Machine tool multi-body dynamics modeling method and system for heterogeneous double five-axis machine tool

Abstract

The invention provides a machine tool multi-body dynamics modeling method and system for a heterogeneous double-five-axis machine tool, and the method comprises the steps: S1, constructing a kinematic chain of the heterogeneous double-five-axis machine tool according to the structural characteristics and motion states of the heterogeneous double-five-axis machine tool; s2, performing three-dimensional modeling on the heterogeneous double five-axis machine tool, and extracting the mass of each component through a model; according to a Nitsche principle-based partition variation method of flexible multi-body dynamics, machine tool kinetic energy and potential energy expressions considering part flexibility are obtained; s3, based on Hertz contact modeling and a contact stiffness theory, establishing a kinetic model of a joint part of each component of the heterogeneous double-five-axis machine tool, and obtaining connection characteristic parameters among the components of the machine tool; and S4, establishing a multi-body dynamic model of the machine tool and solving the model. According to the method, the machine tool multi-body dynamic model is accurately constructed, so that the dynamic behavior in the machine tool movement process is accurately predicted.

Description

Technical Field

[0001] The present invention relates to the technical field of machine tool manufacturing, and in particular to a machine tool multi-body dynamics modeling method and system for a heterogeneous dual five-axis machine tool. Background Art

[0002] Heterogeneous dual five-axis machine tools play a key role in the aerospace field, especially in the shaping of large thin-walled parts. Since these parts have extremely high requirements for quality and precision, heterogeneous dual five-axis machine tools have become special equipment for such processing tasks with their complex motion capabilities and high-precision processing performance. Through the precision processing of heterogeneous dual five-axis machine tools, the reliability of products can be significantly improved and the weight can be reduced, thereby improving the performance and fuel efficiency of aerospace vehicles. Therefore, studying and optimizing the dynamic characteristics of heterogeneous dual five-axis machine tools is of great significance to ensure product quality and performance.

[0003] At present, machine tool dynamics modeling mainly relies on the following two methods: finite element analysis (FEA) and rigid body dynamics model. These methods have a wide range of use in practical applications, but they also have some significant shortcomings.

[0004] 1. Finite element analysis (FEA): Finite element analysis is a commonly used dynamic modeling technology. By decomposing the machine tool structure into multiple finite elements, the stress, deformation and dynamic behavior of the machine tool can be analyzed in detail. The FEA method can provide high-precision modeling results for complex structures and is a powerful tool for understanding the dynamic characteristics of machine tools. However, this method usually requires a lot of computing resources, is time-consuming, and is difficult to apply to dynamic environments that require real-time performance prediction. In addition, the finite element model may not be able to fully reflect all dynamic behaviors in the actual machining process when dealing with the multi-body coupling effects and dynamic characteristics changes of heterogeneous dual five-axis machine tools.

[0005] 2. Rigid body dynamics model: The rigid body dynamics model treats machine tool components as rigid bodies and uses simplified motion equations to describe their motion characteristics. This method is suitable for rapid analysis and preliminary design due to its simple calculation and high efficiency. However, the rigid body model ignores the flexibility of the machine tool structure and the complexity of the connection parts, resulting in insufficient accuracy in high-precision machining and complex multi-body system analysis. In addition, the rigid body model shows obvious limitations when dealing with dynamic interactions and coordinated motions between multiple axes, which limits its application effect in complex machining tasks.

[0006] The invention patent document with publication number CN114895565A discloses a real-time prediction method for the dynamic characteristics of a dual-rotary five-axis machine tool under milling conditions, including the following steps: using the standard DH method to describe the kinematic model of the machine tool; using the Lagrangian method to establish the dynamic equation of the machine tool; using Yoshimura Yunxiao's integral method, Hertz theory and elastic mechanics to establish the dynamic model of the spindle-tool handle, spindle-bearing, guide slider and ball screw joint, and obtain the contact characteristic parameters of the joint; finally, combining the dynamic equation and the contact characteristics of the joint to establish a dynamic model. This patent does not focus on the complexity and multi-body dynamic characteristics of heterogeneous dual five-axis machine tools, and does not achieve accurate prediction and optimization of complex dynamic behaviors during machine tool processing.

[0007] The existing technology has the following disadvantages:

[0008] 1. Insufficient computational complexity and real-time performance: When dealing with complex dynamic problems, finite element analysis requires large amounts of computation and takes a long time, making it difficult to meet the requirements of real-time dynamic prediction.

[0009] 2. Insufficient accuracy and flexibility: The rigid body dynamics model is not accurate enough to describe the dynamic behavior of complex systems and cannot fully consider the flexibility of the machine tool structure and the dynamic coupling effects between multiple bodies.

[0010] Therefore, there are the following improvement needs in the machine tool dynamics modeling method:

[0011] 1. Improve model accuracy: It is necessary to develop a multi-body dynamics model that can simultaneously consider the machine tool structure flexibility, nonlinear connection and electromechanical coupling effects to improve the accuracy of dynamic characteristics prediction.

[0012] 2. Enhance real-time dynamic analysis capabilities: By optimizing the modeling algorithm, reducing the calculation time, improving the model's adaptability to different processing conditions and environments, and realizing real-time performance analysis.

[0013] By improving existing technologies, the modeling accuracy and dynamic performance prediction of heterogeneous dual five-axis machine tools can be significantly improved, providing more reliable technical support for high-end manufacturing fields such as aerospace and promoting the development of high-precision manufacturing technology. Summary of the invention

[0014] In view of the defects in the prior art, the present invention provides a machine tool multi-body dynamics modeling method and system for a heterogeneous dual five-axis machine tool.

[0015] According to a machine tool multi-body dynamics modeling method and system for a heterogeneous dual five-axis machine tool provided by the present invention, the scheme is as follows:

[0016] In a first aspect, a machine tool multi-body dynamics modeling method for a heterogeneous dual five-axis machine tool is provided, the method comprising:

[0017] Step S1: constructing a kinematic chain of the heterogeneous dual five-axis machine tool according to the structural characteristics and motion state of the heterogeneous dual five-axis machine tool;

[0018] Step S2: Perform three-dimensional modeling on the heterogeneous dual five-axis machine tool, and extract the mass of each component through the model; according to the partition variation method based on Nitsche principle of flexible multi-body dynamics, the expressions of kinetic energy and potential energy of the machine tool considering the flexibility of the components are obtained;

[0019] Step S3: Based on Hertz contact modeling and contact stiffness theory, a dynamic model of the joints of the components of the heterogeneous dual five-axis machine tool is established, and then the connection characteristic parameters between the components of the machine tool are obtained;

[0020] Step S4: Based on the expressions of kinetic energy and potential energy of the machine tool system and the dynamics model of the connection characteristics between the components, a multi-body dynamics model of the machine tool is established and the model is solved.

[0021] Preferably, the motion chain in step S1 includes: a milling side open-loop motion chain from the milling side tool coordinate system to the machine tool base coordinate system, a support side open-loop motion chain from the support side end coordinate system to the machine tool base, and a closed-loop mirror motion chain from the tool side to the support side.

