A double-mode self-checking solution method for equivalent parameters of machine tool joint considering macro-micro topography

Abstract

This invention discloses a dual-mode self-verification solution method for equivalent parameters of machine tool joints considering macro- and micro-morphological features, belonging to the field of mechanical equipment structural dynamics modeling and parameter identification. First, the macro-geometric features of the joint surface are extracted and an initial gap function is constructed based on a given flatness error. Then, a global contact load positive prediction model is constructed. Next, based on the definition of tangential contact stiffness, global discrete accumulation is performed to obtain the total normal contact stiffness of the joint, and it is converted into the equivalent Young's modulus and loss factor of a virtual material layer according to the principle of equivalent volumetric strain energy. This invention solves the problem that traditional analytical methods are prone to mathematical singularities and collapse under local contact conditions, achieving high-fidelity and robust extraction of joint dynamic parameters under global conditions, providing solid algorithmic support for predicting the dynamic performance of machine tools and optimizing vibration resistance design.

Description

Technical Field

[0001] This invention belongs to the field of mechanical equipment structural dynamics modeling and parameter identification, and specifically relates to a dual-mode self-verification solution method for equivalent parameters of machine tool joints that considers macroscopic and microscopic morphology. Background Technology

[0002] In the reliability and dynamics engineering design of complex machine tools or mechanical equipment, bolted joints are key weak points affecting the overall dynamic performance of the machine (such as natural frequency, contact stiffness, and damping dissipation characteristics). To accurately simulate these joints in finite element analysis software, the "virtual material layer" method is widely used in engineering for equivalent modeling. Its core idea is to obtain the normal and tangential contact stiffness of the joint surface through theoretical derivation, and then, based on the principle of equivalent volumetric strain energy, to inversely calculate the equivalent Young's modulus and equivalent loss factor of the virtual material layer, thus providing underlying parameter support for the vibration-resistant optimization design of the entire machine tool.

[0003] However, traditional analytical methods for solving the contact stiffness of joints (such as the classic Yoshimura integral method) mainly rely on the "full contact assumption." This assumes that the nominal assembly pressure is large enough to completely flatten all macroscopic features of the joint surface (such as flatness errors or machining waviness). However, in actual machine tool service or assembly processes, macroscopic warping caused by the release of residual stress in large structural components, or periodic waviness left by milling, often inevitably leads to macroscopic geometric deviations at the joint surface. When the nominal assembly pressure is low or the morphological error is large, only some peaks of the joint surface make contact, while the troughs remain suspended, forming a "partial contact" condition. In this case, the traditional analytical calculus method suffers from the destruction of the integral boundary conditions, resulting in negative microscopic deformations within the mathematical model. This leads to distortions in the complex domain (imaginary numbers) or mathematical singularities, causing the solution formula to completely collapse and become ineffective, failing to provide any effective stiffness parameters for industrial software.

[0004] Furthermore, in traditional analytical methods, when deriving double integrals, the nonlinear contact exponent representing microscopic roughness peaks is often forced to be rounded down (e.g., setting m=2) to ensure the existence of physically meaningful closed-form algebraic solutions. This sacrifices the physical fidelity of the real identification parameters obtained through experiments or digital twin technology. Therefore, researching a robust solution method that can completely overcome the limitations of the "full contact assumption," adaptively identify and eliminate local suspended regions, and is compatible with real non-integer microscopic contact parameters, and introducing a theoretical analytical model for closed-loop self-verification and iterative improvement of discrete mesh accuracy to meet the required accuracy, has significant theoretical and engineering value for achieving high-fidelity extraction of machine tool dynamic parameters under complex working conditions. Summary of the Invention

[0005] The purpose of this invention is to overcome the aforementioned deficiencies of existing technologies and propose a dual-mode self-verification solution method for the equivalent parameters of machine tool joints considering both macroscopic and microscopic morphology. This method aims to solve the problem of singular collapse easily occurring in traditional analytical methods under local contact conditions. By integrating a high-resolution discrete non-negative truncation algorithm with a closed-loop analytical verification benchmark, it achieves high-fidelity, robust extraction of dynamic parameters and adaptive precision control under complex working conditions. Finally, it solves for the total normal contact stiffness of the joint and the equivalent parameters of the virtual material layer, with flatness error and nominal contact pressure as independent variables.

