Method for constructing semi-analytical kinetic model containing pose parameters of complete machine tool

Abstract

The invention discloses a method for constructing a semi-analytical kinetic model containing pose parameters of a complete machine tool. The method comprises the following steps: S1, constructing a plurality of groups of pose machine tool three-dimensional models according to a machine tool pose parameter sample set and the positions of structural parts and joint parts in a space; s2, importing the multiple groups of pose machine tool three-dimensional models into a finite element system to perform modal reduction and structural member rigidity and mass matrix extraction to construct a structural member semi-analytical dynamic model; s3, constructing an agent model of a nonlinear mapping relation between the structural part semi-analysis dynamic model and the rigidity and mass matrixes corresponding to the structural part semi-analysis dynamic model according to the structural part semi-analysis dynamic model; s4, constructing a joint part contact stiffness model; and S5, establishing a dynamical model of the complete machine tool by adopting a structural component synthesis method. According to the method, the problem of rapid estimation of global dynamic characteristics can be effectively solved by performing dynamical modeling on the complete machine tool.

Description

Technical Field

[0001] The present invention relates to the field of machine tool design, and particularly to a method for constructing a semi-analytical dynamic model of a whole machine tool including pose parameters. Background Art

[0002] Machine tool dynamic modeling mainly focuses on modeling the characteristics of the machine tool during the dynamic machining process. The dynamic characteristics of the machine tool are the characteristics exhibited during the dynamic machining process and are the key factors affecting the cutting performance of the machine tool. They directly affect the machining accuracy, efficiency, and stability of the machine tool. Therefore, modeling the dynamic characteristics of the machine tool is the basis for achieving precise control and optimization of the machine tool's dynamic performance.

[0003] The application scope of machine tool dynamic modeling is very wide. For example, it can precisely control parameters such as the natural frequency and stiffness of the machine tool to improve the machining accuracy and efficiency of the machine tool; it can reduce the vibration and noise of the machine tool by optimizing the design of the transmission system; it can avoid problems such as resonance during the machining process of the machine tool by predicting and controlling the dynamic characteristics of the machine tool.

[0004] For a multi-axis linkage CNC machining center, its dynamic characteristics vary greatly with the change of position parameters. The existing machine tool dynamic models mainly establish finite element models by means of the analytical method or borrowing commercial software. Among them, the dynamic model established by the analytical method has limited accuracy and cannot reflect the dynamic characteristics of the machine tool with the change of position. Although the dynamic model established by finite element has high accuracy, it needs to re-establish the finite element model after the position parameters change. In the initial design, optimization analysis, and parameter modification stages of the machine tool, establishing a semi-analytical dynamic model with as few degrees of freedom as possible and capable of quickly predicting the low-order dynamic characteristics of the whole machine tool within the entire domain is an important way to improve the calculation and analysis efficiency.

[0005] CN112364547A discloses a method for quickly predicting the global dynamic performance of a whole machine tool. This method first divides the whole machine tool structure into two categories: components and joints, and uses the dynamic condensation method to establish a semi-analytical dynamic model of the components; then selects the constraint method of the joints to construct the deformation coordination equation of the joints; then establishes a semi-analytical dynamic model of the whole machine; finally, based on the established semi-analytical dynamic model of the whole machine, predicts the distribution of the dynamic performance of the whole machine tool within the working space. However, this method has problems that need further optimization when establishing the semi-analytical dynamic model of the components to improve the accuracy and efficiency of prediction.

[0006] CN118657011A discloses a method for determining the vibration response of a machine tool's finite element with variable structure. This method includes importing the overall structure of the machine tool into finite element software for element division to obtain multiple elements; performing modal analysis on the structural components respectively, and determining the stiffness matrix of the joint of the structural components according to the degree-of-freedom stiffness matrix corresponding to each structural component; updating the overall stiffness matrix according to the stiffness matrix of the joint of the structural components, and calculating the updated overall stiffness matrix by the matrix perturbation method, and obtaining the vibration response of each node through the moving least squares method based on the frequency response function and the structural input excitation signal. However, when performing mesh division, there is a problem of further optimizing the mesh quality to improve the calculation accuracy and efficiency.

[0007] In traditional machine tool dynamics modeling methods, when using finite element software to build a model, when the position parameters change, the finite element model needs to be rebuilt, resulting in low efficiency.

[0008] In summary, it is still a problem to be further studied to establish a semi-analytical dynamics model of the whole machine that can quickly and accurately describe the low-order dynamic characteristics of the system with as few degrees of freedom as possible. Summary of the Invention

[0009] To solve the problems of the existing technology, the present invention proposes a method for constructing a semi-analytical dynamics model of a machine tool's whole machine with pose parameters. This method effectively solves the problem of quickly predicting the global dynamic characteristics by performing dynamics modeling on the whole machine of the machine tool. The present invention establishes a semi-analytical dynamics model of the whole machine of the machine tool based on the comprehensive reflection and fitting of the stiffness of each structural component and the joint.