[0022] Preferably, the step S1 further comprises: establishing a parameter model using the DH standard method, and describing the overall kinematic characteristics of the heterogeneous dual five-axis machine tool through homogeneous coordinate transformation;

[0023] Step S1.1: Use the standard DH parameter method to describe the coordinate system transformation between the substructures of the heterogeneous dual five-axis machine tool. i , α i d i and θ i Four parameters;

[0024] Among them, a i is the link length, which is defined as the distance between two adjacent joint axes in the current link coordinate system, that is, the distance from the previous joint axis to the current joint axis along the X axis of the previous link;

[0025] α i The joint torsion angle is defined as the rotation angle from the previous joint axis Z axis to the current joint axis Z axis around the current link's X axis. It is the angle required to rotate the previous link coordinate system around the current link's X axis to be parallel to the current link coordinate system's Z axis.

[0026] d i is the link offset, which is defined as the distance along the Z axis of the current joint axis in the current link coordinate system;

[0027] θ iis the joint angle, which is defined as the angle of rotation around the current joint axis Z axis in the current link coordinate system;

[0028] According to the standard DH parameter method, the coordinate transformation relationship between two adjacent links is represented by a 4×4 homogeneous transformation matrix; this transformation matrix converts one coordinate system to the next coordinate system to represent the geometric relationship between the two links; the homogeneous transformation matrix combines rotation and translation. For two adjacent links i-1 and i, the transformation matrix It is expressed as:

[0029]

[0030] Step S1.2: By analyzing the structure of the heterogeneous dual five-axis machine tool, the kinematic chain transformation relationship between the milling side and the support side of the machine tool is obtained; by multiplying the transformation matrices in sequence, the total transformation matrix from the support side to the milling side coordinate system is obtained.

[0031] Preferably, step S2 comprises:

[0032] Step S2.1: Establish a three-dimensional model of the heterogeneous dual five-axis machine tool, and obtain the mass m of each component based on the established three-dimensional model i ;

[0033] Step S2.2: According to the partition variation method based on Nitsche's principle, the machine tool components need to be decomposed into N subdomains before solving the dynamic model; then the energy functional of the machine tool is

[0034]

[0035] Among them, T i is the kinetic energy of subdomain i, U i is the strain potential energy of subdomain i, W i is the work done by the external force on subdomain i, Π f is the interface potential energy on the boundary of adjacent subdomains; Γ represents the interface of adjacent subdomains, t1 and t2 represent the start and end time of integration;

[0036] Based on Kirchhoff thin plate theory, the kinetic energy of subdomain i is

[0037]

[0038] Among them, u p 、v p and w p is the displacement of point p(x, y, z) in subdomain i in the XYZ direction, and ρ is the material density of the machine tool component;

[0039] The strain energy of subdomain i is expressed as:

[0040]

[0041] Among them, N n and M n (n = x, y, xy) represent the generalized internal forces and internal moments of machine tool components respectively; they are based on the component stress components σ n (n=x,y,xy) is expressed as:

[0042]

[0043] The interface potential energy Π on the boundary of adjacent subdomains f It is expressed as:

[0044] Π f =Π λ -Π κ 6)

[0045] Among them, λ and Π κ are the partition interface potential energy introduced by the partition generalized variation and penalty function terms respectively;

[0046] Π λ and Π κ The calculation method of is related to the division direction of the adjacent subdomain interface. When the subdomain interface is divided along the normal direction of the X direction, Π λ and Π κ The calculation method is expressed as

[0047]

[0048] Among them, Q xz is the equivalent generalized shear force, Δ is the generalized displacement coordination equation of the adjacent subdomain boundaries; these parameters are calculated as follows, κ is the weight parameter on the partition interface, and the value is selected to be greater than the elastic modulus of the material;

[0049]

[0050] Δ u =u m -u m+1 ,Δ v =v m -v m+1

[0051] Δ w =w m -w m+1 ,

[0052] Preferably, the step S3 comprises:

[0053] Step S3.1: Assume that the number of balls in contact in each row of grooves in the guide rail system is the same, which is n; then the force state between the balls on the upper and lower sides of the guide rail is the same;

[0054] The contact pressure between the single ball and the groove is P U Indicated below, the contact pressure between a single ball and the groove is P L Indicates; Z1 and Z2 are the coordinates of the center of gravity of the slider and the track respectively, P is the normal load on the guide rail system, and β is the contact angle;

[0055] Step S3.2: If each ball is always under pressure under the external load, then

[0056] P+2nP L sinβ=2nP U sinβ10)

[0057] Under the action of external load P, the relative deformation of the guide rail system is represented by ΔZ, which is expressed as

[0058] ΔZ=Z1-Z2 11)

[0059] If the functional relationship between the external load and the relative deformation ΔZ is established, the analytical expression of the normal contact stiffness of the guide rail slider can be clearly expressed;

[0060] The normal contact force and deformation of a single ball satisfy

[0061]

[0062] In the formula, α U , α L The contact pressure P of a single ball is U , P L The elastic deformation caused by the action of k h The relationship between the load F and the deformation α of a single ball is called the quasi-stiffness coefficient. Since the force state between the upper and lower balls is the same, the corresponding deformations are also the same.

[0063] In addition, during the assembly process of the guide rail system, a preload is usually applied. Assuming that the normal pressure generated on the contact surface of a single ball under the action of the preload is P0, and the initial deformation caused by the preload is α0, the two also satisfy

[0064]

[0065] Assuming that the initial deformation of all upper and lower balls is the same, which is α0, then under the action of load P, according to the deformation coordination condition, we can get

[0066] (αU -α0)sinβ=(α0-α L )sinβ=ΔZ 14)

[0067] From the above formula we can get

[0068]

[0069] Establish the pressure P on the ball at the upper end of the guide rail U The functional relationship between the external load P and the preload force P0 is expressed as

[0070] P U =f(P,P0)16)

[0071] From the above formula we can get

[0072]

[0073] The above formula establishes an implicit functional relationship between the external load P and the relative deformation ΔZ. If the derivative of ΔZ is further calculated, the expression of the normal contact stiffness of the slider is obtained as follows:

[0074]

[0075] Preferably, step S4 comprises: substituting the normal contact stiffness of the slider into the dynamic model of the joint of the machine tool, solving the partition interface elastic potential energy of the partition variation method based on the Nitsche principle; taking the first-order variation of the energy functional Π, and obtaining the discrete dynamic equation of the machine tool according to the stationary value condition of δΠ=0:

[0076]

[0077] Where q is the set of displacement vectors of all machine tool component subdomains; M and K are the assembly matrices of the generalized mass matrix and stiffness matrix of the laminate subdomain, respectively; K λ and K κ is the assembly matrix of the partition interface matrix; F is the generalized external force matrix; by solving the dynamic equation, the dynamic response of the heterogeneous dual five-axis machine tool under the action of the generalized external force F is obtained.