[0006] Step 1: Morphological Discretization and Micro-contact Constitutive Model Construction. First, the geometric morphological features of the interface are extracted and the initial gap function is determined, followed by high-resolution mesh discretization. Then, based on the deformation compatibility equation and the non-negative truncation mechanism, a single-mesh micro-contact constitutive model that can automatically filter out suspended states is constructed.

[0007] Step 1.1: Shape Feature Extraction and Gap Matrix Construction. Obtain the macroscopic dimensional parameters of the machine tool mating surface, extract its surface morphology geometric features to construct a normalized shape function, and determine the initial gap function of the mating surface based on the given flatness error. Discretize the continuous mating surface into a high-resolution two-dimensional mesh matrix, and extract the initial gap value for each mesh element;

[0008] Step 1.2: Construction of Microscopic Contact Constitutive Model Based on Non-negative Truncation Mechanism. Assuming a macroscopic rigid body approximation, the microscopic deformation of the mesh element is calculated based on the deformation compatibility equation for local microscopic deformation. A non-negative truncation mechanism is introduced in this process, i.e., a maximum value function is used to limit the deformation: when the assumed macroscopic rigid body approximation is less than the initial gap value of the mesh element, the local microscopic deformation of the mesh element is forcibly determined to be zero. Then, based on the power-law contact constitutive relation, a microscopic contact constitutive model of the local contact pressure and local microscopic deformation of a single mesh element is constructed, thereby automatically identifying and eliminating the influence of mesh elements that have not experienced actual contact in locally suspended states.

[0009] Step 2: Forward prediction of macroscopic state and numerical robust root-finding solution. A forward prediction model with macroscopic rigid body approximation quantities as variables is constructed, and a nonlinear numerical root-finding algorithm is used to intelligently iteratively match the set target assembly load to obtain the true macroscopic rigid body approximation quantities.

[0010] Step 2.1: Construction of the global contact load forward prediction model. The contact load is obtained by calculating the local contact pressure of all grid elements in Step 1 on the corresponding grid area, and then discretized and accumulated over the entire domain to obtain the predicted total contact load of the joint;

[0011] Step 2.2: Solving for the true macroscopic rigid body approximation based on nonlinear root-finding. The product of the nominal contact pressure and the nominal contact area set at the actual machine tool joint is used as the target total load. A nonlinear numerical root-finding algorithm is used to intelligently iteratively try to find the macroscopic rigid body approximation until the predicted total contact load matches the target total load, thereby solving for the true macroscopic rigid body approximation of the joint under the current working condition.

[0012] Step 3: Global transformation of equivalent parameters. Based on the obtained real macroscopic rigid body approximation quantities, the local tangent stiffness is calculated and accumulated globally, thus being equivalent to the virtual material parameters required for finite element analysis.

[0013] Step 3.1: Discrete and accumulate tangential normal contact stiffness. Substitute the actual macroscopic rigid body approximation obtained in Step 2 into the local microscopic deformation of the mesh element, calculate the derivative of the local contact pressure with respect to the local microscopic deformation, and obtain the tangential normal contact stiffness of the mesh element. Discretely accumulate the tangential normal contact stiffness of all mesh elements to obtain the total normal contact stiffness of the joint;

[0014] Step 3.2: Virtual material equivalent parameter conversion. Based on the principle of equivalent volumetric strain energy and the macroscopic dimensions of the interface, the obtained normal total contact stiffness is converted into the equivalent Young's modulus and equivalent loss factor of the virtual material layer.

[0015] Step 4: Construction of the dual-mode self-verification framework and adaptive solution of contact state. An analytical model based on Yoshimura Yoshitaka's integral method is constructed in parallel, which together with the aforementioned numerical solution model constitutes the dual-mode self-verification framework. Based on the contact state determination results, closed-loop self-verification iteration of mesh accuracy is performed or robustly reused.

[0016] Step 4.1: Construction of the analytical verification benchmark model and the dual-mode framework. A parallel analytical solution model for the total normal contact stiffness based on Yoshimura Yoshitaka's integral method is constructed. The numerical solution model constructed in steps 1 to 3 and the analytical solution model are respectively used as the first and second modes, forming a dual-mode self-verification framework. The analytical solution model is used as the theoretical verification benchmark.

