应用改进分形理论及连续变形理论的机械结合面切向刚度建模  

Modeling of Tangential Stiffness of Mechanical Joint Surface Using Improved Fractal Theory and Continuous Deformation Theory

作　　者：李志涛 王世军[1] 韩子锐 卫娟娟 赵金娟 李鹏阳[1] LI Zhitao;WANG Shijun;HAN Zirui;WEI Juanjuan;ZHAO Jinjuan;LI Pengyang(School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China;School of Printing, Packaging Engineering and Digital Media Technology, Xi’an University of Technology, Xi’an 710048, China)

机构地区：[1]西安理工大学机械与精密仪器工程学院,西安710048 [2]西安理工大学印刷包装与数字媒体学院,西安710048

出　　处：《西安交通大学学报》2020年第6期107-114,共8页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51675422);陕西省科技厅科技统筹创新工程重点实验室资助项目(2014SZS10-P05)。

摘　　要：针对现有分形理论在建立切向刚度模型时未考虑微凸体变形的连续性以及未考虑结合面在即将发生切向滑移之前静摩擦力导致实际接触面积增大的问题,提出了应用改进分形理论及连续变形理论的切向刚度建模方法。该方法以微凸体连续变形理论为基础,应用改进分形理论分析静摩擦力与实际接触面积之间的关系,并利用赫兹接触理论推导了结合面法向接触载荷;随后,根据切向刚度的产生机理,推导了包含弹塑性过渡阶段的切向接触载荷,结合所推导的法向、切向接触载荷从而建立了结合面切向刚度模型。为验证该方法的合理性,首先建立栓接结合部的有限元模型,利用超景深三维显微系统VHX-5000获取结合面的轮廓数据,经过功率谱密度法获取结合面的分形参数,通过虚拟材料将该方法以及对比方法计算的刚度输入有限元模型中进行仿真,得到栓接结合部在不同扭紧力矩下的前三阶固有频率及振型;随后搭建包含栓接结合部的实验装置,通过锤击实验也获取该装置在不同扭紧力矩的前三阶固有频率及振型。在相同扭紧力矩下的前三阶固有频率对比实验和仿真结果表明:该方法的仿真与实验结果之间最大相对误差为3.84%,相比于田红亮的方法降低了54.45%,说明该方法能够更加准确地预测结合面动态特性。A method for modeling tangential stiffness based on fractal theory and the continuous deformation theory is presented to solve the problem that the existing fractal contact theory does not consider the continuity of asperity deformation,and the problem that the static friction force leads to an increase of real contact area of the binding surface before the tangential slip occurs when establishing the tangential stiffness model.The method bases on the continuous deformation theory of asperity,uses an improved fractal theory to analyze the relationship between static friction force and real contact area Hertz contact theory is used to derive the normal contact load of joint.According to the generating mechanism of tangential stiffness,the tangential contact load with the elastoplastic transition stage is also derived.Then a tangential stiffness model of joint is established by combining the derived normal and tangential contact loads.In order to verify the rationality of the method,a finite element model of bolt joint is built.In the finite model,the profile data of the contact surfaces of the joint are obtained by a ultra-depth three-dimensional microscope system VHX-5000,and then the fractal parameters of joint are obtained by the power spectrum density method.The first three order natural frequencies and vibration shapes of bolt joint are computed under different torques by inputting the stiffnesses of joint resulting from virtual material method and a comparison method into the finite element model for simulation of bolt joint.A experimental device including bolt joint is built,and then the first three order natural frequencies and vibration shapes of the device are also obtained under different torques by hammering experiments.Comparisons between experimental natural frequencies and computing natural frequencies under the same torques show that the maximum relative error of the simulation results is about 3.84%relative to experiment results,and it is 54.45%lower than Tian Hongliang method.These results show t

关 键 词：连续变形理论 改进分形理论 结合面 切向刚度 

分 类 号：TH113.1[机械工程—机械设计及理论]