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

doi:10.3969/j.issn.0372-2112.2019.06.012

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

更新时间：2025-07-02

- Direct-Integrating Approach for Solving State Equation of the Nonlinear Dynamics Model of Gear Systems for Offset Press
- Acta Electronica Sinica Vol. 47, Issue 6, Pages: 1267-1271(2019)
- 作者机构：
  
  1. 北京印刷学院,北京,102600
  2. 清华大学,北京,100084
  3. 北京印刷学院,北京,102600
  4. 清华大学,北京,100084
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61472461, No.61272030)
- DOI：10.3969/j.issn.0372-2112.2019.06.012
  CLC： TP242
- Published：2019
- 稿件说明：
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Direct-Integrating Approach for Solving State Equation of the Nonlinear Dynamics Model of Gear Systems for Offset Press[J]. Acta Electronica Sinica, 2019, 47(6): 1267-1271.
DOI：

Direct-Integrating Approach for Solving State Equation of the Nonlinear Dynamics Model of Gear Systems for Offset Press[J]. Acta Electronica Sinica, 2019, 47(6): 1267-1271. DOI： 10.3969/j.issn.0372-2112.2019.06.012.

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.

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

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 equati

on 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.

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Related Institution

School of Electrical and Information Engineering, Beijing University of Civil Engineering and Architecture

Beijing Key Laboratory of Signal and Information Processing for High-End Printing Equipment, Beijing Institute of Graphic Communication

School of Electrical and Information Engineering Beijing University of Civil Engineering and Architecture Beijing

Beijing Key Laboratory of Signal and Information Processing for High-End Printing Equipment Beijing Institute of Graphic Communication Beijing China

（北京印刷学院信息与机电工程学院，）

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