Machine tool whole machine global static stiffness rapid modeling and optimization method

Abstract

The application discloses a kind of machine tool whole machine global static stiffness quick modeling and optimization method, comprising: machine tool whole machine structure is divided into two categories of substructure and joint, static stiffness model of substructure is established using local rigidity assumption and static condensation method;Joint uses local rigidity assumption, and the static stiffness model of joint is constructed;Establish machine tool whole machine semi-analytical static stiffness model;Based on optimization algorithm and evaluation algorithm, the weak position of machine tool in workspace is calculated under the static stiffness model of determined joint;Based on sensitivity method, the static stiffness parameters of machine tool joint are evaluated, and under a group of position parameters, the influence degree of the static stiffness parameters of each joint on the end static stiffness of machine tool whole machine is obtained;Based on optimization algorithm and evaluation algorithm, the best joint static stiffness parameter of whole machine static stiffness under a group of position parameters in value range is obtained;The static stiffness of the weakest position in workspace is improved.

Description

Technical Field

[0001] This invention relates to the field of machine tools, and in particular to a method for rapid modeling and optimization of the overall static stiffness of a machine tool. Background Technology

[0002] Machine tools are the foundation of the equipment manufacturing industry and hold a crucial position in modern manufacturing. Currently, my country's research on CNC machine tools cannot meet the demands for high precision. Among the many factors affecting machine tool accuracy, static stiffness is one of the key factors. Static stiffness refers to the rigidity performance of a machine tool under static conditions; it reflects the machine tool's ability to resist deformation under load. Insufficient static stiffness leads to larger machining errors, thus affecting machining accuracy and ultimately reducing product quality. Therefore, improving the static stiffness of machine tools is of great significance for improving their machining accuracy and product quality.

[0003] Improving the static stiffness of machine tools requires global static stiffness modeling of the entire machine tool, analyzing the influence of machine tool position parameters and joint stiffness parameters on the overall static stiffness. Currently, machine tool static stiffness can be modeled using three main methods: numerical methods, semi-analytical methods, and analytical methods. However, analytical and numerical methods have different limitations: analytical methods can highly simplify the model and obtain accurate solutions, but the accuracy is limited due to the simplification. Numerical methods require rebuilding the finite element model after changes to the machine tool's position parameters and joint stiffness parameters, resulting in low efficiency in static stiffness calculation. Therefore, researching a global semi-analytical static stiffness modeling method for machine tools, and then rapidly evaluating and optimizing the global static stiffness of the machine tool, is of great significance. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and address the low efficiency of static stiffness calculation. It provides a method for establishing a semi-analytical static stiffness model of the entire machine tool based on static condensation, surrogate model and local stiffness assumption. At the same time, it proposes a method for evaluating and optimizing the static stiffness of the entire machine tool based on optimization algorithm and evaluation algorithm.

[0005] The objective of this invention is achieved through the following technical solution:

[0006] A method for rapid modeling and optimization of the overall static stiffness of a machine tool includes:

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

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

[0009] S3. Based on the static stiffness models of the aforementioned substructures and joints, establish a semi-analytical static stiffness model for the entire machine tool.

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

[0011] S5. The static stiffness parameters of the machine tool joints are evaluated based on the sensitivity method. Under a certain set of position parameters, the influence of the static stiffness parameters of each joint on the static stiffness of the whole machine tool is obtained.

[0012] S6. Based on the optimization algorithm and evaluation algorithm, the static stiffness parameter of the joint with the best overall static stiffness under a certain set of position parameters within the range of values ​​is obtained; at the same time, by combining with step S4, the overall static stiffness at the position parameter with the worst comprehensive static stiffness in the workspace is taken as the output of the corresponding joint static stiffness parameter. The optimization algorithm and evaluation algorithm are nested together, and the obtained joint static stiffness parameter is the one 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 machine tool in the workspace.

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

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

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

[0016] S102. Taking a single substructure as the object, set a 6-degree-of-freedom virtual node at the equivalent center of the joint in the substructure, and rigidly constrain the 6-degree-of-freedom virtual node and 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 joints of the substructure;

[0018] S104. Perform static condensation operation to obtain the condensation static stiffness matrix of the substructure's degrees of freedom;

[0019] S105. Define the spatial position information of the machine tool within each stroke range as position parameters, and use the position parameters as independent variables to analyze the working state of the machine tool under different poses. Use all elements in the stiffness matrix of the degree of freedom as output to construct a surrogate model and obtain the static stiffness model of the substructure.