[0078] In a second aspect, a machine tool multi-body dynamics modeling system for a heterogeneous dual five-axis machine tool is provided, the system comprising:

[0079] Module M1: Construct the kinematic chain of the heterogeneous dual five-axis machine tool according to its structural characteristics and motion state;

[0080] Module M2: 3D modeling of heterogeneous dual five-axis machine tools, and extraction of the mass of each component through the model; based on the partition variation method based on the Nitsche principle of flexible multi-body dynamics, the expressions of the machine tool kinetic energy and potential energy considering the flexibility of the components are obtained;

[0081] Module M3: Based on Hertz contact modeling and contact stiffness theory, a dynamic model of the joints of the components of the heterogeneous dual five-axis machine tool is established to obtain the connection characteristic parameters between the components of the machine tool;

[0082] Module M4: Based on the kinetic energy and potential energy expressions of the machine tool system and the dynamic model of the connection characteristics between the components, a multi-body dynamic model of the machine tool is established and the model is solved.

[0083] Preferably, the kinematic chain in the module M1 includes: a milling side open-loop kinematic chain from the milling side tool coordinate system to the machine tool base coordinate system, a support side open-loop kinematic chain from the support side end coordinate system to the machine tool base, and a closed-loop mirror kinematic chain from the tool side to the support side;

[0084] The module M1 also includes: establishing a parameter model using the DH standard method and describing the overall kinematic characteristics of the heterogeneous dual five-axis machine tool through homogeneous coordinate transformation;

[0085] Module M1.1: Use the standard DH parameter method to describe the coordinate system transformation between the substructures of the heterogeneous dual five-axis machine tool. i , α i d i and θ i Four parameters;

[0086] Among them, a i is the link length, which is defined as the distance between two adjacent joint axes in the current link coordinate system, that is, the distance from the previous joint axis to the current joint axis along the X axis of the previous link;

[0087] α i The joint torsion angle is defined as the rotation angle from the previous joint axis Z axis to the current joint axis Z axis around the current link's X axis. It is the angle required to rotate the previous link coordinate system around the current link's X axis to be parallel to the current link coordinate system's Z axis.

[0088] d i is the link offset, which is defined as the distance along the Z axis of the current joint axis in the current link coordinate system;

[0089] θ i is the joint angle, which is defined as the angle of rotation around the current joint axis Z axis in the current link coordinate system;

[0090] According to the standard DH parameter method, the coordinate transformation relationship between two adjacent links is represented by a 4×4 homogeneous transformation matrix; this transformation matrix converts one coordinate system to the next coordinate system to represent the geometric relationship between the two links; the homogeneous transformation matrix combines rotation and translation. For two adjacent links i-1 and i, the transformation matrix It is expressed as:

[0091]

[0092] Module M1.2: By analyzing the structure of the heterogeneous dual five-axis machine tool, the kinematic chain transformation relationship between the milling side and the support side of the machine tool is obtained; by multiplying the transformation matrices in sequence, the total transformation matrix from the support side to the milling side coordinate system is obtained.

[0093] Preferably, the module M2 comprises:

[0094] Module M2.1: Establish a 3D model of a heterogeneous dual five-axis machine tool and obtain the mass m of each component based on the established 3D model i ;

[0095] Module M2.2: According to the partition variation method based on Nitsche's principle, the machine tool components need to be decomposed into N subdomains before solving the dynamic model; then the energy functional of the machine tool is

[0096]

[0097] Among them, T i is the kinetic energy of subdomain i, U i is the strain potential energy of subdomain i, W i is the work done by the external force on subdomain i, Π f is the interface potential energy on the boundary of adjacent subdomains; Γ represents the interface of adjacent subdomains, t1 and t2 represent the start and end time of integration;

[0098] Based on Kirchhoff thin plate theory, the kinetic energy of subdomain i is

[0099]

[0100] Among them, u p 、v p and w p is the displacement of point p(x, y, z) in subdomain i in the XYZ direction, and ρ is the material density of the machine tool component;

[0101] The strain energy of subdomain i is expressed as:

[0102]

[0103] Among them, N n and M n(n = x, y, xy) represent the generalized internal forces and internal moments of machine tool components respectively; they are based on the component stress components σ n (n=x,y,xy) is expressed as:

[0104]

[0105] The interface potential energy Π on the boundary of adjacent subdomains f It is expressed as:

[0106] Π f =Π λ -Π κ 6)

[0107] Among them, λ and Π κ are the partition interface potential energy introduced by the partition generalized variation and penalty function terms respectively;

[0108] Π λ and Π κ The calculation method of is related to the division direction of the adjacent subdomain interface. When the subdomain interface is divided along the normal direction of the X direction, Π λ and Π κ The calculation method is expressed as

[0109]

[0110] Among them, Q xz is the equivalent generalized shear force, Δ is the generalized displacement coordination equation of the adjacent subdomain boundaries; these parameters are calculated as follows, κ is the weight parameter on the partition interface, and the value is selected to be greater than the elastic modulus of the material;

[0111]

[0112] Δ u =u m -u m+1 ,Δ v =v m -v m+1

[0113] Δ w =w m -w m+1 ,

[0114] Preferably, the module M3 comprises:

[0115] Module M3.1: Assume that the number of balls in contact in each row of grooves in the guide rail system is the same, which is n; then the force state between the balls on the upper and lower sides of the guide rail is the same;

[0116] The contact pressure between the single ball and the groove is PU Indicated below, the contact pressure between a single ball and the groove is P L Indicates; Z1 and Z2 are the coordinates of the center of gravity of the slider and the track respectively, P is the normal load on the guide rail system, and β is the contact angle;

[0117] Module M3.2: If the balls are always under pressure under the external load, then

[0118] P+2nP L sinβ=2nP U sinβ10)

[0119] Under the action of external load P, the relative deformation of the guide rail system is represented by ΔZ, which is expressed as

[0120] ΔZ=Z1-Z2 11)

[0121] If the functional relationship between the external load and the relative deformation ΔZ is established, the analytical expression of the normal contact stiffness of the guide rail slider can be clearly expressed;

[0122] The normal contact force and deformation of a single ball satisfy

[0123]

[0124] In the formula, α U , α L The contact pressure P of a single ball is U , P L The elastic deformation caused by the action of k h The relationship between the load F and the deformation α of a single ball is called the quasi-stiffness coefficient. Since the force state between the upper and lower balls is the same, the corresponding deformations are also the same.

[0125] In addition, during the assembly process of the guide rail system, a preload is usually applied. Assuming that the normal pressure generated on the contact surface of a single ball under the action of the preload is P0, and the initial deformation caused by the preload is α0, the two also satisfy

[0126]

[0127] Assuming that the initial deformation of all upper and lower balls is the same, which is α0, then under the action of load P, according to the deformation coordination condition, we can get

[0128] (α U -α0)sinβ=(α0-α L )sinβ=ΔZ 14)

[0129] From the above formula we can get

[0130]

[0131] Establish the pressure P on the ball at the upper end of the guide rail U The functional relationship between the external load P and the preload force P0 is expressed as

[0132] P U =f(P,P0)16)

[0133] From the above formula we can get

[0134]

[0135] The above formula establishes an implicit functional relationship between the external load P and the relative deformation ΔZ. If the derivative of ΔZ is further calculated, the expression of the normal contact stiffness of the slider is obtained as follows:

[0136]

[0137] The module M4 includes: substituting the normal contact stiffness of the slider into the dynamic model of the joint of the machine tool to solve the partition interface elastic potential energy based on the partition variation method of the Nitsche principle; taking the first-order variation of the energy functional Π, and obtaining the discrete dynamic equation of the machine tool according to the stationary value condition of δΠ=0:

[0138]

[0139] Where q is the set of displacement vectors of all machine tool component subdomains; M and K are the assembly matrices of the generalized mass matrix and stiffness matrix of the laminate subdomain, respectively; K λ and K κ is the assembly matrix of the partition interface matrix; F is the generalized external force matrix; by solving the dynamic equation, the dynamic response of the heterogeneous dual five-axis machine tool under the action of the generalized external force F is obtained.

