螺旋锥齿轮啮合刚度及参数振动稳定性研究  

Mesh stiffness function and stability analysis for parametric vibration of spiral bevel gears

作　　者：王延忠[1,2] 周元子[1] 李国权[3] 郭梅[3] 

机构地区：[1]北京航空航天大学机械工程及自动化学院,北京100191 [2]重庆大学机械工程学院机械传动国家重点实验室,重庆400044 [3]中国航空工业集团公司沈阳发动机设计研究所,沈阳110015

出　　处：《航空动力学报》2010年第7期1664-1669,共6页Journal of Aerospace Power

基　　金：国家自然科学基金(50875009);航空科学基金(20090451009);"十一五"基础科研重点项目(B0620060424);机械传动国家重点实验室开放基金(SKLMT-KFKT-200813)

摘　　要：准确计算时变啮合刚度是齿轮系统动力学研究的基础.针对航空高速重载螺旋锥齿轮,基于轮齿接触分析(TCA)和轮齿加载接触分析(LTCA)通过计算瞬时接触点的轮齿变形柔度建立了时变啮合刚度数值模型;将齿轮时变啮合刚度在一个啮合周期内视为逐段线性,基于Floquet理论推导了含时变刚度参数振动系统的状态转换矩阵解析式;通过修正小轮机床调整参数设计三种接触情况,分析了算例齿轮在相同载荷工况下的接触轨迹、传动误差、重合度和时变啮合刚度;采用二自由度齿轮系统动力学模型考察工作转速范围内的周期运动不稳定区间,分析了时变啮合刚度对螺旋锥齿轮系统参数振动稳定性的影响.Theoretical study of the time-varying mesh stiffness is critical to geared system dynamics.For spiral bevel gears at high speed and heavy load in aero-engines,a numerical solution was applied to investigate the compliance and stiffness for each instantaneous contact,based on the static deflections and directional forces obtained by TCA（tooth contact analysis） and LTCA（loaded tooth contact analysis）.Analytical form for state transition matrix of parametrical excited system including periodically varying stiffness was derived from the assumption that the time-varying mesh stiffness is piece-wise linearity.By adjusting the pinion machine tool settings,different contact patterns,transmission error,contact ratio and mesh stiffness under the same load condition for a pair of spiral bevel gears were treated.The Floquet theorem was applied,therefore,a program to calculate the magnitudes of the characteristic multipliers was used to investigate the instability among the working rotation speed interval,based on a two-degree-of-freedom dynamic system.The influence of time-varying mesh stiffness on parametric vibration stability of the spiral bevel geared system was investigated.

关 键 词：螺旋锥齿轮 参数振动 加载接触分析 时变啮合刚度 FLOQUET理论 稳定性 

分 类 号：V231.92[航空宇航科学与技术—航空宇航推进理论与工程]