Analysis and Optimization of a Five-phase Hybrid Excitation Flux Switching Machine Based on the Consistency and Complementarity Principle

In this study,the general optimal stator poles/rotor teeth(P/T)combination equation of the E-core hybrid excitation flux switching(HEFS)machines are introduced,and a new HEFS machine is proposed and optimized.Firstly,the influences of three different P/T combinations(10/18,10/19,and 10/21)on the HEFS machines are investigated with two-dimensional(2D)finite element analyses(2D-FEA).Meanwhile,the consistency and complementarity principle of the armature windings is analyzed in detail to give reasonable explanations to the simulated results.The general optimal P/T combination equation of the E-core HEFS machines is deduced mathematically to provide an effective guidance on the selection of P/T combinations.The optimal P/T combination calculated by the general equation agrees with the simulated results which confirm the correctness of the mathematical inferences.Finally,the optimizations on the proposed HEFS machine are implemented to obtain higher output torque and better flux-regulation ratio characteristics based on which the cogging torque and torque ripple are reduced significantly.

Separation work analysis of cohesive law and consistently coupled cohesive law

An appropriate coupled cohesive law for predicting the mixed mode failure is established by combining normal separation and tangential separation of surfaces in the cohesive zone model （CZM） and the cohesive element method. The Xu-Needleman exponential cohesive law with the fully shear failure mechanism is one of the most popular models. Based on the proposed consistently coupled rule/principle, the Xu-Needleman law with the fully shear failure mechanism is proved to be a non-consistently coupled cohesive law by analyzing the surface separation work. It is shown that the Xu-Needleman law is only valid in the mixed mode fracture when the normal separation work equals the tangential separation work. Based on the consistently coupled principle and the modification of the Xu-Needleman law, a consistently coupled cohesive （CCC） law is given. It is shown that the proposed CCC law has already overcome the non-consistency defect of the Xu-Needleman law with great promise in mixed mode analyses.