摘要
在考虑齿面摩擦、齿轮时变啮合刚度和齿侧间隙的情况下,推导出了改正的齿轮副系统的非线性动力学模型,应用符号运算软件,编写符号运算程序,得到了齿轮副非线性振动微分方程。该模型在计算摩擦力时,考虑了载荷在啮合区的动态分配,并根据啮合区单双齿交替的特点提出用周期扩大法建立摩擦力、齿轮时变刚度的模型,改正的齿轮非线性动力学模型是一个周期系数分段线性的非自治系统,与以前所建立的模型相比,该模型的参变系数是具有相同周期的周期函数,新的齿轮非线性动力学模型的建立为求解时变的齿轮动力学方程近似解析解带来方便。
A non-linear dynamic model for gear pair system is developed considering surface friction, gear mesh stiffness and backlash. The dynamic distribution of load in the mesh area is taken into consideration in calculating the friction force. Based on the repeated fluctuation of single gear and double gear, period enlargement method is used to establish the friction force and gear meshing stiffness models, respectively. The non-linear dynamics model is a non-autonomous system. Compared with the other models, the coefficient in the system established by period enlargement is a periodic function with the same period. Thus, it becomes possible to apply Energy Method or other methods to obtain the approximate analytical solutions for the time-varying dynamics equations of the gear pair system.
出处
《工程力学》
EI
CSCD
北大核心
2008年第1期217-223,共7页
Engineering Mechanics
基金
国家自然科学基金项目(50475139)
国家重点基础研究发展计划(973计划项目)(2005CB724100)
关键词
非线性模型
时变啮合刚度
摩擦力
齿轮
间隙
non-linear model
time-varying stiffness
friction force
gear
backlash