[0017] Step 4.2: Contact State Determination and Adaptive Solution. The contact state of the joint is determined based on the solved real macroscopic rigid body approximation. When a full contact state is determined, the total normal contact stiffness output in Step 3 is cross-compared with the calculation results of the analytical reference model. If the relative error exceeds a preset threshold, the resolution of the two-dimensional mesh matrix in Step 1 is automatically increased, and iterative calculation is re-executed until the accuracy requirements are met. When a local contact state is determined, local contact features are robustly extracted using a non-negative truncation mechanism, and the mesh matrix resolution that meets the accuracy requirements after iterating with the full contact state parameters is automatically used for re-solution. Finally, the total normal contact stiffness of the joint under the current working condition, as well as the equivalent Young's modulus and equivalent loss factor of the virtual material layer, are output.

[0018] The beneficial effects of this invention are as follows:

[0019] (1) Strong adaptability and robustness under various working conditions: Based on mesh discretization and non-negative truncation mechanism, this method can automatically identify and remove mesh elements that have not made real contact in local suspended states. It completely breaks the mathematical constraint that traditional calculus must satisfy "full contact", effectively avoiding algorithm collapse and mathematical singularity distortion problems under low assembly pressure.

[0020] (2) High fidelity: It breaks through the limitation that the nonlinear contact index must be rounded up in the traditional analytical derivation, and can be perfectly compatible with any experimentally identified real non-integer contact parameters, which greatly improves the physical fidelity of the virtual material equivalent parameters in the whole domain working conditions.

[0021] (3) Innovative dual-mode closed-loop control: It is the first to transform the traditional analytical model into an "accuracy verification scale". The numerical root-finding results are automatically compared with the analytical benchmark in the full contact domain. If the relative error exceeds the tolerance threshold, the grid resolution is automatically increased. This mechanism gives the solution algorithm a very high self-correction capability, ensuring the absolute reliability of the engineering calculation results. Attached Figure Description

[0022] Figure 1 This is a technical framework diagram.

[0023] Figure 2 This is a schematic diagram of the mesh matrix of the bonding surface.

[0024] Figure 3 This is a geometric feature diagram of the metal surface after grinding.

[0025] Figure 4 This is a surface comparison diagram of the total contact stiffness of the joint in the normal direction under the two methods. Detailed Implementation

[0026] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings:

[0027] This invention aims to solve for the normal total contact stiffness of the joint and the equivalent parameters of the virtual material layer, with flatness error and nominal contact pressure as independent variables. This invention constructs a systematic technical framework of "morphological discretization and truncation constitutive model—macroscopic state prediction and root-finding—equivalent parameter conversion—dual-mode accuracy self-verification," such as... Figure 1 As shown, this method achieves high-fidelity and robust solution of dynamic parameters of machine tool joints under arbitrary partial or full contact conditions. First, the morphological features of the joint surface are extracted and discretized into a high-resolution mesh. A non-negative truncation mechanism is introduced to construct a single-mesh micro-contact constitutive model to automatically filter out local suspended regions. Next, a global contact load positive prediction model is constructed, and a nonlinear root-finding algorithm is used to iteratively match the target assembly load to obtain the true macroscopic rigid body approximation. Then, the local tangent stiffness is calculated and discretized and accumulated over the entire domain, converting it into the equivalent Young's modulus and equivalent loss factor of a virtual material layer based on the equivalence principle. Finally, a parallel analytical solution model is constructed as a theoretical verification benchmark, forming a dual-mode self-verification framework together with the aforementioned numerical model. The contact state is determined based on the true macroscopic rigid body approximation. Under full contact conditions, closed-loop self-verification and adaptive adjustment of the mesh resolution are performed for iterative solution. Under partial contact conditions, robust solution is achieved by relying on the non-negative truncation mechanism and using the mesh resolution that meets the accuracy requirements under full contact conditions.

[0028] The specific implementation steps and mathematical model are detailed below:

[0029] Step 1: Morphological discretization and microscopic contact constitutive construction.

[0030] First, the geometric features of the bonding surface are extracted and the initial gap function is determined, followed by high-resolution mesh discretization. Then, based on the deformation compatibility equation and the non-negative truncation mechanism, a single-mesh micro-contact constitutive model that can automatically filter out suspended states is constructed.