[0010] The present invention is implemented by the following technical solutions:

[0011] A method for constructing a semi-analytical dynamics model of a machine tool's whole machine with pose parameters includes the following steps:

[0012] S1. Construct multiple three-dimensional models of pose machine tools according to the pose parameter sample set of the machine tool according to the positions of the structural components and joints of the whole machine of the machine tool in space;

[0013] S2. Import the multiple three-dimensional models of pose machine tools into the finite element system for modal reduction and extraction of the stiffness and mass matrices of the structural components to construct a semi-analytical dynamics model of the structural components;

[0014] S3. Construct a surrogate model of the nonlinear mapping relationship between the stiffness and mass matrices corresponding to the semi-analytical dynamics model of the structural components;

[0015] S4. Construct a contact stiffness model of the joint;

[0016] S5. Establish a dynamics model of the whole machine of the machine tool by using the structural component synthesis method.

[0017] Further, the process of constructing multiple groups of pose machine tool three-dimensional models according to the machine tool pose parameter sample set based on the position of the structural member in space in step S1 includes:

[0018] Step 101: Determine the stroke parameter range of the machine tool at each pose, conduct experimental design and establish a pose parameter sample set. Use the optimal Latin hypercube experimental design method for parameter sampling, select the sampled parameters, and for each structural movement stroke of the machine tool, determine the displacement stroke range of the structural member in each direction, and preliminarily determine the distribution interval of each pose parameter;

[0019] Step 102: Generate random numbers: Assume that the position of the machine tool in the n direction is an n-dimensional number, that is, an n-dimensional space is formed, and the number of sampling times is M. According to the principle of the optimal Latin hypercube experimental design method, each dimension is divided into M equal intervals, and the length of each interval is 1 / M. Randomly select N values from the first interval to form the first column of a matrix A, and then extract the same number of values from the second interval as the second column of the matrix A, and so on until all columns of the matrix A are filled. Shuffle the order of each row of the matrix A to obtain a matrix B. Each column vector of the matrix B represents a sample point, and the matrix B represents the final M sampled sample points. In this way, M groups of sample points of the n-dimensional position parameters of the machine tool are obtained;

[0020] Step 103: Modify the positions of the structural members of the machine tool in space according to the pose parameter sample set established in step 101 and step 102 to obtain multiple groups of pose machine tool three-dimensional models.

[0021] Further, the process of importing the multiple groups of pose machine tool three-dimensional models into the finite element system for modal reduction and extracting the stiffness and mass matrices of the structural members to construct a semi-analytical dynamic model of the structural member in step S2 includes:

[0022] Step 201: The component structural member i in the serial kinematic chain is connected to the component structural members i - 1 and i + 1 through the joints i and i + 1 respectively. The local reference frames Ki and Ki + 1 are placed at the centers of the joints i and i + 1 respectively. The undamped dynamic equation of the component structural member is expressed in the local reference frame Ki + 1 as:

[0023]

[0024] Among them, k (i) and m (i) are the stiffness and mass matrices of the structural member, f (i) and u (i) are the force vector and the nodal displacement vector of the structural member respectively;

[0025] Step 202: Substitute u (i)Divided into two subgroups, the external node displacement vector u is obtained according to the following formula E (i) and the internal node displacement vector u I (i) , where:

[0026]

[0027] where, is expressed as:

[0028]

[0029] where: and are the node displacement vectors of the finite element node groups at the joints i and i + 1 respectively, represents the node group displacement vector of the structural member node N at the joint i + 1;

[0030] Step 203, construct a reduced dynamic model by condensing a single structural member to a point on the joint surface, including: for the same type of joint surface of a single structural member, if there are multiple, assuming that the condensed nodes have a consistent deformation field, a "middle node" can be set at the equivalent center position of the joint, and multiple joint surfaces are condensed to this middle node; for different types of joint surfaces, first condense the joint surfaces of the same type to the same middle node according to the above steps, and then perform secondary condensation on the different types of middle nodes, and two middle nodes can be condensed into one point.

