre-tool position point; 16. Compensation post-tool position point. Detailed Implementation

[0057] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0058] The multi-frame structural component of this invention has a diameter of 2000mm or more, a height of 1000mm or more, a positional accuracy requirement of less than 0.05mm, and undergoes complex deformation during processing. Figure 1 This is a flowchart of the multi-frame structural component regional deformation compensation method based on spatiotemporal interaction coefficients according to the present invention. The specific steps are as follows:

[0059] The first step is to determine the influence domain of spatiotemporal interaction, and to set reference points and feature points based on the surface characteristics.

[0060] During the processing, the material of the wall panel is gradually removed, the residual stress in the cutting layer is gradually released, the internal stress balance is broken, and the part deforms to restore the equilibrium state. When a part of the multi-frame structure deforms due to material removal, its adjacent areas will also deform. When processing one grid of the multi-frame structure, it affects the four surrounding grids. The deformation value outside the four grids affected by the deformation is less than the positional accuracy requirement.

[0061] In a multi-frame structure, the center of the grid is furthest from the rib, has the weakest rigidity, and experiences the most severe deformation. Therefore, the center of the grid is set as the grid reference point. When material is removed from one grid in a multi-frame structure, its adjacent areas will deform. Since there is no external force during release, the curvature change rates on the left and right sides of the rib shared by adjacent grids are equal. The intersection of the line connecting the center reference points of two adjacent grids on the curved surface and the center line of the rib width is set as the boundary feature point, representing the curvature relationship between adjacent grids.

[0062] The second step is to establish a spatiotemporal interaction model by defining the feature domain and then solve for the spatiotemporal interaction coefficients.

[0063] When a new stress equilibrium state is formed, the additional stress generated at this time can be considered to act on the remaining material as an equivalent torque. The equivalent torque on the mesh rib can be obtained by removing the stress in the material, and is expressed as:

[0064]

[0065]

[0066] Among them, M α and M β To remove stress in the α and β directions of the material, H is the blank thickness of the multi-frame structural component, h is the remaining material thickness of the rib plate of the multi-frame structural component, and σ α and σ β To remove stress in the α and β directions of the material;

[0067] The reference point at the center of the mesh of a multi-frame structural component represents the maximum deformation value inside the mesh. The deformation state of the mesh reference point relative to the boundary feature point is expressed as follows:

[0068]

[0069] Where u1 is the deformation along the line connecting the first grid center reference point and the boundary feature point α, v1 is the deformation along the line connecting the first grid center reference point and the boundary feature point β, w1 is the deformation of the first grid center reference point in the thickness direction, D1 is the stiffness after material removal from the first grid, L1 is the arc length distance between the two boundary feature points of the first grid on the curved surface, and μ is the Poisson's ratio of the material.

[0070] Calculate the deformation values ​​of the second to fourth grids in sequence.

[0071] While processing the second mesh, the first mesh continues to deform; simultaneously, after processing the second mesh, the second mesh also affects the first mesh. The spatiotemporal interaction coefficient characterizes the mutual influence between the two meshes during processing. Considering processing time and the distance between meshes, the spatiotemporal interaction coefficient is expressed as:

[0072]

[0073] Where, ρ 2,1 ρ represents the spatiotemporal interaction coefficient that influences the second grid after the first grid is processed. 1,2 The spatiotemporal interaction coefficient represents the impact of the second mesh processing on the first mesh, h1 and h2 are the wall thicknesses after the mesh processing, t1 and t2 are the times of the two meshes before and after processing, and C is a coefficient determined by the material and structure of the multi-frame structural component.

[0074] The third step is to divide the compensation area within the influence domain, using the deformation gradient of the reference point as a constraint.

[0075] After determining the spatiotemporal interaction coefficient between the two meshes, and processing all the meshes, the last mesh processed will undergo severe deformation due to the cumulative deformation influence of the previously processed meshes. The displacement of the reference point of the last processed mesh is expressed as:

[0076]

[0077] Where ξ4 is the displacement along the α direction of the line connecting the fourth grid reference points, and ζ4 is the displacement along the β direction of the line connecting the fourth grid reference points. This represents the displacement of the fourth grid reference point in the thickness direction;

[0078] By determining the spatiotemporal interaction coefficient, the deformation values ​​of all processed mesh feature points are obtained. The last processed mesh has the most severe cumulative deformation due to deformation, and its central feature point has the largest displacement. Using the feature point deformation values ​​calculated in the second step, the deformation values ​​of all points on the line connecting the central feature point of the last processed mesh and the boundary feature point of the fourth adjacent mesh can be obtained. The deformation value of the boundary feature point of the fourth adjacent mesh is considered to be 0. The allowable tolerance Φ = 0.05 mm is used as the deformation gradient within the region. All points on the connecting line are divided into q regions, and the difference in deformation value within each region is less than the deformation gradient.

[0079] The fourth step involves adjusting the compensation value based on the deviation between the actual and analytical positions of the feature points, thereby achieving regional compensation processing.

