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
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.
李壮举, 田舜禹, 赵伟, 曹少中. 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, CAO Shao-zhong. Direct-Integrating Approach for Solving State Equation of the Mechanics Model of Web Offset Press's Folding Mechanism with Clearance. Acta Electronica Sinica, 2018, 46(12): 3037-3043.
[1] 袁英才.卷筒纸印刷机含间隙折页机构动力学研究及稳健设计[D].长沙:中南大学,2011. Yuan Ying-cai.Dynamics Research and Robust Desing of Web Offset Press's Folding Mechanism with Clearance[D].Changsha:Central South University,2011.(in Chinese)
[2] 曹少中,涂序彦.非线性控制系统状态方程直接积分解法[J].控制与决策,2011,26(10):1591-1595. CAO Shao-zhong,TU Xu-yan.Direct-integrating approach for solving state equation of nonlinear control systems[J].Control and Decision,2011,26(10):1591-1595.(in Chinese)
[3] 洪奕光,程代展.非线性系统的分析与控制[M].北京:科学出版社,2005.167-185.
[4] 曹少中,赵伟.球型机器人状态方程直接积分解法[J].电子学报,2016,44(12):3020-3025. CAO Shao-zhong,ZHAO Wei.Direct-integrating approach for solving state equation ofthe mechanics model of spherical robot[J].Acta Electronic Sinica,2016,44(12):3020-3025.(in Chinese))
[5] Srivastava H M,Niukkanen A W.Some clebsch-gordan type linearization relations and associated families of Dirichlet integrals[J].Mathematical and Computer Modelling,2003,37(3-4):245-250.
[6] Doyle F J,Allgower F,Morari M.Normal form approach to approximate input-output linearization for maximum phase nonlinear SISO systems[J].IEEE Trans on Automatic Control,1996,41(2):305-309.
[7] Albeverio S,Bozhok R,Koshmanenko V.The rigged hilbert spaces approach in singular perturbation theory[J].Mathematical Physics,2006,58(2):227-246.
[8] Lin T C,David H Schultz,Zhang W Q.Numerical solutions of linear and nonlinear singular perturbation problems[J].Computer and Mathematics Applications,2008,55(11):2574-2592.
[9] Stephen Schecter.Traveling-wave solutions of convection-diffusion systems by center manifold reduction[J].Nonlinear Analysis,2002,49(1):35-59.
[10] Kahram an A,Singh R.Non-linear dynamics of a spur gear pair[J].Journal of Sound and Vibration,1990,142(1):49-75
[11] Kahram an A,Singh R.Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system[J].Journal of Sound and Vibration,1991,146(1):135-156
[12] Padmanabhan C,Singh R.Spectral coupling issues in a two-degree-of-freedom system with clearance non-linearity[J].Journal of Sound and Vibration,1992,155(2):209-230
[13] Vinayak H,S ingh R,Padmanabhan C.Linear dynamic analysis of multi-mesh transmissions containing external rigid gears[J].Journal of Sound and Vibration,1995,185(1):1-32