端曲面齿轮传动系统的非线性动态特性

Nonlinear Dynamic Characteristics of the Curve-face Gear Transmission System

为了研究端曲面齿轮传动系统的非线性动态特性以及参数对系统动态特性的影响,建立了端曲面齿轮系统的非线性动力学模型;选取无量纲啮合频率为控制参数,通过分岔图、相图、时间历程图、Poincaré映射图,研究了系统的动力学特性。研究表明,系统经跳跃分岔由无冲击状态转迁为单边冲击状态,随后经连续的倍化分岔通向混沌运动;当增大综合传动误差或减小转矩时,系统无冲击状态区域逐渐收缩,跳跃分岔值和倍化分岔值发生超前,使系统提前发生跳跃现象;无冲击—单边冲击的转迁方式发生改变,亚谐运动区域逐渐扩展并发生前移,系统运动类型增多,运动周期数增大,混沌运动区域逐渐扩大,系统稳定性下降。

In order to study the nonlinear dynamic characteristics of the curve-face gear transmission system and the influence of parameters on the dynamic characteristics of the system,a nonlinear dynamic model of the curve-face gear system is established.The dimensionless meshing frequency is selected as the control parameter,and the bifurcation diagram,phase diagram,time history diagram and Poincarédiagram are analyzed.The mapping graph is used to study the dynamic characteristics of the system.The results show that the system changes from the non-impact state to the unilateral impact state by jumping bifurcation,and then leads to chaotic motion by continuous doubling bifurcation.When the comprehensive transmission error is increased or the torque is reduced,the non-impact state region of the system shrinks gradually,and the jumping bifurcation value and doubling bifurcation advance,which make the system jump ahead of time.The mode of transition from non-shock to unilateral shock changes,the subharmonic motion region expands gradually and moves forward,the types of motion increase,the number of motion cycles increases,the chaotic motion region expands gradually,and the stability of the system decreases.