[0140] Compared with the prior art, the present invention has the following beneficial effects:

[0141] 1. The present invention comprehensively considers the flexibility and nonlinear interaction of various machine tool components to construct a more accurate multi-body dynamics model, thereby overcoming the problem of insufficient accuracy caused by ignoring these factors in traditional modeling methods;

[0142] 2. The present invention achieves accurate prediction of the dynamic behavior of the machine tool motion process by accurately modeling the dynamics of the connection parts of the machine tool components;

[0143] 3. By accurately predicting the dynamic behavior of the machine tool, the present invention has significant advantages in improving machining accuracy and stability, reducing machining defects caused by dynamic errors, and improving product quality consistency and reliability;

[0144] 4. The present invention effectively improves the accuracy of dynamic modeling, enhances real-time prediction capabilities and optimizes processing control, providing important technical support for high-precision manufacturing.

[0145] Other beneficial effects of the present invention will be explained in the specific implementation manner through the introduction of specific technical features and technical solutions. Through the introduction of these technical features and technical solutions, those skilled in the art should be able to understand the beneficial technical effects brought about by the technical features and technical solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0146] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0147] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0148] Figure 2 It is the geometric model and kinematic chain diagram of the heterogeneous dual five-axis machine tool;

[0149] Figure 3 It is the contact model of the joints between the components of heterogeneous dual five-axis machine tools. DETAILED DESCRIPTION

[0150] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0151] The embodiment of the present invention provides a machine tool multi-body dynamics modeling method for a heterogeneous dual five-axis machine tool, referring to Figure 1 As shown, the specific contents of this method are as follows:

[0152] Step S1: According to the structural characteristics and motion state of the heterogeneous dual five-axis machine tool, the motion chain of the heterogeneous dual five-axis machine tool is constructed; the parameter model is established using the DH standard method, and the overall kinematic characteristics of the heterogeneous dual five-axis machine tool are described through homogeneous coordinate transformation.

[0153] The milling side of the heterogeneous dual five-axis machine tool adopts a five-axis machine tool with an AC double-swing head structure (the rotating axes are A1 and C1 axes), and the support side also adopts a five-axis machine tool with an AC double-swing head structure (the rotating axes are A2 and C2 axes). The machine tool structure code is [t-A1-C1-Z1-Y1-X1-b-X2-Y2-Z2-C2-A2-w].

[0154] Reference Figure 2As shown in the figure, based on its dual five-axis structure, the kinematic model of the mirror milling machine tool contains three motion chains, namely the open-loop motion chain on the milling side from the tool coordinate system on the milling side to the basic coordinate system of the machine tool, the open-loop motion chain on the support side from the end coordinate system on the support side to the machine tool base, and the closed-loop mirror motion chain from the tool side to the support side.

[0155] Step S1.1: Use the standard DH parameter method to describe the coordinate system transformation between the substructures of the heterogeneous dual five-axis machine tool. i , α i d i and θ i Four parameters;

[0156] Among them, a i is the link length, which is defined as the distance between two adjacent joint axes in the current link coordinate system, that is, the distance from the previous joint axis to the current joint axis along the X axis of the previous link;

[0157] α i The joint torsion angle is defined as the rotation angle from the previous joint axis Z axis to the current joint axis Z axis around the current link's X axis. It is the angle required to rotate the previous link coordinate system around the current link's X axis to be parallel to the current link coordinate system's Z axis.

[0158] d i is the link offset, which is defined as the distance along the Z axis of the current joint axis in the current link coordinate system;

[0159] θ i is the joint angle, which is defined as the angle of rotation around the current joint axis Z axis in the current link coordinate system;

[0160] According to the standard DH parameter method, the coordinate transformation relationship between two adjacent links is represented by a 4×4 homogeneous transformation matrix; this transformation matrix converts one coordinate system to the next coordinate system to represent the geometric relationship between the two links; the homogeneous transformation matrix combines rotation and translation. For two adjacent links i-1 and i, the transformation matrix It is expressed as:

[0161]

[0162] Step S1.2: By analyzing the structure of the heterogeneous dual five-axis machine tool, the kinematic chain transformation relationship between the milling side and the support side of the machine tool is obtained; by multiplying the transformation matrices in sequence, the total transformation matrix from the support side to the milling side coordinate system is obtained.

[0163] Step S2: Perform three-dimensional modeling of the heterogeneous dual five-axis machine tool and extract the mass of each component through the model; according to the partition variation method based on the Nitsche principle of flexible multi-body dynamics, the machine tool kinetic energy and potential energy expressions considering the flexibility of the components are obtained.

[0164] The step S2 specifically includes:

[0165] Step S2.1: Establish a three-dimensional model of the heterogeneous dual five-axis machine tool, and obtain the mass m of each component based on the established three-dimensional model i ;

[0166] Step S2.2: According to the partition variation method based on Nitsche's principle, the machine tool components need to be decomposed into N subdomains before solving the dynamic model; then the energy functional of the machine tool is

[0167]

[0168] Among them, T i is the kinetic energy of subdomain i, U i is the strain potential energy of subdomain i, W i is the work done by the external force on subdomain i, Π f is the interface potential energy on the boundary of adjacent subdomains; Γ represents the interface of adjacent subdomains, t1 and t2 represent the start and end time of integration;

[0169] Based on Kirchhoff thin plate theory, the kinetic energy of subdomain i is

[0170]

[0171] Among them, u p 、v p and w p is the displacement of point p(x, y, z) in subdomain i in the XYZ direction, and ρ is the material density of the machine tool component;

[0172] The strain energy of subdomain i is expressed as:

[0173]

[0174] Among them, N n and M n (n = x, y, xy) represent the generalized internal forces and internal moments of machine tool components respectively; they are based on the component stress components σ n (n=x,y,xy) is expressed as:

[0175]

[0176] The interface potential energy Π on the boundary of adjacent subdomains f It is expressed as:

[0177] Π f =Π λ -Π κ 6)

[0178] Among them,λ and Π κ are the partition interface potential energy introduced by the partition generalized variation and penalty function terms respectively;

[0179] Π λ and Π κ The calculation method of is related to the division direction of the adjacent subdomain interface. When the subdomain interface is divided along the normal direction of the X direction, Π λ and Π κ The calculation method is expressed as

[0180]

[0181] Among them, Q xz is the equivalent generalized shear force, Δ is the generalized displacement coordination equation of the adjacent subdomain boundaries; these parameters are calculated as follows, κ is the weight parameter on the partition interface, and the value is selected to be greater than the elastic modulus of the material;

[0182]

[0183] Δ u =u m -u m+1 ,Δ v =v m -v m+1

[0184] Δ w =w m -w m+1 ,

[0185] Step S3: Based on Hertz contact modeling and contact stiffness theory, a dynamic model of the joints of the components of the heterogeneous dual five-axis machine tool is established to obtain the connection characteristic parameters between the components of the machine tool.

