齿隙系统的建模与自振荡分析

摘要

针对齿隙系统都有自振荡倾向的问题,给出了自振荡的条件.分析并说明了当齿隙处于系统中不同的位置上时要用不同的非线性特性来描述.当有力矩传递时齿隙的模型应该是用死区特性来描述,死区特性夹在两个动态环节之间形成了所谓的三明治系统.如果齿隙位于系统的输出端,则齿隙就具有滞环特性.无论是死区特性或滞环特性的场合,系统都有可能出现自振荡.分析指出这种三明治系统是由多重反馈回路所构成的,因而存在着固有的稳定性问题.采用描述函数法分析了这种三明治系统产生自振荡的条件,结论是齿隙的这种三明治系统与带滞环特性的系统一样,也是很容易起振的,并给出了改善起振条件的可能措施.%For the problems that all systems with backlash are likely to oscillate,the conditions for self-oscillation were discussed.It shows that there are different nonlinear characteristics for the backlash at different positions of the system.If there are torques transmitted through the gear train,the backlash must be modeled as a dead zone,where the system is of sandwich structure: a dead zone between two dynamic blocks.If the gear train is at the output of the system,then the backlash is modeled as a hysteresis characteristic.Whenever in the dead-zone case or hysteresis case,the systems all are likely to oscillate under certain conditions.It is pointed out that for the sandwich system,there are multiple feedback loops surrounding a dead zone,so the stability problem may exist naturally with such system structures.The describing function method is used to analyze the limit cycles of the sandwich system.It shows that the system with sandwiched backlash also has the tendency to oscillate just like a system with hysteresis.Measures to alleviate the problem of self-oscillation were also discussed.