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

ZHANG Jun CHEN Tao WANG Jian

Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (19) : 77-88.

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (19) : 77-88.

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

  • ZHANG Jun  CHEN Tao  WANG Jian
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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.

Key words

helical planetary gear train / dynamic transmission error / response surface method / gear modification

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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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