[0080] The regional compensation amount is determined by the deformation values ​​of benchmark points within the defined region; the regional compensation value is ξ. q ζ q and Use a trigger probe to measure the coordinate information P of the grid corner points. R (x R ,y R ,z R ), to obtain the measured displacement value δ of the grid corner points within the region. R , is represented as:

[0081]

[0082] Where P0(x0,y0,z0) represents the theoretical coordinates of the grid corner points.

[0083] The deformation values ​​at the corner points of the computational region in the finite element model are expressed as follows:

[0084]

[0085] Among them, P F (x F ,y F ,z F ) represents the theoretical coordinates of the grid corner points.

[0086] The model is corrected by obtaining the deviation value through actual measurement. The error δ between the finite element model and the actual state of the workpiece is expressed as:

[0087] δ=δ R -δ F (8)

[0088] The deformation value of the regional reference point is modified using the error value, and the compensation value of the region is also corrected, becoming ξ′. q ,ζ′ q and

[0089] The machining code is offset using the corrected compensation value. Since the tool position points after offset are determined in the coordinate system of the area reference point, the compensation value needs to be mapped to the Cartesian coordinate system R of the machining code. 3 In the region, the curve connecting the reference point and the unoffset tool position is r1(t) = (u1(t), v1(t), w1(t)). The state of the tool position on the curve can be represented by a Frenet frame, and the unit tangent vector of the curve is r. α1 The unit normal vector is r β1 The arc length of the line connecting the regional reference point and the tool point on the surface is known, and can be expressed according to the first fundamental form of the surface as follows:

[0090]

[0091]

[0092] Where E, F, and G are the coefficients of the first fundamental form of the surface, α and β are the coordinate directions of the surface, and a is the parameter at the tool point with respect to t, which is obtained by solving the equation.

[0093] After determining the result of 'a', the coordinates of the unoffset tool position point under the Frenet frame of the regional reference point can be obtained. Similarly, the curve connecting the regional reference point and the offset tool position point is r2(t) = (u2(t), v2(t), w2(t)), and the arc length L′ of the line connecting the regional reference point and the offset tool position point on the surface can be expressed as:

[0094]

[0095] Where b is the parameter of the offset tool position point with respect to t, and the coordinates of the offset tool position point can also be obtained through the frame of the regional reference point;

[0096] By establishing Frenet frames at reference points on the two curves, the relationship between the compensation value and the reference point coordinate system can be obtained. Furthermore, the compensation value of the tool position point in the Cartesian coordinate system of the machining code can be obtained, expressed as:

[0097]

[0098] in, Let β be the angle between β and the positive x-axis of the Cartesian coordinate system, and let θ be the angle between α and the positive z-axis.

[0099] Finally, the machining is performed according to the CNC machining program generated after the offset tool position. By repeating the work from step two to step four, the overall deformation of large thin-walled parts can be completed by regional compensation machining, achieving precise control of deformation. At the same time, it also provides support for precise compensation of tool position for wall thickness deformation, thus meeting actual machining needs.

