A Three-dimensional Fractal Model Of The Normal Contact Characteristics Of Two Contacting Rough Surfaces

Mechanical joint surfaces exist in large numbers in mechanical structures.The contact stiffness and damping generated by the mechanical joint surface have an important influence on the accuracy and performance of the whole machine.The mechanical joint surface is composed of two rough surfaces that are in contact with each other,and there are micro-protrusions of different sizes and shapes on the rough surface.In this paper,based on the idealized models of cone and spherical asperities,two three-dimensional fractal models of normal contact characteristics of two contacting rough surfaces is established.The following research and analysis are made through numerical simulation,model comparison and experimental verification.(1)First,the asperities on the rough surface are equivalent to cones.Combining the fractal theory and the improved W-M function,a three-dimensional fractal model of the normal stiffness of the joint surface based on the asperity of the cone is established.Secondly,according to the three-dimensional fractal geometry theory and the normal contact damping loss mechanism,a three-dimensional fractal model of the normal damping of the joint surface based on the conic asperity is established.This model ignores the joint surface itself tiny mass.Furthermore,through comparison with previous models and experimental data,the reliability of the modeling method in this paper was verified,and through numerical simulation to study the influence of related variables on the normal contact stiffness and damping of the joint surface.(2)First,according to the common characteristics of elastic mechanics and plastic mechanics expressions,a new model of asperity elastic-plastic contact is developed.The proposed model can solve the problem of discontinuous,leap and non-monotone contact load,mean contact pressure and contact area in three separated phases,i.e.perfectly elastic phase,elastoplastic phase and fully plastic phase.Secondly,by introducing the first loading and unloading model of a single asperity,the energy storage and loss expressions of the asperity in the elasto-plastic stage are derived.Considering the deformation process of asperities,a rough surface normal damping model considering the elastoplastic deformation mechanism and deformation process is established.Furthermore,through comparison with previous models and experimental data,the reliability of the modeling method in this paper was verified.(3)Through the simulation comparison between the models,it is found that when the fractal dimension is 2.1-2.5,the stiffness solved by the conical model is larger than that solved by the spherical model,while when the fractal dimension is 2.6-2.9,the stiffness solved by the conical model is smaller than that solved by the spherical model,and the difference between them is smaller when the fractal dimension is larger than 2.6.The normal energy consumption solved by the conical model is smaller than the normal energy consumption solved by the spherical model.The normal damping solved by the conical model is smaller than the normal damping solved by the spherical model.The normal damping energy loss considering the elastoplastic deformation stage is smaller than the normal damping energy loss considering only the elastic and plastic stages.The normal contact damping considering the elastoplastic deformation stage is larger than that only considering the elastic and plastic stages.