[0020] Furthermore, in step S101, the degrees of freedom retained by the substructure are set at the joints between the substructures to take into account the connection of each substructure; at the same time, they are set at the end of the machine tool to take into account the displacement of the machine tool and the two ends of the workpiece.

[0021] In step S102, if the substructure number is denoted as i, then the virtual node is denoted as... The local coordinate system of a 6-DOF virtual node is denoted as m is the number of the corresponding joint in substructure i, and the k-th finite element node at the location of the joint in the substructure is denoted as . The local coordinate system of the k-th finite element node is denoted as...

[0022] In step S103, the displacement of any finite element node with 6 degrees of freedom on the joint of the corresponding substructure is represented by the displacement of the created virtual node with 6 degrees of freedom:

[0023]

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

[0025] For the local coordinate system of a 6-DOF virtual node Local coordinate system of the k-th finite element node When transformations between virtual nodes occur only through translation, and the rotational displacement of the virtual node is θ, tanθ is approximately represented by θ; virtual node Finite element node of the k-th junction displacement transformation matrix between Represented as:

[0026]

[0027] In the formula, I is the identity matrix, and O is the zero matrix. To obtain the corresponding finite element node of the joint Pointing to virtual nodes The antisymmetric matrix of the position vector;

[0028] From finite element nodes Pointing to virtual nodes antisymmetric matrix of displacement vector Represented as

[0029]

[0030] In the formula, Indicates from finite element nodes Pointing to virtual nodes The X-direction position vector, Indicates from finite element nodes Pointing to virtual nodes The position vector in the Y direction, Indicates from finite element nodes Pointing to virtual nodes The Z-direction position vector;

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

[0032] Furthermore, in step S105, firstly, the location parameters and their value ranges are selected; secondly, experimental points are selected using experimental design methods; and after modifying the finite element model of any substructure based on the obtained experimental points, the degree-of-freedom condensed stiffness matrix at the corresponding experimental points is obtained through static condensation. Finally, the method of creating a surrogate model is used to interpolate or fit each element of the location parameters and the corresponding degree-of-freedom condensed stiffness matrix to obtain the static stiffness model of the substructure, expressed as:

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

[0034] In the formula, K (i) U represents the condensed matrix of static stiffness degrees of freedom of substructure i. (i) F represents the displacement vector that preserves the degrees of freedom of substructure i. (i) This indicates that the substructure i retains the force vectors on the degrees of freedom;

[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 methodology, Kriging method, neural network method, and radial basis function interpolation method.

[0036] When the position parameters change, the static stiffness matrix of the degrees of freedom of the relevant substructure will change accordingly.

[0037] Furthermore, step S2 includes two cases:

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

[0039] S202. If there are several joints between substructures, and treating a certain joint as a rigid connection has no effect on the result, then the stiffness of these joints is transformed by coordinate system transformation, and the stiffness matrix of these joints is obtained by using the principle of parallel spring superposition. At this time, the surface in the substructure corresponding to the position of these joints is rigid as a whole.

[0040] Furthermore, step S4 includes:

[0041] S401. Treat the tool and workpiece as rigid bodies, and under a given set of determined joint parameters, obtain the relative displacement of the end of the machine tool at the cutting position by combining a set of force vectors with coordinate system transformation. Then, by transforming the position parameters, obtain the distribution of the relative displacement of the end of the machine tool at the cutting position in the workspace. Then, substitute it and the force into the force balance equation to obtain the distribution of the static stiffness of the whole machine in the workspace.

[0042] S402. For the identification of the weak stiffness location of a certain degree of freedom, by calculating the maximum value of the relative displacement of the end of the machine tool at the cutting position under the action of force, the weak static stiffness location of the workspace and the corresponding static stiffness of the end of the machine are obtained.

[0043] S403. For the identification of weak stiffness locations in several degrees of freedom, the location with the worst overall stiffness performance in the workspace is obtained based on optimization and evaluation algorithms, and the corresponding static stiffness parameters of the end of the whole machine are obtained; wherein the optimization algorithms include, but are not limited to, genetic algorithm, differential evolution algorithm, ant colony algorithm, particle swarm optimization algorithm and simulated annealing algorithm; the evaluation algorithms include, but are not limited to, analytic hierarchy process, fuzzy comprehensive evaluation method, TOPSIS method, grey relational analysis method and rank sum ratio method.

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

[0045] The substructure static stiffness module is used to divide the machine tool's overall structure into two main categories: substructures and joints. It establishes the substructure static stiffness model using the local rigidity assumption and static condensation method.

[0046] The joint static stiffness module is used to construct a static stiffness model of the joint by applying the assumption of local rigidity to the joint.

