螺旋锥齿轮啮合刚度及参数振动稳定性研究

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. 

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

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 vibration system including periodically varying stiffness was derived, on the assumption that the time-varying mesh stiffness is piece-wise linearity. By adjusting the pinion machine tool settings, different contact pattern, transmission error, contact ratio and mesh stiffness under the same load condition for a pair of spiral bevel gears was treated. The Floquet theorem was applied, therefore, a program to calculate the magnitudes of the characteristic multipliers was applied 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 is investigated.