[0031] Furthermore, the process of constructing the contact stiffness model of the joint in step S4 includes:

[0032] Step 401, construct the contact stiffness matrix of the joint according to the following formula, that is: taking the structural member i as the object, assuming the plane where the joint i + 1 of the structural member i and the structural member j is a rigid surface, for the same type of joint, a six-degree-of-freedom "center node" is specified at the joint, and this node is at the equivalent geometric center of the joint;

[0033]

[0034] where: n in the subscript represents the nth type of joint type of this joint, and respectively represent the linear displacement and angular displacement of the "center node" i+1,n in the local coordinate system K , is the linear displacement of the kth node on the joint i + 1 of the structural member i is the angular displacement vector from the node to the "center node" ;

[0035] Step 402: Using the dynamic condensation method and based on the principle of rigid multi-point constraints, each external finite element node on the joint i+1 of structural member i is condensed to the central node;

[0036] The condensed external node displacement vector can be expressed as:

[0037]

[0038] Where: represents the six-dimensional node displacement vector of the "central node" on structural member i , represents the six-dimensional node displacement vector of the external node displacement vector on structural member i changing to the "central node" reduction matrix;

[0039] Step 403: Establish the relationship of the six-dimensional node displacement vector of the "central node" of structural member j according to the following formula:

[0040]

[0041] Where: represents the six-dimensional node force vector on the "intermediate node" , represents the six-dimensional node force vector on the "central node" , K i+1,n represents the contact stiffness matrix of joint i+1;

[0042] Step 404: The relationship between the node force and the node displacement can be constructed according to the following formula through the contact stiffness matrix K i+1,n It can be expressed as:

[0043]

[0044] Where: K i+1,n is the 6×6 contact stiffness matrix calculated above. If there are multiple types of joints, then according to the principle of deformation superposition:

[0045]

[0046] Where: K i+1 is the equivalent contact stiffness matrix of joint i+1, X i+1 is the coordinate transformation matrix of different local coordinate systems, N is the number of joint types, and this stiffness matrix is the linear superposition of the interface stiffness matrices in the local coordinate system.

[0047] Furthermore, the process of establishing the dynamic model of the whole machine tool by using the structural component synthesis method in step S5 includes:

[0048] Step 501: Construct the dynamic model of the machine tool by assembling the stiffness, mass matrices of the above structural components and the contact stiffness matrix of the joints.

[0049] Step 502: Under the global coordinate system K, construct the dynamic model of the whole machine including the pose parameters in all directions of the machine tool according to the following formula:

[0050]

[0051] where K and M are the stiffness matrix and mass matrix of the whole machine tool, and F and U are the force vector and node displacement vector of the whole machine tool; a dynamic model of the whole machine including the pose parameters in all directions of the machine tool is constructed.

[0052] Beneficial effects

[0053] 1) The present invention can effectively solve the problem that it is difficult to reflect the change of the dynamic characteristics of the whole machine tool in the full working range in the existing technology of dynamic modeling of the whole machine tool. By using the optimal Latin hypercube experimental design method to establish a sample set of pose parameters and establishing a surrogate model of the nonlinear mapping relationship between the position parameters of the machine tool structural components and their corresponding stiffness and mass matrices, etc., the change of the dynamic characteristics of the machine tool in different poses can be accurately described.

[0054] 2) The present invention can effectively solve the problem that it is difficult to accurately describe the nonlinear coupling effect of the machine tool structure in different poses in the existing technology. By constructing the contact stiffness matrix of the joints and using the structural component synthesis method to establish the dynamic model of the whole machine tool, etc., the nonlinear coupling effect of the machine tool structure in different poses can be accurately described.

[0055] 3) It can improve the accuracy and efficiency of the dynamic modeling of the whole machine tool. By using the dynamic condensation method to establish the finite element model of each structural component and extract the reduced mass and stiffness matrices, etc., the modeling process can be effectively optimized, and the accuracy and efficiency of modeling can be improved.

[0056] 4) It can improve the calculation accuracy and efficiency of the dynamic modeling of the whole machine tool. By using the modal reduction method to establish the semi-analytical dynamic model of the structural components and using the rigid multi-point constraint to form a reduced dynamic model at the joints of the structural components, etc., the quality of mesh generation can be effectively optimized, and the calculation accuracy and efficiency can be improved. Description of the drawings

[0057] Figure 1 It is a schematic diagram of the division of the machine tool structural components involved in the present invention.

[0058] Figure 2Schematic diagram of the machine tool kinematic chain involved in the present invention.

[0059] Figure 3 Schematic diagram of the Latin hypercube experimental design sampling involved in the present invention.

[0060] Figure 4 Schematic diagram of structural member i involved in the present invention.

[0061] Figure 5 Schematic diagram of the condensation of the guide rail slider joint surface in the present invention.

[0062] Figure 6 Schematic diagram of the rigid multi-point constraint of the joint surface involved in the present invention.