[0047] The machine tool semi-analytical static stiffness module is used to establish a machine tool semi-analytical static stiffness model based on the static stiffness models of substructures and joints.

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

[0049] The evaluation module is used to evaluate the static stiffness parameters of the machine tool joints using a sensitivity method. Under a certain set of position parameters, it obtains the degree of influence of the static stiffness parameters of each joint on the static stiffness of the end of the machine tool.

[0050] The optimization module uses optimization and evaluation algorithms to find the best static stiffness parameter for the joint of the machine under a certain set of positional parameters within a given range. Simultaneously, combined with the calculation module, the static stiffness of the machine at the position with the worst overall static stiffness in the workspace is used as the output of the corresponding static stiffness parameter for the joint. By nesting the optimization and evaluation algorithms, the obtained static stiffness parameter for the joint is the one that can improve the static stiffness at the weakest position in the workspace, i.e., improve the lower limit of the static stiffness of the machine tool as a whole in the workspace.

[0051] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method for rapid modeling and optimization of the overall static stiffness of the machine tool.

[0052] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for rapid modeling and optimization of the overall static stiffness of the machine tool.

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

[0054] 1. Rapid Modeling and Optimization: This invention, through the construction of a semi-analytical static stiffness model of the entire machine, avoids the tedious operation of re-establishing the finite element model after changes in joint parameters or positional parameters, significantly improving the efficiency of static stiffness modeling for the entire 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. Identifying Weak Static Stiffness Locations: By using a static stiffness weakness location identification method based on optimization and evaluation algorithms, the weakest static stiffness location in the machine tool workspace can be quickly found, and the impact of static stiffness parameters of each joint on the overall machine end static stiffness can be evaluated, providing precise guidance for optimization.

[0056] 3. Improve the static stiffness of the weakest position: Based on nested optimization and evaluation algorithms, this invention can calculate and optimize the solution to improve the static stiffness of the weakest position in the workspace within the range of static stiffness parameters of the joint, thereby raising the minimum static stiffness limit of the machine tool workspace and enhancing the overall machine performance.

[0057] 4. Cost and resource savings: By employing techniques such as static condensation, surrogate models, and local rigidity assumptions, the modeling process is simplified, reducing computational costs. There is no need to repeatedly build complex finite element models, significantly reducing the design cycle and overall manufacturing costs.

[0058] 5. Support for multiple sensitivity analysis methods: This invention introduces multiple sensitivity analysis methods (such as the 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 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.). Moreover, the selection of substructures can be freely changed as the research content changes, which 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 novel approach to static stiffness modeling proposed in this invention can provide new technical support for machine tool design, breaking through the limitations of traditional methods in terms of accuracy and efficiency, and laying the foundation for improving the design quality and product competitiveness of machine tools. Attached Figure Description

[0061] Figure 1 This is a flowchart illustrating the rapid modeling and optimization method for the overall static stiffness of the machine tool in this embodiment.

[0062] Figure 2 This is a schematic diagram of the overall machine tool model.

[0063] Figure 3 This is a schematic diagram of the movable joint.

[0064] Figure 4 This is a schematic diagram of the static stiffness model of the joint.

[0065] Figure 5 This is a schematic diagram of the overall topology of the machine tool. Detailed Implementation

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

[0067] Traditional static stiffness modeling primarily relies on the full finite element method. This embodiment provides a method for establishing a semi-analytical static stiffness model of a machine tool, enabling the evaluation of the static stiffness of the entire machine tool in the workspace. Simultaneously, by using joint parameters as independent variables, and taking the displacement difference between the spindle and the machining end of the worktable in the local coordinate system at the cutting position (retaining degrees of freedom) as the output for sensitivity analysis, the influence of each joint parameter on the overall static stiffness performance of the machine tool in the workspace can be obtained. Furthermore, the static stiffness of the entire machine tool can be optimized.

[0068] This embodiment proposes a method for rapid modeling and optimization of the overall static stiffness of a machine tool, such as... Figure 1 As shown, the specific content includes the following steps:

[0069] S1. A static stiffness model of the substructure is established based on the local stiffness assumption and the 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 slide 5, an upper slide 6, and a worktable 7. This embodiment divides the machine tool into two main categories: substructures and connecting parts. Substructures are abstract representations of machine tool components. A substructure can be one or more of the following: spindle, worktable, slide, column, spindle box, and bed. Connecting parts include moving connecting parts, fixed connecting parts, and rotating connecting parts. The types of connecting parts include, but are not limited to, bearing connections, bolt connections, guide rail-slider connections, and lead screw-nut connections.

