Instantaneous mode contamination and parametric combination instability of spinning cyclically symmetric ring structures with expanding application to planetary gear ring

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• 作者：Shiyu Wang^a ; ^b ; ^{wangshiyu@tju.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Wenjia Sun^a ; ^b ; Yaoyao Wang^a ; ^b
• 关键词：Spinning cyclically symmetric ring structures ; Perturbation method ; Mode superposition method ; Instantaneous mode contamination ; Parametric combination instability
• 刊名：Journal of Sound and Vibration
• 出版年：2016
• 出版时间：4 August 2016
• 年：2016
• 卷：375
• 期：Complete
• 页码：366-385
• 全文大小：890 K

文摘

This work addresses the free and parametric elastic vibrations of the spinning cyclically symmetric ring structures. The focus is on the instantaneous mode contamination, parametric combination instability and their connections. An analytical model is developed by using the Hamilton’s principle for the in-plane bending deflection, the distinction of which is in the arbitrary distributions of the attached mass and stiffness. A special case with equally-spaced discrete mass particles and spinning springs is detailed. The uneven tangential force and the time-invariant deflection caused by the mass particles are formulated. The results imply that the order of such deflection is equal to the number of the mass particles. The instantaneous mode contamination and parametric combination instability are captured by the perturbation and superposition mode shapes of the stationary smooth ring by introducing complex coefficients. The contamination rule is similar to that of the stationary structure but the contamination strength is time-variant due to the spinning springs. New analytical results and quantitative explanations on the contamination and instability especially their connections are presented. As an application of the proposed method, the free and parametric vibrations of the planetary gear ring are formulated. Main results are demonstrated by means of the numerical simulations and compared with the existing studies.