胶印机齿轮系统非线性模型与动力学分析

项目名称： 胶印机齿轮系统非线性模型与动力学分析

项目编号： No.61472461

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 计算机科学学科

项目作者： 曹少中

作者单位： 北京印刷学院

项目金额： 60万元

中文摘要： 针对胶印机齿轮系统的非线性动态特性，运用集中质量法、牛顿第二定律、微分方程及级数理论和方法，深入开展胶印机齿轮系统非线性动力学建模及其分析算法研究：首先，以胶印机一对传动齿轮为对象，考虑变啮合刚度、齿侧间隙、动态传递误差等非线性因素，建立胶印机齿轮系统单自由度非线性动力学模型；其次，以单色胶印机齿轮系统为对象，考虑齿轮系统存在齿侧间隙和滚动轴承的径向间隙，假设传动轴和轴承均对称于齿轮中心平面，建立单色胶印机齿轮系统三自由度非线性动力学模型；然后，以多色胶印机齿轮系统为对象，建立多色胶印机齿轮系统多自由度非线性动力学模型；针对胶印机非线性动力学模型不能得到精确解的问题，通过对其微分方程的右边关于自变量进行泰勒展开，然后进行直接积分，可得到任意级近似解，根据不同的计算精度要求，可以得到不同的求解算法。通过对胶印机齿轮系统的非线性动力学建模、分析，为胶印机的非线性动力学分析提供了一种新的方法。

中文关键词： 胶印机；齿轮系统；非线性模型；微分方程；任意级近似解

英文摘要： For the nonlinear dynamic characteristics of gear system for offset press, Using the lumped mass method, Newton's second law, the differential equations and series theory and method, carry out the gear system nonlinear dynamic modeling and analysis of offset printing machine algorithm research.. First of all, to offset a pair of transmission gear as object, a nonlinear dynamic model of gear system for offset printing machine with single degree of freedom was established wherein the time-varying meshing stiffness, backlash, dynamic transmission error and other nonlinear factors were considered. Secondly, to offset the single color offset printing machine gear system as object, a nonlinear dynamic model of gear system for a single color offset printing machine with three degree of freedom was established wherein the gear system backlash and rolling bearing radial clearance were considered, and assuming the shaft and bearings symmetrically on the gear center plane. Then, to offset the gear system of a multi-color offset printing machine as the object, a nonlinear dynamic model of the gear system for multi-color offset printing machine with multi degree of freedom was established. Finally, Considering the exact solution of nonlinear dynamic model for offset printing machine cannot be obtained,the right side of differential equation is transferred into Taylor expansion, and integrated directly,the any order approximate solutions can be obtained, according to the different accuracy requirement, the different algorithm can be applied. In this project, by establishing and analyzing the nonlinear dynamic model of the gear system for offset press, and the new analyzing method of nonlinear dynamic system for offset press is provided.

英文关键词： offset press;gear systems;nonlinear model;differential equation;any approximative solution