基于各向异性虚拟材料的机械结构固定结合面动态特性高精度预测

To high-grade NC machine tools, the dynamic property (vibration shape, natural frequency and damping ratio) is a key of whole machine tools, therefor, the dynamic performance in joint interface becomes a research hot point in machine tools. Now, it is difficult for current models of joint interfaces to satisfy the high-grade need of a set of joint interfaces in NC machine tools and there lacks a parameterized model because of the diversity of joint interface's type in NC machine tools and some parameters of describing joint interface model. A new anisotropic virtual material modeling approach on fixed joint interface in machine tools is conducted. Four aspects of works are studied as follows. A dynamic parametric modeling method on fixed joint interface in machine tools is suggested. Using Hertz contact theory and fractal theory, an analytic model of virtual material's elastic modulus, shear modulus, Poisson ratio, thickness and density is proposed if some engineering data of materials are treated as known parameters. A theoretical method to identify such two important characteristic parameters of analytic solution model as fractal dimension and fractal roughness is given. The analytic solutions for virtual material are effectively verified. Many component joint interfaces and machine tools selected as some research examples, the theoretical mode shapes are correlatively analyzed with the experimental ones all around to attain the theoretical predicting accurancy. A complete novel theoretical method can greatly improve the dynamic modeling accurancy in whole machine tools.

对高端数控机床而言，动态特性(振型、固有频率、阻尼比等)是整机性能的关键，结合面动力学性能成为机床的研究热点。由于数控机床的结合面类型众多，描述结合面模型的参数多样化，现有结合面的模型既不能满足高端要求，也没有参数化模型，故急需一种高精度的参数化建模方法。本项目将构建一种新颖的固定结合面各向异性虚拟材料建模方法。本项目拟在以下几个方面展开研究：提出一种基于各向异性虚拟材料的机床固定结合面动力学参数化建模法；应用赫兹接触理论和分形理论，以材料的一些工程数据为已知参数，建立虚拟材料弹性模量、切变模量、泊松比、厚度、密度的解析解模型；给出识别解析解模型中2个重要表征参数(分形维数和分形粗糙度)的理论方法；对虚拟材料理论解进行有效性验证，以多类零件结合面、整机为研究对象，对一系列试验试件的理论模态与实验模态进行相关性分析，给出理论预测精度。本项目架构的全新理论方法可显著提高机床整机动力学建模精度。

结合部的动力学特性显著影响机械结构的动力学行为。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。