含裂纹故障齿轮系统的非线性动力学研究

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考虑时变啮合刚度、间隙非线性及传动误差的影响,针对试验齿轮箱中的单对齿轮传动建立齿轮副扭转振动的参数化动力学模型,对裂纹故障的非线性动力学机理进行研究。采用平均法分析齿轮裂纹模型的主共振及1/2亚谐共振的动力学响应;给出裂纹演化过程对齿轮系统啮合刚度及动力学行为的影响;通过幅频特性曲线、时域图、相轨迹图、Poincaré截面图及频谱图综合分析含有裂纹故障齿轮的振动特征;通过奇异性理论分析裂纹程度及传动误差所产生的内部激励与系统动力学分岔的关系,从而揭示了不同裂纹程度和传动误差所引起的不同分岔模式;最后通过试验提取含有裂纹故障齿轮的振动特征,试验结果验证了理论分析的结果,从而为齿轮系统裂纹故障的识别提供理论依据。 According to spur gear pair of laboratorial gearbox,a dynamic model with time-varying mesh stiffness,nonlinear clearance and transmission error is established,and its nonlinear dynamic mechanism is also researched.The dynamic response of gear model is analyzed under primary resonance and 1/2 sub-harmonious resonance by means of averaging method,and shows the effect of crack evolvement on mesh stiffness and dynamic characteristic of gear system.The vibration features of gear pair with cracked failure are analyzed by amplitude frequency curve,time domain,phase contrail,Poincare mapping and frequency spectrum.Singularity theory analysis shows the relation between crack extents as well as the internal force formed by transmission error and the dynamic bifurcation of gear system,which indicates different bifurcation under different crack extent and transmission error.At last,mechanism research results are proved by the vibration characteristic of fault signals measured on gearbox experiment,which supply a theory base to crack fault diagnosis of gearbox.