内外激励作用下多自由度齿轮系统的非线性动力学特性  

Non-linear dynamic features of a gear system with multi-DOF subjected to internal and external excitation

作　　者：向玲[1] 贾轶[1] 李媛媛[1] 冯晓冉[1] 高雪媛 邸薇薇 

机构地区：[1]华北电力大学机械工程系,河北保定071003

出　　处：《振动与冲击》2016年第13期153-159,205,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(51475164);河北省自然科学基金(E2013502226)

摘　　要：采用周期扩大法,建立了齿轮副的六自由度非线性动力学模型,模型考虑了齿轮副间的时变啮合刚度、齿侧间隙、齿面摩擦等非线性因素;对模型中的相关周期项作傅里叶级数展开,并采用数值积分方法研究六自由度齿轮传动系统的运动随转速、支撑刚度的分岔特性。结合poincaré截面图、分岔图、FFT频谱及最大Lyapunov指数图,系统地分析了支撑刚度对齿轮系统的影响。结果发现,随着激励频率的提高,系统经过多次跳跃进入混沌,提高支撑刚度会使系统的跳跃点数目增加,并且使系统的混沌区减小且整体后移,致使系统推迟进入混沌;再者会使系统通向混沌的道路多样化,除了拟周期通道之外,还出现了激变性、阵发性的混沌道路及"周期5-拟周期-锁相-不稳定吸引子-混沌"的非常规混沌道路。另外支撑刚度的提高会使系统的1/2次谐振加强,致使谐振频率下的动态啮合力(DMF)增大,但会使一些混沌区的DMF逐渐减小,并且使啮合轮齿经历"双边冲击-单边冲击-无冲击"的状态变化。Based on the period-enlargement method,a 6-DOF nonlinear dynamic model of a spur gear pair was developed considering rectangular-wave mesh stiffness,backlash,sliding friction and other no-linear factors. Periodic terms in the dynamic equations were expanded with Fourier series and numerical integration was used to investigate the influences of system parameters including rotating speed and supporting stiffness on the bifurcation features of the system.The Poincaré maps, bifurcation diagrams, FFT spectrum and the largest Lyapunov exponents were achieved to systematically analyze the effects of supporting stiffness on the gear system. It was shown that the system goes into chaos motion after several ＂frequency hoppings ＂ with increase in exciting frequency; besides,as the supporting stiffness increases,the number of ＂frequency hoppings＂increases accordingly,the regions of exciting frequency corresponding to chaos motion are smaller and delayed,in other words,the system enters later chaotic motion due to the larger supporting stiffness; moreover,the roads to chaos become diverse,in addition to quasi-periodic route,there exist intermittent and catastrophic chaos routes and the non-typical ‘period 5 quasiperiodic-locked-unsteady attractor-chaos＇ chaos route; with increase in supporting stiffness,the resonance of the system at w /2（ w is the exciting frequency） becomes stronger and the dynamic meshing force（ DMF） increases accordingly,but the DMF in some chaotic regions decreases gradually,the gear system exhibits a state change of ＂double-side impact-single-side impact-no impact＂.

关 键 词：齿轮副 非线性动力学 摩擦 间隙 支撑刚度 

分 类 号：TH113[机械工程—机械设计及理论]