Contact Stiffness Modeling Of Joint Interfaces Considering Base Lengths Of Asperities

Because there are a large number of joint interfaces in the machine tool structure,the deformation of the joint interfaces will cause the corresponding parts to have displacement,which will lead to machining errors.In order to improve the machining accuracy of machine tools,it is important to study the contact mechanism of the joint interfaces theoretically and establish the contact stiffness model to characterize its deform-resisting ability for analysis and prediction of the static and dynamic characteristics of machine tool structure.In view of the fact that the base length and interaction of asperities have not been taken into account in the previous theoretical model of contact stiffness of joint interfaces,this paper makes a study on it.The main research work is as follows:(1)In the traditional MB fractal model,the smaller scale asperities are ignored,and the cosine function is used to describe the counter of asperities,which leads to a large blank area inside the asperities of cosine shape.In order to eliminate the influence of this large blank area,this paper introduces the base length of asperities by referring to the existing literature.Based on the KE model,the normal contact stiffness model of joint interfaces considering three deformation mechanisms of asperities is established.The numerical simulation results show that when given a fixed contact load,the contact area and contact stiffness of joint interfaces increase first and then decrease with the increase of the fractal dimension,and the contact stiffness is an increasing function of contact load,material characteristic parameter and hardness coefficient.It is a subtraction function of characteristic length scale parameter,and the model is closer to the actual situation.(2)Based on the theory of elasticity,the relationship between actual deformation and average surface contact load under the interaction of asperities is obtained.The expressions of normal contact load on the base length and contact area of asperities are derived,and the normal contact stiffness model of joint interfaces is established.The numerical simulation results show that the normal contact stiffness of joint interfaces inquiring the interaction and base length of asperities is always less than the stiffness without inquiring interaction.Take fractal dimension 1.85 as the critical point.When the fractal dimension is1.1?1.85,the nonlinearity of normal contact stiffness increases,while when the fractal dimension is 1.85?1.9,the nonlinearity of normal contact stiffness decreases.At the same time,the calculated results of model are in good agreement with the existing experimental data.(3)Based on the above models,the tangential contact stiffness of asperities is deduced according to the relationship between tangential deformation and tangential load,and then the tangential contact stiffness of joint interfaces model inquiring the interaction and base length of asperities is established.The numerical simulation results show that the tangential contact stiffness of joint interfaces inquiring the interaction and base length of asperities is always less than the stiffness without inquiring interaction.When the fractal dimension increases from 1.1 to 1.85,the tangential contact stiffness increases,while when the fractal dimension exceeds 1.85 to 1.9,the tangential contact stiffness decreases,and the correctness of model is verified by experimental data.