A method for generating robot grinding parameters based on stiffness variation of large thin-walled parts

Abstract

The present invention discloses a method for generating robot grinding parameters based on the stiffness variation of large thin-walled parts in the field of robot grinding of large thin-walled parts. The method comprises the following steps: Step 1: extracting a grinding plane; Step 2: performing equal-width decomposition of the workpiece transversely along the robot grinding motion direction; Step 3: discretizing the workpiece along the variable thickness direction using the finite difference method; Step 4: extracting the discrete thin plate stiffness matrix using the finite element analysis method; Step 5: reducing the stiffness matrix dimension using the principal component analysis method; Step 6: constructing a stiffness variation trend line for the complete workpiece; and combining dynamic process generation constraints with the dynamic contact force variation trend to construct a complete grinding dynamic contact force applied along the grinding motion trajectory. The initial value of the obtained dynamic contact force curve is the basic contact force value in the dynamic process generation constraints, and the variation trend of the curve is determined by the workpiece stiffness variation trend line.

Description

Technical Field

[0001] The invention relates to a method for generating a robot grinding process for large thin-walled parts with variable stiffness characteristics in the field of robot grinding of large thin-walled parts. Background Art

[0002] In my country's uniquely high-end equipment manufacturing sectors, such as aerospace, defense, energy, and advanced rail transit, large, thin-walled parts account for a significant portion of the market. These include rocket engine nozzles, rocket / missile fuel tanks, aircraft skins, wind turbine blades, high-speed rail bodies, and ship propellers. After forming, these parts require grinding to achieve process requirements, such as improved surface quality, paint adhesion, and dimensional accuracy.

[0003] The stiffness of large, thin-walled parts exhibits significant variations as the grinding position changes. This variable stiffness makes it difficult to achieve uniform material removal from large, thin-walled parts using conventional processing methods with predefined process parameters. This requires that the grinding process parameters for large, thin-walled parts can be dynamically adjusted as the workpiece's variable stiffness changes. Currently, no effective methods or technologies exist for this, and actual processing often relies on trial and error, relying on manual experience. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for generating robot grinding parameters based on the stiffness change of large thin-walled parts, which can ensure the consistency of grinding quality parameters such as material removal amount and surface roughness.

[0005] To achieve the above object, the present invention provides a method for generating robot grinding parameters based on the stiffness change of large thin-walled parts, comprising the following steps:

[0006] Step 1, extracting the grinding plane;

[0007] Step 2, decomposing the workpiece into equal widths laterally along the grinding motion direction of the robot;

[0008] Step 3: discretize along the variable thickness direction based on the finite difference method;

[0009] Step 4, using finite element analysis to extract the discrete thin plate stiffness matrix;

[0010] Step 5, dimensionality reduction of stiffness matrix based on principal component analysis;

[0011] Step 6: Construct the stiffness change trend line of the complete workpiece.

[0012] Compared with the existing technology, the present invention has the beneficial effect of establishing corresponding dynamic process generation constraints (basic contact force value and contact force range) based on the characteristics and process requirements of different grinding methods, obtaining the trend line of the workpiece stiffness change along the grinding motion trajectory, and thus obtaining the trend of the dynamic contact force change. The dynamic process generation constraints and the dynamic contact force change trend are combined to construct a complete grinding dynamic contact force applied along the grinding motion trajectory. The initial value of the obtained dynamic contact force curve is the basic contact force value in the dynamic process generation constraints, and the curve's trend is determined by the workpiece stiffness change trend line.

[0013] As a further improvement of the present invention, the specific contents of step 1 are as follows:

[0014] The governing equation of the thin plate in plate and shell theory is shown in Equation 1 below:

[0015]

[0016] Where D(x,y) is the bending stiffness of the thin plate, which is a function of the spatial coordinates; ω is the deflection, μ is the Poisson's ratio of the material, and q(x,y) is the load.

[0017] In this way, the contact surface of the actual workpiece can be separated and the shell problem can be converted into a thin plate problem, thereby simplifying the calculation.

[0018] As a further improvement of the present invention, step 2 includes the following contents:

[0019] The robot's grinding motion trajectory divides the workpiece into several processing areas according to the grinding width, and the robot's grinding force trajectory is applied to the workpiece surface according to the motion trajectory. Therefore, the force trajectory planning problem can be decomposed according to the motion trajectory, and the workpiece stiffness change trend line on each linear motion trajectory can be solved separately.

