A Research On Orthotropic Joint Modeling Method Based On Fractal Theory

The profile features of the plane grinding surface and the modeling method of the joint are studied.The relationships between the contact stiffness and real contact area,contact load are researched,and then the finite element modeling method containing the virtual material is established by theoretical,experimental and simulation methods.A new modeling method for fixed joint with orthotropic characteristic is proposed.Firstly,the profile features of the grinding surface in different directions are studied.The profile data are measured in different directions by profiler.The statistical parameters in different directions are calculated by probability density method,the fractal parameters in different directions are calculated by PSD method,the spectral characteristics in different directions are analyzed by FFT.The research of statistical method shows that the statistical parameters in different direction are different,and the profile features are different,however,the profiles approach to normal distribution.The research of the fractal characteristics show that the fractal parameters of the profiles in different directions are different,and the fractal parameters are different.Spectral analysis shows that the spectral characteristics of the profiles have obvious differences in different directions.The spectrum of the profiles contain high frequency components and low frequency components,and the proportion of low frequency components are much less than the high frequency components.The profile data in two orthogonal directions are imported into ANSYS,and the relationships between the normal load,tangential load and deformation are calculated,the results show that the normal and tangential contact stiffness in 90 degree direction are greater than the stiffness in 0 degree direction.Secondly,the contact stiffness models of the orthotropic surface are established.The asperities are equivalent to elliptical asperities,and the analytical models of the normal and tangential stiffenss are established by contact mechanics.The normal and tangential stiffness models of the contact surface are established by fractal theory.The influence parameters on the stiffness are analyzed by MATLAB.The results show that the contact stiffness can be improved by increasing the normal contact load,decreasing the tangential load,improving the material parameters.In order to verify the validity of the theoretical model,the finite element model is established,the relationships between the contact stiffness and real contact area,contact loads are analyzed.The results of the theoretical model and the results of the FE model are compared to verify the correctness of the theoretical model.Subsequently,the constitutive relations of the orthotropic contact surface are established.The physical structure of the grinding surface is analyzed,the geometric fluctuations of the profile and the mechanics property of the surface are analyzed.A method for determining the thickness of the contact layer is proposed.The contact layer is equivalent to the orthotropic virtual material containing 9 indendent parameters.The virtual material parameters are derived by the relationships between the stiffness and the load.A constitutive model of the orthotropic material is established.Finally,a finite element modeling method for fixed joint is proposed and verified by experiment.In order to verify the rationality of the contact stiffness and the correctness of the constitutive model,an experimental model containing fixed joint is established,and then the modal shapes and natural frequencies are obtained by experimental modal analysis.Based on the experimental model,a finite element model including virtual material is established in ANSYS.In finite element model,the contact layer is equivalent to the orthotropic virtual material,and the contact stiffness and the constitutive relations are introduced into the finite element model,the modal shapes and natural frequencies of the finite element model are calculated.It is shown that the experimental modal shapes are consistent with the modal shapes of finite element model,and the relative errors between the experimental frequencies and frequencies of the finite element model are less than 10 percents.The experimental results have a good agreement with the results of the finite element model,which prove the correctness of the theoretical model.An effective modeling method for the fixed joint is proposed in the paper.The finite element method is combined with the theoretical method,which can realize the integration of the whole machine structural analysis and the finite element method.