电子学报 ›› 2019, Vol. 47 ›› Issue (6): 1267-1271.DOI: 10.3969/j.issn.0372-2112.2019.06.012

• 学术论文 • 上一篇    下一篇

胶印机齿轮系统非线性模型直接积分解法

赵伟1, 曹少中1, 孙富春2, 晋振杰1, 王明道1   

  1. 1. 北京印刷学院, 北京 102600;
    2. 清华大学, 北京 100084
  • 收稿日期:2017-12-13 修回日期:2018-07-04 出版日期:2019-06-25 发布日期:2019-06-25
  • 作者简介:赵伟 男,1983年9月出生,山东泰安人,讲师.2015年获得北京邮电大学博士学位,清华大学博士后在站,主要从事机器人、控制学方向研究工作E-mail:zhaoweihu@163.com;曹少中 男,1965年2月生于河北保定,博士,2005年毕业于北京理工大学信息工程学院,现为北京印刷学院信息工程学院教授.主要研究方向为非线性系统理论,机器人控制理论.E-mail:caoshaozhong@bigc.edu.cn
  • 基金资助:
    国家自然科学基金面上项目(No.61472461,No.61272030)

Direct-Integrating Approach for Solving State Equation of the Nonlinear Dynamics Model of Gear Systems for Offset Press

ZHAO Wei1, CAO Shao-zhong1, SUN Fu-chun2, JIN Zhen-jie1, WANG Ming-dao1   

  1. 1. Beijing Institute of Graphic Communication, Beijing 102600, China;
    2. Tsinghua University, Beijing 100084, China
  • Received:2017-12-13 Revised:2018-07-04 Online:2019-06-25 Published:2019-06-25

摘要: 卷筒纸印刷机折页机构是一种存在耦合的非线性齿轮系统.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,考虑变啮合刚度、齿侧间隙、动态传递误差等非线性因素,建立卷筒纸印刷机折页机构齿轮系统单自由度非线性动力学模型.引入由状态量、控制量与自变量时间为坐标构成的"广义状态空间",将卷筒纸印刷机折页机构齿轮系统动力学模型变为广义状态空间上的系统状态方程.在广义状态空间将方程的右端展开为时间的Taylor级数,进一步直接积分获得非线性控制系统状态方程关于自变量时间的级数解,最终获得状态方程的解析解.使用Matlab软件,对状态方程的解析解进行仿真,得到齿轮转动的角速度与角加速度与时间关系曲线.得到的曲线与实际情况进行对比,验证了动力学模型与状态方程解析解的正确性.

关键词: 齿轮系统, 动力学模型, 非线性系统, 状态方程, 直接积分

Abstract: web-offset press is a kind of coupling nonlinear dynamic system.We use the lumped mass method,Newton's second law,the differential equations and series theory and method to establish the gear system nonlinear dynamic modeling of web-offset printing machine wherein the time-varying meshing stiffness,backlash,dynamic transmission error and other nonlinear factors were considered.the concept of general time-state space comprising of state variables,control variable and time t is established.Then the model of web-offset printing machine can be transformed into a state equation of nonlinear system.In order to solve the state equation of nonlinear control systems,at the operation point of general time-state space,the right side of the state equation can be expanded as Taylor series about time.Then the series solution of the nonlinear control state equation,for which the solution is expression in time series,can be obtained by using direct-integrating approach.Then we use Matlab to simulate the equation of the web-offset printing machine's gear system.We obtain the curves of the relationship of gear's angular velocity and time and the relationship of angular acceleration and time.we contrast these curves and the facts.the contrast result verifies the validity of the dynamic model and the analytic solution of the system equation.

Key words: gear system, dynamic model, nonlinear systems, state equation, direct-integrating

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