[0020] This allows the workpiece to be decomposed into equal widths transverse to the robot's grinding motion direction, thereby further simplifying the workpiece.

[0021] As a further improvement of the present invention, step 3 includes the following contents:

[0022] In order to further simplify the solution model, the variable thickness thin plate unit is discretized by the finite difference method according to the direction of thickness change on the decomposed thin plate unit, and the variable thickness thin plate is discretized into several thin plate units of equal thickness. The finite difference method is a commonly used differential equation discretization method. By replacing the differential quotient in the differential equation with the difference quotient, the differential equation is discretized. The partial derivatives of each order at the origin of the differential discretization can be expressed as the following formula 2 using the difference,

[0023]

[0024] Where λc is the differential step length, ω i is the deflection value at the ith differential node, and the subscript (..)0 indicates the differential discrete node number 0. Substituting Equation 2 into Equation 1, we can obtain the differential equation at the differential discrete origin, as shown in Equation 3 below.

[0025] 20ω0-8(ω1+ω2+ω3+ω4)+2(ω5+ω6+ω7+ω8)

[0026] +(ω9+ω 10 +ω 11 +ω 12 )=q i λ c 4 / D i

[0027] Where q i , D i are the load value and bending stiffness value at the i-th differential node respectively;

[0028] After the differential grid and the node numbers are given, the differential equations at each node can be written in the form of Equation 3, and the deflection values ​​at each node can be obtained by solving the differential equations, so that the boundary conditions of each discrete thin plate can be determined during finite element analysis.

[0029] This can further simplify the solution model. The variable thickness thin plate unit is discretized using the finite difference method according to the direction of thickness change on the decomposed thin plate unit, and the variable thickness thin plate is discretized into several thin plate units of equal thickness. The variable stiffness thin plate problem is simplified to an equal stiffness thin plate problem. At the same time, the boundary conditions of each discrete thin plate unit during finite element analysis are determined, preparing for the next step of applying the finite element method to calculate the stiffness matrix of the discrete thin plate unit.

[0030] As a further improvement of the present invention, step 4 includes the following contents:

[0031] When performing finite element analysis, the boundary node displacements of the thin plate element calculated by the differential discretization method in step 3 will be used as the boundary conditions of the finite element analysis. The finite element method is also a numerical calculation method based on the idea of ​​discretization. The finite element method is based on variational equations and can obtain higher numerical calculation accuracy. Therefore, the finite element method is used in the calculation of the thin plate stiffness matrix in this step.

[0032] In finite element analysis, there are two stiffness matrices, namely the unit stiffness matrix Ke and the overall stiffness matrix K. The unit stiffness matrix can be obtained by applying the virtual work principle to the finite element nodes as shown in Equation 4 below:

[0033] K e =∫∫BT DBdxdy

[0034] Where B is the deformation matrix and D is the elastic matrix. For a four-node element, their matrix forms are as shown in Equations 5 and 6 below:

[0035]

[0036]

[0037] Where N is the element shape function, x, y are the node coordinates, i, p are the node names, E is the material elastic modulus, t is the plate thickness, and μ is the Poisson's ratio;

[0038] For a four-node thin plate element, each node has three degrees of freedom, namely deflection ω, rotation angle θx of the plate mid-surface normal around the x-axis, and rotation angle θy around the y-axis. Therefore, the dimension of the element stiffness matrix is ​​12×12. The overall stiffness matrix is ​​formed by combining the corresponding elements in the element stiffness matrix. Its calculation formula is shown in Equation 7 below.

[0039]

[0040] Where n is the number of nodes.

[0041] In this way, higher numerical calculation accuracy can be obtained through the finite element method based on variational equations.

[0042] As a further improvement of the present invention, step 5 includes the following contents:

[0043] From Equation 7, we can see that the size of the overall stiffness matrix is ​​3n×3n. Even after differential discretization, the dimension of the stiffness matrix is ​​still very large and cannot be expressed as a trend line of the workpiece stiffness change. Therefore, the stiffness matrix needs to be reduced in dimension. The stiffness matrix has the characteristics of symmetry and sparsity. Among the dimensionality reduction methods of this type of matrix, the PCA method is used. It uses an orthogonal matrix to map data in a high-dimensional space to a low-dimensional space, thereby simplifying the high-dimensional matrix.