[0070] S2. The joint is based on the assumption of local rigidity. If multiple joints can be rigidly connected, the static stiffness model of the joint is obtained by establishing the 6-DOF stiffness matrix of the joint based on the stiffness superposition method of parallel springs.

[0071] S3. Based on the static stiffness models of the aforementioned substructures and joints, establish a semi-analytical static stiffness model for the entire machine tool.

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

[0073] S5. Evaluate the static stiffness parameters of machine tool joints based on sensitivity methods. Under a certain set of position parameters, obtain the degree of influence of the static stiffness parameters of each joint on the overall static stiffness of the machine tool. Sensitivity methods include, but are not limited to, 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 evaluation algorithm, the static stiffness parameter of the joint with the best overall static stiffness under a certain set of position parameters within the range of values ​​is obtained; at the same time, by combining with step S4, the overall static stiffness at the position parameter with the worst comprehensive static stiffness in the workspace is taken as the output of the corresponding joint static stiffness parameter. The optimization algorithm and evaluation algorithm are nested together, and the obtained joint static stiffness parameter is the one 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 machine tool in the workspace.

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

[0076] S101. Taking a single substructure in the machine tool as the object, establish the degree-of-freedom condensed stiffness matrix of the substructure through static condensation. The degrees of freedom retained by the substructure need to be set at the joints between substructures, taking into account the connection between each substructure; at the same time, they also need to be set at the machining end of the machine tool, taking into account the displacement of the machine tool and the workpiece.

[0077] S102. A 6-DOF virtual node is set at the equivalent center of the joint location in the substructure, and the 6-DOF virtual node is rigidly constrained to the 6 degrees of freedom of the finite element node at the joint location in the substructure. If the substructure is denoted as i, the virtual node is denoted as... The local coordinate system of a 6-DOF virtual node is denoted as m is the number of the corresponding joint in substructure i, and the k-th finite element node at the location of the joint in the substructure is denoted as . The local coordinate system of the k-th finite element node is denoted as... Virtual nodes at the same junction of two substructures should coincide in spatial position.

[0078] S103. Use a 6-DOF virtual node to represent all finite element nodes at the joints 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, Representing finite element nodes The 6-DOF displacement vector Represents virtual nodes The 6-DOF displacement vector Represents virtual nodes With finite element nodes The displacement transformation matrix between them.

[0082] For the local coordinate system With local coordinate system The transformation between them is only achieved through translation, and when the rotational displacement of the virtual node is very small, the virtual node... Finite element node of the k-th junction displacement transformation matrix between It can be represented as

[0083]

[0084] In the formula, I is the identity matrix, and O is the zero matrix. To obtain the corresponding finite element node of the joint Pointing to virtual nodes The antisymmetric matrix of the position vector.

[0085] From finite element nodes Pointing to virtual nodes antisymmetric matrix of displacement vector It can be represented as

[0086]

[0087] In the formula, Indicates from finite element nodes Pointing to virtual nodes The X-direction position vector, Indicates from finite element nodes Pointing to virtual nodes The position vector in the Y direction, Indicates from finite element nodes Pointing to virtual nodes The Z-direction position vector.

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

[0089] When using the computer software HyperMesh for static condensation in this embodiment, it is important to ensure that the X, Y, and Z axes of the coordinate systems of each substructure model are in the same direction.

[0090] The joint is rigidly connected by using a rigid multi-point constraint method, and the degrees of freedom of the corresponding virtual nodes are set to be retained.

[0091] When several joints in a substructure can be considered as rigid connections, the above principle can be used to perform static polycondensation again.

[0092] S105. Define the spatial position information of the machine tool within each stroke range as position parameters, and use the position parameters as independent variables to analyze the working state of the machine tool under different poses. Use all elements in the stiffness matrix of the degree of freedom as output to construct a surrogate model and obtain the static stiffness model of the substructure.

[0093] The specific process is as follows: First, the location parameters and their value ranges are selected. Second, experimental points are selected using experimental design methods. Based on the obtained experimental points, the finite element model of any substructure is modified. Then, the condensed stiffness matrix of the corresponding degree of freedom at the experimental points is obtained through static condensation. Finally, a surrogate model is created to interpolate or fit each element of the location parameters and the corresponding condensed stiffness matrix to obtain the 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. Surrogate model methods include, but are not limited to, response surface methodology, 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 elements at the joint (such as the RBE2 element in HyperMesh software) may sometimes change position as the position parameters change. Figure 3 This is a schematic diagram of the movable joint. If the position parameters at the movable joint change, the position of the joint on substructure i changes, causing a change in the position of the rigid constraint element corresponding to the joint, i.e., the condensed 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 element remains unchanged, meaning the condensed stiffness matrix of substructure j does not change. Besides changes in the rigid constraint element causing changes in the substructure, changes in the internal structure of the substructure and rotations in space can also lead to changes in the substructure stiffness matrix.