[0031] Step 1.1: Shape feature extraction and gap matrix construction.

[0032] Given a set of known nominal contact pressures Flatness error Initial gap function of the mating surface It can be described as flatness error The function.

[0033]

[0034] in This is a normalized shape function constructed by extracting the geometric features of the surface morphology of the bonding surface.

[0035] Discretize the continuous bonding surface into a high-resolution mesh matrix, such as Figure 2 As shown, Figure 2The length of the inter-face is , width is The length of the grid cell is , width is .

[0036] Based on the initial gap function of the mating surface The initial gap of each grid cell is represented by the initial gap at the center point of each grid cell, that is, the initial gap of the grid cell starting from the origin of the coordinate system. Liede Initial gap of row grid cells for:

[0037]

[0038] Step 1.2: Construction of microscopic contact constitutive model based on nonnegative truncation mechanism.

[0039] Assuming the nominal contact pressure is Flatness error is At that time, the macroscopic rigid body approximation is Based on the deformation compatibility equation of local micro-deformation, a maximum value function is introduced as a non-negative truncation mechanism to obtain the true local micro-deformation of the mesh element. for:

[0040]

[0041] The physical meaning of this mathematical operation lies in: when the assumed macroscopic rigid body approaches a certain value... Smaller than the initial gap value of the mesh cell When this condition is met, it indicates that the mesh element is in a locally suspended state, and its local micro-deformation will be forcibly determined and limited to zero by the above formula.

[0042] Based on the power-law contact principle of micro-roughness peaks, local contact pressure of mesh elements is constructed. Local micro-deformation of mesh elements Microscopic contact constitutive model:

[0043]

[0044] in, and This is the contact constant related to surface roughness. Through this step, the system automatically identifies and eliminates the influence of mesh elements that are not in actual contact under local suspended states on the overall force at the mathematical level, thus avoiding singular distortions in subsequent calculations.

[0045] Step 2: Positive prediction of macroscopic state and numerical robust root-finding solution.

[0046] A positive prediction model with macroscopic rigid body approximation as the variable is constructed, and a nonlinear numerical root-finding algorithm is combined to intelligently iteratively match the set target assembly load to obtain the true macroscopic rigid body approximation.

[0047] Step 2.1: Construction of the global contact load positive prediction model.

[0048] Based on the local contact pressure of the mesh elements obtained in step 1.2 The contact load borne by this mesh element is:

[0049]

[0050] By discretizing and summing the contact loads of all mesh elements on the joint surface in step 1, the assumed macroscopic rigid body approximation of the joint system can be obtained. The predicted total contact load is as follows:

[0051]

[0052] Step 2.2: Solving for the approximate quantities of real macroscopic rigid bodies based on nonlinear root-finding.

[0053] Using the nominal contact pressure set in step 1.1 With nominal contact area The product of these is taken as the physical target total load. Construct the macroscopic static equilibrium equations and determine whether the equations are satisfied:

[0054]

[0055] If the equation holds, it means that the assumed macroscopic rigid body approximation is true. If it is accurate, then it is inaccurate; otherwise, it is inaccurate. In this case, a nonlinear numerical root-finding algorithm (such as the bisection method, secant method, etc.) is used to intelligently iteratively try to approximate the macroscopic rigid body's approximate value within a physically reasonable range, and then continue to provide... , , ...by continuously reducing the residual between the predicted total contact load and the target total load until the macroscopic rigid body approximation that satisfies the equation is found, the true macroscopic rigid body approximation of the joint under the current working condition is robustly solved, denoted as... .

[0056] Step 3: Global conversion of equivalent parameters.

[0057] Based on the obtained real macroscopic rigid body approximation quantities, the local tangent stiffness is calculated and accumulated globally, thus becoming equivalent to the virtual material parameters required for finite element analysis.

[0058] Step 3.1: Discrete accumulation of tangential normal contact stiffness.

[0059] According to the definition of contact mechanics, the tangential normal contact stiffness of a mesh element... The effect of the partial derivative of local contact pressure on local micro-deformation on the mesh area is as follows:

[0060]

[0061] The true macroscopic rigid body approximation obtained in step 2 Substituting the local micro-deformation of the mesh elements and discretizing and summing the tangential normal contact stiffness of all mesh elements on the joint surface, the total normal contact stiffness of the joint is obtained:

[0062]

[0063] Step 3.2: Virtual material equivalent parameter conversion.

