Analytical Investigation On Dynamic Properties Of Elastic Ring Gear

Time-varying excitations are the dominant excitations in gears system. Theseforces can be transmitted into casing and other attachments via ring structures formingthe primary vibratory transmitting paths. Therefore, the dynamic properties of the ringgear should be examined with an aim to suppress the noise and vibration. For thisreason, the relationships between key parameters and the response should be clarifiedin order to optimize the dynamic design and determine the suitable operatingcondition. The main contents are:(1) The ring gear is modeled as elastic rotating ring subject to discrete movingtime-varying stiffness. The mathematical model having in-planeinextensional deflections is developed by using the Hamilton’s principle, inwhich Coriolis effect is included.(2) The modal properties are examined by using the direct perturbation method.The relationships between the basic parameters and the modal propertiesincluding the natural frequency splitting and mode contamination are found,which naturally present a simple rule governing the suppression or evenelimination of the frequency splitting and mode contamination.(3) The parametric stability is also investigated. The focus is on the dynamictuning effect of the mesh phase and contact ratio on the dynamic response.The connections between the basic parameters, including the tooth numberand pinion number, and the parametric stability are clarified, whichcontribute to the parameters selection from the dynamic perspective.(4) The effect of the pinion group pattern on the dynamic properties of the ringstructures. The relationships between the structural topology and the naturalfrequency splitting and mode contamination are found. Further, a newconcept of equivalent group is proposed, which can be utilized to suppressthe frequency splitting and mode contamination.The main contents of this thesis are an extensional study of the National NaturalScience Foundation of China (Dynamic Topology Optimization of Rotational Ultrasonic System, Grant No.51175370). The effect of the key parameters on thenatural frequency splitting, mode contamination, and parametric stability are clarified,which contributes to the development of the dynamic tuning for general symmetricsystems.