卷筒纸印刷机折页机构运动学方程直接积分解法

doi:10.3969/j.issn.0372-2112.2018.12.030

电子学报 ›› 2018, Vol. 46 ›› Issue (12): 3037-3043.DOI: 10.3969/j.issn.0372-2112.2018.12.030

卷筒纸印刷机折页机构运动学方程直接积分解法

李壮举¹, 田舜禹¹, 赵伟², 曹少中²

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

收稿日期:2017-09-19 修回日期:2018-02-08 出版日期:2018-12-25
- 作者简介:
- 李壮举 男,1975年生于河南南阳.工学博士.研究方向为多变量系统解耦控制、复杂系统的控制研究、机器人技术研究.E-mail:lizhuangju@bucea.edu.cn;田舜禹 男,1992年生于北京.硕士研究生.研究方向为复杂系统的控制研究、机器人技术研究.E-mail:630377414@qq.com;赵伟男,1983年生于山东泰安.工学博士.北京印刷学院信息工程学院讲师.研究方向为机器人技术.E-mail:zhaoweihu@163.com;曹少中 男,1965年生于河北保定.工学博士.北京印刷学院信息工程学院教授.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:
- 北京市教委项目 (No.KM201810016010）; 国家自然科学基金 (No.61272030，No.61472461）

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

LI Zhuang-ju¹, TIAN Shun-yu¹, ZHAO Wei², CAO Shao-zhong²

1.School of Electrical and Information Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044;
2.Beijing Key Laboratory of Signal and Information Processing for High-End Printing Equipment, Beijing Institute of Graphic Communication, Beijing 102600, China

Received:2017-09-19 Revised:2018-02-08 Online:2018-12-25 Published:2018-12-25
- Supported by:
- Project of Beijing Municipality Education Commission (No.KM201810016010); National Natural Science Foundation of China (No.61272030, No.61472461)

摘要/Abstract

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t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.

关键词: 卷筒纸印刷机折页机构, 动力学模型, 非线性系统, 状态方程, 直接积分

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 t 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.

Key words: web offset press's folding mechanism, dynamic model, nonlinear systems, state equation, direct-integrating

中图分类号:

TP273

李壮举, 田舜禹, 赵伟, 等. 卷筒纸印刷机折页机构运动学方程直接积分解法[J]. 电子学报, 2018, 46(12): 3037-3043.

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.

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卷筒纸印刷机折页机构运动学方程直接积分解法

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

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