[0186] Reference Figure 3 As shown, step S3 specifically includes:

[0187] Step S3.1: The overall force of the linear rolling guide system can be simplified as follows: Figure 3 The mechanical model shown in the figure assumes that there are 4 rows of grooves in the guide rail system, and the number of balls involved in contact in each row of grooves is the same (all n), so the force state between the balls on the top and bottom of the guide rail is the same.

[0188] The contact pressure between the single ball and the groove is P U Indicated below, the contact pressure between a single ball and the groove is P L express; Figure 3 Where Z1 and Z2 are the coordinates of the center of gravity of the slider and the track, P is the normal load on the guide system, and β is the contact angle.

[0189] Step S3.2: If each ball is always under pressure under the external load, then

[0190] P+2nP L sinβ=2nP U sinβ10)

[0191] Under the action of external load P, the relative deformation of the guide rail system is represented by ΔZ, which is expressed as

[0192] ΔZ=Z1-Z2 11)

[0193] If the functional relationship between the external load and the relative deformation ΔZ is established, the analytical expression of the normal contact stiffness of the guide rail slider can be clearly expressed;

[0194] The normal contact force and deformation of a single ball satisfy

[0195]

[0196] In the formula, α U , α L The contact pressure P of a single ball is U , P L The elastic deformation caused by the action of k h The relationship between the load F and the deformation α of a single ball is called the quasi-stiffness coefficient; since the force state between the upper and lower balls is the same, the corresponding deformations are also the same.

[0197] In addition, during the assembly process of the guide rail system, a preload is usually applied. Assuming that the normal pressure generated on the contact surface of a single ball under the action of the preload is P0, and the initial deformation caused by the preload is α0, the two also satisfy

[0198]

[0199] Assuming that the initial deformation of all upper and lower balls is the same, which is α0, then under the action of load P, according to the deformation coordination condition, we can get

[0200] (α U -α0)sinβ=(α0-α L )sinβ=ΔZ 14)

[0201] From the above formula we can get

[0202]

[0203] Establish the pressure P on the ball at the upper end of the guide rail U The functional relationship between the external load P and the preload force P0 is expressed as

[0204] P U =f(P,P0)16)

[0205] From the above formula we can get

[0206]

[0207] The above formula establishes an implicit functional relationship between the external load P and the relative deformation ΔZ. If the derivative of ΔZ is further calculated, the expression of the normal contact stiffness of the slider is obtained as follows:

[0208]

[0209] Step S4: Based on the expressions of kinetic energy and potential energy of the machine tool system and the dynamics model of the connection characteristics between the components, a multi-body dynamics model of the machine tool is established and the model is solved.

[0210] Substitute the normal contact stiffness of the slider into the dynamic model of the joint of the machine tool to solve the partition interface elastic potential energy based on the partition variation method of the Nitsche principle; take the first-order variation of the energy functional Π, and according to the stationary value condition of δΠ=0, the discrete dynamic equation of the machine tool is obtained as follows:

[0211]

[0212] Where q is the set of displacement vectors of all machine tool component subdomains; M and K are the assembly matrices of the generalized mass matrix and stiffness matrix of the laminate subdomain, respectively; K λ and K κ is the assembly matrix of the partition interface matrix; F is the generalized external force matrix; by solving the dynamic equation, the dynamic response of the heterogeneous dual five-axis machine tool under the action of the generalized external force F is obtained.

[0213] The present invention also provides a machine tool multi-body dynamics modeling system for heterogeneous dual five-axis machine tools, which can be implemented by executing the process steps of the machine tool multi-body dynamics modeling method for heterogeneous dual five-axis machine tools, that is, those skilled in the art can understand the machine tool multi-body dynamics modeling method for heterogeneous dual five-axis machine tools as a preferred implementation of the machine tool multi-body dynamics modeling system for heterogeneous dual five-axis machine tools. The system specifically includes the following contents:

[0214] Module M1: According to the structural characteristics and motion state of the heterogeneous dual five-axis machine tool, the motion chain of the heterogeneous dual five-axis machine tool is constructed; the parameter model is established using the DH standard method, and the overall kinematic characteristics of the heterogeneous dual five-axis machine tool are described through homogeneous coordinate transformation.

[0215] The milling side of the heterogeneous dual five-axis machine tool adopts a five-axis machine tool with an AC double-swing head structure (the rotating axes are A1 and C1 axes), and the support side also adopts a five-axis machine tool with an AC double-swing head structure (the rotating axes are A2 and C2 axes). The machine tool structure code is [t-A1-C1-Z1-Y1-X1-b-X2-Y2-Z2-C2-A2-w].

[0216] Reference Figure 2 As shown in the figure, based on its dual five-axis structure, the kinematic model of the mirror milling machine tool contains three motion chains, namely the open-loop motion chain on the milling side from the tool coordinate system on the milling side to the basic coordinate system of the machine tool, the open-loop motion chain on the support side from the end coordinate system on the support side to the machine tool base, and the closed-loop mirror motion chain from the tool side to the support side.

[0217] Module M1.1: Use the standard DH parameter method to describe the coordinate system transformation between the substructures of the heterogeneous dual five-axis machine tool. i , α i d i and θ i Four parameters;

[0218] Among them, a i is the link length, which is defined as the distance between two adjacent joint axes in the current link coordinate system, that is, the distance from the previous joint axis to the current joint axis along the X axis of the previous link;

[0219] α i The joint torsion angle is defined as the rotation angle from the previous joint axis Z axis to the current joint axis Z axis around the current link's X axis. It is the angle required to rotate the previous link coordinate system around the current link's X axis to be parallel to the current link coordinate system's Z axis.

[0220] d i is the link offset, which is defined as the distance along the Z axis of the current joint axis in the current link coordinate system;

[0221] θ i is the joint angle, which is defined as the angle of rotation around the current joint axis Z axis in the current link coordinate system;

[0222] According to the standard DH parameter method, the coordinate transformation relationship between two adjacent links is represented by a 4×4 homogeneous transformation matrix; this transformation matrix converts one coordinate system to the next coordinate system to represent the geometric relationship between the two links; the homogeneous transformation matrix combines rotation and translation. For two adjacent links i-1 and i, the transformation matrix It is expressed as:

[0223]

[0224] Module M1.2: By analyzing the structure of the heterogeneous dual five-axis machine tool, the kinematic chain transformation relationship between the milling side and the support side of the machine tool is obtained; by multiplying the transformation matrices in sequence, the total transformation matrix from the support side to the milling side coordinate system is obtained.

[0225] Module M2: Perform three-dimensional modeling of the heterogeneous dual five-axis machine tool and extract the mass of each component through the model; according to the partition variation method based on the Nitsche principle of flexible multi-body dynamics, the machine tool kinetic energy and potential energy expressions considering the flexibility of the components are obtained.

