| The rotating machinery is widely used in the practical engineering fields,such as the planetary gear transmission,hydraulic motor,rolling bearings,permanent magnet motor,and the ultrasonic motor.This machinery usually employs cyclic ring topology,structures.Parametric vibration can be induced due to the contact/non-contact,distributed/discrete,or stationary/rotating loads.The effect of the key parameters on the modal behavior and dynamic stability is studied in order to clarify the relationships between the cyclic topology and dynamic performance.The main contents include:(1)An elastic model of the structure is developed by using Hamliton principal in the inertial coordinates,based on which the parametric vibration is investigated.The eigenvalue is obtained by using the coordinate transformation and general vibration theory,and the modal properties and parametric instability are studied.The results imply that the natural frequencies split due to the rotating supports.The divergence and flutter instabilities can occur for some rotation speeds.Besides,the unstable regions and dynamic response are calculated by using the Floquét theory and numerical method with an aim to verify the theorical results.(2)The parametric vibration is investigated by the proposed perturbation method.The eigenvalues are obtained based on the ring-fixed coordinates,and the natural frequency splitting,parametric vibration and their relationships are analyzed.The results imply that the unstable behaviors occur at the splitting natural frequencies instead of the repeated ones.Besides,the classical problem of the rotating ring with stationary support and the inverse problem are examined.The results verify that the former is stable but the latter can be unstable,which are compared with the existing results in the open literature.(3)The simplification of the complete model with parametric excitation is examined.The eigenvlaues are obtained for different models by using direct perturbation and mode superposition.The equivalence between the complete and simplified models are examined in the presence of weak support.The results imply that the flexual and extensional natural frequencies cannot split simultaneously.The natural frequencies are veering for the complete model but interect with each other for the simplified models.According to the simplified models,different dynamic behaviors regarding different vibration modes can be found before or after the crossover point.Additionally,the same estimation on the stability can be made based on different models.That is,the parametric instability can only occur at the splitting natural frequencies rather than the repeated ones.This thesis is a part of research of the National Natural Science Foundation of China(Dynamic Topology Optimization of Rotational Ultrasonic System,Grant No.51175370),and a part of the preliminary research of the National Natural Science Foundation of China(Investigation on Dynamic Tuning and Grouped Configuration of Cyclically Symmetric Machinery,Grant No.51675368).The studies provide some new directions and ideas for the topology optimization of the transmission/support/diriving mechanisms. |
