| There are various ring shaped periodic structures in engineering field,such as automobile wheel hub,vibratory gyroscopes,motor stators and rotors,gear ring and so on.Under the influence of concentrated force,this kind of structures are prone to the problems of uneven stress distribution and vibration instability.In this thesis,the ring shaped periodic structure and the ring stator of permanent magnet motor are taken as examples to study the static and dynamic characteristics.The main contents are as follows:In this thesis,the stress distribution of the ring shaped structures under load are analyzed by D’Alembert principle.Based on the assumption of inextensional deformation,the mathematical models of tangential and radial loaded ring shaped structures are established by the cross-section method,and the stress distribution and elastic deformation are determined.Aiming at the large deformation of the ring shaped structures,the static models of the extensional deformation are established by the crosssection method,and the stress distribution and elastic deformation are obtained by the operator method.The above results provide a simple method for stress and deformation analysis of ring shaped structures subjected to multiple loads.That is,based on the stress distribution of the ring shaped structure subjected to a single load,the stress distribution under the multiple load is obtained by the superposition method.The analytical results of the cross-section method and the superposition method are verified by an example.The dynamic stability of the ring shaped stator of permanent magnet motor is studied by eigenvalue analysis.The mathematical model is established by using Hamilton’s principle,and a method to eliminate the instability of magnetic-induced vibration by changing the topological structure of permanent magnet is studied.Two kinds of topological structures,grouping and mirror,are proposed.Among them,the number of permanent magnets,the number of groups and the angle between adjacent permanent magnets in the group can be changed to eliminate vibration instability.And the parameters of mirror topology to eliminate vibration instability are the number of permanent magnets and the angle between adjacent permanent magnets in the group.In the mirror topology,due to the multiple arrangement of the angles between adjacent permanent magnets in the group,the intra-group uniform,increasing and general topology are further proposed to eliminate vibration instability.On the basis of the analytical model,the eigenvalues of the above two topologies are used to prove the effectiveness of vibration instability suppression. |
