Contact Behaviors Of Power-law Hardening Elastic-Plastic Materials Considering Real Surface Topography

Contact stiffness widely exists in engineering applications, such as the joints of machine tools, bearings and gear and so on, which has the important effects on the performance of the mechanical equipment. All contact surfaces are rough in the microscopy scale, which contains many asperities on them. When the surfaces contact with each other, in fact, it is the asperities on the surfaces contact with each others. What’s more, some engineering materials show the power-law hardening properties in the hardening phase, however, the studies about the contact between power-law hardening materials are still not sufficient. First, the normal contact and the tangential contact of the single asperity are both studied to analyze the contact behaviors of the power-law hardening materials. Secondly, the geometrical characteristics and the position of the asperities are analyzed, and the interaction between the asperities is considered the contact between rough surfaces. Finally, based on the above study about the normal and tangential contact of the power-law hardening asperities, and the shoulder-shoulder contact style, the normal contact stiffness model for single asperity contact is built, and then considering the geometrical characteristics and the position of the asperities, and the interaction effect of asperities, the normal contact stiffness model of power-law hardening surfaces are obtained. The normal stiffness model is verified by the experiments.First, the normal and tangential contact between a single asperity and a rigid flat is considered. For the normal contact, the finite element method is applied to analyze the contact parameters such as contact load and contact area in the loading and unloading process, and get the empirical expressions about the contact parameters by fitting the finite element results. Meanwhile, the effect of the stain hardening exponent and the Poisson’s ratio on the normal contact parameters is considered. The results show that in the normal loading and unloading process, the stain hardening exponent significantly affects the normal contact parameters, and the Poisson’s ratio has little effect on the normal contact parameters. For the tangential contact, the single tangential loading process and the cyclic tangential loading and unloading process are considered. The tangential contact parameters such as contact load, contact area, Mises stress and contact pressure are studied with the finite element method in the single tangential loading process, and the effect of the stain hardening exponent on the tangential parameters are analyzed. Also, the empirical expressions of the contact load and contact area are obtained, which are accurate in a large range of the normal load. In the cyclic tangential loading and unloading process, the tangential parameters such as the contact load, energy loss, plastic deformation and contact area are studied with the finite element model, and the effect of the stain hardening exponent on the tangential parameters are analyzed.Then the contact between the power-law hardening surfaces is considered. For one hand, the analytical model of surface contact considering the asperity interaction effect. The real surface topography is measured first, and the asperities can be identified and the geometrical characteristics and the position of the asperities can be obtained. Then the asperity interaction, i.e. the effect of the asperity contact on the substrate deformation is considered, and the normal and tangential parameters of the surface contact can be obtained. Based on the analytical model, the effect of the material properties on the asperity interaction such as strain hardening exponent, the ratio of Young’s modulus and yield strength, and the Poisson’s ratio are analyzed. The results show that the real surface topography and the choice of the baseline of the substrate play important roles in the asperity interaction effects. Meanwhile, the influence of Young’s modulus and yield strength on the asperity interaction is significant, while the influence of the Poisson’s ratio is not so large. On the other hand, the numerical model of the surface contact is established. The original surface topography is simplified by the wavelet analysis, and the reverse engineering technology is used to rebuild the rough surface. Then the finite element model is established to study the normal and tangential contact between the rigid flat and the simplified rough surface, and the normal and tangential contact parameters are obtained. The comparison between the analytical model and the numerical model, it can be proved that the analytical model is accurate.Finally, the normal contact stiffness of the joint for power-law hardening materials is studied. Based on the shoulder-shoulder asperity contact style, the empirical expressions of the normal and tangential parameters which are obtained by the contact of a single asperity and a rigid flat are modified. Considering the position and the geometrical characteristics of the asperities on the rough surfaces, and the asperity interaction effects, the normal contact stiffness model is built. To verify the built normal stiffness model, the experiments on the small universal joint and the slide way-fixed surface joint are conducted. On one hand, for the small universal joint, the normal stiffness can be predicted by the normal stiffness model, and is compared with the experimental results. The comparison shows that the normal stiffness model can correspond with the experiments, implying the normal stiffness model is accurate. On the other hand, for the slide way-fixed surface joint, the experimental modal analysis is conducted, and the modal parameters for the first three orders are obtained. Meanwhile, based on the normal stiffness model, a finite element model about normal stiffness of the joint are built where the normal stiffness are considered by the spring elements, and the finite element results about the modal parameters can be obtained. By comparing the finite element results with the experimental results, it can be found the normal stiffness model is accurate.