谐波齿轮系统的快慢振荡机制研究
A STUDY OF DYNAMICAL MECHANISMS OF THE FAST-SLOW OSCILLATIONS OF HARMONIC GEAR SYSTEM
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摘要: 谐波齿轮减速器是一种新型的传动装置, 因其具有诸多的优点, 因而得到了广泛应用. 谐波齿轮减速器涉及不同振荡尺度之间的耦合作用, 这通常会诱发复杂的快慢振荡, 严重影响了谐波齿轮系统的正常工作. 本文考虑涉及扭转刚度非线性因素的谐波齿轮系统, 旨在研究系统的快慢动力学, 揭示新型的快慢振荡机制. 首先, 构建了非线性扭转刚度下的谐波齿轮系统的快慢动力学模型. 然后, 通过改变扭转刚度系数, 得到了系统从常规振荡向快慢振荡的转迁过程. 接着, 简要地论述了有关快慢系统的基础理论. 在此基础上, 采用快慢分析法研究了快子系统的动力学特性, 揭示了快慢振荡的产生机制. 研究表明, 当系统参数改变时, 快子系统的平衡点曲线并未发生失稳或分岔; 然而, 在某一点附近, 平衡点曲线能够产生急剧量变, 其特征是平衡点在局部小范围内可以在正坐标值与负坐标值之间快速转迁. 在此基础上, 揭示了一种诱发快慢振荡的新型动力学机制, 比较了这种诱发机制与其他相关机制之间的区别. 本文丰富了系统通向快慢振荡的路径, 为实际谐波齿轮传动系统中的快慢振荡机理与控制研究提供参考.Abstract: A harmonic gear reducer is an advanced driving device, and it has been widely used because of many advantages. A harmonic gear reducer involves the coupling of different oscillation scales. This usually induces complex fast-slow oscillations, which have great impact on the proper operation of the system. In this paper, a harmonic gear system with the nonlinear factor of torsional stiffness is considered. The purpose of this paper is to study fast-slow dynamics of the system and to reveal a novel dynamical mechanism of the fast-slow oscillations. To begin with, the fast-slow dynamical model of the harmonic gear reducer with the nonlinear factor of torsional stiffness is built. Then, the transition of the system from normal oscillations to the fast-slow oscillations is obtained by varying the torsional stiffness. Subsequently, we give a brief description of the basic theory related to fast-slow systems. Based on this, dynamical characteristics of the fast subsystem are investigated by the fast-slow analysis and the generation mechanisms of fast-slow oscillations are revealed. Our results show that, when the system parameter is varied, the equilibrium curve of the fast subsystem does not lose its stability or bifurcate. However, near some point, a sharp quantitative change can be observed in the equilibrium point curve, characterized by the fact that the equilibrium point is able to undertake a fast transition between positive and negative coordinate values in a local small area of the equilibrium point curve. Based on this, we reveal a novel dynamical mechanism underlying the appearance of fast-slow oscillations, and compare the mechanism with other related dynamical mechanisms of fast-slow oscillations. Our results enrich the routes of dynamical systems to the fast-slow oscillations, and besides our study provides important reference to the research on the dynamical mechanisms and control of fast-slow oscillations in the actual systems of harmonic gear drive.