Rapid modeling and optimizing method for global static stiffness of complete machine tool

Abstract

The invention discloses a complete machine tool global static rigidity rapid modeling and optimizing method, which comprises the following steps of: dividing a complete machine tool structure into two categories, namely a substructure and a joint part, and establishing a substructure static rigidity model by adopting a local rigidity hypothesis and static polycondensation method; constructing a static rigidity model of the joint part by adopting a local rigidity hypothesis for the joint part; establishing a semi-analytical static stiffness model of the whole machine tool; on the basis of an optimization algorithm and an evaluation algorithm, under the determined static rigidity model of the joint part, the weak position of the static rigidity of the machine tool in the working space is obtained through calculation; based on a sensitivity method, evaluating static stiffness parameters of the machine tool joint parts, and under a certain group of position parameters, obtaining the influence degree of the static stiffness parameters of each joint part on the static stiffness of the tail end of the whole machine tool; based on an optimization algorithm and an evaluation algorithm, a joint part static stiffness parameter with the best complete machine static stiffness under a certain group of position parameters within a value range is obtained; and the static rigidity of the weakest position in the working space is improved.

Description

Technical Field

[0001] The invention relates to the field of machine tools, and in particular to a method for rapid modeling and optimization of the global static stiffness of a complete machine tool. Background Art

[0002] Machine tools are the foundation of the equipment manufacturing industry and play a very important role in contemporary manufacturing. my country's CNC machine tool research cannot currently meet the high-precision requirements. Among the many factors that affect the accuracy of machine tools, the static stiffness performance of machine tools is one of the key factors. Static stiffness refers to the stiffness performance of machine tools under static conditions. It reflects the ability of machine tools to resist deformation when bearing loads. Insufficient static stiffness of machine tools will lead to large errors in processing, thereby affecting processing accuracy and reducing product quality. Therefore, improving the static stiffness of machine tools is of great significance to improving their processing accuracy and product quality.

[0003] To improve the static stiffness of machine tools, it is necessary to model the global static stiffness of the whole machine tool and analyze the influence of the position parameters of the machine tool and the stiffness parameters of the joints on the static stiffness of the whole machine. At present, the static stiffness of machine tools can be modeled mainly by numerical method, semi-analytical method and analytical method. However, the analytical method and numerical method have limitations to varying degrees: the analytical method can highly simplify the model and obtain an accurate solution, but the accuracy is limited due to the simplification of the model. The numerical method needs to re-establish the finite element model after the position parameters and the stiffness parameters of the joints of the machine tool model are changed, and there is a problem of low efficiency in static stiffness calculation. Therefore, it is of great significance to study a semi-analytical static stiffness modeling method for the whole machine tool, so as to quickly evaluate the global static stiffness of the machine tool and optimize it. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art. In view of the shortcoming of low static stiffness calculation efficiency, a method for establishing a global semi-analytical static stiffness model of a machine tool based on static condensation, proxy model and local rigidity assumption is provided. At the same time, a method for evaluating and optimizing the global static stiffness of the whole machine based on optimization algorithm and evaluation algorithm is proposed.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] A method for rapid modeling and optimization of the global static stiffness of a machine tool, comprising:

[0007] S1. The whole structure of the machine tool is divided into two categories: substructure and joint. The substructure is the representation form of the machine tool components. The static stiffness model of the substructure is established based on the local rigidity assumption and the static condensation method.

[0008] S2. Based on the local rigidity assumption, a static stiffness model of the joint is constructed;

[0009] S3. A semi-analytical static stiffness model of the whole machine tool is established based on the static stiffness model of the aforementioned substructure and the static stiffness model of the joint;

[0010] S4. According to the aforementioned semi-analytical static stiffness model of the whole machine, the static stiffness distribution of the whole machine in the workspace is obtained, and based on the optimization algorithm and the evaluation algorithm, under the determined static stiffness model of the joint, the weak position of the static stiffness of the machine tool in the workspace is calculated;

[0011] S5. Evaluate the static stiffness parameters of the joints of the machine tool based on the sensitivity method, and obtain the influence of the static stiffness parameters of each joint on the static stiffness of the whole machine tool under a certain set of position parameters;

[0012] S6. Based on the optimization algorithm and the evaluation algorithm, the static stiffness parameters of the joint with the best static stiffness of the whole machine under a certain set of position parameters within the value range are obtained; at the same time, by combining step S4, the static stiffness of the whole machine at the position parameter with the worst comprehensive static stiffness in the workspace is used as the output of the corresponding static stiffness parameters of the joint, and the optimization algorithm and the evaluation algorithm are nested to obtain the static stiffness parameters of the joint that can improve the static stiffness at the weakest position in the workspace, that is, to improve the lower limit of the static stiffness of the whole machine in the workspace.

[0013] Furthermore, the substructure includes but is not limited to a spindle, a worktable, a slide, a column, a spindle box, and a bed; the types of joints include but are not limited to bearing connection, bolt connection, guide rail and slider connection, and screw nut connection.

[0014] Further, step S1 includes the following steps:

[0015] S101. Taking a single substructure in a machine tool as an object, determine the degrees of freedom that need to be retained;

[0016] S102. Taking a single substructure as an object, a virtual node with 6 degrees of freedom is set at the equivalent center of the joint in the substructure, and the virtual node with 6 degrees of freedom is rigidly constrained with the 6 degrees of freedom of the finite element node at the joint in the substructure;

[0017] S103. Use a 6-DOF virtual node to represent all finite element nodes on the joint in the substructure;

[0018] S104. Performing a static condensation operation to obtain a degree of freedom condensation static stiffness matrix of the substructure;

[0019] S105. Define the spatial position information of the machine tool within each travel range as position parameters, and use the position parameters as independent variables to analyze the working status of the machine tool in different postures. Take all elements in the degree of freedom condensation stiffness matrix as output, construct a proxy model, and obtain the static stiffness model of the substructure.