[0095] After static condensation and the creation of a proxy model, the static stiffness model of the substructure can be expressed as follows:

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

[0097] In the formula, K (i) U represents the condensed matrix of static stiffness degrees of freedom of substructure i. (i) F represents the displacement vector that preserves the degrees of freedom of substructure i. (i) This indicates that the substructure i retains the force vectors on the degrees of freedom.

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

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

[0100] S202. If there are multiple joints between substructures, and treating a certain joint as a rigid connection will not have a significant impact on the result, the stiffness of these joints can be equivalently combined. In this case, the surface of the substructure corresponding to the location of these joints will exhibit rigidity as a whole.

[0101] like Figure 4 As shown, taking the movable joint as an example, Figure 3 The interface between substructure i and substructure j is abstracted as a schematic diagram. A 6-DOF virtual node is created at the equivalent center of this interface group within the substructure. If the two substructures are numbered i and j, then the virtual nodes in the two substructures can be denoted as follows: and n is the numbering of this joint group in substructures i and j. Simultaneously, a 6-DOF virtual node is created at the equivalent center of the corresponding single joint in each of the two substructures. The corresponding virtual nodes can then be denoted as... and b is the number of a single joint in the corresponding joint group.

[0102] It is important to note that the virtual nodes corresponding to the mating surfaces in the two substructures must coincide spatially, and there must be a 6-DOF spring connection between the coinciding virtual nodes. The 6-DOF spring represents the equivalent stiffness of each mating surface. Represents virtual nodes With virtual nodes The spring stiffness between Represents virtual nodes With virtual nodes The spring stiffness between Represents virtual nodes With virtual nodes The local coordinate system at that location Represents virtual nodes With virtual nodes The local coordinate system at that location.

[0103] For rigid surfaces, virtual nodes With virtual nodes The displacements can all be generated by virtual nodes. With virtual nodes The displacement is represented by the same value, and because the spatial positions are the same, the displacement transformation matrices at the corresponding joint positions are identical. Let the displacement transformation matrix between virtual nodes be denoted as... The transformation of the spring's stiffness matrix in different coordinate systems can then be expressed as follows:

[0104]

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

[0106] For a given local coordinate system that can be obtained simply by translating the other local coordinate system, and where the rotational displacement of the nodes is small, the displacement transformation matrix... It can be represented as

[0107]

[0108] In the formula, I is the identity matrix, and O is the zero matrix. For virtual nodes or virtual node Pointing to virtual nodes or virtual node The antisymmetric matrix of the position vector.

[0109] When the stiffness of the joint changes with factors such as position parameters, the stiffness parameter of the joint 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 that 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 away at the same time (i.e., the degree of freedom corresponding to the stiffness of the joint being 0 is not retained).

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

[0111] Assuming that the joints between each substructure can be equivalent to a 6-DOF spring, where... and This represents the nodes corresponding to the two retained degrees of freedom of substructure i. and Let K represent the nodes corresponding to the two retained degrees of freedom of substructure j. The stiffness matrix K of substructure i of the machine tool at this time... (i) It can be represented as

[0112]

[0113] In the formula, 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 degrees of freedom retained in substructure i.

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

[0115]

[0116] In the formula, K i,j This represents the 6-DOF spring stiffness matrix at the junction between substructure i and substructure j. The superscripts (i) and (j) indicate whether the symbol belongs to substructure i or substructure j, respectively. F E U represents the 6-dimensional force vector acting on the virtual nodes in the corresponding substructure. E This represents the 6-dimensional displacement vector of the virtual node in the corresponding substructure.

[0117] The parameterized stiffness matrix K of the machine tool G It can be represented as

[0118]

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

[0120] KU=F(10)

[0121] In the formula, 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] Generally, the force applied by the machine tool is located at the end of the machine tool. Treating the tool and workpiece as rigid bodies, and setting the degrees of freedom at both ends of the machine as retained degrees of freedom, the forces in the first three degrees of freedom are of equal magnitude and opposite direction, while the forces in the latter three degrees of freedom are related to the difference between the actual cutting position and the position of the node corresponding to the retained degree of freedom. When the retained degree of freedom is subjected to forces related to position parameters, it can be represented by a function of the position parameters. Substituting the force vector into Equation 10 yields the displacement of the machine tool end 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 represented by the local coordinate system at the actual cutting position. Since the tool and the workpiece are considered as rigid bodies, the displacement of the end of the machine tool at the cutting position can be obtained by coordinate system transformation, and then its relative displacement can be calculated.

