Effects of random tooth profile errors on the dynamic behaviors of planetary gears

• Published in: Journal of sound and vibration 2018-02, Vol.415, p.91-110
• Main Authors: Xun, Chao, Long, Xinhua, Hua, Hongxing
• Format: Article
• Language: English
• Subjects: Amplitudes; Computer simulation; Contact loss; Dynamic transmission error; Errors; Finite element method; Gear teeth; Gear trains; Monte Carlo simulation; Multiscale analysis; Planetary gear train; Probability distribution; Random error; Statistical analysis; Stiffness; Stochastic models; Tooth profile modification; Upper bounds; Vibration
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2017.11.022

In this paper, a nonlinear random model is built to describe the dynamics of planetary gear trains (PGTs), in which the time-varying mesh stiffness, tooth profile modification (TPM), tooth contact loss, and random tooth profile error are considered. A stochastic method based on the method of multiple scales (MMS) is extended to analyze the statistical property of the dynamic performance of PGTs. By the proposed multiple-scales based stochastic method, the distributions of the dynamic transmission errors (DTEs) are investigated, and the lower and upper bounds are determined based on the 3σ principle. Monte Carlo method is employed to verify the proposed method. Results indicate that the proposed method can be used to determine the distribution of the DTE of PGTs high efficiently and allow a link between the manufacturing precision and the dynamical response. In addition, the effects of tooth profile modification on the distributions of vibration amplitudes and the probability of tooth contact loss with different manufacturing tooth profile errors are studied. The results show that the manufacturing precision affects the distribution of dynamic transmission errors dramatically and appropriate TPMs are helpful to decrease the nominal value and the deviation of the vibration amplitudes. •A random-nonlinear model is built to describe the dynamics of planetary gear train.•The method of multiple scales is extended to study the statistical property of dynamic response.•A link is built between the manufacturing procession and dynamic response.