[0020] Furthermore, in step S101, the degree of freedom retained by the substructure is set at the joint position between the substructures to take into account the connection conditions of each substructure; and is also set at the end position of the machine tool to take into account the displacement conditions at the two end points of the machine tool tool and the workpiece;

[0021] In step S102, if the substructure number is recorded as i, the virtual node is recorded as The local coordinate system of the virtual node with 6 degrees of freedom is recorded as m is the number of the corresponding joint in substructure i, and the kth finite element node at the location of the joint of the substructure is recorded as The local coordinate system of the kth finite element node is recorded as

[0022] In step S103, any 6-DOF displacement of a finite element node on the joint in the corresponding substructure is represented by the created virtual node 6-DOF displacement:

[0023]

[0024] In the formula, Represents a finite element node The 6-DOF displacement vector, Indicates virtual node The 6-DOF displacement vector, Indicates virtual node With finite element nodes The displacement transformation matrix between them;

[0025] Local coordinate system for a virtual node with 6 degrees of freedom and the local coordinate system of the kth finite element node When the virtual node is transformed only by translation and the rotation displacement of the virtual node is θ, tanθ is approximately represented by θ; The kth joint finite element node The displacement transformation matrix between It is expressed as:

[0026]

[0027] Where I is the identity matrix, O is the zero matrix, is the finite element node from the corresponding joint Point to virtual node The antisymmetric matrix of the position vector;

[0028] From the finite element node Point to virtual node The antisymmetric matrix of the displacement vector Expressed as

[0029]

[0030] In the formula, Represents the finite element node Point to virtual node The X-direction position vector, Represents the finite element node Point to virtual node The Y position vector of Represents the finite element node Point to virtual node The Z direction position vector;

[0031] In step S104, when static condensation is performed, the rigid multi-point constraint method is used to set the joints to be rigidly connected, and the degrees of freedom of the corresponding virtual nodes are set to reserved degrees of freedom; when several joints in the substructure can be regarded as rigid connections, static condensation is performed again using the above principle.

[0032] Further, in step S105, firstly, the position parameters are selected and their value ranges are determined, then the experimental points are selected using the experimental design method, and the finite element model of any substructure is modified according to the obtained experimental points, and the degree of freedom condensation stiffness matrix under the corresponding experimental points is obtained by static condensation, and finally, the position parameters and each element of the corresponding degree of freedom condensation stiffness matrix are interpolated or fitted by the method of creating a proxy model to obtain the static stiffness model of the substructure, which is expressed as:

[0033] K (i) U (i) =F (i)

[0034] In the formula, K (i) represents the static stiffness degree of freedom condensation matrix of substructure i, U (i) represents the displacement vector of the reserved degrees of freedom of substructure i, F (i) represents the force vector on the reserved degree of freedom of substructure i;

[0035] The experimental design methods include but are not limited to Latin hypercube design, uniform design and orthogonal experimental design; the methods for creating surrogate models include but are not limited to response surface method, Kriging method, neural network method and radial basis function interpolation method;

[0036] When the position parameters change, the degree of freedom condensed static stiffness matrix of the relevant substructure will change with the change of the position parameters.

[0037] Further, step S2 includes two cases:

[0038] S201. Based on step S1, the position of the joint in the substructure is set as a rigid surface, and the corresponding single joint is represented by a set of 6-DOF springs, and the stiffness parameters of the 6-DOF springs are obtained by calculation or querying relevant manuals;

[0039] S202. If there are several joints between the substructures, and considering some of the joints as rigid connections has no effect on the results, the stiffness of these joints is transformed into a coordinate system, and then the stiffness matrix of these joints is obtained by using the parallel spring superposition principle. At this time, the surface of the substructure corresponding to the position of these joints is rigid as a whole.

[0040] Further, step S4 includes:

[0041] S401. The tool and the workpiece are regarded as rigid bodies, and under a given set of joint parameters, a set of force vectors are given and combined with coordinate system transformation to obtain the relative displacement of the machine tool end at the cutting position, and then the position parameters are transformed to obtain the distribution of the relative displacement of the machine tool end at the cutting position in the workspace, and then the relative displacement and the force are substituted into the force balance equation to obtain the static stiffness distribution of the whole machine in the workspace;

[0042] S402. For identification of a weak position of rigidity of a certain degree of freedom, obtain the weak position of static rigidity of the workspace and the corresponding static rigidity of the entire machine end by obtaining the maximum relative displacement of the machine end at the cutting position under the action of force;

[0043] S403. For the identification of weak stiffness positions of several degrees of freedom, the position with the worst comprehensive stiffness performance in the workspace is obtained based on the optimization algorithm and the evaluation algorithm, and the corresponding static stiffness parameters of the entire terminal are obtained; wherein the optimization algorithm includes but is not limited to genetic algorithm, differential evolution algorithm, ant colony algorithm, particle swarm algorithm and simulated annealing algorithm; the evaluation algorithm includes but is not limited to hierarchical analysis method, fuzzy comprehensive evaluation method, TOPSIS method, grey correlation method and rank sum ratio method.