[0044] The calculation process of the PCA method is as follows: First, each column of the stiffness matrix is ​​averaged, that is, each value in each column of the matrix is ​​subtracted from the average value of all values ​​in the column, where the average value of the jth value in the i-th column is the average value of the center x j (i’) The calculation formula is as shown in Equation 8 below:

[0045]

[0046] Where x j (i)is the jth value of the i-th column of the stiffness matrix, m is the number of all samples contained in the i-th column, and then the covariance matrix is ​​calculated as shown in Equation 9 below:

[0047]

[0048] Where c i is the data variable, and the covariance can be calculated by the following formula 10:

[0049]

[0050] Where Exp is the mathematical expectation. After the covariance matrix is ​​constructed, perform eigenvalue decomposition on it. Sort the eigenvalues ​​and find the orthogonalized unit eigenvector w of the largest first n eigenvalues ​​λa i , and form it into an eigenvector matrix, as shown in Equation 11 below

[0051] W=(w1,w2,w3...w n )

[0052] The number of rows in this matrix is ​​the number of dimensions to which the matrix needs to be reduced. Since the stiffness matrix needs to be reduced to one dimension to be expressed as a trend line of the workpiece stiffness change, the first row of the eigenvector transpose matrix, i.e., w1, is taken in the actual calculation. After obtaining the eigenvector matrix, all elements in the stiffness matrix can be mapped to the low-dimensional space to obtain the reduced-dimensional data matrix, as shown in the following formula 12.

[0053] N=(z (1) , z (2) ,...z (n) )

[0054] Where z (i) is a variable in the new matrix, and its mapping relationship with the data in the stiffness matrix can be expressed as Equation 13 shown below:

[0055] z (i) =w1x j (i)

[0056] Through the above-mentioned dimensionality reduction method, the 3n×3n stiffness matrix can be reduced to the 3n-dimensional vector required for calculation, and the changing trend of the value of each element in the 3n vector can be used to represent the changing trend of the workpiece stiffness.

[0057] As a further improvement of the present invention, step 6 includes the following contents:

[0058] The high-order stiffness matrix of the discrete thin plate can be reduced to a vector form. In order to obtain the workpiece stiffness change trend curve with the grinding position, the continuous grinding motion trajectory is first discretized into 3n points, which correspond one by one to the 3n elements in the vector obtained after the stiffness matrix is ​​reduced in dimension. The polynomial fitting method is used to construct the element values ​​into the form of a continuous curve, thereby obtaining the stiffness change trend line of the discrete thin plate unit under a single grinding trajectory. Then, the stiffness change trend lines of each discrete thin plate unit are spliced ​​together according to the complete grinding motion trajectory to construct a complete workpiece stiffness change trend line. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Flow chart of the method of the present invention.

[0060] Figure 2 This is a flow chart of the algorithm of the present invention.

[0061] Figure 3 This is an example diagram of the robot processing trajectory of the present invention.

[0062] Figure 4 This is a comparison chart of the calculation effects of the method of the present invention.

[0063] Figure 5 A dynamic process parameter map is generated for the present invention. DETAILED DESCRIPTION

[0064] The present invention will be further described below in conjunction with the accompanying drawings:

[0065] like Figure 1-5 A robot grinding parameter generation method based on the stiffness change of large thin-walled parts is shown, including the following contents:

[0066] Step 1: Extract the grinding surface.

[0067] The governing equation of the thin plate in plate and shell theory is shown in Equation 1 below:

[0068]

[0069] Where D(x,y) is the bending stiffness of the thin plate, which is a function of the spatial coordinates; ω is the deflection, μ is the Poisson's ratio of the material, and q(x,y) is the load.

[0070] Step 2: Decompose the workpiece into equal widths laterally along the grinding motion direction of the robot.

[0071] The robot's grinding motion trajectory divides the workpiece into several processing areas according to the grinding width, and the robot's grinding force trajectory is applied to the workpiece surface according to the motion trajectory. Therefore, the force trajectory planning problem can be decomposed according to the motion trajectory, and the workpiece stiffness change trend line on each linear motion trajectory can be solved separately. It should be pointed out that the strip units decomposed by width are located in different positions in the entire plate structure, so the boundary conditions of the differential equation are different. Figure 3 Taking the workpiece shown in as an example, the slat units at both ends can be regarded as three-sided simply supported and one-sided free, while the slat unit in the middle position can be regarded as four-sided simply supported.

[0072] Step 3: discretize along the variable thickness direction based on the finite difference method.

