基于等效横观各向同性虚拟材料的固定结合部建模方法

Modeling Method of Fixed Joint Interfaces Based on Equivalent Transversely Isotropic Virtual Material

为提高固定结合部的建模精度以及通用性,考虑固定结合部在法向和切向的不同特性,提出利用横观各向同性虚拟材料等效的固定结合部动力学参数化建模方法,将固定结合部两接触面的微观接触部分等效为一种等截面的横观各向同性虚拟材料,等效虚拟材料与两侧零件均为固定连接。基于接触分形理论和固定结合部接触刚度分形模型,根据横观各向同性材料弹性常数的定义,理论推导了等效虚拟材料弹性常数以及密度的理论计算模型。在此基础上,对具有固定结合部的试验模型进行了有限元建模与模态分析,进而将理论分析模态与试验模态进行比较,结果表明:试验模型的理论模态与实验模态的前6阶振型完全一致,相应固有频率的相对误差的绝对值在10%以内,说明了建模方法的正确有效性,为数控机床固定结合部动力学建模提供了一种新的方法,实现了固定结合部动力学建模与有限元分析软件的无缝衔接集成。

To improve the fixed joint interfaces＇ modeling precision and versatility, considering the different characteristics of the fixed joint interfaces in normal and tangential directions, the dynamics parametric modeling method of fixed joint interfaces based on equivalent transversely isotropic virtual material is proposed. The micro contact portion of two contact surfaces in fixed joint interfaces is regarded as a virtual transversely isotropic material with a unchanged section, which is rigidly linked with two components situated at both sides of the fixed joint interfaces. Based on contact fractal theory and contact stiffness fractal model, according to the definition of transversely isotropic material＇s elastic constants, the theoretical calculation models of equivalent virtual material＇s elastic constants and density are put forward. On above basis, finite element modeling and modal analysis of one experimental model that has fixed joint interface are conducted, and then, the theoretical modals are compared with the experimental modals. The results show that the theoretical modals＇ first six order vibration shapes are in excellent coherence with the experimental modals＇, and the absolute values of the relative errors of corresponding natural frequency are less than 10%, which shows the correctness and effectiveness of the modeling method. This method provides a new method for CNC machine tools＇ fixed joint interfaces dynamic modeling, and the seamless integration of fixed joint interfaces dynamic modeling and finite element analysis software is achieved.