[0063] Figure 7 Schematic diagram of the comprehensive connection of structural members in the present invention. Specific embodiments

[0064] The following is combined with the attached Figure 1 ~Attached Figure 7 The following description is made for the present invention:

[0065] The present invention provides a method for constructing a semi-analytical dynamic model of the position parameters of a whole machine tool. The method includes:

[0066] S1. According to the machine tool pose parameter sample set, construct multiple groups of pose machine tool three-dimensional models according to the positions of the structural members and joints of the whole machine tool structure in space; and perform pose parameter experimental design and sampling. The structural members include the bed (1), the column (2), the crossbeam (3), the spindle box (4), the tool head (5), the workbench (6), the turntable (7), etc., as Figure 1 shown. The schematic diagram of the whole machine tool topology structure can be specifically described by the schematic diagram of the machine tool kinematic chain, as Figure 2 shown. It shows the dynamic relationship between the machine tool cutting tool kinematic chain and the workpiece kinematic chain. The machine tool dynamic model framework is established through the two kinematic chains T and W. The blue arrows in the figure represent the local reference systems, which define the directions and motions of each cutting structural member; the joints cover the moving joints, the rotating joints and the fixed joints. Determine the stroke parameter range of the machine tool at each pose, perform experimental design and establish a pose parameter sample set. To ensure the uniformity and representativeness of the sampling results and consider the coupling relationship of the machine tool structures at different poses, the optimal Latin hypercube experimental design method (OLHS) can be used for parameter sampling, including the following steps:

[0067] Step 101. Select the parameters for sampling; for the motion strokes of each structure of the machine tool, first determine the displacement stroke range of the structural members in each direction, and initially determine the distribution intervals of each pose parameter to ensure that the selected parameters have a certain comprehensiveness and representativeness.

[0068] Step 102: Generate random numbers; Assume the positions of the machine tool in the x, y, z... n directions are dimensions, that is, an N-dimensional space is formed, and the number of sampling times is M. According to the principle of the OLHS method, each dimension is divided into M equal intervals, and the length of each interval is 1 / M. Then, N values A are randomly selected from the first interval (0 to 1 / M). 11 , A 21 , … A N1 These form 1 set as the first column of matrix A. Then, the same number of values are selected from the second interval as the second column of matrix A. And so on until all columns of matrix A are filled. The entire sampling process is as shown in Figure 3 shown. The final result of matrix A is as follows:

[0069]

[0070] Then, the order of each row of matrix A is shuffled to obtain matrix B:

[0071]

[0072] Each column vector of matrix B represents a sample point, and matrix B represents the M sample points of the final sampling. In this way, M groups of sample points for the multi-dimensional position parameters of the machine tool in the x, y, z,... n directions are obtained. Each combination represents a set of complete position parameter configurations, ensuring the global and local variability of the samples under different combinations.

[0073] Step 103: Modal reduction of structural components and extraction of mass and stiffness matrices. According to the pose parameter sample set established in Step 101 and Step 102, modify the positions of each structural component of the machine tool in space to obtain multiple groups of three-dimensional models of the machine tool with pose changes. S2: Import the multiple groups of pose machine tool three-dimensional models into finite element software for modal reduction and extraction of structural component stiffness and mass matrices; at the same time, based on the constraint interface synthesis method and rigid multi-point constraints, use the method of modal reduction (CMS) to establish a semi-analytical dynamic model of the structural components.

[0074] Step 201: The structural component i in the serial kinematic chain is connected to the structural components i - 1 and i + 1 through the joints i and i + 1 respectively. The local reference frames K i and K i+1 are placed at the centers of the joints i and i + 1 respectively. The undamped dynamic equation of the structural component is expressed in the local reference frame K i+1 as:

[0075]

[0076] where, k (i) and m (i) are the stiffness and mass matrices of the structural component, f (i) and u (i)They are the force vector and the node displacement vector of the structural member respectively.

[0077] Step 202: To reduce the model complexity, u can be (i) divided into two subgroups, namely the external node displacement vector u E (i) and the internal node displacement vector u I (i) , as Figure 4 shown, where:

[0078]

[0079] Among them, is expressed as:

[0080]

[0081] Among them and are the node displacement vectors of the finite element node groups at the joints i and i + 1 respectively, represents the node group displacement vector of the structural member node N at the joint i + 1.