[0226] The module M2 specifically includes:

[0227] Module M2.1: Establish a 3D model of a heterogeneous dual five-axis machine tool and obtain the mass m of each component based on the established 3D model i ;

[0228] Module M2.2: According to the partition variation method based on Nitsche's principle, the machine tool components need to be decomposed into N subdomains before solving the dynamic model; then the energy functional of the machine tool is

[0229]

[0230] Among them, T i is the kinetic energy of subdomain i, U i is the strain potential energy of subdomain i, W i is the work done by the external force on subdomain i, Π f is the interface potential energy on the boundary of adjacent subdomains; Γ represents the interface of adjacent subdomains, t1 and t2 represent the start and end time of integration;

[0231] Based on Kirchhoff thin plate theory, the kinetic energy of subdomain i is

[0232]

[0233] Among them, u p 、v p and w p is the displacement of point p(x, y, z) in subdomain i in the XYZ direction, and ρ is the material density of the machine tool component;

[0234] The strain energy of subdomain i is expressed as:

[0235]

[0236] Among them, N n and M n (n = x, y, xy) represent the generalized internal forces and internal moments of machine tool components respectively; they are based on the component stress components σ n (n=x,y,xy) is expressed as:

[0237]

[0238] The interface potential energy Π on the boundary of adjacent subdomains f It is expressed as:

[0239] Π f =Π λ -Π κ 6)

[0240] Among them, λ and Π κ are the partition interface potential energy introduced by the partition generalized variation and penalty function terms respectively;

[0241] Π λ and Π κ The calculation method of is related to the division direction of the adjacent subdomain interface. When the subdomain interface is divided along the normal direction of the X direction, Π λ and Π κ The calculation method is expressed as

[0242]

[0243] Among them, Q xz is the equivalent generalized shear force, Δ is the generalized displacement coordination equation of the adjacent subdomain boundaries; these parameters are calculated as follows, κ is the weight parameter on the partition interface, and the value is selected to be greater than the elastic modulus of the material;

[0244]

[0245] Δ u =u m -u m+1 ,Δ v =v m -v m+1

[0246] Δ w =w m -w m+1 ,

[0247] Module M3: Based on Hertz contact modeling and contact stiffness theory, a dynamic model of the joints of the heterogeneous dual five-axis machine tool is established to obtain the connection characteristic parameters between the machine tool components.

[0248] Reference Figure 3 As shown, the module M3 specifically includes:

[0249] Module M3.1: The overall force of the linear rolling guide system can be simplified as follows: Figure 3The mechanical model shown in the figure assumes that there are 4 rows of grooves in the guide rail system, and the number of balls involved in contact in each row of grooves is the same (all n), so the force state between the balls on the top and bottom of the guide rail is the same.

[0250] The contact pressure between the single ball and the groove is P U Indicated below, the contact pressure between a single ball and the groove is P L express; Figure 3 Where Z1 and Z2 are the coordinates of the center of gravity of the slider and the track, P is the normal load on the guide system, and β is the contact angle.

[0251] Module M3.2: If the balls are always under pressure under the external load, then

[0252] P+2nP L sinβ=2nP U sinβ10)

[0253] Under the action of external load P, the relative deformation of the guide rail system is represented by ΔZ, which is expressed as

[0254] ΔZ=Z1-Z2 11)

[0255] If the functional relationship between the external load and the relative deformation ΔZ is established, the analytical expression of the normal contact stiffness of the guide rail slider can be clearly expressed;

[0256] The normal contact force and deformation of a single ball satisfy

[0257]

[0258] In the formula, α U , α L The contact pressure P of a single ball is U , P L The elastic deformation caused by the action of k h The relationship between the load F and the deformation α of a single ball is called the quasi-stiffness coefficient; since the force state between the upper and lower balls is the same, the corresponding deformations are also the same.

[0259] In addition, during the assembly process of the guide rail system, a preload is usually applied. Assuming that the normal pressure generated on the contact surface of a single ball under the action of the preload is P0, and the initial deformation caused by the preload is α0, the two also satisfy

[0260]

[0261] Assuming that the initial deformation of all upper and lower balls is the same, which is α0, then under the action of load P, according to the deformation coordination condition, we can get

[0262] (α U -α0)sinβ=(α0-α L )sinβ=ΔZ 14)

[0263] From the above formula we can get

[0264]

[0265] Establish the pressure P on the ball at the upper end of the guide rail U The functional relationship between the external load P and the preload force P0 is expressed as

[0266] P U =f(P,P0)16)

[0267] From the above formula we can get

[0268]

[0269] The above formula establishes an implicit functional relationship between the external load P and the relative deformation ΔZ. If the derivative of ΔZ is further calculated, the expression of the normal contact stiffness of the slider is obtained as follows:

[0270]

[0271] Module M4: Based on the kinetic energy and potential energy expressions of the machine tool system and the dynamic model of the connection characteristics between the components, a multi-body dynamic model of the machine tool is established and the model is solved.

[0272] Substitute the normal contact stiffness of the slider into the dynamic model of the joint of the machine tool to solve the partition interface elastic potential energy based on the partition variation method of the Nitsche principle; take the first-order variation of the energy functional Π, and according to the stationary value condition of δΠ=0, the discrete dynamic equation of the machine tool is obtained as follows:

[0273]

[0274] Where q is the set of displacement vectors of all machine tool component subdomains; M and K are the assembly matrices of the generalized mass matrix and stiffness matrix of the laminate subdomain, respectively; K λ and K κ is the assembly matrix of the partition interface matrix; F is the generalized external force matrix; by solving the dynamic equation, the dynamic response of the heterogeneous dual five-axis machine tool under the action of the generalized external force F is obtained.

[0275] An embodiment of the present invention provides a machine tool multi-body dynamics modeling method and system for a heterogeneous dual five-axis machine tool. By comprehensively considering the flexibility of the components of the heterogeneous dual five-axis machine tool and the interaction between the components, a machine tool multi-body dynamics model is accurately constructed, thereby achieving accurate prediction of the dynamic behavior of the machine tool during movement.

[0276] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0277] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A machine tool multi-body dynamics modeling method for heterogeneous dual five-axis machine tools, characterized in that: include: Step S1: constructing a kinematic chain of the heterogeneous dual five-axis machine tool according to the structural characteristics and motion state of the heterogeneous dual five-axis machine tool; Step S2: Perform three-dimensional modeling on the heterogeneous dual five-axis machine tool, and extract the mass of each component through the model; according to the partition variation method based on Nitsche principle of flexible multi-body dynamics, the expressions of kinetic energy and potential energy of the machine tool considering the flexibility of the components are obtained; Step S3: Based on Hertz contact modeling and contact stiffness theory, a dynamic model of the joints of the components of the heterogeneous dual five-axis machine tool is established, and then the connection characteristic parameters between the components of the machine tool are obtained; Step S4: Based on the expressions of kinetic energy and potential energy of the machine tool system and the dynamics model of the connection characteristics between the components, a multi-body dynamics model of the machine tool is established and the model is solved.

2. The machine tool multi-body dynamics modeling method for heterogeneous dual five-axis machine tools according to claim 1 is characterized in that: The kinematic chain in step S1 includes: a milling side open-loop kinematic chain from the milling side tool coordinate system to the machine tool base coordinate system, a support side open-loop kinematic chain from the support side end coordinate system to the machine tool base, and a closed-loop mirror kinematic chain from the tool side to the support side.

