变双曲圆弧齿线圆柱齿轮非线性振动特性分析

为得到变双曲圆弧齿线圆柱齿轮（CHATT）工作时的振动规律，以便设计出运行平稳可靠、传动高效的齿轮，对其非线性振动特性展开研究。通过齿轮副承载接触分析，计算啮合线上轮齿的时变啮合刚度和轴向误差激励，并依据啮合冲击计算模型得到啮入冲击激励。基于集中参数理论建立CHATT的12自由度的弯扭轴多因素耦合振动模型，再依据牛顿第二定律建立包含上述三种内部激励的振动微分方程组。采用变步长四阶Runge-Kutta法对量纲一化后的方程组求解，对比主动轮和从动轮各自垂直、扭转和轴向上的振动特性数值解，结果表明：主动轮和从动轮的振动规律始终保持一致，竖直和扭转方向上作拟周期运动，轴向振动处于稳态响应的近混沌状态。进一步研究齿线半径、负载转矩和输入转速等三个参数变化对系统振动特性的影响规律，分析结果表明：轴向振动从多周期运动向近混沌运动演变，其振动的规律性更容易受到上述三个参数变化的影响。变双曲圆弧齿线圆柱齿轮振动模型的建立、求解和参数影响分析为后续的动态设计、预测不同参数下的振动响应趋势以及降噪提供一定的理论依据。

Analysis of Nonlinear Vibration on a Cylindrical Gear with Variational Hyperbola and Circular-arc-tooth-trace

In order to get the vibration rule of a cylindrical gear with variational hyperbola and circular-arc-tooth-trace (CHATT) at work and design a stable and efficient gear,it''s necessary to analyze its nonlinear vibration characteristics.The time-varying stiffness of meshing curve and axial error excitation were calculated by load tooth contact analysis (LTCA),and meshing impact excitation was received according to meshing impact model.The twelve-degree of bending-torsion-shaft multi-factor coupling dynamical model of CHATT was established based on the theory of concentrated parameter,and vibration differential equations were built on the basis of Newton''s second law.Then,equations were solved by adopting fourth-order Runge-Kutta algorithm with variable step lengths.Vibration displacement,vibration velocity,vibration acceleration,dynamic load of bearing,vibration displacement & velocity phase and Poincaré section of driving gear and driven gear were calculated,and response amplitude spectrums of above signals were obtained with FFT method.The comparison of numerical solutions of driving gear and driven gear in verticality,torsion,and axial direction showed that the vibration law of driving gear always keeps consistent with driven gear,quasi-periodic motion occurs in verticality and torsion direction,and vibration in axial direction shows a nearly chaotic state of steady state response.Moreover,the influence rule on system vibration characteristics was researched by changing tooth-trace radius,loading torque and inputing speed,and results of vibration displacement & velocity phase indicated that vibration regularity of driving gear and driven gear in axial direction gradually becomes poor,which evolutes from quasi-periodic motion to nearly chaotic motion.The regularity of axial direction vibration is more susceptible by changing these three parameters.The establishment and solution of CHATT vibration model and parameter influencing analysis provide theoretical foundation for the later dynamic design,prediction of vibration response under different parameters,and noise reduction.