Modal properties of a multi-stage power-split planetary gear set

Lina Zhang,Ruoyu Sheng,Yong Wang,Kai Wu,Qilin Huang

doi:10.1177/1687814017698876

Lina Zhang, Ruoyu Sheng + Show 3 more

Open Access

https://doi.org/10.1177/1687814017698876

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Abstract

Planetary gears are recognized as one of the most effective forms of power transmission. A dynamic model of an N-stage power-split planetary gear set is proposed in this article. Three-dimensional translations and axial rotation of all members, mesh stiffness, bearing stiffness, and the interstage coupling stiffness are considered. Subsequently, equations of motion of the whole system are derived. Natural frequencies and vibration modes are obtained by solving the eigenvalue problem governed by corresponding equations. According to the modal properties, all vibration modes of the N-stage system can be categorized as N + 2 groups: the overall axial translational–rotational mode, the overall radical translational mode, and the ith-stage planet mode ( Ni > 3). Furthermore, the typical vibration modes of a two-stage system are graphed. It is also found that the radical interstage coupling stiffness has an impact on natural frequencies of the overall radical translational modes, while the axial and twist coupling stiffness only affect the natural frequencies of the overall axial translational–rotational modes.

Highlights

Planetary gears are widely used in aerospace and wind turbine industries because of their high reliability, high torque, and compactness.1 The closed-form planetary gears are more competent due to the power-split characteristic and higher transmission ratios
The results show that mode types of the N-stage planetary gear train (PGT) can be classified into N + 2 groups: the overall axial translational–rotational mode, the overall radical translational mode, and the ith-stage planet mode (Ni . 3)
From the results of modal characteristic analyses, the vibration modes of the N-stage PGTs are categorized as N + 2 groups: the overall axial translational– rotational mode, the overall radical translational mode, and the ith-stage planet mode (Ni . 3)

Summary

Introduction

Planetary gears are widely used in aerospace and wind turbine industries because of their high reliability, high torque, and compactness. The closed-form planetary gears are more competent due to the power-split characteristic and higher transmission ratios. Lin and Parker developed the transverse–torsional dynamic models of single-stage planetary gears and analytically investigated the natural frequency spectra and vibration modes with spaced and diametrically opposed planets. Kiracofe and Parker established the rotational dynamic model compound and multi-stage planetary gears, and investigated the structured vibration mode and natural frequency properties of the system. With those analyses, researchers further investigated the vibration reduction by detecting the influences of system parameters on dynamic response, such as mesh stiffness fluctuation, mesh phasing relationships, and contact ratios. A dynamic model of a multi-stage power-split planetary gear set considering the threedimensional translation and axial rotation is established to investigate the modal properties of the system.

Equations of motion for ring gear in stage 2

Equations of motion for planets in stage 1

12. Dynamic equations for planets of stage N

10. Dynamic equations for ring gear of stage N

Conclusion