[0064] Set the thickness of the virtual material layer to .

[0065] The length of the virtual material layer is , width is ,area for:

[0066]

[0067] Axial stiffness of virtual material layer for:

[0068]

[0069] in, It represents the equivalent Young's modulus of the virtual material layer.

[0070] According to the principle of equivalent volumetric strain energy, we get:

[0071]

[0072] The equivalent Young's modulus of the virtual material layer is obtained by inverse calculation. for:

[0073]

[0074] The stiffness and damping of the joint exhibit a strong nonlinear correlation. A power-law correlation model is used to obtain the equivalent loss factor of the virtual material layer. for:

[0075]

[0076] in, and is the empirical constant for damping at the joint.

[0077] Step 4: Construction of the dual-mode self-verification framework and adaptive solution of contact state.

[0078] A parallel analytical model based on Yoshimura Yoshitaka's integral method is constructed, which together with the aforementioned numerical solution model constitutes a dual-mode self-verification framework. Based on the contact state determination results, closed-loop self-verification iteration of mesh accuracy is performed or robustly continued.

[0079] Step 4.1: Analyze and verify the benchmark model and construct the dual-mode framework.

[0080] A parallel analytical solution model for the total normal contact stiffness based on Yoshimura Yoshitaka's integral method is constructed as a theoretical verification benchmark:

[0081] Initial gap function of the mating surface It can be described as flatness error The function.

[0082]

[0083] in This is the normalized shape function.

[0084] The contact state of the mating surfaces depends on the macroscopic rigid body approximation. With initial gap The relationship between the local micro-deformation and the deformation compatibility equation can be used to obtain the local micro-deformation amount. for:

[0085]

[0086] Based on the power law formula, local contact pressure With local micro deformation It follows a power-law relationship:

[0087]

[0088] in, and This is the contact constant related to surface roughness. It represents the local micro-deformation. Substituting, we get:

[0089]

[0090] By definition, normal contact stiffness per unit area Local contact pressure For local micro deformation The derivative:

[0091]

[0092] Local micro deformation Substituting, we get:

[0093]

[0094] Yoshimura Yoshitaka's integral method is based on the entire nominal contact area. Integrate to obtain macroscopic properties.

[0095] Integral normal contact stiffness per unit area The total normal contact stiffness of the joint is obtained. .

[0096]

[0097] in, The area where actual contact occurred.

[0098] Integral local contact pressure Get contact load .

[0099]

[0100] Nominal contact pressure The calculation formula is:

[0101]

[0102] For the parametric equation system:

[0103]

[0104] The objective function is obtained by solving the nonlinear mapping:

[0105]

[0106] Step 4.2: Contact state determination and adaptive solution.

[0107] The true macroscopic rigid body approximation quantity obtained from step 2 Determine the contact state of the joint:

[0108] ①When When the system determines that true contact is achieved at any point in the joint, it enters a full contact state. At this time, the system automatically triggers the analytical verification benchmark model, cross-compares the total normal contact stiffness output in step 3 with the calculation results of the analytical benchmark model. If the relative error between the two exceeds the preset tolerance threshold, the system automatically feeds back to step 1, increases the resolution of the two-dimensional mesh matrix (reduces l and w), and re-executes the iterative calculation until the set calculation accuracy requirements are met.

[0109] ②When At this point, the joint is determined to be in a state of local contact. The analytical verification benchmark model fails due to the violation of integral boundary conditions. The system robustly extracts the local contact features based on the non-negative truncation mechanism and automatically resolves the problem using the grid matrix resolution that meets the accuracy requirements after iterating the parameters of the full contact state.

[0110] Finally, the system outputs the total normal contact stiffness of the joint under the current working condition, as well as the equivalent Young's modulus and equivalent loss factor of the virtual material layer.

[0111] Implementation Case:

[0112] The basic physical and geometric parameters of the joint are shown in Table 1:

[0113] Table 1. Basic physical and geometric parameters of the joint.