[0044] The present invention also provides a device for rapid modeling and optimization of the global static stiffness of a machine tool, comprising:

[0045] Substructure static stiffness module, which is used to divide the whole structure of the machine tool into two categories: substructure and joint, and establish the substructure static stiffness model by adopting the local rigidity assumption and static condensation method;

[0046] The static stiffness module of the joint is used to adopt the local rigidity assumption for the joint and construct the static stiffness model of the joint;

[0047] The semi-analytical static stiffness module of the whole machine tool is used to establish the semi-analytical static stiffness model of the whole machine tool according to the static stiffness model of the substructure and the static stiffness model of the joint;

[0048] The calculation module is used to obtain the static stiffness distribution of the whole machine in the workspace according to the semi-analytical static stiffness model of the whole machine, and to calculate the weak position of the static stiffness of the machine tool in the workspace under the static stiffness model of the determined joint based on the optimization algorithm and the evaluation algorithm;

[0049] An evaluation module is used to evaluate the static stiffness parameters of the machine tool joints by using a sensitivity method, and obtain the influence of the static stiffness parameters of each joint on the static stiffness of the machine tool end under a certain set of position parameters;

[0050] The optimization module is used to use the optimization algorithm and the evaluation algorithm to obtain the static stiffness parameters of the joint with the best static stiffness of the whole machine under a certain set of position parameters within the value range; at the same time, combined with the calculation module, the static stiffness of the whole machine at the position parameter with the worst comprehensive static stiffness in the workspace is used as the output of the corresponding static stiffness parameters of the joint, and the optimization algorithm and the evaluation algorithm are nested. The static stiffness parameters of the joint obtained are the ones that can improve the static stiffness at the weakest position in the workspace, that is, improve the lower limit of the static stiffness of the whole machine in the workspace.

[0051] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the method for rapid modeling and optimization of the global static stiffness of the entire machine tool are implemented.

[0052] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method for rapid modeling and optimization of the global static stiffness of the entire machine tool are implemented.

[0053] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0054] 1. Rapid modeling and optimization: This invention avoids the tedious operation of re-establishing the finite element model after the joint parameters or position parameters are changed by constructing a semi-analytical static stiffness model of the whole machine, greatly improving the efficiency of static stiffness modeling of the whole machine tool. This technology is applicable to multiple stages such as initial design, optimization analysis and structural modification, significantly shortening the design cycle.

[0055] 2. Identify weak locations of static stiffness: Through the static stiffness weak location identification method based on optimization algorithm and evaluation algorithm, the weakest location of static stiffness in the machine tool workspace can be quickly found, and the influence of the static stiffness parameters of each joint on the static stiffness of the entire machine end can be evaluated, providing precise guidance for optimization.

[0056] 3. Improve the static stiffness of the weakest position: Based on the nested optimization algorithm and the evaluation algorithm, the present invention can calculate and optimize the solution to improve the static stiffness of the weakest position in the working space within the value range of the static stiffness parameters of the joint, thereby improving the lowest static stiffness lower limit of the machine tool working space and enhancing the performance of the whole machine.

[0057] 4. Save costs and resources: Through static condensation, proxy models, and local rigidity assumptions, the modeling process is simplified and the calculation cost is reduced. There is no need to repeatedly build complex finite element models, which significantly reduces the overall cost of design cycle and production.

[0058] 5. Multi-method sensitivity analysis support: The present invention introduces a variety of sensitivity analysis methods (such as finite difference method, SOBOL method, etc.), which can not only refine the quantitative analysis of the influence of joint parameters on static stiffness, and be used to find the weak links of the whole machine tool, but also support flexible application for different design requirements.

[0059] 6. Strong versatility and adaptability: The static stiffness model and optimization method are applicable to various types of joints (such as bearing connections, guide rail slider connections, etc.) and various substructures (such as spindles, columns, etc.), and the selection of substructures can be freely changed as the research content changes. It has strong versatility and adaptability and can be widely used in the design and optimization of different machine tools.

[0060] 7. Innovative technical support: The new idea of ​​static stiffness modeling proposed in this invention can provide new technical support for machine tool design, break through the limitations of traditional methods in accuracy and efficiency, and lay the foundation for improving the design quality of machine tools and product competitiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 Schematic diagram of the process of the method for rapid modeling and optimization of the global static stiffness of the whole machine tool of this embodiment.

[0062] Figure 2 This is a schematic diagram of the structure of the whole machine model.

[0063] Figure 3 Schematic diagram of the mobile joint.

[0064] Figure 4 Schematic diagram of the static stiffness model of the joint.

[0065] Figure 5 This is a schematic diagram of the overall topological structure of the machine tool. DETAILED DESCRIPTION

[0066] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0067] Traditional static stiffness modeling mainly relies on the full finite element method. This embodiment provides a method for establishing a semi-analytical static stiffness model of a whole machine tool, which can evaluate the static stiffness of the whole machine tool in the workspace. At the same time, the joint parameters are used as independent variables, and the displacement difference of the spindle and the worktable processing end retaining the degree of freedom in the local coordinate system at the cutting position is used as the output for sensitivity analysis to obtain the influence of each joint parameter on the static stiffness performance of the whole machine in the workspace. Furthermore, the static stiffness of the whole machine tool can be optimized.

[0068] This embodiment proposes a method for rapid modeling and optimization of the global static stiffness of a machine tool. Figure 1 As shown, the specific contents include the following steps:

[0069] S1. Establish the substructure static stiffness model based on the local rigidity assumption and static condensation method; Figure 2 A schematic diagram of a machine tool is shown, including a spindle 1, a spindle box 2, a column 3, a bed 4, a lower slide 5, an upper slide 6, and a workbench 7. This embodiment divides the machine tool into two categories: substructures and joints, where the substructure is an abstract representation of the machine tool components. The substructure can be one or more of the spindle, workbench, slide, column, spindle box, and bed; the joint includes a moving joint, a fixed joint, and a rotating joint; the types of joints include but are not limited to bearing connection, bolt connection, guide rail slider connection, and lead screw nut connection.