[0100] 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 method for regional compensation of overall deformation of large thin-walled components based on spatiotemporal interaction, characterized in that, The steps are as follows: The first step is to determine the influence domain of spatiotemporal interaction, and to set reference points and boundary feature points based on the surface characteristics. For multi-frame structural components in large thin-walled parts, during the machining process, as material is removed, the residual stress in the cutting layer is gradually released, the internal stress balance is broken, and the multi-frame structural component returns to the equilibrium state after deformation; when a part of the multi-frame structural component deforms due to material removal, its adjacent areas will also deform; when the multi-frame structural component is machining one grid, it affects the surrounding n grids. The center of the grid in a multi-frame structure is furthest from the rib, has the weakest rigidity, and experiences the most severe deformation. Therefore, the center of the grid is set as the grid reference point. When the material of a grid in a multi-frame structure is removed, its adjacent areas will deform. Since there is no external force during release, the deformation on both sides of the rib shared by adjacent grids is the same. Therefore, the intersection of the line connecting the center reference points of two adjacent grids on the curved surface and the center line of the rib width is set as the boundary feature point. The second step is to establish a spatiotemporal interaction model between feature domains and solve for the spatiotemporal interaction coefficients. When a new stress equilibrium state is formed, the additional stress generated at this time can be considered to act on the remaining material as an equivalent torque. The equivalent torque on the mesh rib is obtained by removing the stress from the material and is expressed as: Among them, M α and M β To remove the equivalent torque generated by stress in the α and β directions in the material, H is the blank thickness of the multi-frame structural member, h is the remaining material thickness of the rib plate of the multi-frame structural member, and σ α and σ β To remove stress in the α and β directions of the material; The reference point at the center of the multi-frame structural member mesh represents the maximum deformation value inside the mesh. The deformation state of the reference point relative to the boundary feature point is expressed as: Among them, u i The deformation in the α direction of the line connecting the reference point and the boundary feature point, v i The deformation in the β direction of the line connecting the reference point and the boundary feature point, w i D represents the deformation of the reference point in the thickness direction. i To ensure the stiffness of the remaining material after the mesh material is removed, L i Let μ be the arc distance between two boundary feature points on the curved surface, and μ be the Poisson's ratio of the material. While processing the next mesh, the previously processed mesh continues to deform; simultaneously, after processing the next mesh, the next mesh also affects the previously processed mesh. The spatiotemporal interaction coefficient characterizes the mutual influence between two meshes during processing. Considering processing time and the distance between meshes, the spatiotemporal interaction coefficient is expressed as: Where, ρ i+1,i ρ is the spatiotemporal interaction coefficient that represents the effect of the previous mesh processing on the subsequent mesh. i,i+1 h represents the spatiotemporal interaction coefficient that represents the influence of the subsequent mesh processing on the previous mesh. i and h i+1 t represents the wall thickness after the front and rear meshes are processed. i and t i+1 The time intervals before and after processing are given, m is the number of reference points between the two meshes before and after processing, and C is a coefficient determined by the material and structure of the multi-frame structure. The third step is to divide the compensation area within the influence domain, using the deformation gradient of the reference point as a constraint. After determining the spatiotemporal interaction coefficient between the two meshes, and processing all the meshes, the final processed mesh undergoes severe deformation due to the cumulative influence of the deformation of the previously processed meshes. The displacement of the reference point of the final processed mesh is expressed as: Where, ξ n Let ζ be the displacement along the line α connecting the reference points. n The displacement along the line β connecting the reference points. The displacement of the reference point in the thickness direction is n, and the number of grids is n. By determining the spatiotemporal interaction coefficient, the deformation values ​​of all processed mesh feature points are obtained. The last processed mesh has the most severe cumulative deformation impact, and its reference point has the largest displacement. Using the feature point deformation values ​​calculated in the second step, the deformation values ​​of all points on the line connecting the reference point of the last processed mesh and the boundary feature point of the adjacent nth mesh can be obtained. It is assumed that the deformation value of the boundary feature point of the adjacent nth mesh is 0. The allowable tolerance Φ is used as the deformation gradient in the region. All points on the line are divided into q compensation regions. The difference in deformation values ​​in each compensation region is less than the deformation gradient. The fourth step involves adjusting the compensation value based on the deviation between the actual and analytical positions of the feature points, thereby achieving regional compensation processing. The compensation amount of the compensation area is determined by the deformation value of the reference point within the divided compensation area. The compensation value of the q-th compensation area is ξ. q ζ q and Use a trigger probe to measure the coordinate information P of the grid corner points. R (x R ,y R ,z R ), to obtain the measured displacement value δ of the grid corner points within the region. R , is represented as: Where P0(x0,y0,z0) represents the theoretical coordinates of the grid corner point; The deformation values ​​at the corner points of the computational region in the finite element model are expressed as follows: Among them, P F (x F ,y F ,z F () represents the predicted coordinates of the grid corner points; The model is corrected by obtaining the deviation value through actual measurement. The error δ between the finite element model and the actual state of the workpiece is expressed as: d=d R -d F (8) The deformation value of the regional reference point is modified using the error value, and the compensation value of the compensation area is corrected to ξ′. q ,ζ′ q and The machining code is offset using the compensation values ​​of the corrected compensation region. Since the tool position points after offset are determined in the coordinate system of the region's reference point, the compensation values ​​of the compensation region need to be mapped to the Cartesian coordinate system R of the machining code. 3 In the region, the curve connecting the reference point and the unoffset tool position is r1(t) = (u1(t), v1(t), w1(t)). The state of the tool position on the curve is represented by a Frenet frame, and the unit tangent vector of the curve containing the unoffset tool position is r. α1 The unit normal vector is r β1 The arc length of the line connecting the regional reference point and the tool point on the surface is known, and can be expressed according to the first fundamental form of the surface as follows: Where E, F, and G are the coefficients of the first basic form of the surface, α and β are the coordinate directions of the surface, and a is the parameter at the tool point with respect to t, which is obtained by solving the equation; After determining 'a', the coordinates of the unoffset tool position point under the Frenet frame of the regional reference point are obtained. Similarly, the curve containing the line connecting the regional reference point and the offset tool position point is r2(t)=(u2(t),v2(t),w2(t)). The arc length L′ of the line connecting the regional reference point and the offset tool position point on the surface is expressed as: Where b is the parameter of the offset tool position point with respect to t, and the coordinates of the offset tool position point can also be obtained through the frame of the regional reference point; By establishing a Frenet frame at the reference points on the two curves, the relationship between the compensation value and the reference point coordinate system is obtained. Furthermore, the compensation value of the tool position point in the Cartesian coordinate system of the machining code is obtained, expressed as: in, Let β be the angle between β and the positive x-axis of the Cartesian coordinate system, and let θ be the angle between α and the positive z-axis of the Cartesian coordinate system. Finally, the machining is carried out according to the CNC machining program generated after the offset tool position. The work of steps two to four is repeated to complete the overall deformation and regional compensation machining of large thin-walled parts, realize the precise control of deformation, and at the same time provide support for the precise compensation of tool position for wall thickness deformation, thus meeting the actual machining requirements.

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