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

[0125] S401. Treating the tool and workpiece as rigid bodies, and given a set of defined joint parameters, the relative displacement of the end of the machine tool at the cutting position can be obtained by combining a set of force vectors with 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, by substituting it and the force into the force balance equation, the static stiffness distribution of the whole machine in the workspace can be obtained.

[0126] S402. For identifying the weak point of stiffness in a certain degree of freedom, the maximum value of the relative displacement of the end of the machine tool at the cutting position under a certain force can be obtained to obtain the weak point of static stiffness in the workspace and the corresponding static stiffness of the end of the machine.

[0127] S403. For identifying weak points in stiffness across multiple degrees of freedom, the location with the worst overall stiffness performance in the workspace can be obtained based on optimization and evaluation algorithms, along with the corresponding static stiffness parameters at the end of the entire machine. Optimization algorithms include, but are not limited to, genetic algorithms, differential evolution algorithms, ant colony optimization algorithms, particle swarm optimization algorithms, and simulated annealing algorithms. Evaluation algorithms include, but are not limited to, analytic hierarchy process (AHP), fuzzy comprehensive evaluation method, TOPSIS method, grey relational analysis method, and rank-sum ratio method.

[0128] Preferably, embodiments of this application also provide a device for rapid modeling and optimization of the overall static stiffness of a machine tool, which, based on the above modeling and optimization method, includes:

[0129] The substructure static stiffness module is used to divide the machine tool's overall structure into two main categories: substructures and joints. It establishes the substructure static stiffness model using the local rigidity assumption and static condensation method.

[0130] The static stiffness module of the joint is used to assume local rigidity of the joint. If multiple joints can be rigidly connected, the static stiffness model of the joint is obtained by establishing a 6-DOF stiffness matrix of the joint based on the stiffness superposition method of parallel springs.

[0131] The machine tool semi-analytical static stiffness module is used to establish a machine tool semi-analytical static stiffness model based on the static stiffness models of substructures and joints.

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

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

[0134] The optimization module is used to determine the optimal static stiffness parameters for the joints within a given set of positional parameters, based on optimization and evaluation algorithms. Simultaneously, in conjunction with the calculation module, it outputs the static stiffness parameters for the joints at the location with the worst overall static stiffness in the workspace. By nesting optimization and evaluation algorithms, the resulting static stiffness parameters for the joints are those that can improve the static stiffness at the weakest point in the workspace, thus raising the lower limit of the overall static stiffness of the machine tool in the workspace, thereby completing the optimization.

[0135] Preferably, embodiments of this application also provide a specific implementation of an electronic device capable of implementing all steps in the rapid modeling and optimization method for the overall static stiffness of the machine tool described in the above embodiments. The electronic device specifically includes the following:

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

[0137] The processor, memory, and communication interface communicate with each other via a bus; the communication interface is used to realize information transmission between 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, it implements all the steps in the rapid modeling and optimization method for the overall static stiffness of the machine tool in the above embodiments.

[0139] Embodiments of this application also provide a computer-readable storage medium capable of implementing all steps of the rapid modeling and optimization method for the overall static stiffness of the machine tool in the above embodiments. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements all steps of the rapid modeling and optimization method for the overall static stiffness of the machine tool in the above embodiments.

[0140] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. In particular, hardware + program embodiments are relatively simple in description because they are fundamentally similar to method embodiments; relevant parts can be referred to the descriptions in the method embodiments.

[0141] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0142] While this application provides method operation steps as shown in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-inventive labor. The order of steps listed in the embodiments is merely one possible execution order among many and does not represent the only execution order. In actual device or client product execution, the method can be executed sequentially as shown in the embodiments or drawings, or in parallel (e.g., in a parallel processor or multi-threaded processing environment).