[0073] In order to further simplify the solution model, the thin plate unit after the above simplification is still a variable thickness plate. In order to further simplify the solution model, the variable thickness thin plate unit is discretized on the decomposed thin plate unit according to the direction of thickness change using the finite difference method, and the variable thickness thin plate is discretized into several thin plate units of equal thickness. The main purpose of the differential calculation here is to simplify the variable stiffness thin plate problem into an equal stiffness thin plate problem, and at the same time determine the boundary conditions of each discrete thin plate unit during finite element analysis, in preparation for the next step of applying the finite element method to calculate the stiffness matrix of the discrete thin plate unit. The finite difference method is a commonly used differential equation discretization method. By using the difference quotient instead of the derivative in the differential equation, the differential equation is discretized. The partial derivatives of each order at the origin of the differential discretization can be expressed by the difference as can be expressed as the following formula 2,

[0074]

[0075] Where λc is the differential step length, ω i is the deflection value at the ith differential node, and the subscript (..)0 indicates the differential discrete node number 0. Substituting Equation 2 into Equation 1, we can obtain the differential equation at the differential discrete origin, as shown in Equation 3 below.

[0076] 20ω0-8(ω1+ω2+ω3+ω4)+2(ω5+ω6+ω7+ω8)

[0077] +(ω9+ω 10 +ω 11 +ω 12 )=q i λ c 4 / D i

[0078] Where q i , D i are the load value and bending stiffness value at the i-th differential node respectively;

[0079] After the differential grid and the node numbers are given, the differential equations at each node can be written in the form of Equation 3, and the deflection values ​​at each node can be obtained by solving the differential equations, so that the boundary conditions of each discrete thin plate can be determined during finite element analysis.

[0080] Step 4: Use finite element analysis to extract the discrete thin plate stiffness matrix.

[0081] The stiffness of the thin plate is the main parameter in the thin plate deflection equation, which characterizes the relationship between load and deformation. Therefore, the stiffness of the thin plate needs to be solved to establish the relationship between force and deformation. When performing finite element analysis, the displacement of the thin plate unit boundary node calculated in the differential discretization method in step 3 will be used as the boundary condition of the finite element analysis; the finite element method is also a numerical calculation method based on the idea of ​​discretization. The finite element method is based on variational equations and can obtain higher numerical calculation accuracy. Therefore, the finite element method is used in the calculation of the thin plate stiffness matrix in this step;

[0082] In finite element analysis, there are two stiffness matrices, namely the unit stiffness matrix Ke and the overall stiffness matrix K. The unit stiffness matrix can be obtained by applying the virtual work principle to the finite element nodes as shown in Equation 4 below:

[0083] K e =∫∫B T DBdxdy

[0084] Where B is the deformation matrix and D is the elastic matrix. For a four-node element, their matrix forms are as shown in Equations 5 and 6 below:

[0085]

[0086]

[0087] Where N is the element shape function, x, y are the node coordinates, i, p are the node names, E is the material elastic modulus, t is the plate thickness, and μ is the Poisson's ratio;

[0088] For a four-node thin plate element, each node has three degrees of freedom, namely deflection ω, rotation angle θx of the plate mid-surface normal around the x-axis, and rotation angle θy around the y-axis. Therefore, the dimension of the element stiffness matrix is ​​12×12. The overall stiffness matrix is ​​formed by combining the corresponding elements in the element stiffness matrix. Its calculation formula is shown in Equation 7 below.

[0089]

[0090] Where n is the number of nodes.

[0091] Step 5, dimensionality reduction of stiffness matrix based on principal component analysis;

[0092] From Equation 7, we can see that the size of the overall stiffness matrix is ​​3n×3n. Even after differential discretization, the dimension of the stiffness matrix is ​​still very large and cannot be expressed as a trend line of the workpiece stiffness change. Therefore, the stiffness matrix needs to be reduced in dimension. The stiffness matrix has the characteristics of symmetry and sparsity. Among the dimensionality reduction methods of this type of matrix, the PCA method is used. It uses an orthogonal matrix to map data in a high-dimensional space to a low-dimensional space, thereby simplifying the high-dimensional matrix.