[0114]

[0115] After grinding, the metal surface will form a large number of dense, unidirectional parallel textures, such as Figure 3 As shown. Taking the joint formed on two metal surfaces after grinding as an example, a cosine function with periodic characteristics is used to characterize the microtexture. When the texture directions of the two joint surfaces are the same, the normalized shape function of the joint is constructed as follows:

[0116]

[0117] The initial resolution of the mesh matrix was set to 100×100, totaling 10,000 mesh cells. The tolerance threshold was set to 2‱. To comprehensively explore the performance of the method under different assembly conditions, two typical conditions—high assembly pressure (full contact) and low assembly pressure (partial contact)—were selected for verification.

[0118] To construct a high assembly pressure, low error operating condition, the nominal contact pressure is set. Flatness error The macroscopic rigid body approximation quantity is obtained using the numerically robust root-finding algorithm of this invention. Subsequently, the system determines that the current macroscopic rigid body approximation exceeds the given flatness error, and the trough at the joint is completely flattened, entering a full contact state. At this point, the system automatically triggers the analytical datum model for self-verification. The calculated numerical solution yields the total normal contact stiffness of the joint. The total normal contact stiffness of the joint obtained by analytical solution The relative error of the total normal contact stiffness of the joint obtained by the two methods was 10.716‱, which failed the self-verification. The system automatically increased the resolution of the two-dimensional mesh matrix and re-executed the iterative calculation. When the resolution of the two-dimensional mesh matrix was increased to 600×600, with a total of 360,000 mesh elements, the numerical solution obtained the total normal contact stiffness of the joint. The total normal contact stiffness of the joint obtained by analytical solution The relative error of the total contact stiffness in the normal direction of the joint obtained by the two methods was 1.8156‱, and the self-verification passed successfully, verifying that the iterated 600×600 mesh resolution fully meets the accuracy requirements for high-fidelity engineering calculations. Finally, the equivalent Young's modulus of the virtual material layer was obtained. The equivalent loss factor of the virtual material layer .

[0119] To construct a low assembly pressure, high error operating condition, the nominal contact pressure is set. Flatness error Under this operating condition, the nominal contact pressure of 5 MPa is insufficient to flatten a flatness error of 10 μm. If the traditional analytical formula is forcibly applied for derivation, problems will arise due to the presence of variations within the integration domain. When the base of a calculus formula is negative, it produces complex solutions, causing the mathematical model to completely suffer from singular distortion and collapse, making it impossible to output effective stiffness. However, the numerical solution method of this invention, relying on a non-negative truncation mechanism, automatically identifies and eliminates trough-hanging meshes, robustly calculating the true macroscopic rigid body approximation. The system determines that the joint is in a partial contact state. At this point, it automatically recalculates using the 600×600 grid resolution obtained after iterating the parameters for the full contact state to meet the accuracy requirements. The algorithm ultimately successfully and stably outputs the total normal contact stiffness of the joint under this complex working condition. At this point, the total normal contact stiffness of the joint obtained by the comparative analytical method is... This demonstrates a significant improvement in accuracy between numerical methods and traditional analytical methods under local contact conditions. Finally, the equivalent Young's modulus of the virtual material layer is obtained. The equivalent loss factor of the virtual material layer .

[0120] To further demonstrate the robustness of the method of this invention, under wide-area operating conditions (with a nominal contact pressure of...), Flatness error is Given 1600 pairs of data within a given range, a full-domain scan is performed, and a surface comparison diagram of the total contact stiffness of the joint normal direction under the two methods is plotted, such as... Figure 4 As shown. By Figure 4It is evident that traditional analytical methods (grid lines) suffer severe distortion in the local contact domain, completely deviating from physical reality. In contrast, the numerically robust solution method (colored surface) proposed in this invention not only perfectly coincides with the theoretical analytical benchmark in the entire contact domain (verifying extremely high fidelity), but also maintains excellent numerical stability and smoothness in the local contact domain. This method completely solves the problem of algorithm collapse caused by local contact in traditional joint dynamic simulation, providing reliable underlying parameter support for accurate prediction of the overall dynamic performance of machine tools.

