圆柱面结合部接触应力的三维分形模型

THR EE-DIMENSIONAL FRACTAL MODEL OF CONTACT STRESS OF CYLINDER JOINT

为了对机械结构中圆柱结合部的承载能力进行研究,基于Hertz接触理论,并结合修正的三维分形理论,应用三维分形曲面来模拟实际工程中的结合面,在综合考虑宏观特性因素与微观形貌因素的情况下,建立了圆柱结合部接触应力的三维分形模型,并与Hertz接触模型进行了对比分析,证明了所建立模型的合理性。通过Matlab仿真分析得到,从宏观特性因素上,可以选用内接触圆柱结合部,或增大小圆柱体的半径来降低接触应力,提高承载能力;从微观形貌因素上,可以减小分形尺度参数,或减小材料特性参数来降低接触应力。分形维数对接触应力的影响比较复杂:当2.1≤D≤2.5时,增大分形维数,可以降低接触应力;当2.5≤D≤2.9时,减小分形维数,可以降低接触应力。

In order to study the carrying capacity of the cylinder joint in the mechanical structure,based on Hertz contact theory and combined with the modifed three-dimensional fractal theory,the three-dimensional fractal theory was applied to simulate the actual engineering joint surface,and a thee-dimensional fractal model of the contact stress of the cylinder joint was established under the comprehensive consideration of the macroscopic characteristics and the microscopic morphology factors.And a comparative analysis was conducted with the Hertz contact model,proving the rationality of the established model.Through Matlab simulation analysis,from the macro characteristics,the contact stress can be reduced and the carrying capacity can be:improved by using the form of internal contact cylinder joint or by increasing the radius of the cylinder.From the aspect of microscopic morphology,the contact stress can be reduced by reducing the fractal dimension parameter and the material characteristic parameter.The influence of the fractal dimension of the micro-topography parameter on the contact stress is.complex.When2.1≤D≤2.5,increasing the fractal dimension can reduce the contact stress.When 2.5≤D≤2.9,reducing the fractal dimension can reduce the contact stress.