[0093] The calculation process of the PCA method is as follows: First, each column of the stiffness matrix is ​​averaged, that is, each value in each column of the matrix is ​​subtracted from the average value of all values ​​in the column, where the average value of the jth value in the i-th column is the average value of the center x j (i’) The calculation formula is as shown in Equation 8 below:

[0094]

[0095] Where x j (i) is the jth value of the i-th column of the stiffness matrix, m is the number of all samples contained in the i-th column, and then the covariance matrix is ​​calculated as shown in Equation 9 below:

[0096]

[0097] Where c i is the data variable, and the covariance can be calculated by the following formula 10:

[0098]

[0099] Where Exp is the mathematical expectation. After the covariance matrix is ​​constructed, perform eigenvalue decomposition on it. Sort the eigenvalues ​​and find the orthogonalized unit eigenvector w of the largest first n eigenvalues ​​λa i , and form the eigenvector matrix as shown in Equation 11 below

[0100] W=(w1,w2,w3...w n )

[0101] The number of rows of this matrix is ​​the number of dimensions to which the matrix needs to be reduced. Since the stiffness matrix needs to be reduced to one dimension to be expressed as a trend line of the workpiece stiffness change, the first row of the eigenvector transpose matrix, i.e., w1, is taken in the actual calculation. After obtaining the eigenvector matrix, all elements in the stiffness matrix can be mapped to the low-dimensional space to obtain the reduced-dimensional data matrix, as shown in the following formula 12.

[0102] N=(z (1) , z (2) ,...z(n) )

[0103] Where z (i) is a variable in the new matrix, and its mapping relationship with the data in the stiffness matrix can be expressed as Equation 13 shown below:

[0104] z (i) =w1x j (i)

[0105] Through the above-mentioned dimensionality reduction method, the 3n×3n stiffness matrix can be reduced to the 3n-dimensional vector required for calculation, and the changing trend of the value of each element in the 3n vector can be used to represent the changing trend of the workpiece stiffness.

[0106] Step 6: Construct the stiffness change trend line of the complete workpiece.

[0107] The high-order stiffness matrix of the discrete thin plate can be reduced to a vector form. In order to obtain the workpiece stiffness change trend curve with the grinding position, the continuous grinding motion trajectory is first discretized into 3n points, which correspond one by one to the 3n elements in the vector obtained after the stiffness matrix is ​​reduced in dimension. The polynomial fitting method is used to construct the element values ​​into the form of a continuous curve, thereby obtaining the stiffness change trend line of the discrete thin plate unit under a single grinding trajectory. Then, the stiffness change trend lines of each discrete thin plate unit are spliced ​​together according to the complete grinding motion trajectory to construct a complete workpiece stiffness change trend line.

[0108] The present invention establishes corresponding dynamic process generation constraints (basic contact force value and contact force range) based on the characteristics of different grinding forms and process requirements, obtains the change trend line of the workpiece stiffness along the grinding motion trajectory, and thus obtains the change trend of the dynamic contact force. The dynamic process generation constraints are combined with the dynamic contact force change trend to construct a complete grinding dynamic contact force applied along the grinding motion trajectory. The initial value of the obtained dynamic contact force curve is the basic contact force value in the dynamic process generation constraints, and the change trend of the curve is determined by the workpiece stiffness change trend line. The method flow chart is as follows: Figure 1 shown.

[0109] The dynamic process parameters of robot grinding are control parameters calculated by corresponding algorithms based on input information such as process requirements and process parameters. The parameters include grinding dynamic force constraints (basic contact force value and contact force range) and force change trend lines, etc., and are further combined with the robot grinding motion trajectory to generate a complete grinding force trajectory. The core algorithm is: the calculation method of the workpiece stiffness change trend line.

[0110] The core issue for calculating the trend line of workpiece stiffness variation is how to perform the calculation simply and efficiently. Robotic thin-walled workpiece grinding is a typical task mode in which a robot interacts with a dynamic environment. However, unlike the interaction mode between a robot and a completely unknown environment, a large thin-walled workpiece is a known contact environment. Therefore, when studying the problem of robot interaction with dynamic environments, the stiffness of the thin-walled workpiece can be used as a known condition for force trajectory planning. Usually, obtaining the stiffness value of a thin-walled workpiece requires numerical calculation, such as the commonly used finite element method. However, the stiffness matrix of a large thin-walled workpiece obtained by the finite element method is a high-order matrix, and its dimension will increase significantly with the increase in the number of analysis nodes. This will not only significantly increase the difficulty and time of calculation, but also cannot be expressed as a stiffness variation trend line within a plane that is easy to calculate. Therefore, it is necessary to reduce the dimensionality of the workpiece stiffness matrix so that the trend of the workpiece stiffness changing with the grinding contact point can be expressed as a curve, which can be applied to the grinding force trajectory planning method proposed in this chapter.