[0070] S2. Based on the local rigidity assumption of the joint, if multiple joints can be rigidly connected, a 6-DOF stiffness matrix of the joint is established based on the stiffness superposition method of parallel springs to obtain the static stiffness model of the joint;

[0071] S3. A semi-analytical static stiffness model of the whole machine tool is established based on the static stiffness model of the aforementioned substructure and the static stiffness model of the joint;

[0072] S4. According to the aforementioned semi-analytical static stiffness model of the whole machine, the static stiffness distribution of the whole machine in the workspace is obtained, and based on the optimization algorithm and the evaluation algorithm, under the determined static stiffness model of the joint, the weak position of the static stiffness of the machine tool in the workspace is calculated;

[0073] S5. Evaluate the static stiffness parameters of the joints of the machine tool based on the sensitivity method, and obtain the influence of the static stiffness parameters of each joint on the static stiffness of the whole machine tool under a certain set of position parameters; the sensitivity method includes but is not limited to the finite difference method, MOAT method, correlation coefficient method, regression analysis method, importance estimation method and SOBOL method;

[0074] S6. Based on the optimization algorithm and the evaluation algorithm, the static stiffness parameters of the joint with the best static stiffness of the whole machine under a certain set of position parameters within the value range are obtained; at the same time, by combining step S4, the static stiffness of the whole machine at the position parameter with the worst comprehensive static stiffness in the workspace is used as the output of the corresponding static stiffness parameters of the joint, and the optimization algorithm and the evaluation algorithm are nested to obtain the static stiffness parameters of the joint that can improve the static stiffness at the weakest position in the workspace, that is, to improve the lower limit of the static stiffness of the whole machine in the workspace.

[0075] Specifically, step S1 specifically includes the following steps:

[0076] S101. Taking a single substructure in the machine tool as the object, the degree of freedom condensation stiffness matrix of the substructure is established by the static condensation method. The degree of freedom retained by the substructure needs to be set at the joint position between the substructures, which takes into account the connection of each substructure; it also needs to be set at the processing end of the machine tool, which takes into account the displacement of the tool and the workpiece of the whole machine tool.

[0077] S102. Set a virtual node with 6 degrees of freedom at the equivalent center of the joint in the substructure, and rigidly constrain the virtual node with 6 degrees of freedom and the 6 degrees of freedom of the finite element node at the joint in the substructure. If the substructure is numbered as i, the virtual node is denoted as The local coordinate system of the virtual node with 6 degrees of freedom is recorded as m is the number of the corresponding joint in substructure i, and the kth finite element node at the location of the joint of the substructure is recorded as The local coordinate system of the kth finite element node is recorded as The virtual nodes at the same joint position of two substructures should coincide in space.

[0078] S103. Use a 6-DOF virtual node to represent all finite element nodes on the joint in the substructure; specifically:

[0079] The 6-DOF displacement of any finite element node on the joint of the corresponding substructure can be represented by the 6-DOF displacement of the created virtual node:

[0080]

[0081] In the formula, Represents a finite element node The 6-DOF displacement vector, Indicates virtual node The 6-DOF displacement vector, Indicates virtual node With finite element nodes The displacement transformation matrix between them.

[0082] For local coordinate system With local coordinate system The virtual node is transformed only by translation, and the rotation displacement of the virtual node is very small. The kth joint finite element node The displacement transformation matrix between It can be expressed as

[0083]

[0084] Where I is the identity matrix, O is the zero matrix, is the finite element node from the corresponding joint Point to virtual node The antisymmetric matrix of the position vector.

[0085] From the finite element node Point to virtual node The antisymmetric matrix of the displacement vector It can be expressed as

[0086]

[0087] In the formula, Represents the finite element node Point to virtual node The X-direction position vector, Represents the finite element node Point to virtual node The Y direction position vector, Represents the finite element node Point to virtual node The Z direction position vector.

[0088] S104. Perform a static condensation operation to obtain the degree of freedom condensation static stiffness matrix of the substructure.

[0089] When the computer software HyperMesh is used for static polycondensation in this embodiment, it should be noted that the directions of the X, Y, and Z axes of the coordinate systems of the substructure models should be the same.

[0090] The rigid connection of the joint is set by using the rigid multi-point constraint method, and the degree of freedom of the corresponding virtual node is set to the reserved degree of freedom.

[0091] When several joints in a substructure can be regarded as rigid connections, static polycondensation can be performed again using the above principle.

[0092] S105. Define the spatial position information of the machine tool within each travel range as position parameters, and use the position parameters as independent variables to analyze the working status of the machine tool in different postures. Take all elements in the degree of freedom condensation stiffness matrix as output, construct a proxy model, and obtain the static stiffness model of the substructure.

[0093] The specific process is as follows: first, the position parameters are selected and their value ranges are determined. Secondly, the experimental points are selected using the experimental design method. After the finite element model of any substructure is modified according to the obtained experimental points, the degree of freedom condensation stiffness matrix under the corresponding experimental points is obtained through static condensation. Finally, the position parameters and each element of the corresponding degree of freedom condensation stiffness matrix are interpolated or fitted by the method of creating a proxy model to obtain a semi-analytical static stiffness model of the substructure. The experimental design methods include but are not limited to Latin hypercube design, uniform design and orthogonal experimental design. The proxy model methods include but are not limited to response surface method, kriging method, neural network method and radial basis function interpolation method.