[0082] Step 203: Construct a reduced dynamic model by condensing a single structural member to a point on the joint surface, including: for the same type of joint surface of a single structural member, if there are multiple ones, assuming that the condensed nodes have a consistent deformation field, a "middle node" can be set at the equivalent center position of the joint to condense multiple joint surfaces to this middle node; for different types of joint surfaces, first condense the joint surfaces of the same type to the same middle node according to the above steps, and then perform secondary condensation on the middle nodes of different types. Two middle nodes can be condensed into one point. Specifically:

[0083] Use finite element software to perform the above modal reduction process, condense the internal nodes of the structural member to reduce the degrees of freedom, and form a reduced dynamic model at the joint of the structural member through rigid multi-point constraints (RBE2 or RBE3 elements). For the same type of joint surface of a single structural member, if there are multiple ones, assuming that the condensed nodes have a consistent deformation field, a "middle node" can be set at the equivalent center position of the joint to condense multiple joint surfaces to this middle node; for different types of joint surfaces, first condense the joint surfaces of the same type to the same middle node according to the above steps, and then perform secondary condensation on the middle nodes of different types. GY reduction, CBM reduction or CMS reduction methods, etc. can be used to condense two middle nodes into one point, so that the single structural member is condensed to a point on the joint surface.

[0084] As Figure 5As shown in the figure, take the joint surface i+1 of the structural member i as an example. For the joint surface of a single guide rail slider, based on the assumption of rigid multi-point constraints, the degrees of freedom of multiple nodes at the joint are condensed into a few condensed nodes. These condensed nodes can be further simplified, and a new condensed node is created at the center of the joint part, condensing the single guide rail joint surface into a point The joint surface of a single slider is condensed into a point Assume the joint surface and the joint surface have a consistent deformation field, and a condensed node, i.e., the central node, is created at the center of the joint surface i+1 As Figure 6 shown. Then the rigid multi-point constraint can be used again at the joint surface, and finally multiple identical joint surfaces are condensed onto a central node of the joint surface i+1, thus realizing the simplification of degrees of freedom.

[0085] S3. Construct a surrogate model for the nonlinear mapping relationship between the stiffness and mass matrices corresponding to the semi-analytical dynamics model of the structural member;

[0086] Fitting of the stiffness and mass matrix surrogate models of the machine tool substructure with pose parameters. According to the stiffness and mass matrices of multiple groups of machine tool structural members in different poses extracted in step 2, establish the nonlinear mapping relationship between the position parameters of the machine tool structural members and their corresponding stiffness and mass matrices. Use a neural network model to perform surrogate modeling on the relationship between the pose parameters and the stiffness and mass matrices. This surrogate model should fully reflect the nonlinear variation characteristics of each element in the matrix and ensure that when the pose parameters change, the overall dynamic characteristics of the system are accurately predicted.

[0087] Through this method, a surrogate model of the whole machine tool with pose parameters is finally obtained. This model accurately reflects the nonlinear relationship between each element in the overall stiffness and mass matrix of the machine tool and the corresponding pose parameters. Formulas (1) and (2) roughly represent this relationship:

[0088]

[0089] Among them, k 11 to k nn are the elements in the stiffness matrix of the structural member, m 11 to m nn are the elements in the mass matrix of the structural member, x1 is the position parameter of the structural member, and f 11 (x1) to f nn (x1) are the nonlinear mappings between the position parameter and the elements in the stiffness matrix, and g 11 (x1) to gnn(x1) are the same by analogy.

[0090] S4. Construct a contact stiffness model for the joint part, including:

[0091] Step 401. Construct the contact stiffness matrix of the joint: Taking structural member i as the object, assume the plane where the joint i+1 between structural member i and structural member j is a rigid plane. For the same type of joint, specify a six-degree-of-freedom "central node" at the joint, and this node is at the equivalent geometric center of the joint, denoted as At each finite element node of joint i+1, its displacement and rotation can be expressed through the constraint relationship between this "central node" and other nodes:

[0092]

[0093] where: n in the subscript represents the nth type of joint of this joint, and respectively represent the linear displacement and angular displacement of the "central node" i+1,n in the local coordinate system K ; is the linear displacement of the kth node on the joint i+1 of structural member i, is the angular displacement vector from node to the "central node" .

[0094] Step 402. In the finite element software, adopt the dynamic condensation method. According to the principle of rigid multi-point constraints, each external finite element node on the joint i+1 of structural member i can be condensed to this central node

[0095] The condensed external node displacement vector can be expressed as:

[0096]

[0097] where: represents the six-dimensional node displacement vector of the "central node" on structural member i, represents the reduction matrix of the six-dimensional node displacement vector when the external node displacement vector on structural member i changes to the "central node" .

[0098] Step 403. Taking structural member j as the object and following the same process, the six-dimensional node displacement vector of the "central node" of structural member j can be obtained through dynamic condensation. Equivalent the contact stiffness of joint i+1 connecting structural member i and structural member j to a six-degree-of-freedom spring. According to Newton's third law, the "central node" and the "central node" There is a deformation relationship as follows:

[0099]

[0100] Among them, represents the six-dimensional nodal force vector on the "intermediate node" represents the six-dimensional nodal force vector on the "central node", and K i+1,n i+1,n i+1,n represents the contact stiffness matrix of joint i + 1.