Claims

1. A dual-mode self-verification solution method for equivalent parameters of machine tool joints considering macro- and micro-morphological features, characterized in that, This method is used to solve for the total normal contact stiffness of the joint and the equivalent parameters of the virtual material layer, with flatness error and nominal contact pressure as independent variables. The solution method includes: Step 1: Obtain the macroscopic dimensional parameters of the machine tool mating surface, extract its surface morphology geometric features, and construct a normalized shape function. Combine this with the given flatness error to determine the initial gap function of the mating surface. Discretize the continuous mating surface into a high-resolution two-dimensional mesh matrix and extract the initial gap value of each mesh element. Assuming the macroscopic rigid body approximation, based on the deformation compatibility equation of local microscopic deformation, introduce a non-negative truncation mechanism to obtain the local microscopic deformation of the mesh element. Then, based on the power-law contact constitutive relation, construct a microscopic contact constitutive model of the local contact pressure and local microscopic deformation of a single mesh element. Step 2: Construct a global nominal contact pressure prediction model with the macroscopic rigid body approximation as the independent variable; calculate the contact load on the corresponding grid area of ​​all grid elements in Step 1 and discretize and accumulate it to obtain the total contact load of the joint; take the product of the nominal contact pressure and the nominal contact area set in the actual machine tool joint as the target total load, and use a nonlinear numerical root-finding algorithm to intelligently iterate and try to find the macroscopic rigid body approximation until the predicted total contact load matches the target total load, thereby solving for the real macroscopic rigid body approximation of the joint under the current working condition; Step 3: Substitute the actual macroscopic rigid body approximation obtained in Step 2 into the local microscopic deformation of the mesh element, calculate the derivative of the local contact pressure with respect to the local microscopic deformation to obtain the tangential normal contact stiffness of the mesh element, and discretize and accumulate all mesh elements to obtain the total normal contact stiffness of the joint; according to the principle of equivalent volumetric strain energy, convert it into the equivalent Young's modulus and equivalent loss factor of the virtual material layer; Step 4: Construct a parallel analytical solution model for the total normal contact stiffness based on Yoshimura Yoshitaka's integral method. The numerical solution model constructed in steps 1 to 3 and the analytical solution model are used as the first and second modes, respectively, forming a dual-mode self-verification framework. The analytical solution model is used as the theoretical verification benchmark. The contact state of the joint is determined based on the solved real macroscopic rigid body approximation. When it is determined to be a full contact state, the total normal contact stiffness output in step 3 is cross-compared with the calculation results of the analytical benchmark model. If the relative error exceeds the preset threshold, the resolution of the two-dimensional mesh matrix in step 1 is automatically increased and the iterative calculation is re-executed until the accuracy requirements are met. When it is determined to be a local contact state, the local contact features are robustly extracted based on the non-negative truncation mechanism, and the mesh matrix resolution that meets the accuracy requirements after iterating the parameters of the full contact state is automatically used for the solution. Finally, the total normal contact stiffness of the joint under the current working condition, as well as the equivalent Young's modulus and equivalent loss factor of the virtual material layer, are output.

2. The dual-mode self-verification solution method for equivalent parameters of machine tool joints considering macro- and micro-morphology as described in claim 1, characterized in that, The non-negative truncation mechanism introduced in step 1 specifically uses a maximum value function to limit the local micro-deformation of the mesh element. When the assumed macroscopic rigid body approach value is less than the initial gap value of the mesh element, the local micro-deformation of the mesh element will be forcibly determined to be zero, thereby automatically identifying and eliminating the influence of mesh elements that have not made real contact in the local suspended state on the total contact load and normal total contact stiffness of the joint.

3. The dual-mode self-verification solution method for equivalent parameters of machine tool joints considering macro- and micro-morphology as described in claim 1, characterized in that, The dual-mode self-verification framework constructed in step 4 specifically ensures the robustness and high fidelity of the solution through the following two mechanisms: First, for the full contact state, the analytical solution model is used as the theoretical verification benchmark. By cross-comparing with the numerical solution results and judging the error threshold, the resolution of the two-dimensional grid matrix is ​​driven to iteratively increase, thereby realizing the adaptive closed-loop adjustment of the accuracy of discrete numerical calculation. Second, for the local contact state, when the analytical solution model fails due to the destruction of the integral boundary conditions caused by local dangling, the grid matrix resolution that meets the accuracy requirements obtained by iteration under the full contact state is directly used for the solution. This completely avoids the collapse of mathematical singularity in the traditional analytical method while ensuring the computational accuracy of the robust extraction of equivalent parameters under the local contact condition.

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