Nonlinear Virtual Material Based Modeling Of Mechanical Joints And Application

With the rapid development of technology, the machine tool industry is going inthe high-precision and reliability direction. As joint surface provides more than half ofthe stiffness and nearly all of the damping of a the whole machine tool. It is necessaryto research into the dynamics mechanism and establish engineering model of jointsurface. Based on fractal theory and Hertz contact theory, a nonlinear virtual materialbased model applied on fractional load mechanical joints is proposed which consistsof upper and lower parts of joint and nonlinear virtual material in the middle.Compared with traditional models, the nonlinear virtual material based model comesnearer the mechanism of joints, which is more simple and precise to solve engineeringproblems. The main contents are as follows:（1）The fractal dimension and fractal roughness parameters are calculated fromthe rough surface profile by using logarithmic form of power density spectrum. Inorder to explore the truncated area of a single asperity, total elastic and plastictruncated area of asperities, the unit area scale is advanced.（2） A mechanical joints model of nonlinear virtual material is built. Thefunctional relationships of elastic modulus, stress and unit area scale of this model arederived, and the effecting law of fractal parameters is inquired. The nonlinearity ofvirtual material model is reflected in two patterns: Virtual material of joints reflectnonlinear dynamic characteristic when the preload force changes. Different stress ofdifferent joint regions lead to different elastic modulus under specific preload force,which reflects nonlinear dynamic characteristic.（3）In this paper, the nonlinear stress-strain curves of virtual material is derived.The stress-strain curve exhibits a significantly difference between virtualmaterial and common material, which verified the accuracy of nonlinear elasticmodulus and stress derived from the virtual material model.（4）As structurally symmetrical specimen has limitations in terms of expressionjunction dynamic characteristics, the paper specially designed unsymmetricalstructure specimen: L-shaped specimen and frame-shaped specimen. The L-shapedspecimen is small form-factor with double bolt construction, and the dimension offrame-shaped specimen with8-bolt construction is similar to the machine tool joints. In this paper, the nonlinear virtual material model is applied on the L-shapedspecimen and the frame-shaped specimen in two situations: uniform preload andcouple. Compared to the experimental results, the error of finite element analysisresults is between0.4%-8%, which indicates that the model is of high accuracy.