3. The machine tool multi-body dynamics modeling method for heterogeneous dual five-axis machine tools according to claim 1 is characterized in that: The step S1 further comprises: establishing a parameter model by using the DH standard method, and describing the overall kinematic characteristics of the heterogeneous dual five-axis machine tool by homogeneous coordinate transformation; Step S1.1: Use the standard DH parameter method to describe the coordinate system transformation between the substructures of the heterogeneous dual five-axis machine tool. i , α i d i and θ i Four parameters; Among them, a i is the link length, which is defined as the distance between two adjacent joint axes in the current link coordinate system, that is, the distance from the previous joint axis to the current joint axis along the X axis of the previous link; α i The joint torsion angle is defined as the rotation angle from the previous joint axis Z axis to the current joint axis Z axis around the current link's X axis. It is the angle required to rotate the previous link coordinate system around the current link's X axis to be parallel to the current link coordinate system's Z axis. d i is the link offset, which is defined as the distance along the Z axis of the current joint axis in the current link coordinate system; θ i is the joint angle, which is defined as the angle of rotation around the current joint axis Z axis in the current link coordinate system; According to the standard DH parameter method, the coordinate transformation relationship between two adjacent links is represented by a 4×4 homogeneous transformation matrix; this transformation matrix converts one coordinate system to the next coordinate system to represent the geometric relationship between the two links; the homogeneous transformation matrix combines rotation and translation. For two adjacent links i-1 and i, the transformation matrix It is expressed as: Step S1.2: By analyzing the structure of the heterogeneous dual five-axis machine tool, the kinematic chain transformation relationship between the milling side and the support side of the machine tool is obtained; by multiplying the transformation matrices in sequence, the total transformation matrix from the support side to the milling side coordinate system is obtained.

4. The machine tool multi-body dynamics modeling method for heterogeneous dual five-axis machine tools according to claim 1 is characterized in that: The step S2 comprises: Step S2.1: Establish a three-dimensional model of the heterogeneous dual five-axis machine tool, and obtain the mass m of each component based on the established three-dimensional model i ; Step S2.2: According to the partition variation method based on Nitsche's principle, the machine tool components need to be decomposed into N subdomains before solving the dynamic model; then the energy functional of the machine tool is Among them, T i is the kinetic energy of subdomain i, U i is the strain potential energy of subdomain i, W i is the work done by the external force on subdomain i, Π f is the interface potential energy on the boundary of adjacent subdomains; Γ represents the interface of adjacent subdomains, t1 and t2 represent the start and end time of integration; Based on Kirchhoff thin plate theory, the kinetic energy of subdomain i is Among them, u p 、v p and w p is the displacement of point p(x, y, z) in subdomain i in the XYZ direction, and ρ is the material density of the machine tool component; The strain energy of subdomain i is expressed as: Among them, N n and M n (n = x, y, xy) represent the generalized internal forces and internal moments of machine tool components respectively; they are based on the component stress components σ n (n=x,y,xy) is expressed as: The interface potential energy Π on the boundary of adjacent subdomains f It is expressed as: P f =P λ -P κ 6) Among them, λ and Π κ are the partition interface potential energy introduced by the partition generalized variation and penalty function terms respectively; Π λ and Π κ The calculation method of is related to the division direction of the adjacent subdomain interface. When the subdomain interface is divided along the normal direction of the X direction, Π λ and Π κ The calculation method is expressed as Among them, Q xz is the equivalent generalized shear force, Δ is the generalized displacement coordination equation of the adjacent subdomain boundaries; these parameters are calculated as follows, κ is the weight parameter on the partition interface, and the value is selected to be greater than the elastic modulus of the material; Δ u =u m -u m+1 ,Δ v =v m -v m+1 5. The machine tool multi-body dynamics modeling method for heterogeneous dual five-axis machine tools according to claim 1 is characterized in that: The step S3 comprises: Step S3.1: Assume that the number of balls in contact in each row of grooves in the guide rail system is the same, which is n; then the force state between the balls on the upper and lower sides of the guide rail is the same; The contact pressure between the single ball and the groove is P U Indicated below, the contact pressure between a single ball and the groove is P L Indicates; Z1 and Z2 are the coordinates of the center of gravity of the slider and the track respectively, P is the normal load on the guide rail system, and β is the contact angle; Step S3.2: If each ball is always under pressure under the external load, then P+2nP L sinβ=2nP U sinβ10) Under the action of external load P, the relative deformation of the guide rail system is represented by ΔZ, which is expressed as ΔZ=Z1-Z2 11) If the functional relationship between the external load and the relative deformation ΔZ is established, the analytical expression of the normal contact stiffness of the guide rail slider can be clearly expressed; The normal contact force and deformation of a single ball satisfy In the formula, α U , α L The contact pressure P of a single ball is U , P L The elastic deformation caused by the action of k h The relationship between the load F and the deformation α of a single ball is called the quasi-stiffness coefficient. Since the force state between the upper and lower balls is the same, the corresponding deformations are also the same. In addition, during the assembly process of the guide rail system, a preload is usually applied. Assuming that the normal pressure generated on the contact surface of a single ball under the action of the preload is P0, and the initial deformation caused by the preload is α0, the two also satisfy Assuming that the initial deformation of all upper and lower balls is the same, which is α0, then under the action of load P, according to the deformation coordination condition, we can get (a U -α0)sinβ=(α0-α L )sinβ=ΔZ 14) From the above formula we can get Establish the pressure P on the ball at the upper end of the guide rail U The functional relationship between the external load P and the preload force P0 is expressed as P U =f(P,P0)16) From the above formula we can get The above formula establishes an implicit functional relationship between the external load P and the relative deformation ΔZ. If the derivative of ΔZ is further calculated, the expression of the normal contact stiffness of the slider is obtained as follows:

6. The machine tool multi-body dynamics modeling method for heterogeneous dual five-axis machine tools according to claim 4 is characterized in that: The step S4 comprises: substituting the normal contact stiffness of the slider into the dynamic model of the joint of the machine tool, solving the partition interface elastic potential energy based on the partition variation method of the Nitsche principle; taking the first-order variation of the energy functional Π, and obtaining the discrete dynamic equation of the machine tool according to the stationary value condition of δΠ=0: Where q is the set of displacement vectors of all machine tool component subdomains; M and K are the assembly matrices of the generalized mass matrix and stiffness matrix of the laminate subdomain, respectively; K λ and K κ is the assembly matrix of the partition interface matrix; F is the generalized external force matrix; by solving the dynamic equation, the dynamic response of the heterogeneous dual five-axis machine tool under the action of the generalized external force F is obtained.

7. A machine tool multi-body dynamics modeling system for heterogeneous dual five-axis machine tools, characterized in that: include: Module M1: Construct the kinematic chain of the heterogeneous dual five-axis machine tool according to its structural characteristics and motion state; Module M2: 3D modeling of heterogeneous dual five-axis machine tools, and extraction of the mass of each component through the model; based on the partition variation method based on the Nitsche principle of flexible multi-body dynamics, the expressions of the machine tool kinetic energy and potential energy considering the flexibility of the components are obtained; Module M3: Based on Hertz contact modeling and contact stiffness theory, a dynamic model of the joints of the components of the heterogeneous dual five-axis machine tool is established to obtain the connection characteristic parameters between the components of the machine tool; Module M4: Based on the kinetic energy and potential energy expressions of the machine tool system and the dynamic model of the connection characteristics between the components, a multi-body dynamic model of the machine tool is established and the model is solved.