[0143] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied 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 storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0145] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0146] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A machine tool whole machine global static stiffness rapid modeling and optimization method, characterized in that, Comprise: S1. The machine tool whole machine structure is divided into two categories of substructure and joint, wherein the substructure is the expression form of machine tool components, and the substructure static stiffness model is established based on the local rigidity assumption and the static condensation method; comprising the following steps: S101. Taking a single substructure in the machine tool as the object, determine the degrees of freedom that need to be retained; S102. Taking a single substructure as the object, setting a 6-DOF virtual node at the equivalent center of the joint position in the substructure, and rigidly constraining the 6-DOF virtual node with the 6-DOF of the finite element node at the joint position in the substructure; S103. A 6-DOF virtual node is used to complete the representation of all finite element nodes on the joint in the substructure; the 6-DOF displacement of any finite element node on the joint in the substructure is represented by the 6-DOF displacement of the created virtual node: ； wherein denotes the 6-DOF displacement vector of a finite element node , denotes the 6-DOF displacement vector of a virtual node , denotes the 6-DOF displacement vector of a virtual node , denotes the displacement transformation matrix between a virtual node and a finite element node The local coordinate system of the virtual node of 6 degrees of freedom The local coordinate system of the kth finite element node The displacement conversion matrix between the virtual node and the kth joint finite element node The local coordinate system of the kth joint finite element node The displacement conversion matrix between the virtual node and the kth joint finite element node is expressed as: ； where I is an identity matrix and O is a zero matrix, is the position vector of the finite element node pointing to the virtual node antisymmetric matrix of the position vector of the virtual node From the finite element nodes pointing to virtual nodes anti-symmetric matrix of displacement vectors is represented as ； wherein represents an X-direction position vector from the finite element node to the virtual node , represents a Y-direction position vector from the finite element node to the virtual node , represents a Z-direction position vector from the finite element node to the virtual node ; S104. Perform static condensation operation to obtain the degree of freedom condensation static stiffness matrix of the substructure; S105. Define the spatial position information of the machine tool within each stroke range as the position parameter, and use the position parameter as the independent variable to analyze the working state of the machine tool in different poses, and use all elements in the degree of freedom condensation stiffness matrix as the output to construct the surrogate model, and obtain the static stiffness model of the substructure; S2. Based on the local rigidity assumption, construct the static stiffness model of the joint; including; S201. Based on step S1, set the joint position in the substructure as a rigid surface, and represent the corresponding single joint by using a set of 6-DOF springs, and the stiffness parameters of the 6-DOF springs are obtained by calculation or consulting relevant manuals; S202. If there are several joints between the substructures, and if some of the joints are considered to be rigidly connected, it has no effect on the result, then the stiffness of these joints is converted in the coordinate system, and the stiffness matrix of the combination of these joints is obtained by using the parallel spring superposition principle, at this time the whole on the surface corresponding to these joint positions in the substructure is rigid; S3. According to the static stiffness model of the substructure and the static stiffness model of the joint, establish the semi-analytical static stiffness model of the machine tool whole machine; S4. According to the aforementioned semi-analytical static stiffness model of the whole machine, obtain the static stiffness distribution of the machine tool whole machine in the working space, based on the optimization algorithm and the evaluation algorithm, under the static stiffness model of the determined joint, calculate the weak position of the machine tool static stiffness in the working space; S5. Based on the sensitivity method, evaluate the static stiffness parameters of the machine tool joint, and obtain the influence degree of each joint static stiffness parameter on the machine tool static stiffness under a certain group of position parameters; S6. Based on the optimization algorithm and the evaluation algorithm, obtain the best joint static stiffness parameter under a certain group of position parameters in the value range; at the same time, through the combination of step S4, the static stiffness of the machine tool in the worst position parameter in the working space is taken as the output of the corresponding joint static stiffness parameter, and the optimization algorithm and the evaluation algorithm are nested to obtain the joint static stiffness parameter that can improve the static stiffness at the weakest position in the working space, that is, improve the lower limit of the static stiffness of the machine tool in the working space.

2. The machine tool global static stiffness rapid modeling and optimization method according to claim 1, characterized in that, The substructure includes a main shaft, a workbench, a slide, a column, a main shaft box, and a bed; and the types of the joint include bearing connection, bolt connection, guide rail and sliding block connection, and screw nut connection.

3. The machine tool global static stiffness rapid modeling and optimization method according to claim 1, characterized in that, In step S101, the degrees of freedom reserved by the substructures are set at the joint positions between the substructures to consider the connection of each substructure, and are set at the end positions of the machine tool to consider the displacement of the tool and the workpiece at the end positions. In step S102, if the number of the substructure is denoted as i, the virtual node is denoted as , the local coordinate system of the virtual node with 6 degrees of freedom is denoted as , m is the number of the corresponding joint in the substructure i, the kth finite element node at the position of the joint of the substructure is denoted as , and the local coordinate system of the kth finite element node is denoted as . In step S104, when static condensation is performed, the joints are set to be rigidly connected by using a rigid multi-point constraint method, and the degrees of freedom of the corresponding virtual nodes are set to be the reserved degrees of freedom; when several joints in the substructure can be regarded as rigidly connected, the above principle is used to perform static condensation again.

