Method for calculating normal contact stiffness of mechanical joint surface based on ellipsoid contact and fractal theory

Abstract

The invention discloses a mechanical joint surface normal contact stiffness calculation method based on ellipsoid contact and fractal theories, and belongs to the field of dynamic and static characteristic analysis of numerical control machine tools. Comprising the steps that a real contact micro-convex body is equivalent to contact of an ellipsoid and a rigid plane, and a contact micro-convex body normal rigidity model considering long and short axes of the ellipsoid is established; introducing a domain expansion factor, constructing a mechanical joint surface normal contact stiffness three-dimensional fractal correction model, and calculating a fractal dimension D and a roughness coefficient G; analyzing and extracting a space stress distribution matrix of the joint surface by adopting a refined finite element model; calculating the normal contact stiffness of the mechanical joint surface, and obtaining the inherent frequency in combination with a finite element method; and performing a modal hammering test to verify the accuracy of the calculation method. According to the method, the ellipsoidal hypothesis of the contact micro-convex body is provided, the scale independence and the normal contact mechanical behavior of the surface microstructure are fully considered, and calculation of the normal contact rigidity of the formed mechanical joint surface provides theoretical support for dynamic and static characteristic analysis of a numerical control machine tool.

Description

Technical Field

[0001] The present invention relates to the field of dynamic and static characteristic analysis of numerically controlled machine tools, and in particular to a method for calculating the normal contact stiffness of a mechanical joint surface based on ellipsoidal contact and fractal theory. Background Art

[0002] The dynamic and static characteristics of CNC machine tools have a significant impact on the stability of machining accuracy. How to improve the dynamic and static characteristics of the entire machine has become an important bottleneck in the iterative upgrade of domestic CNC machine tools. Existing research shows that the contact stiffness of the mechanical joint surface accounts for 60-80% of the total stiffness of the entire machine, which is the weak link of CNC machine tools. The contact stiffness of the mechanical joint surface is divided into two categories: normal and tangential according to the load mode. Among them, the joint surfaces on the CNC machine tool guide rail-basic large parts and basic large parts-basic large parts mainly bear normal loads. Therefore, the present invention mainly focuses on the theoretical calculation of the normal contact stiffness of the mechanical joint surface in the field of CNC machine tools. However, current research is mostly based on Hertz contact to equate micro-convex bodies to spheres, which is difficult to meet the high-precision calculation requirements when applied in domestic high-end CNC machine tools.

[0003] The factors that affect the normal contact stiffness of mechanical joints involve multiple dimensions such as preload and surface morphology. Currently, statistical methods, fractal methods, multi-scale methods and virtual material methods have been developed, among which the fractal method is the most widely used, such as patents CN201910242143.6, CN201911301377.X and CN202411328592.X. Considering the difficulty of analyzing theoretical models, patent CN201610985606.4 proposes a numerical solution method combined with finite elements. However, existing finite element analysis methods all use an automatic division method that sets the grid size, which makes it difficult to achieve a synergistic effect between computational efficiency and accuracy. Taking into account the size relationship of real micro-convex bodies and the feasibility of refined finite element model construction methods, a method for calculating the normal contact stiffness of mechanical joints based on ellipsoidal contact and fractal theory is provided, assuming that the micro-convex bodies are ellipsoids. Summary of the Invention

[0004] The goal of this invention is to provide a method for calculating the normal contact stiffness of mechanical joints based on ellipsoidal contact and fractal theory in the field of CNC machine tools, so as to solve the problem that the accuracy and efficiency of numerical solutions are difficult to coordinate and the calculation accuracy requirements of high-end CNC machine tools cannot be met.

[0005] The present invention describes a method for calculating the normal contact stiffness of a mechanical interface based on ellipsoidal contact and fractal theory, which equates the contact convex body to the contact between an ellipsoid and a rigid plane, uses scale-independent three-dimensional fractal theory to establish a normal contact stiffness model for the mechanical interface, and combines it with a refined finite element model for solution.

