引入各向同性虚拟材料的固定结合部模型

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The dynamical performance of the joint surface has considerable impact on the dynamical behavior of mechanical structure.An isotropic virtual material hypothesis-based analytical dynamical modeling method for immovable joint surface in machine tools was proposed in order to enhance the modeling precision of ensemble machine tools.The microcontact section of two contact planes in immovable joint surface were regarded as a virtual isotropic material,which is rigidly linked with two components situated at both sides of the immovable joint surface.By adding an element,a complicated assembled part including a joint surface could be equalized as a simple component without a joint surface so as to simplify the complicated problem on the immovable joint surface.The interaction between normal and tangential performances of immovable joint surface was considered,some analytical expressions of elastic modulus,Poisson ratio,thickness and density was put forward for virtual material according to Hertz contact theory and fractal geometry theory.The theoretical mode for a whole machine tool can be derived by inserting analytical formulas of virtual material＇s parameters into finite element software.The theoretical modes were compared with the experimental results in terms of qualitative comparison of similar mode and quantitative comparison of corresponding natural frequency.The theoretical first six order vibration shapes are in excellent coherence with the experimental results,and the relative errors between the theoretical first six-rank natural frequencies and the experimental those are from -8.1％ to 8.1％.The good agreement of theoretical results with the experimental ones verified the analytical formulae of virtual material＇s parameters.The virtual material＇s model will lay a theoretical foundation for the accurate dynamical modeling of immovable joint surface in CNC machine tools.为提高整机的建模精度,提出利用各向同性虚拟材料假设的机床固定结合部动力学建模的解析法.将固定结合部的两个接触面的微观接触部分假设为一种虚拟的各向同性材料,虚拟材料与固定结合部两侧的零件皆为固定连接.通过增加一个元件可将含结合部的复杂部件等效为不含结合部的简单零件,达到将复杂的固定结合部问题简单化的目的.考虑固定结合部法向和切向特性的相互影响,应用赫兹接触理论和分形几何理论推导虚拟材料弹性模量、泊松比、厚度、密度等参数的解析解.将虚拟材料参数的解析解导入到有限元软件中,可获得整机的理论模态.对实验试件的理论模态与实验模态进行比较（相似振型定性比较,相应的固有频率定量比较）.比较结果表明：理论模态与实验模态的前6阶振型一致,理论模态与实验模态前6阶固有频率的相对误差在-8.1％～8.1％之间.验证虚拟材料参数解析解的有效性,虚拟材料模型可为计算机数控机床固定结合部的精确动力学建模提供一定的理论基础.