Research On Tangential Modeling Of Mechanical Joint Surfaces Based On Improved Fractal And Continuous Deformation Theory

According to the existing literatures,when the tangential contact stiffness model is established,the tangential contact stiffness of the asperity in the elastoplastic transition stage is not considered,and the increase of the actual contact area caused by the static friction force of the joint surface before the tangential slip is not considered too.This paper presents a tangential contact stiffness model of the joint surface using improved fractal theory and continuous deformation theory.The model is based on the continuously asperity deformation theory,and the improved fractal theory is used to analyze the relationship between the static friction force and the actual contact area.The Hertz contact theory is used to derive the normal contact load of the joint surface,and then according to the generation mechanism of tangential contact stiffness,the tangential contact load including the elastoplastic transition stage is derived.The normal and tangential contact loads are combined to establish the tangential contact stiffness model of the joint surface and verify the model.This article has studied from the following aspects:(1)The difference between the statistical and fractal characteristics of the rough surface obtained by the same processing method is studied.The three-dimensional profile data of different sample surfaces are obtained by using a super depth-of-field 3D microscope,and the data is processed by least square method to obtain contour data of different resolutions from different sample surfaces,and then the statistical parameters are evaluated.In addition,two-dimensional profile data in different directions are sampled at anywhere on the surface of different samples,and then the data is displayed in double logarithmic coordinates system.The fractal parameters are calculated by the PSD method.The results showed that the statistical and fractal characteristics of different sample surfaces are consistent obtained by the same processing method.Therefore,the contact characteristics per unit area can be extended to the entire contact surface through integration,which provides a theoretical basis for the subsequent theoretical modeling of the contact characteristics of rough surfaces.(2)The continuous deformation theory is used to establish the tangential contact stiffness model of the joint surface.The contact deformation process of a single asperity is analyzed.According to the generation mechanism of tangential contact stiffness,it is found that tangential contact stiffness still exists in the elastoplastic transition stage.Based on the Hertz contact theory,the normal contact load and the tangential contact load between the joint surfaces are deduced,and a tangential contact stiffness model based on continuous deformation theory is built.Numerical simulations show that improve of the machining accuracy of the contact surface will increase the tangential contact stiffness between the joint surfaces,and the tangential contact stiffness between the joint surfaces increases with the increase of the normal load and the decrease of tangential load.In order to verify the rationality of the model in this chapter,the surface profile data is introduced into the finite element software through APDL language to establish the finite element model.Compared to the model of Tian Hongliang,it is found that the theoretical model of tangential contact stiffness established in this chapter has certain advantages over the existing theoretical models..(3)An improved tangential contact stiffness model of joint surface is established by applying improved fractal theory and continuous deformation theory.According to the improved fractal theory,the problem of the increase of the actual area caused by the static friction from the joint surfaces is considered.In strict accordance with the Hertz contact theory,the actual contact area of the joint surface before the tangential slip is derived and the normal contact load and tangential contact load between the joint surfaces are derived.Thus,an improved tangential contact stiffness model is established.Numerical simulations show that reduction of the friction factor can effectively improve the tangential contact stiffness of the joint surface.(4)The experimental device including bolted joints is used to verify the rationality and superiority of the model in this paper.According to the basic principle of the experimental mode,the first three orders of natural frequencies and mode shapes under different pretightening torque are obtained through experiment.The experimental device is reasonably simplified to create a finite element model containing the contact layer of the virtual material,and the established tangential contact stiffness model is introduced into the virtual contact layer through APDL language to simulate the first three orders of natural frequencies and mode shapes under different pretightening torque.The simulation results show that the two tangential contact stiffness models established in this paper are closer to the experimental results than the models proposed in the existing literature.Since the model in Chapter 4 is improved based on the model in Chapter 3,the simulated results are closer to the experimental results and more suitable the actual contact situation.The method proposed in this paper which the tangential contact stiffness of the joint surface is established by the improved fractal theory and continuous deformation theory provides an effective and convenient method for the joint surface modeling,which can accurately predict the dynamic performance of the whole machine.