基于最小动态传动误差波动量的斜齿行星轮系齿轮修形研究

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (19) : 77-88.

论文

张俊陈涛汪建

作者信息 +

Tooth modification of helical planetary gear train based on minimum dynamic transmission error fluctuation

ZHANG Jun CHEN Tao WANG Jian

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文章历史 +

摘要

为抑制系统的振动和噪声，以动态传动误差波动量为指标，研究了斜齿行星轮系的齿轮修形策略。采用集中参数法建立了斜齿行星轮系的弯—扭—轴—摆耦合动力学模型，进而运用Runge-Katta法求解了各齿轮副的动态传动误差。借助Romax软件，数值仿真了轮系中各齿面的接触载荷。结果表明，未修形时，轮系中各啮合副的动态传动误差波动量大、齿面载荷分布不均、存在明显的啮入啮出冲击。因此，针对该斜齿行星轮系制定了齿向鼓形、齿廓渐开线的修形策略。基于齿轮啮合原理，推导了修形函数在啮合线上的分量，并将其计入行星轮系的动力学模型，再通过数值计算，获得计入齿轮修形效应的各啮合副动态传动误差。运用响应面法拟合出齿轮修形量与啮合副动态传动误差波动量之间含交叉项的二次多项式函数，取其最小值对应的设计变量值为内、外啮合副独立修形时的最佳修形量。在此基础上，以内、外啮合副独立修形时的最佳修形量为设计变量均值，进一步拟合出斜齿行星轮系综合修形的响应面函数，并通过求解函数最小值获得轮系最佳修形量组合。最后，比较了修形前、后斜齿行星轮系的动态特性。结果表明：本文所提的修形方法能有效改善齿面受载状况，使各齿轮副的动态传动误差波动量降低到4 μm以内。

Abstract

In order to reduce the vibration and noise of planetary gear train, a comprehensive tooth modification strategy to minimize the dynamic transmission error fluctuation of meshing gear pairs is proposed. An analytical bending-torsion-translation-swing coupling dynamic model of a helical planetary gear train is established, with which the dynamic transmission error of each gear pair is solved by using the Runge-Kutta method. Meanwhile, the contact pressure on the engaging tooth surface is numerically simulated by using the software of Romax. The theoretical calculations and numerical simulations indicate that without tooth modifications, there exist noticeable fluctuation of dynamic transmission errors and uneven load distributions of the tooth surfaces, leading to meshing impacts at engage-in and engage-out positions. Accordingly, a comprehensive modification strategy of crowned modification in the lead direction and involute modification in the profile direction is proposed. Based on the meshing theory, the component of the modification function along the line of action is derived, which is further incorporated into the aforementioned dynamic model to recalculate the dynamic transmission errors of meshing gear pairs. A quadratic polynomial function with crossed terms is derived with the response surface method to describe the quantitative relationship between the amounts of tooth modification and the dynamic transmission error fluctuation. By minimizing the quadratic polynomial function, the optimal tooth modification parameters of an individual gear pair can be determined. The optimal modification parameters of the internal and the external gear pairs are further set as the mean value of the modification design variables to fit the response surface function of the planetary gear system. The optimized modification parameters for the helical planetary gearings are obtained with the minimum fluctuation of transmission errors. Finally, the dynamic characteristics of a helical planetary gear train with and without modifications are compared. The comparison results show that the proposed tooth modification strategy can effectively improve the contact status of engaging surfaces and reduce the dynamic transmission error fluctuations of each gear pair within 4 μm.

导出引用

张俊陈涛汪建. 基于最小动态传动误差波动量的斜齿行星轮系齿轮修形研究[J]. 振动与冲击, 2019, 38(19): 77-88

ZHANG Jun CHEN Tao WANG Jian. Tooth modification of helical planetary gear train based on minimum dynamic transmission error fluctuation[J]. Journal of Vibration and Shock, 2019, 38(19): 77-88

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