| With the rapid development of the national economy,the population of large and medium-sized cities is increasing,and the traffic problem in cities is becoming increasingly serious.In order to meet the needs of people's work and life,many cities are building subways,light rails and intercity high-speed trains in recent years.Now the era of rail transit has arrived and thus the research needs of rail transit technology are more urgent.For rail transit,the research of traction system is very important,especially the research of traction machine.This paper takes a primary permanent magnet vernier linear machine as the research object.The thrust and no-load back electromotive force(back-EMF)are two important aspects of the machine to achieve electromechanical energy conversion.In this paper,the formulae of no-load back-EMF and thrust of the machine are derived emphatically.The multi-harmonic permanent magnet vernier linear machine can achieve richer harmonics by using the non-uniformly distributed permanent magnet arrays along the airgap,and its performance is better than that of the conventional primary permanent magnet vernier linear machine.The main research results of this paper are as follows:1.The structure of the multi-harmonic permanent magnet vernier linear machine is described in detail and compared with that of conventional permanent magnet vernier linear machine.At the same time,the mathematical models of magneto-motive force(MMF)and permeability are established based on the topology of the two machines.From this mathematical models,the MMF and permeability formulas are derived.In addition,the harmonics in MMF and permeability are analyzed by formula.Then the no-load airgap magnetic density formulas are derived from the MMF and permeability formulas.The harmonics contained in the airgap flux density are analyzed and compared with the finite element method(FEM)results.2.The airgap flux modulation principle of the multi-harmonic permanent magnet vernier linear machine is analyzed by theoretical analysis and FEM.At the same time,the phase angle analysis of the two machines are researched by theoretical analysis and FEM,so as to distinguish the moving and stationary harmonics,which is beneficial to the analysis of the effect of each harmonic on the no-load back-EMF.3.The formula of no-load back-EMF is derived and verified by the equivalent model method.Several models corresponding to the effective harmonic order are established and compared with the FEM results of the original model and the theoretical analysis results.Finally,the formula method and the equivalent model method are basically in agreement with FEM results,which verify the effectiveness of the no-load back-EMF formula and the equivalent model method.4.The thrust formula is derived by using the relation between the back-EMF and the thrust.The theoretical results of thrust analysis are compared with the results of FEM.At the same time,through the FEM and theoretical analysis,the electromagnetic performance of the two machines are analyzed and compared,such as thrust,cogging force,loss,efficiency and so on.The results show that the thrust density of the multi-harmonic primary permanent magnet vernier linear machine is 15% higher than that of the conventional primary permanent magnet vernier linear machine.In addition,the thermal analysis of the machine and the irreversible demagnetization capability of the permanent magnets are also carried out,and the results show that the permanent magnets are not easy to generate demagnetization under normal working conditions.5.The prototype of the multi-harmonic permanent magnet vernier linear machine is manufactured and the existing equipment in the laboratory are used to build the relevant experimental test platform.The speed,no-load back-EMF,thrust and efficiency are measured.The test results are consistent with the theoretical analysis and the FEM,which has verified the correctness of the magnetic field modulation theory analysis. |
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