[0094] It should be noted that when the position parameters change, the rigid constraint unit at the joint (such as the RBE2 unit in the HyperMesh software) sometimes changes position as the position parameters change. Figure 3 is a schematic diagram of a mobile joint. If the position parameters at the mobile joint change, the position of the joint on substructure i changes, causing the position of the rigid constraint unit corresponding to the joint to change, that is, the degree of freedom condensation stiffness matrix of substructure i changes. However, the position of the joint on substructure j does not change, so the position of the rigid constraint unit does not change, that is, the degree of freedom condensation stiffness matrix of substructure j does not change. In addition to the change of the rigid constraint unit that will cause the substructure to change, the change of the internal structure of the substructure and the rotation in the spatial position will also cause the substructure stiffness matrix to change.

[0095] After static polycondensation and creation of proxy models, the static stiffness model of the substructure can be expressed as

[0096] K (i) U (i) =F (i) (4)

[0097] In the formula, K (i) represents the static stiffness degree of freedom condensation matrix of substructure i, U (i) represents the displacement vector of the reserved degrees of freedom of substructure i, F (i) represents the force vector on the reserved degrees of freedom of substructure i.

[0098] Specifically, step S2 includes the following two situations:

[0099] S201. Based on step S1, the position of the joint in the substructure is set as a rigid surface, and the corresponding single joint is represented by a group of 6-DOF springs, and the stiffness parameters of the 6-DOF springs are obtained by calculation or querying relevant manuals.

[0100] S202. If there are multiple joints between substructures, and considering some of the joints as rigid connections will not have a significant impact on the results, the stiffness of these joints can be equivalently combined. In this case, the surfaces corresponding to the positions of these joints in the substructure are rigid as a whole.

[0101] like Figure 4 As shown, taking the mobile joint as an example, Figure 3 The interface between substructure i and substructure j is abstracted as a schematic diagram. A virtual node with 6 degrees of freedom is created at the equivalent center of this joint group in the substructure. If the two substructures are numbered i and j, the virtual nodes in the two substructures can be recorded as and n is the number of this joint group in substructure i and substructure j. At the same time, a 6-DOF virtual node is created at the equivalent center of the corresponding single joint in the two substructures. The corresponding virtual nodes can be recorded as and b is the number of a single joint in the corresponding joint group.

[0102] It should be noted that the virtual nodes corresponding to the joint surfaces in the two substructures need to overlap in space, and there is a 6-DOF spring connection between the overlapping virtual nodes. The 6-DOF spring is the equivalent stiffness of each joint surface. Indicates virtual node With virtual node The spring stiffness between Indicates virtual node With virtual node The spring stiffness between Indicates virtual node With virtual node The local coordinate system at Indicates virtual node With virtual node The local coordinate system at .

[0103] For rigid surfaces, virtual nodes With virtual node The displacement of the virtual node With virtual node The displacement of is represented by , and because the spatial position is the same, the displacement transformation matrix at the corresponding joint position is the same. The displacement transformation matrix between virtual nodes is recorded as Then the transformation of the spring stiffness matrix in different coordinate systems can be expressed as

[0104]

[0105] In the formula, Indicates virtual node With virtual node The spring stiffness matrix between , z represents the number of joints in this joint group, Indicates virtual node With virtual node The spring stiffness matrix between .

[0106] If one of the local coordinate systems can be obtained by translating only the other local coordinate system, and the rotational displacement of the node is very small, the displacement transformation matrix It can be expressed as

[0107]

[0108] Where I is the identity matrix, O is the zero matrix, From virtual node or virtual node Point to virtual node or virtual node The antisymmetric matrix of the position vector.

[0109] For the case where the joint stiffness changes with factors such as position parameters, the joint stiffness parameters can be expressed as a function of the position parameters; when the stiffness of the joint in a certain degree of freedom is 0 (no constraint is imposed on a certain degree of freedom), the corresponding joint matrix and the degree of freedom of the virtual node of this joint in the corresponding substructure can be condensed at the same time (that is, the degree of freedom corresponding to the joint stiffness of 0 is not retained).

[0110] Specifically, in step S3, this embodiment will Figure 2 The machine tool is abstracted into a topological structure model, such as Figure 5 As shown, Figure 5 Substructure 1, substructure 4, and substructure 7 represent Figure 2 The spindle 1, bed 4 and worktable 7 are included.

[0111] Assume that the joints between each substructure can be equivalent to a 6-DOF spring, where and represents the nodes corresponding to the two retained degrees of freedom of substructure i, and represents the nodes corresponding to the two reserved degrees of freedom of substructure j. At this time, the stiffness matrix K of substructure i of the machine tool is (i) It can be expressed as

[0112]

[0113] Where K is the stiffness matrix, the superscript (i) indicates that the symbol belongs to substructure i, and the subscripts 1 and 2 indicate the node numbers corresponding to the reserved degrees of freedom in substructure i.

[0114] The joint stiffness between substructure i and substructure j can be equivalent to a 6-DOF spring, and the deformation coordination relationship between the corresponding virtual nodes of the spring is:

[0115]

[0116] In the formula, K i,j represents the 6-DOF spring stiffness matrix of the joint between substructure i and substructure j. The superscript (i) and superscript (j) represent the symbol belonging to substructure i or substructure j, respectively. F E It represents the 6-dimensional force vector of the virtual node in the corresponding substructure, U E Represents the 6-dimensional displacement vector of the virtual node in the corresponding substructure.