[0101] Step 404, using Hooke's law, the relationship between nodal force and nodal displacement can be expressed through the contact stiffness matrix K i+1,n as:

[0102]

[0103] Among them: K i+1,n is the 6×6 contact stiffness matrix calculated above. If there are multiple types of joints, then according to the principle of superposition of deformations, we can get:

[0104]

[0105] Among them: K i+1 is the equivalent contact stiffness matrix of joint i + 1, X i+1 is the coordinate transformation matrix of different local coordinate systems, and N is the number of joint types. This stiffness matrix is the linear superposition of the interface stiffness matrices in the local coordinate system.

[0106] S5. Establish the dynamic model of the whole machine tool by using the structural component synthesis method:

[0107] Establish the dynamic model of the whole machine tool by using the structural component synthesis method. Build the dynamic model of the machine tool by assembling the above structural component stiffness, mass matrix and joint contact stiffness matrix. Figure 7 shows the connection process of the synthesis of the machine tool structural components. Each structural component is connected through the contact stiffness matrix of the joint, ensuring the compatibility of the machine tool structural components. In the global coordinate system K, the undamped dynamic equation of the whole machine tool can be expressed as:

[0108]

[0109] Among them, \(K\) and \(M\) are the stiffness matrix and mass matrix of the whole machine tool, and \(F\) and \(U\) are the force vector and node displacement vector of the whole machine tool. The block matrix corresponding to the external condensed nodes in \(M\) is a diagonal matrix, and the block matrix corresponding to the external condensed nodes in \(K\) is a band matrix. Therefore, the low-order dynamic model of the whole machine tool uses a relatively small number (12N) of degrees of freedom to describe, and thus a dynamic model of the whole machine including the pose parameters in all directions of the machine tool is constructed.

[0110] Embodiment 1: A method for constructing a semi-analytical dynamic model of a whole machine tool including pose parameters, comprising the following steps:

[0111] Step 1: Divide the structure of the whole machine tool into two categories: structural parts and joints, and conduct experimental design and sampling of pose parameters.

[0112] Step 101: Determine the range of travel parameters of the machine tool at each pose, conduct experimental design and establish a sample set of pose parameters. The optimal Latin hypercube experimental design method is used for parameter sampling, and the sampled parameters are selected. For the movement stroke of each structure of the machine tool, it is determined that the X-axis travel range is 0 - 2000 mm, the Y-axis travel range is 0 - 1500 mm, the Z-axis travel range is 0 - 1200 mm, the A-axis rotation angle range is 0 - 360°, the B-axis rotation angle range is 0 - 240°, and the C-axis rotation angle range is 0 - 360°. The distribution intervals of each pose parameter are initially determined;

[0113] Step 102: Generate random numbers. Assume that the position of the machine tool in 5 directions is a 5-dimensional space, and the number of sampling times is 100. According to the principle of the optimal Latin hypercube experimental design method, each dimension is divided into 100 equal intervals, and the length of each interval is 1 / 100. Randomly select 6 values from the first interval (0 - 0.01) to form a set as the first column of matrix \(A\). Then, select the same number of values from the second interval (0.01 - 0.02) as the second column of matrix \(A\), and so on, until all columns of matrix \(A\) are filled. Shuffle the order of each row of matrix \(A\) to obtain matrix \(B\). Each column vector of matrix \(B\) represents a sample point, and matrix \(B\) represents the final 100 sampled sample points. In this way, 100 groups of sample points of the 6-dimensional position parameters of the machine tool are obtained;

[0114] Step 103: Modify the positions of each structural part of the machine tool in space according to the sample set of pose parameters established in Step 101 and Step 102 to obtain 100 three-dimensional models of the machine tool with pose changes.

[0115] Step 2: Modal reduction of structural parts and extraction of mass and stiffness matrices

[0116] Step 201: Import the model into the finite element software ABAQUS for modal reduction and extraction of the stiffness and mass matrices of the structural components. Based on the constraint interface synthesis method and rigid multi-point constraints, a semi-analytical dynamic model of the structural components is established using the modal reduction method. The internal nodes of the structural components are condensed to reduce the degrees of freedom, and a reduced dynamic model is formed at the joint of the structural components through the rigid multi-point constraint RBE2 element.

[0117] Step 202: For the same type of joint surfaces of a single structural component, if there are multiple ones, assuming that the condensed nodes have a consistent deformation field, an "intermediate node" can be set at the equivalent center position of the joint to condense multiple joint surfaces to this intermediate node; for different types of joint surfaces, first condense the joint surfaces of the same type to the same intermediate node according to the above steps, and then perform secondary condensation on the intermediate nodes of different types. Using the GY reduction method, condense the two intermediate nodes into one point, so that the single structural component is condensed to a point on the joint surface.