[0006] The present invention provides a method for calculating the normal contact stiffness of a mechanical interface based on ellipsoidal contact and fractal theory, and the specific steps are as follows:

[0007] S10 equates the real contact asperity to the contact between an ellipsoid and a rigid plane, and establishes a normal stiffness model of the contact asperity taking into account the major and minor axes of the ellipse.

[0008] S101 uses the ellipsoid surface equation to fit the micro-convex body, and the real contact micro-convex body is equivalent to the contact between the ellipsoid and the rigid plane.

[0009] S102 establishes a functional relationship model between the normal deformation of the contact micro-convex body and the major and minor axes of the ellipse.

[0010] S103 divides the normal deformation into three stages: elastic, elastoplastic, and plastic, and constructs the critical cross-sectional area equations of adjacent stages.

[0011] Critical cross-sectional area a′ between elasticity and elastoplasticity ec The model is

[0012]

[0013] Where H is the hardness of the softer material; γ is the dimensional parameter of the spectral density; E0 is the equivalent elastic modulus; and e is the eccentricity related to the major axis a0 and minor axis b0 of the ellipse.

[0014] Elastic-plastic critical cross-sectional area a′ pc The model is

[0015]

[0016] S104 establishes the normal contact stiffness model of a single contact micro-convex body in the elastic and elastoplastic stages.

[0017] S20 introduces a domain expansion factor to construct a three-dimensional fractal correction model of the normal contact stiffness of the mechanical interface.

[0018] Normal contact stiffness K of the mechanical interface in the elastic stage e The three-dimensional fractal correction model is

[0019]

[0020] Normal contact stiffness K of the mechanical interface in the elastic-plastic stage ep The three-dimensional fractal correction model is

[0021]

[0022] The three-dimensional fractal correction model of the normal contact stiffness of the mechanical interface is:

[0023]

[0024] S30 obtains the three-dimensional morphology data of the bonding surface through experiments and calculates the fractal dimension D and roughness coefficient G.

[0025] S40 uses a refined finite element model to analyze and extract the spatial stress distribution matrix of the joint surface.

[0026] S401 proposed a method for constructing a refined finite element model of a mechanical structure using the combined Solidworks-Hypermesh-Ansys software and setting material properties.

[0027] S402 uses Targe170 and Contact174 units to establish contact pairs.

[0028] S403 static analysis obtains the contact stress distribution cloud diagram of the bonding surface.

[0029] S404 extracts the spatial stress distribution matrix of the bonding surface based on the contact stress distribution cloud diagram of the bonding surface.

[0030] S50 calculates the normal contact stiffness of the mechanical joint surface and obtains the natural frequency by combining the finite element method.

[0031] S60 was subjected to modal hammer tests to verify the accuracy of the calculation method.

[0032] The beneficial effects of the technical solution provided by the present invention are: on the one hand, it provides a method for calculating the normal contact stiffness of the mechanical joint surface, which converts the traditional spherical contact equivalent method into an ellipsoidal contact equivalent, which is closer to the dimensional relationship of a single micro-convex body; on the other hand, it is combined with a refined finite element model to achieve the synergy of solution efficiency and accuracy, thereby improving the accuracy of the calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a flow chart of the calculation method for the normal contact stiffness of the mechanical joint surface.

[0034] Figure 2 The microscopic morphology of the mechanical bonding surface and the enlarged image of a single micro-protrusion.

[0035] Figure 3 Schematic diagram of the deformation of a single equivalent ellipsoid in contact with a rigid plane.

[0036] Figure 4 Engineering drawing of a frame-type structural test piece connected by threaded fasteners.

[0037] Figure 5 This is a bar chart of the natural frequency numerical solution and experimental test results. DETAILED DESCRIPTION

[0038] The following combination Figure 1The flow chart of the calculation method of the normal contact stiffness of the mechanical joint surface is shown in Figure 2 The microscopic morphology of the mechanical interface and the enlarged view of a single micro-protrusion shown provide a detailed description of the technical solutions in the embodiments of the present invention. It should be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit it. Based on the embodiments of the present invention, other embodiments derived by those skilled in the art without inventive effort are also within the scope of protection of the present invention.