4. The machine tool global static stiffness rapid modeling and optimization method according to claim 1, characterized in that, In step S105, firstly, the position parameters are selected and the value ranges thereof are determined; secondly, experimental points are selected by using an experimental design method, and after the finite element model of any substructure is modified according to the obtained experimental points, the degrees of freedom condensation stiffness matrix under the corresponding experimental points is obtained through static condensation; finally, a proxy model is created to interpolate or fit the position parameters and each element of the corresponding degrees of freedom condensation stiffness matrix, so as to obtain the static stiffness model of the substructure, which is expressed as: ； wherein represents the static stiffness condensed matrix of substructure i for the degrees of freedom, represents the displacement vector of the retained degrees of freedom of substructure i, represents the force vector on the retained degrees of freedom of substructure i; The experimental design method includes Latin hypercube design, uniform design, and orthogonal experimental design; and the method of creating a proxy model includes response surface method, Kriging method, neural network method, and radial basis function interpolation method. When the position parameters change, the degrees of freedom condensation static stiffness matrix of the relevant substructure changes with the change of the position parameters.

5. The machine tool global static stiffness rapid modeling and optimization method according to claim 1, characterized in that, Step S4 includes: S401. The tool and the workpiece are regarded as rigid bodies, and under the condition of a given set of joint parameters, the relative displacement of the machine tool end at the cutting position is obtained by giving a set of force vectors and combining coordinate system conversion, and then the distribution of the relative displacement of the machine tool end at the cutting position in the working space is obtained by transforming the position parameters, and then the distribution is substituted into the force balance equation to obtain the static stiffness distribution of the whole machine in the working space; S402. For the identification of the stiffness weak position of a certain degree of freedom, the maximum value of the relative displacement of the machine tool end at the cutting position under the action of force is obtained, and the static stiffness weak position in the working space and the corresponding whole machine end static stiffness are obtained; S403. For the identification of the stiffness weak position of several degrees of freedom, the position with the worst comprehensive stiffness performance in the working space is obtained based on an optimization algorithm and an evaluation algorithm, and the corresponding whole machine end static stiffness parameter is obtained; the optimization algorithm includes genetic algorithm, differential evolution algorithm, ant colony algorithm, particle swarm algorithm, and simulated annealing algorithm; and the evaluation algorithm includes analytic hierarchy process, fuzzy comprehensive evaluation method, TOPSIS method, grey correlation method, and rank sum ratio method.

6. A device for rapid modeling and optimization of global static stiffness of a machine tool, based on the method for rapid modeling and optimization of global static stiffness of a machine tool according to any one of claims 1-5, characterized in that, The static stiffness module of the substructure is used to divide the machine tool structure into two categories of substructures and joints, and to establish a static stiffness model of the substructure by using local rigidity assumption and static condensation method; The static stiffness module of the joint is used to construct a static stiffness model of the joint by using local rigidity assumption; The static stiffness module of the joint is used to construct a static stiffness model of the joint by using local rigidity assumption; The machine tool whole machine semi-analytical static stiffness module is used for establishing a machine tool whole machine semi-analytical static stiffness model according to a static stiffness model of a substructure and a static stiffness model of a joint; The calculation module is used for obtaining a whole machine static stiffness distribution in a working space according to the whole machine semi-analytical static stiffness model, and calculating a weak position of the machine tool static stiffness in the working space based on an optimization algorithm and an evaluation algorithm under the determined static stiffness model of the joint; The evaluation module is used for evaluating the static stiffness parameters of the machine tool joint by a sensitivity method, and obtaining an influence degree of the static stiffness parameters of each joint on the whole machine end static stiffness under a certain group of position parameters; The optimization module is used for obtaining the best joint static stiffness parameters of the whole machine static stiffness under a certain group of position parameters in a value range by using the optimization algorithm and the evaluation algorithm; meanwhile, the whole machine static stiffness at a position parameter with the worst comprehensive static stiffness in the working space is combined with the calculation module as an output of the corresponding joint static stiffness parameter, and the joint static stiffness parameters obtained by nested use of the optimization algorithm and the evaluation algorithm are the joint static stiffness parameters capable of improving the static stiffness at the weakest position in the working space, i.e. improving the lower limit of the whole machine static stiffness in the working space.

7. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the steps of the machine tool whole machine global static stiffness rapid modeling and optimization method in any one of claims 1 to 5.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the machine tool whole machine global static stiffness rapid modeling and optimization method in any one of claims 1 to 5.

Images