考虑磨合的变角减速器齿面形貌模拟及振动特性分析

Simulation of tooth surface topography and analysis of vibration characteristics for variable-angle speed reducer considering running-in

  • 摘要: 为研究磨合对变角减速器齿面形貌及振动特性的影响,首先,采用结构函数法计算磨合后齿面的分形参数,并结合分形理论与齿轮渐开线方程,模拟实际粗糙齿面的形貌特征;其次,建立了一个包含16自由度的弯-扭-轴耦合的锥齿轮-转子-轴承动力学模型,该模型考虑了齿面形貌、时变啮合刚度等因素;再次,通过势能法结合微凸体分布函数计算时变啮合刚度,分析磨合前后刚度的变化规律,并利用分形函数构造齿轮粗糙啮合间隙;最后,采用龙格-库塔(Runge-Kuta)数值积分法求解模型,并通过试验验证,对比磨合前后系统的振动特性变化规律。结果表明,基于结构函数法计算的分形参数能够有效模拟变角减速器微观齿面的微观形貌。磨合过程显著改变了齿面形貌,降低了齿面粗糙度和齿轮啮合间隙,同时减少了时变啮合刚度。随着齿面粗糙度的降低,系统啮合频率的幅值明显下降,振动特性得以显著改善。试验结果与理论分析有较好的一致性,为变角减速器磨合工艺的研究提供了理论依据。

     

    Abstract: In order to study the influence of running-in on the tooth surface morphology and vibration characteristics of the variable angle reducer, firstly, the fractal parameters of the tooth surface after running-in were calculated by using the structure function method, and the actual rough tooth surface morphology was simulated by combining the fractal theory and the gear involute equation. Secondly, a dynamic model of bevel gear-rotor-bearing with 16 degrees of freedom was established, which takes into account tooth surface morphology and time-varying meshing stiffness. Thirdly, the time-varying meshing stiffness was calculated by the potential energy method combined with the distribution function of the micro-convex body, and the time-varying meshing stiffness change before and after running-in was analyzed, the fractal function was used to construct the rough meshing gap of the gear. Finally, the Runge-Kuta numerical integration method was used to solve the model, and the vibration characteristics of the system before and after running-in were compared by experiments. The results show that the fractal parameters calculated by the structure function method can effectively simulate the microscopic tooth surface morphology of the variable angle reducers. The running-in process significantly changes the shape of the tooth surface, reduces the roughness of the tooth surface and the meshing clearance of the gear, and reduces the time-varying meshing stiffness. With the reduction of tooth surface roughness, the amplitude of meshing frequency of the system decreases obviously, and the vibration characteristics are improved significantly. The experimental results are in good agreement with the theoretical analysis, which provides a theoretical basis for the study of running-in technology of variable angle reducers.

     

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