[0039] A method for calculating normal contact stiffness based on ellipsoid contact and a three-dimensional fractal model, wherein the steps for implementing the method include:

[0040] S10 equates the real contact asperity to the contact between an ellipsoid and a rigid plane, and establishes a normal stiffness model of the contact asperity taking into account the major and minor axes of the ellipse.

[0041] S101 uses the ellipsoid surface equation to fit the micro-convex body, and the real contact micro-convex body is equivalent to Figure 3 The ellipsoid in is in contact with the rigid plane. The major axis of the elliptical contact surface is defined as a0, and the minor axis is defined as b0.

[0042] S102 establishes a functional relationship model between the normal deformation of the contact micro-convex body and the major and minor axes of the ellipse.

[0043] S103 divides the normal deformation into three stages: elastic, elastoplastic, and plastic, and constructs the critical cross-sectional area equations of adjacent stages.

[0044] Critical cross-sectional area a′ between elasticity and elastoplasticity ec The model is

[0045]

[0046] Where H is the hardness of the softer material; γ is the dimensional parameter of the spectral density; E0 is the equivalent elastic modulus; and e is the eccentricity related to the major axis a0 and minor axis b0 of the ellipse.

[0047] Elastic-plastic critical cross-sectional area a′ pc The model is

[0048]

[0049] Set the equivalent elastic modulus E0 = 2.1 × 10 11 Pa, equivalent Poisson's ratio v = 0.28, spectral density size parameter γ = 1.5, hardness of the foot soft material H = 1.96×10 9 ; Parameter related to Poisson's ratio k = 0.454 + 0.41v.

[0050] S104 establishes the normal contact stiffness model of a single contact micro-convex body in the elastic and elastoplastic stages.

[0051] S20 introduces a domain expansion factor to construct a three-dimensional fractal correction model of the normal contact stiffness of the mechanical interface.

[0052] Normal contact stiffness K of the mechanical interface in the elastic stage e The three-dimensional fractal correction model is

[0053]

[0054] Normal contact stiffness K of the mechanical interface in the elastic-plastic stage ep The three-dimensional fractal correction model is

[0055]

[0056] The three-dimensional fractal correction model of the normal contact stiffness of the mechanical interface is:

[0057]

[0058] S30 obtains the three-dimensional morphology data of the bonding surface through experiments and calculates the fractal dimension D and roughness coefficient G.

[0059] S40 build Figure 4 The refined finite element model of the frame-type structural component shown in the figure extracts the spatial stress distribution matrix of the joint surface through static analysis.

[0060] S401 proposed a method for constructing a refined finite element model of frame-type structural parts using the combined Solidworks-Hypermesh-Ansys software, and set the material to 45 steel.

[0061] S402 uses Targe170 and Contact174 units to establish contact pairs.

[0062] S403 static analysis obtains the contact stress distribution cloud diagram of the bonding surface.

[0063] S404 extracts the spatial stress distribution matrix of the bonding surface based on the contact stress distribution cloud diagram of the bonding surface.

[0064] S50 calculates the normal contact stiffness of the joint surface of the frame-type structural component and obtains the natural frequency of the frame-type structural component based on the modal analysis module. The first four natural frequencies are 419.452Hz, 419.912Hz, 621.642Hz, and 622.121Hz.

[0065] S60 uses the LMS vibration test system to conduct hammer tests on frame-type structural components, and the first four natural frequencies obtained are 430.183Hz, 430.347Hz, 634.914Hz, and 636.645Hz.

[0066] Furthermore, the calculation results of the traditional WK model are 411.561Hz, 412.472Hz, 609.875Hz, and 611.124Hz.

[0067] The results of the method of the present invention, the test data and the traditional WK model calculation are plotted into a bar graph, as shown in Figure 5 The results show that the average calculation error of this method is reduced from 4.11% to 2.32% compared with the traditional ball contact model, and the similarity with the experimental value is higher, increasing from 95% to more than 97%.