[0118] Step 3: Establish a surrogate model for the non-linear mapping relationship between the position parameters of the machine tool structural components and their corresponding stiffness and mass matrices. According to the 100 groups of stiffness and mass matrices of the machine tool structural components in different poses extracted in Step 2, use the RBF neural network model to perform surrogate modeling on the relationship between the pose parameters and the stiffness and mass matrices. This surrogate model should fully reflect the non-linear change characteristics of each element in the matrix and ensure that when the pose parameters change, the overall dynamic characteristics of the system are accurately predicted, obtaining a surrogate model of the whole machine tool including pose parameters, which accurately reflects the non-linear relationship between each element of the overall stiffness and mass matrix of the machine tool and the corresponding pose parameters.

[0119] Step 4: Construct the contact stiffness matrix of the joint

[0120] Step 401: Take the spindle box of the structural component as the object, assume the plane where the joint of the spindle box of the structural component and the column of the structural component is a rigid surface. For the same type of joint, specify a six-degree-of-freedom "center node" at the joint, and this node is at the equivalent geometric center of the joint.

[0121] Step 402: In the finite element software ABAQUS, use the dynamic condensation method. According to the principle of rigid multi-point constraints, each external finite element node on the joint of the spindle box of the structural component can be condensed to this center node.

[0122] Step 403: Taking the structural column as the object and following the same process, the six-dimensional nodal displacement vector of the "central node" of the structural column can be obtained through dynamic condensation. The contact stiffness of the joint connecting the main spindle box of the structure and the structural column is equivalent to a six-degree-of-freedom spring. According to Newton's third law, there is a deformation relationship between the "central node" of the spindle box and the "central node" of the column. Using Hooke's law, the relationship between the nodal force and the nodal displacement can be expressed by the contact stiffness matrix. The contact stiffness matrix of this joint is a 6×6 matrix, and the numerical range is 5×10^7~5×10^8 N / m.

[0123] Step 5: By assembling the above structural stiffness, mass matrix, and joint contact stiffness matrix, a dynamic model of the machine tool is constructed. In the global coordinate system K, the undamped dynamic equation of the entire machine tool can be expressed as: The relationship between the stiffness matrix K (12×12), mass matrix M (12×12), force vector F (12×1), and nodal displacement vector U (18×1) of the whole machine tool is: Among them, the block matrix corresponding to the externally condensed nodes in M is a diagonal matrix, and the block matrix corresponding to the externally condensed nodes in K is a band matrix. Thus, a dynamic model of the whole machine including the pose parameters in all directions of the machine tool is constructed.

[0124] Although the present invention has been described above, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative rather than restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many variations without departing from the purpose of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. A method for constructing a semi-analytical dynamic model of a whole machine tool with pose parameters, characterized in that The method includes the following steps: S1. According to the machine tool pose parameter sample set, construct multiple groups of three-dimensional pose machine tool models according to the positions of the structural components and joints of the whole machine tool in space; S2. Import the multiple groups of three-dimensional pose machine tool models into the finite element system for modal reduction and extraction of the stiffness and mass matrices of the structural components to construct a semi-analytical dynamic model of the structural components; S3. Construct a surrogate model of the non-linear mapping relationship between the stiffness and mass matrices corresponding to the semi-analytical dynamic model of the structural components; S4. Construct a contact stiffness model of the joint; S5. Establish a dynamic model of the whole machine tool by using the structural component synthesis method.

2. The method for constructing a semi-analytical dynamic model of a whole machine tool with pose parameters according to claim 1, characterized in that The process of constructing multiple groups of three-dimensional pose machine tool models according to the positions of the structural components in space in step S1 includes: Step 101. Determine the stroke parameter range of the machine tool at each pose, conduct experimental design and establish a pose parameter sample set, use the optimal Latin hypercube experimental design method for parameter sampling, select the sampled parameters, and for the movement stroke of each structural component of the machine tool, determine the displacement stroke range of the structural components in each direction, and preliminarily determine the distribution interval of each pose parameter; Step 102. Generate random numbers: Assume that the position of the machine tool in the n direction is an n-dimensional number, that is, an n-dimensional space is formed, and the number of sampling times is M. According to the principle of the optimal Latin hypercube experimental design method, each dimension is divided into M equal intervals, and the length of each interval is 1 / M. Randomly select N values from the first interval to form a set as the first column of matrix A, and then extract the same number of values from the second interval as the second column of matrix A, and so on until all columns of matrix A are filled. Shuffle the order of each row of matrix A to obtain matrix B. Each column vector of matrix B represents a sample point, and matrix B represents the final M sampled sample points. In this way, M groups of sample points of the n-dimensional position parameters of the machine tool are obtained; Step 103. According to the pose parameter sample set established in steps 101 and 102, modify the positions of the structural components of the machine tool in space to obtain multiple groups of three-dimensional pose machine tool models.