[0117] Parameterized stiffness matrix K of machine tool G It can be expressed as

[0118]

[0119] The semi-analytical static stiffness model of the whole machine can be expressed as

[0120] KU=F(10)

[0121] Where K represents the parameterized static stiffness matrix; U represents the displacement vector corresponding to the degree of freedom after static condensation; and F represents the external force vector acting on the degree of freedom after static condensation.

[0122] In general, the force applied by the machine tool is located at the end of the machine tool. When the tool and workpiece are regarded as rigid bodies and the degrees of freedom at the two ends of the whole machine are set as the reserved degrees of freedom, the forces of the first three degrees of freedom are the same in magnitude and opposite in direction, and the forces of the last three degrees of freedom are related to the difference between the actual cutting position and the position of the node corresponding to the reserved degree of freedom. When the reserved degree of freedom is subjected to a force related to the position parameter, it can be expressed by a function of the position parameter. Substituting the force vector into equation 10 can obtain the displacement of the end of the machine tool under the corresponding stiffness matrix.

[0123] In addition, when calculating the relative displacement of the end of the machine tool, the displacement of the two points needs to be expressed using the local coordinate system at the actual cutting position. Since the tool and workpiece are regarded as rigid bodies, the displacement of the end of the machine tool at the cutting position can be obtained through coordinate system transformation, and then its relative displacement can be calculated.

[0124] Specifically, step S4 includes the following steps:

[0125] S401. The tool and workpiece are regarded as rigid bodies, and given a set of certain joint parameters, the relative displacement of the end of the machine tool at the cutting position can be obtained by giving a set of force vectors combined with the coordinate system transformation. Then, by transforming the position parameters, the distribution of the relative displacement of the end of the machine tool at the cutting position in the workspace can be obtained. Then, it is substituted with the force into the force balance equation to obtain the static stiffness distribution of the whole machine in the workspace.

[0126] S402. For the identification of the weak position of stiffness of a certain degree of freedom, the maximum value of the relative displacement of the end of the machine tool at the cutting position under the action of a certain force can be obtained, thereby obtaining the weak position of the static stiffness in the workspace and the corresponding static stiffness of the end of the whole machine.

[0127] S403. For the identification of weak rigidity positions of multiple degrees of freedom, the position with the worst comprehensive rigidity performance in the workspace can be obtained based on the optimization algorithm and the evaluation algorithm, and the corresponding static rigidity parameters of the entire terminal can be obtained. The optimization algorithm includes but is not limited to genetic algorithm, differential evolution algorithm, ant colony algorithm, particle swarm algorithm and simulated annealing algorithm. The evaluation algorithm includes but is not limited to hierarchical analysis method, fuzzy comprehensive evaluation method, TOPSIS method, grey correlation method and rank sum ratio method.

[0128] Preferably, the embodiment of the present application also provides a device for rapid modeling and optimization of the global static stiffness of a whole machine tool, based on the above-mentioned modeling and optimization method, including:

[0129] Substructure static stiffness module, which is used to divide the whole structure of the machine tool into two categories: substructure and joint, and establish the substructure static stiffness model by adopting the local rigidity assumption and static condensation method;

[0130] The static stiffness module of the joint is used to adopt the local rigidity assumption for the joint. If multiple joints can be rigidly connected, the 6-DOF stiffness matrix of the joint is established based on the stiffness superposition method of parallel springs to obtain the static stiffness model of the joint.

[0131] The semi-analytical static stiffness module of the whole machine tool is used to establish the semi-analytical static stiffness model of the whole machine tool according to the static stiffness model of the substructure and the static stiffness model of the joint;

[0132] The calculation module is used to obtain the static stiffness distribution of the whole machine in the workspace according to the semi-analytical static stiffness model of the whole machine, and to calculate the weak position of the static stiffness of the machine tool in the workspace under the static stiffness model of the determined joint based on the optimization algorithm and the evaluation algorithm;

[0133] An evaluation module is used to evaluate the static stiffness parameters of the joints of the machine tool based on the sensitivity method, and obtain the influence of the static stiffness parameters of each joint on the static stiffness of the end of the machine tool under a certain set of position parameters; the sensitivity methods include but are not limited to the finite difference method, MOAT method, correlation coefficient method, regression analysis method, importance estimation method and SOBOL method;

[0134] Optimization module. It is used to obtain the static stiffness parameters of the joint with the best static stiffness of the whole machine under a certain set of position parameters within the value range based on the optimization algorithm and the evaluation algorithm; at the same time, combined with the calculation module, the static stiffness of the whole machine at the position parameter with the worst comprehensive static stiffness in the workspace is used as the output of the corresponding static stiffness parameters of the joint, and the optimization algorithm and the evaluation algorithm are nested. The static stiffness parameters of the joint obtained are the ones that can improve the static stiffness at the weakest position in the workspace, that is, improve the lower limit of the static stiffness of the whole machine in the workspace, and complete the optimization.

[0135] Preferably, the embodiments of the present application also provide a specific implementation of an electronic device capable of implementing all steps in the method for rapid modeling and optimization of the global static stiffness of a whole machine tool in the above embodiment, and the electronic device specifically includes the following contents:

[0136] Processor, memory, communications interface and bus;

[0137] Among them, the processor, memory, and communication interface communicate with each other through the bus; the communication interface is used to realize information transmission between related devices such as server-side devices, metering devices, and user-side devices.

[0138] The processor is used to call the computer program in the memory. When the processor executes the computer program, all steps in the method for rapid modeling and optimization of the global static stiffness of the whole machine tool in the above embodiment are implemented.

