人字齿行星传动固有特性及模态突变现象分析  

Analysis of Natural Characteristic and Loci Veering / Crossing of Double Helical Planetary Gear Train

作　　者：刘振州 张俊[1] 

机构地区：[1]安徽工业大学机械工程学院,安徽马鞍山243032

出　　处：《机械传动》2015年第10期9-15,共7页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51375013;50905122);安徽省自然科学基金(1208085ME64)

摘　　要：建立了NGW型人字齿行星传动的平移-扭转耦合动力学模型。依托所建模型,推导出系统的运动微分方程,进而通过求解特征值问题获知系统的固有频率和振型。根据传动系统的运动特征,将NGW型人字齿行星传动的自由振动归纳为3种典型振动模式,即:中心构件轴向扭转振动模式、中心构件径向平移振动模式和行星轮振动模式。在模态跃迁、相交原则的基础上,从振动模式和模态能量角度进一步分析了两种固有频率轨迹突变现象对传动特性的影响。结果表明,模态相交现象发生时,固有频率振动模式和模态能量均发生突变式交换;模态跃迁现象发生时,模态能量发生突变但不交换,且突变较平缓,而振动模式不变。最后,通过具体实例仿真验证了所得结论的正确性。论文工作可有效预估人字齿行星传动系统的固有频率及模态、能量突变位置,从而为减噪抑振及参数优化提供基本的理论依据。A translational- rotational- coupling dynamics model for a NGW double helical planetary gear train（ DHPGT） is developed to investigate the free vibration characteristics. Based on the established model,the differential equations of motion of the system are derived. Through the solution of the system eigenvalue problem,the natural frequency and vibration mode are acquired corresponding. According to the characteristics of transmission system,the vibration modes of a DHPGT can be classified into three categories,i. e.,the central components axial torsional vibration mode,the central components translational mode and the planet wheel vibration mode. Based on the loci veering / crossing principle,the influences of loci veering and loci crossing on the transmission characteristic are analyzed from the perspective of modal strain energy and vibration modes.The simulation results demonstrate that vibration modes and modal energy exchange abruptly when a loci crossing occurs,while vibration modes and modal energy change step- by- step but do not exchange when a loci veering occurs. The conclusions are then verified by numerical simulation of an example system. The present research can accurately forecast natural frequency and the point of modal and modal energy mutation,a fundamental theoretical basis for the parameter optimization,noise reduction and vibration suppression for the DHPGT is provided.

关 键 词：人字齿行星传动 固有频率 振动模式 模态跃迁 模态相交 

分 类 号：TH132.425[机械工程—机械制造及自动化]