Direct-Integrating Approach for Solving State Equation of the Mechanics Model of Web Offset Press's Folding Mechanism with Clearance

LI Zhuang-ju; TIAN Shun-yu; ZHAO Wei; CAO Shao-zhong

doi:10.3969/j.issn.0372-2112.2018.12.030

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Direct-Integrating Approach for Solving State Equation of the Mechanics Model of Web Offset Press's Folding Mechanism with Clearance

更新时间：2025-07-16

- Direct-Integrating Approach for Solving State Equation of the Mechanics Model of Web Offset Press's Folding Mechanism with Clearance
- Acta Electronica Sinica Vol. 46, Issue 12, Pages: 3037-3043(2018)
- 作者机构：
  
  1. 北京建筑大学电信学院,北京,100044
  2. 北京印刷学院高端印刷装备信号与信息处理北京市重点实验室,北京,102600
  3. 北京建筑大学电信学院,北京,100044
  4. 北京印刷学院高端印刷装备信号与信息处理北京市重点实验室,北京,102600
- 作者简介：
- 基金信息：
  
  Project of Beijing Municipality Education Commission (No.KM201810016010);National Natural Science Foundation of China (No.61272030, No.61472461)
- DOI：10.3969/j.issn.0372-2112.2018.12.030
  CLC： TP273
- Published Online：25 December 2018，
  
  Published：2018
- 稿件说明：
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LI Zhuang-ju, TIAN Shun-yu, ZHAO Wei, et al. Direct-Integrating Approach for Solving State Equation of the Mechanics Model of Web Offset Press's Folding Mechanism with Clearance[J]. Acta Electronica Sinica, 2018, 46(12): 3037-3043.
DOI：

LI Zhuang-ju, TIAN Shun-yu, ZHAO Wei, et al. Direct-Integrating Approach for Solving State Equation of the Mechanics Model of Web Offset Press's Folding Mechanism with Clearance[J]. Acta Electronica Sinica, 2018, 46(12): 3037-3043. DOI： 10.3969/j.issn.0372-2112.2018.12.030.

摘要

针对运动副间隙和轴承滚子变形引起的折页机构非线性动态响应问题，提出刚性杆与弹簧组合假设，建立了折页机构间隙动力学模型.对含二阶偏微分方程组的含间隙折页机构动力学模型，采用非线性系统直接积分法进行求解.非线性系统分析的核心归结为系统状态方程的求解问题，对于一般非线性控制系统，通过引入由状态量、控制量与自变量时间

为坐标构成的广义状态空间，在广义状态空间处将方程的右端展开为关于时间的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.以卷筒纸印刷机折页机构这种存在耦合的非线性系统为例，利用本文提出的解法得出了输入量与输出量的解析解，并仿真验证了方法的正确性.

Abstract

To the nonlinear dynamic response of folder system caused by the pair clearance and the bearing stiffness

the hypothesis of rigid role and spring combination is put forward

and the dynamics model of folder mechanism with clearance is established. The dynamics model which contains second order partial differential equations is solved by direct-integrating approach method. The kernel of nonlinear system analysis is the solving of system state equation. Therefore

for a general nonlinear control system

the concept of general time-state space comprising of state variables

control variables

and Time

is introduced. In order to solve the

state equation of nonlinear control system

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 the series

can be obtained by using direct-integrating approach. Dynamics model of the folder mechanism is a typical nonlinear system. Then we obtain the curves of input quantity and output quantity of this dynamics model by the direct-integrating method.

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Related Institution

Beijing Institute of Graphic Communication

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Beijing Institute of Graphic Communication Beijing China

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（北京印刷学院信息与机电工程学院，）

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