8. The machine tool multi-body dynamics modeling system for heterogeneous dual five-axis machine tools according to claim 7, characterized in that: The kinematic chain in the module M1 includes: an open-loop kinematic chain on the milling side from the tool coordinate system on the milling side to the machine tool base coordinate system, an open-loop kinematic chain on the support side from the end coordinate system on the support side to the machine tool base, and a closed-loop mirror kinematic chain from the tool side to the support side; The module M1 also includes: establishing a parameter model using the DH standard method and describing the overall kinematic characteristics of the heterogeneous dual five-axis machine tool through homogeneous coordinate transformation; Module M1.1: Use the standard DH parameter method to describe the coordinate system transformation between the substructures of the heterogeneous dual five-axis machine tool. i , α i d i and θ i Four parameters; Among them, a i is the link length, which is defined as the distance between two adjacent joint axes in the current link coordinate system, that is, the distance from the previous joint axis to the current joint axis along the X axis of the previous link; α i The joint torsion angle is defined as the rotation angle from the previous joint axis Z axis to the current joint axis Z axis around the current link's X axis. It is the angle required to rotate the previous link coordinate system around the current link's X axis to be parallel to the current link coordinate system's Z axis. d i is the link offset, which is defined as the distance along the Z axis of the current joint axis in the current link coordinate system; θ i is the joint angle, which is defined as the angle of rotation around the current joint axis Z axis in the current link coordinate system; According to the standard DH parameter method, the coordinate transformation relationship between two adjacent links is represented by a 4×4 homogeneous transformation matrix; this transformation matrix converts one coordinate system to the next coordinate system to represent the geometric relationship between the two links; the homogeneous transformation matrix combines rotation and translation. For two adjacent links i-1 and i, the transformation matrix It is expressed as: Module M1.2: By analyzing the structure of the heterogeneous dual five-axis machine tool, the kinematic chain transformation relationship between the milling side and the support side of the machine tool is obtained; by multiplying the transformation matrices in sequence, the total transformation matrix from the support side to the milling side coordinate system is obtained.

9. The machine tool multi-body dynamics modeling system for heterogeneous dual five-axis machine tools according to claim 7, characterized in that: The module M2 comprises: Module M2.1: Establish a 3D model of a heterogeneous dual five-axis machine tool and obtain the mass m of each component based on the established 3D model i ; Module M2.2: According to the partition variation method based on Nitsche's principle, the machine tool components need to be decomposed into N subdomains before solving the dynamic model; then the energy functional of the machine tool is Among them, T i is the kinetic energy of subdomain i, U i is the strain potential energy of subdomain i, W i is the work done by the external force on subdomain i, Π f is the interface potential energy on the boundary of adjacent subdomains; Γ represents the interface of adjacent subdomains, t1 and t2 represent the start and end time of integration; Based on Kirchhoff thin plate theory, the kinetic energy of subdomain i is Among them, u p 、v p and w p is the displacement of point p(x, y, z) in subdomain i in the XYZ direction, and ρ is the material density of the machine tool component; The strain energy of subdomain i is expressed as: Among them, N n and M n (n = x, y, xy) represent the generalized internal forces and internal moments of machine tool components respectively; they are based on the component stress components σ n (n=x,y,xy) is expressed as: The interface potential energy Π on the boundary of adjacent subdomains f It is expressed as: P f =P λ -P κ 6) Among them, λ and Π κ are the partition interface potential energy introduced by the partition generalized variation and penalty function terms respectively; Π λ and Π κ The calculation method of is related to the division direction of the adjacent subdomain interface. When the subdomain interface is divided along the normal direction of the X direction, Π λ and Π κ The calculation method is expressed as Among them, Q xz is the equivalent generalized shear force, Δ is the generalized displacement coordination equation of the adjacent subdomain boundaries; these parameters are calculated as follows, κ is the weight parameter on the partition interface, and the value is selected to be greater than the elastic modulus of the material; Δ u =u m -u m+1 ,Δ v =v m -v m+1 10. The machine tool multi-body dynamics modeling system for heterogeneous dual five-axis machine tools according to claim 7, characterized in that: The module M3 comprises: Module M3.1: Assume that the number of balls in contact in each row of grooves in the guide rail system is the same, which is n; then the force state between the balls on the upper and lower sides of the guide rail is the same; The contact pressure between the single ball and the groove is P U Indicated below, the contact pressure between a single ball and the groove is P L Indicates; Z1 and Z2 are the coordinates of the center of gravity of the slider and the track respectively, P is the normal load on the guide rail system, and β is the contact angle; Module M3.2: If the balls are always under pressure under the external load, then P+2nP L sinβ=2nP U sinβ10) Under the action of external load P, the relative deformation of the guide rail system is represented by ΔZ, which is expressed as ΔZ=Z1-Z2 11) If the functional relationship between the external load and the relative deformation ΔZ is established, the analytical expression of the normal contact stiffness of the guide rail slider can be clearly expressed; The normal contact force and deformation of a single ball satisfy In the formula, α U , α L The contact pressure P of a single ball is U , P L The elastic deformation caused by the action of k h The relationship between the load F and the deformation α of a single ball is called the quasi-stiffness coefficient. Since the force state between the upper and lower balls is the same, the corresponding deformations are also the same. In addition, during the assembly process of the guide rail system, a preload is usually applied. Assuming that the normal pressure generated on the contact surface of a single ball under the action of the preload is P0, and the initial deformation caused by the preload is α0, the two also satisfy Assuming that the initial deformation of all upper and lower balls is the same, which is α0, then under the action of load P, according to the deformation coordination condition, we can get (a U -α0)sinβ=(α0-α L )sinβ=ΔZ 14) From the above formula we can get Establish the pressure P on the ball at the upper end of the guide rail U The functional relationship between the external load P and the preload force P0 is expressed as P U =f(P,P0)16) From the above formula we can get The above formula establishes an implicit functional relationship between the external load P and the relative deformation ΔZ. If the derivative of ΔZ is further calculated, the expression of the normal contact stiffness of the slider is obtained as follows: The module M4 includes: substituting the normal contact stiffness of the slider into the dynamic model of the joint of the machine tool to solve the partition interface elastic potential energy based on the partition variation method of the Nitsche principle; taking the first-order variation of the energy functional Π, and obtaining the discrete dynamic equation of the machine tool according to the stationary value condition of δΠ=0: Where q is the set of displacement vectors of all machine tool component subdomains; M and K are the assembly matrices of the generalized mass matrix and stiffness matrix of the laminate subdomain, respectively; K λ and K κ is the assembly matrix of the partition interface matrix; F is the generalized external force matrix; by solving the dynamic equation, the dynamic response of the heterogeneous dual five-axis machine tool under the action of the generalized external force F is obtained.

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