3. A method for constructing a semi-analytical dynamics model of a whole machine tool with pose parameters according to claim 1, characterized in that, The process of importing the multiple groups of three-dimensional pose machine tool models into the finite element system for modal reduction and extraction of the stiffness and mass matrices of the structural components to construct a semi-analytical dynamic model of the structural components in step S2 includes: Step 201. The component structural component i in the serial motion chain is connected to the component structural components i-1 and i+1 through the joints i and i+1 respectively, and the local reference systems Ki and Ki+1 are placed at the centers of the joints i and i+1 respectively. The undamped dynamic equation of the component structural component is expressed in the local reference system Ki+1 as: where k (i) and m (i) are the stiffness and mass matrices of the structural member, f (i) and u (i) are the force vector and the nodal displacement vector of the structural member, respectively; Step 202: Divide u (i) into two subgroups and obtain the external node displacement vector u E (i) and the internal node displacement vector u I (i) , where: Among them, is represented as: Wherein: and are respectively the nodal displacement vectors of the finite element node groups at the joints i and i + 1, represents the nodal group displacement vector of the structural member node N at the joint i + 1; Step 203. Construct a reduced dynamic model in which a single structural component is condensed to a point on the joint surface, including: For the same type of joint surface of a single structural component, if there are multiple, assume that the condensed nodes have a consistent deformation field, and set an "intermediate node" at the equivalent center position of the joint. Condense multiple joint surfaces to this intermediate node; For different types of joint surfaces, first condense the same type of joint surfaces to the same intermediate node according to the above steps, and then perform secondary condensation on the different types of intermediate nodes, and condense two intermediate nodes into one point.

4. A method for constructing a semi-analytical dynamic model of a whole machine tool with pose parameters according to claim 1, characterized in that, The process of constructing the contact stiffness model of the joint in step S4 includes: Step 401: Construct the contact stiffness matrix of the joint according to the following formula. That is, taking structural member i as the object, assume the plane where the joint i+1 between structural member i and structural member j is a rigid surface. For the same type of joint, specify a six-degree-of-freedom "central node" at the joint, and this node is at the equivalent geometric center of the joint. where: n in the subscript represents the nth type of joint of the joint, and respectively represent the linear displacement and angular displacement of the "central node" i+1,n in the local coordinate system K ; is the linear displacement of the kth node on the joint i+1 of the structural member i ; is the angular displacement vector pointing from the slave node to the "central node"; Step 402: Adopt the dynamic condensation method. According to the principle of rigid multi-point constraint, each external finite element node on the joint i+1 of structural member i is condensed to this central node. The displacement vector of the external nodes after condensation can be expressed as: Wherein: Denote the six - dimensional nodal displacement vector of the "central node" on structural member i ; Denote the reduction matrix of the six - dimensional nodal displacement vector when the external nodal displacement vector on structural member i changes to the "central node" ; Step 403. Establish the six-dimensional nodal displacement vector of the "central node" of structural member j according to the following formula: as follows: Relationship: Wherein: represents the six - dimensional nodal force vector on the "intermediate node", represents the six - dimensional nodal force vector on the "central node", K i+1,n represents the contact stiffness matrix of joint i + 1; Step 404, the relationship between the nodal force and the nodal displacement can be constructed according to the following formula through the contact stiffness matrix K i+1,n It is expressed as: Where: K i+1,n is the 6×6 contact stiffness matrix calculated above. If there are multiple types of joint parts, it can be obtained according to the deformation superposition principle: Where: K i+1 is the equivalent contact stiffness matrix of the joint i + 1, X i+1 is the coordinate transformation matrix of different local coordinate systems, N is the number of joint types, and this stiffness matrix is the linear superposition of the interface stiffness matrices in the local coordinate system.

5. A method for constructing a semi-analytical dynamics model of a whole machine tool including pose parameters according to claim 1, characterized in that, The process of establishing the dynamic model of the whole machine tool by using the structural member synthesis method in step S5 includes: Step 501: Construct the dynamic model of the machine tool by assembling the stiffness, mass matrices of the above structural members and the contact stiffness matrix of the joint. Step 502: Under the global coordinate system K, construct the dynamic model of the whole machine tool including the pose parameters in each direction of the machine tool according to the following formula: where K and M are the stiffness matrix and mass matrix of the whole machine tool, and F and U are the force vector and node displacement vector of the whole machine tool; the dynamic model of the whole machine tool including the pose parameters in each direction of the machine tool is constructed.

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