[0111] The specific algorithm is as follows: the variable stiffness shell is discretized into equal stiffness thin plate units using the differential discretization method, and the finite element analysis boundary conditions of each thin plate unit are obtained, thereby simplifying the large-scale thin-walled workpiece overall finite element analysis with a large amount of calculation to a small-scale analysis of discrete thin plate units; further, the principal component analysis (PCA) method is used to reduce the dimension of the high-order stiffness matrix to obtain the stiffness change trend line of each discrete thin plate unit; finally, the stiffness change trend lines of all discrete thin plate units are spliced ​​along the direction of the grinding motion trajectory to construct a complete workpiece stiffness change trend line. The specific process is as follows: Figure 2 shown.

[0112] The present invention enables the grinding process parameters of large thin-walled parts to be dynamically adjusted as the variable stiffness characteristics of the workpiece change, so that the grinding force can be dynamically adjusted according to the thickness of the workpiece, ensuring the consistency of grinding quality parameters such as material removal amount and surface roughness.

[0113] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed herein, those skilled in the art can make some substitutions and modifications to some of the technical features therein according to the disclosed technical content without creative labor, and these substitutions and modifications are all within the protection scope of the present invention.

Claims

1. A method for generating robot grinding parameters based on the stiffness variation of large thin-walled parts, characterized by: Including the following content, Step 1, extracting the grinding plane; Step 2, decomposing the workpiece into equal widths laterally along the grinding motion direction of the robot; Step 3: discretize along the variable thickness direction based on the finite difference method; Step 4, using finite element analysis to extract the discrete thin plate stiffness matrix; Step 5, dimensionality reduction of stiffness matrix based on principal component analysis; Step 6, constructing the stiffness variation trend line of the complete workpiece; Step 1 includes the following: The governing equation of the thin plate in plate and shell theory is shown in Equation 1 below: Where D(x,y) is the bending stiffness of the thin plate, which is a function of the spatial coordinates; ω is the deflection, μ is the Poisson's ratio of the material, and q(x,y) is the load; Step 2 includes the following, The robot's grinding motion trajectory divides the workpiece into several processing areas according to the grinding width, and the robot's grinding force trajectory is applied to the workpiece surface according to the motion trajectory. Therefore, the force trajectory planning problem is decomposed according to the motion trajectory, and the workpiece stiffness change trend line on each linear motion trajectory is solved separately; Step 3 includes the following, In order to further simplify the solution model, the variable thickness thin plate unit is discretized into several thin plate units of equal thickness using the finite difference method according to the direction of thickness change on the decomposed thin plate unit. Step 4 includes the following, When performing finite element analysis, the boundary node displacements of the thin plate element calculated by the differential discretization method in step 3 will be used as the boundary conditions of the finite element analysis; Step 6 includes the following, The high-order stiffness matrix of the discrete thin plate has been reduced to a vector form. In order to obtain the workpiece stiffness change trend curve with the grinding position, the discrete points of the continuous grinding motion trajectory are matched one by one with the elements in the vector obtained after the stiffness matrix is ​​reduced in dimension. The polynomial fitting method is used to construct the element values ​​into the form of a continuous curve, thereby obtaining the stiffness change trend line of the discrete thin plate unit under a single grinding trajectory. Then, the stiffness change trend lines of each discrete thin plate unit are spliced ​​together according to the complete grinding motion trajectory to construct a complete workpiece stiffness change trend line.

2. The method for generating robot grinding parameters based on the stiffness variation of large thin-walled parts according to claim 1, characterized in that: The specific contents of step 3 are as follows: The finite difference method is a discretization method for differential equations. It discretizes the differential equations by replacing the differential quotients in the differential equations with the difference quotients. The partial derivatives of each order at the origin of the differential discretization can be expressed as the following formula 2 using the difference. Where λc is the differential step length, ω i is the deflection value at the ith differential node, and the subscript (..)0 indicates the differential discrete node number 0. Substituting Equation 2 into Equation 1, we can obtain the differential equation at the differential discrete origin, as shown in Equation 3 below. 20ω0-8(ω1+ω2+ω3+ω4)+2(ω5+ω6+ω7+ω8) +(ω9+ω 10 +oh 11 +oh 12 )=q i l c 4 / D i Where q i , D i are the load value and bending stiffness value at the i-th differential node respectively; After the differential grid and the node numbers are given, the differential equations at each node can be written in the form of Equation 3, and the deflection values ​​at each node can be obtained by solving the differential equations, thereby determining the boundary conditions of each discrete thin plate during finite element analysis.

