Forced oscillations with time-varying mesh stiffness and backlash in gear systems  

作　　者：赵莹 温建民 王晓明 刘宏 王薇凌 

机构地区：[1]Robotics Institute,Harbin Institute of Technology [2]School of Automobile Engineering,Harbin Institute of Technology at Weihai [3]School of Electrical Engineering,Harbin Institute of Technology

出　　处：《Journal of Harbin Institute of Technology(New Series)》2009年第4期481-484,共4页哈尔滨工业大学学报（英文版）

摘　　要：A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influence such as time-varying mesh stiffness,backlash and dynamic transmission error(DTE) were obtained.The method of multiple scales was employed to solve the nonlinear differential equations with parametric excitation in gear systems,by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained.The nonlinear influence of stiffness variation,the damping and the internal excitation on the system response was shown by frequency-response curves.Compared with numerical examples,the approximate analytical solutions are in good agreement with exact solutions,which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influence such as time-varying mesh stiffness,backlash and dynamic transmission error（DTE） were obtained.The method of multiple scales was employed to solve the nonlinear differential equations with parametric excitation in gear systems,by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained.The nonlinear influence of stiffness variation,the damping and the internal excitation on the system response was shown by frequency-response curves.Compared with numerical examples,the approximate analytical solutions are in good agreement with exact solutions,which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.

关 键 词：gear system method of multiple scales analytical solutions exact solutions frequency-response curves 

分 类 号：O175.14[理学—数学] TH132.41[理学—基础数学]