[0139] An embodiment of the present application also provides a computer-readable storage medium capable of implementing all steps of the method for rapid modeling and optimization of the global static stiffness of a whole machine tool in the above-mentioned embodiment. A computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, all steps of the method for rapid modeling and optimization of the global static stiffness of a whole machine tool in the above-mentioned embodiment are implemented.

[0140] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the hardware + program embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0141] The above is a description of a specific embodiment of the specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the embodiments and still achieve the desired results. In addition, the processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0142] Although the present application provides method operation steps such as embodiments or flow charts, more or fewer operation steps may be included based on conventional or non-creative labor. The order of steps listed in the embodiments is only one way of executing the order of many steps and does not represent the only execution order. When the actual device or client product is executed, it can be executed in the order of the method shown in the embodiments or the drawings or in parallel (for example, in a parallel processor or multi-threaded processing environment).

[0143] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0144] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0145] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0146] The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solution of the present invention. The above specific embodiments are merely illustrative and not restrictive. Without departing from the scope of the present invention and the scope of protection of the claims, a person of ordinary skill in the art can also make many forms of specific changes under the guidance of the present invention, which all fall within the scope of protection of the present invention.

Claims

1. A method for rapid modeling and optimization of the global static stiffness of a machine tool, characterized in that: include: S1. The whole structure of the machine tool is divided into two categories: substructure and joint. The substructure is the representation form of the machine tool components. The static stiffness model of the substructure is established based on the local rigidity assumption and the static condensation method. S2. Based on the local rigidity assumption, a static stiffness model of the joint is constructed; S3. A semi-analytical static stiffness model of the whole machine tool is established based on the static stiffness model of the aforementioned substructure and the static stiffness model of the joint; S4. According to the aforementioned semi-analytical static stiffness model of the whole machine, the static stiffness distribution of the whole machine in the workspace is obtained, and based on the optimization algorithm and the evaluation algorithm, under the determined static stiffness model of the joint, the weak position of the static stiffness of the machine tool in the workspace is calculated; S5. Evaluate the static stiffness parameters of the joints of the machine tool based on the sensitivity method, and obtain the influence of the static stiffness parameters of each joint on the static stiffness of the whole machine tool under a certain set of position parameters; S6. Based on the optimization algorithm and the evaluation algorithm, the static stiffness parameters of the joint with the best static stiffness of the whole machine under a certain set of position parameters within the value range are obtained; at the same time, by combining step S4, the static stiffness of the whole machine at the position parameter with the worst comprehensive static stiffness in the workspace is used as the output of the corresponding static stiffness parameters of the joint, and the optimization algorithm and the evaluation algorithm are nested to obtain the static stiffness parameters of the joint that can improve the static stiffness at the weakest position in the workspace, that is, to improve the lower limit of the static stiffness of the whole machine in the workspace.

2. According to claim 1, a method for rapid modeling and optimization of the global static stiffness of a machine tool is characterized in that: The substructures include but are not limited to a spindle, a worktable, a slide, a column, a spindle box, and a bed; the types of joints include but are not limited to bearing connection, bolt connection, guide rail and slider connection, and lead screw and nut connection.

3. According to claim 1, a method for rapid modeling and optimization of the global static stiffness of a machine tool is characterized in that: Step S1 includes the following steps: S101. Taking a single substructure in a machine tool as an object, determine the degrees of freedom that need to be retained; S102. Taking a single substructure as an object, a virtual node with 6 degrees of freedom is set at the equivalent center of the joint in the substructure, and the virtual node with 6 degrees of freedom is rigidly constrained with the 6 degrees of freedom of the finite element node at the joint in the substructure; S103. Use a 6-DOF virtual node to represent all finite element nodes on the joint in the substructure; S104. Performing a static condensation operation to obtain a degree of freedom condensation static stiffness matrix of the substructure; S105. Define the spatial position information of the machine tool within each travel range as position parameters, and use the position parameters as independent variables to analyze the working status of the machine tool in different postures. Take all elements in the degree of freedom condensation stiffness matrix as output, construct a proxy model, and obtain the static stiffness model of the substructure.

4. According to claim 3, a method for rapid modeling and optimization of the global static stiffness of a machine tool is characterized in that: In step S101, the degree of freedom retained by the substructure is set at the joint position between the substructures to take into account the connection conditions of each substructure; and is also set at the end position of the machine tool to take into account the displacement conditions at the two end points of the machine tool tool and the workpiece; In step S102, if the substructure number is recorded as i, the virtual node is recorded as The local coordinate system of the virtual node with 6 degrees of freedom is recorded as m is the number of the corresponding joint in substructure i, and the kth finite element node at the location of the joint of the substructure is recorded as The local coordinate system of the kth finite element node is recorded as In step S103, any 6-DOF displacement of a finite element node on the joint in the corresponding substructure is represented by the created virtual node 6-DOF displacement: In the formula, Represents a finite element node The 6-DOF displacement vector, Indicates virtual node The 6-DOF displacement vector, Indicates virtual node With finite element nodes The displacement transformation matrix between them; Local coordinate system for a virtual node with 6 degrees of freedom and the local coordinate system of the kth finite element node When the virtual node is transformed only by translation and the rotation displacement of the virtual node is θ, tanθ is approximately represented by θ; The kth joint finite element node The displacement transformation matrix between It is expressed as: Where I is the identity matrix, O is the zero matrix, is the finite element node from the corresponding joint Point to virtual node The antisymmetric matrix of the position vector; From the finite element node Point to virtual node The antisymmetric matrix of the displacement vector Expressed as In the formula, Represents the finite element node Point to virtual node The X-direction position vector, Represents the finite element node Point to virtual node The Y direction position vector, Represents the finite element node Point to virtual node The Z direction position vector; In step S104, when static condensation is performed, the rigid multi-point constraint method is used to set the joints to be rigidly connected, and the degrees of freedom of the corresponding virtual nodes are set to reserved degrees of freedom; when several joints in the substructure can be regarded as rigid connections, static condensation is performed again using the above principle.