3. The method for generating robot grinding parameters based on the stiffness variation of large thin-walled parts according to claim 2, characterized in that: Step 4 specifically includes the following: The finite element method is also a numerical calculation method based on the idea of ​​discretization. The finite element method is based on variational equations and can obtain higher numerical calculation accuracy. Therefore, the finite element method is used in the calculation of the thin plate stiffness matrix in this step; In finite element analysis, there are two stiffness matrices, namely the unit stiffness matrix Ke and the overall stiffness matrix K. The unit stiffness matrix is ​​obtained by applying the virtual work principle to the finite element nodes as shown in Equation 4 below: K e =∫∫B T DBdxdy Where B is the deformation matrix and D is the elastic matrix. For a four-node element, their matrix forms are as shown in Equations 5 and 6 below: Where N is the element shape function, x, y are the node coordinates, i, p are the node names, E is the material elastic modulus, t is the plate thickness, and μ is the Poisson's ratio; For a four-node thin plate element, each node has three degrees of freedom, namely deflection ω, rotation angle θx of the plate mid-surface normal around the x-axis, and rotation angle θy around the y-axis. Therefore, the dimension of the element stiffness matrix is ​​12×12. The overall stiffness matrix is ​​formed by combining the corresponding elements in the element stiffness matrix. Its calculation formula is shown in Equation 7 below. Where n is the number of nodes.

4. The method for generating robot grinding parameters based on the stiffness variation of large thin-walled parts according to claim 3, characterized in that: Step 5 includes the following, From Equation 7, we can see that the size of the overall stiffness matrix is ​​3n×3n. Even after differential discretization, the dimension of the stiffness matrix is ​​still very large and cannot be expressed as a trend line of the workpiece stiffness change. Therefore, the stiffness matrix needs to be reduced in dimension. The stiffness matrix has the characteristics of symmetry and sparsity. Among the dimensionality reduction methods of this type of matrix, the PCA method is used. It uses an orthogonal matrix to map data in a high-dimensional space to a low-dimensional space, thereby simplifying the high-dimensional matrix. The calculation process of the PCA method is as follows: First, each column of the stiffness matrix is ​​averaged, that is, each value in each column of the matrix is ​​subtracted from the average value of all values ​​in the column, and the average value of the jth value in the i-th column is centered. The calculation formula is as shown in Equation 8 below: Where, is the jth value of the i-th column of the stiffness matrix, m is the number of all samples contained in the i-th column, and then the covariance matrix is ​​calculated as shown in Equation 9 below: Where c i is the data variable, and the covariance can be calculated by the following formula 10: those(c i ,c j )=Exp{[c i -Exp(c i )][c j -Exp(c j )]} Where Exp is the mathematical expectation. After the covariance matrix is ​​constructed, the eigenvalue decomposition is performed on it, the eigenvalues ​​are sorted, and the orthogonalized unit eigenvector w of the largest first n eigenvalues ​​λa is obtained. i , and form it into a feature vector Matrix, as shown in Equation 11 <h2 style=";text-align:left;direction:ltr">W=(w1,w2,w3...w<h2 style=";text-align:left;direction:ltr"> n <h2 style=";text-align:left;direction:ltr"> ) The number of rows in this matrix is ​​the number of dimensions to which the matrix needs to be reduced. Since the stiffness matrix needs to be reduced to one dimension to be expressed as a trend line of the workpiece stiffness change, the first row of the eigenvector transpose matrix, i.e., w1, is taken in the actual calculation. After obtaining the eigenvector matrix, all elements in the stiffness matrix are mapped to the low-dimensional space to obtain the reduced-dimensional data matrix, as shown in the following formula 12. N=(z (1) ,With (2) ,...With (n) ) Where z (i) is a variable in the new matrix, and its mapping relationship with the data in the stiffness matrix can be expressed as Equation 13 shown below: Through the above-mentioned dimensionality reduction method, the 3n×3n stiffness matrix is ​​reduced to the 3n-dimensional vector required for calculation, and the changing trend of the value of each element in the 3n vector is used to represent the changing trend of the workpiece stiffness.

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