Claims

1. A method for calculating the normal contact stiffness of a mechanical interface based on ellipsoidal contact and fractal theory, characterized in that: The following steps are involved: S10 equates the real contact asperity to the contact between an ellipsoid and a rigid plane, and establishes a normal stiffness model of the contact asperity taking into account the major and minor axes of the ellipse. S20 introduces a domain expansion factor to construct a three-dimensional fractal correction model of the normal contact stiffness of the mechanical interface; S30 obtains the three-dimensional topography data of the bonding surface through experiments and calculates the fractal dimension D and roughness coefficient G; S40 uses a refined finite element model to analyze and extract the spatial stress distribution matrix of the joint surface; S50 calculates the normal contact stiffness of the mechanical joint surface and obtains the natural frequency by combining the finite element method; S60 was subjected to modal hammer tests to verify the accuracy of the calculation method.

2. The method for calculating the normal contact stiffness of a mechanical interface based on ellipsoidal contact and fractal theory according to claim 1, characterized in that: Step S10 includes the following steps: S101 uses the ellipsoid surface equation to fit the asperity, and equates the real contact asperity to the contact between the ellipsoid and the rigid plane; S102 establishes a functional relationship model between the normal deformation of the contact asperity and the major and minor axes of the ellipse; S103 divides the normal deformation into three stages: elastic, elastoplastic, and plastic, and constructs the critical cross-sectional area equations of adjacent stages; S104 establishes the normal contact stiffness model of a single contact micro-convex body in the elastic and elastoplastic stages.

3. The method for calculating the normal contact stiffness of a mechanical interface based on ellipsoidal contact and fractal theory according to claim 1 or 2, characterized in that: The critical cross-sectional area a′ between elasticity-elastoplasticity and elastic-plasticity-plasticity in step S103 ec , a′ pc The model is Where H is the hardness of the softer material; γ is the dimensional parameter of the spectral density; E0 is the equivalent elastic modulus; and e is the eccentricity related to the major axis a0 and minor axis b0 of the ellipse.

4. The method for calculating the normal contact stiffness of a mechanical interface based on ellipsoidal contact and fractal theory according to claim 1 or 3, characterized in that: Step S20 determines the elastic deformation and elastoplastic deformation ranges according to the critical cross-sectional area, and derives the normal contact stiffness K of the mechanical joint surface in the elastic stage by integration. e and the normal contact stiffness K in the elastic-plastic stage ep The three-dimensional fractal correction model of Where Ψ is the domain expansion factor, a l ′ is the maximum cross-sectional area, H G2 is the coefficient related to the fractal parameters of the bonding surface; Therefore, the normal contact stiffness model of the mechanical joint surface is established, namely 5. The method for calculating the normal contact stiffness of a mechanical interface based on ellipsoidal contact and fractal theory according to claim 1, characterized in that: The fractal dimension D and the roughness coefficient G in step S30 are obtained by processing the three-dimensional topography data using the power spectrum density method.

6. The method for calculating the normal contact stiffness of a mechanical interface based on ellipsoidal contact and fractal theory according to claim 1, characterized in that: Step S40 includes the following steps: S401 proposes a method for constructing a refined finite element model of a mechanical structure using the Solidworks-Hypermesh-Ansys software combination and sets material properties; S402 uses Targe170 and Contact174 units to establish contact pairs; S403 static analysis to obtain contact stress distribution cloud diagram of the joint surface; S404 extracts the spatial stress distribution matrix of the bonding surface based on the contact stress distribution cloud diagram of the bonding surface.

7. A method for calculating normal contact stiffness of mechanical joint surfaces based on ellipsoidal contact and fractal theory according to claim 1, 4, 5 or 6, characterized in that: In step S50 , the normal contact stiffness of the joint surface is calculated, assigned to the refined finite element model of the mechanical structure, and the natural frequency of the mechanical structure is obtained through the modal analysis module.

8. The method for calculating the normal contact stiffness of a mechanical interface based on ellipsoidal contact and fractal theory according to claim 1 or 7, characterized in that: In step S60 , a vibration test bench is built to obtain the dynamic characteristics of the mechanical structure through a hammer test to verify the effectiveness and accuracy of the method.

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