5. According to claim 3, a method for rapid modeling and optimization of the global static stiffness of a machine tool is characterized in that: In step S105, firstly, the position parameters are selected and their value ranges are determined. Secondly, the experimental points are selected using the experimental design method. After the finite element model of any substructure is modified according to the obtained experimental points, the degree of freedom condensation stiffness matrix under the corresponding experimental points is obtained by static condensation. Finally, the position parameters and each element of the corresponding degree of freedom condensation stiffness matrix are interpolated or fitted by creating a proxy model to obtain the static stiffness model of the substructure, which is expressed as: K (i) U (i) =F (i) In the formula, K (i) represents the static stiffness degree of freedom condensation matrix of substructure i, U (i) represents the displacement vector of the reserved degrees of freedom of substructure i, F (i) represents the force vector on the reserved degree of freedom of substructure i; The experimental design methods include but are not limited to Latin hypercube design, uniform design and orthogonal experimental design; the methods for creating surrogate models include but are not limited to response surface method, Kriging method, neural network method and radial basis function interpolation method; When the position parameters change, the degree of freedom condensed static stiffness matrix of the relevant substructure will change with the change of the position parameters.

6. The method for rapid modeling and optimization of the global static stiffness of a machine tool according to claim 1, characterized in that: Step S2 includes two cases: S201. Based on step S1, the position of the joint in the substructure is set as a rigid surface, and the corresponding single joint is represented by a set of 6-DOF springs, and the stiffness parameters of the 6-DOF springs are obtained by calculation or querying relevant manuals; S202. If there are several joints between the substructures, and considering some of the joints as rigid connections has no effect on the results, the stiffness of these joints is transformed into a coordinate system, and then the stiffness matrix of these joints is obtained by using the parallel spring superposition principle. At this time, the surface of the substructure corresponding to the position of these joints is rigid as a whole.

7. The method for rapid modeling and optimization of the global static stiffness of a machine tool according to claim 1, characterized in that: Step S4 includes: S401. The tool and the workpiece are regarded as rigid bodies, and under a given set of joint parameters, a set of force vectors are given and combined with coordinate system transformation to obtain the relative displacement of the machine tool end at the cutting position, and then the position parameters are transformed to obtain the distribution of the relative displacement of the machine tool end at the cutting position in the workspace, and then the relative displacement and the force are substituted into the force balance equation to obtain the static stiffness distribution of the whole machine in the workspace; S402. For identification of a weak position of stiffness of a certain degree of freedom, by obtaining the maximum relative displacement of the end of the machine tool at the cutting position under the action of force, the weak position of static stiffness in the workspace and the corresponding static stiffness of the end of the whole machine are obtained; S403. For the identification of weak stiffness positions of several degrees of freedom, the position with the worst comprehensive stiffness performance in the workspace is obtained based on the optimization algorithm and the evaluation algorithm, and the corresponding static stiffness parameters of the entire terminal are obtained; wherein the optimization algorithm includes but is not limited to genetic algorithm, differential evolution algorithm, ant colony algorithm, particle swarm algorithm and simulated annealing algorithm; the evaluation algorithm includes but is not limited to hierarchical analysis method, fuzzy comprehensive evaluation method, TOPSIS method, grey correlation method and rank sum ratio method.

8. A device for rapid modeling and optimization of the global static stiffness of a whole machine tool, based on the method for rapid modeling and optimization of the global static stiffness of a whole machine tool as claimed in any one of claims 1 to 7, characterized in that: include: Substructure static stiffness module, which is used to divide the whole structure of the machine tool into two categories: substructure and joint, and establish the substructure static stiffness model by adopting the local rigidity assumption and static condensation method; The static stiffness module of the joint is used to adopt the local rigidity assumption for the joint and construct the static stiffness model of the joint; The semi-analytical static stiffness module of the whole machine tool is used to establish the semi-analytical static stiffness model of the whole machine tool according to the static stiffness model of the substructure and the static stiffness model of the joint; The calculation module is used to obtain the static stiffness distribution of the whole machine in the workspace according to the semi-analytical static stiffness model of the whole machine, and to calculate the weak position of the static stiffness of the machine tool in the workspace under the static stiffness model of the determined joint based on the optimization algorithm and the evaluation algorithm; An evaluation module is used to evaluate the static stiffness parameters of the machine tool joints by using a sensitivity method, and obtain the influence of the static stiffness parameters of each joint on the static stiffness of the machine tool end under a certain set of position parameters; The optimization module is used to use the optimization algorithm and the evaluation algorithm to obtain the static stiffness parameters of the joint with the best static stiffness of the whole machine under a certain set of position parameters within the value range; at the same time, combined with the calculation module, the static stiffness of the whole machine at the position parameter with the worst comprehensive static stiffness in the workspace is used as the output of the corresponding static stiffness parameters of the joint, and the optimization algorithm and the evaluation algorithm are nested. The static stiffness parameters of the joint obtained are the ones that can improve the static stiffness at the weakest position in the workspace, that is, improve the lower limit of the static stiffness of the whole machine in the workspace.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method for rapid modeling and optimization of the global static stiffness of a machine tool as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for rapid modeling and optimization of the global static stiffness of a machine tool as described in any one of claims 1 to 7 are implemented.

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