Research On Numerical And Analytical Combined Method Of Magnetic Field Computation For Rotational Electrical Machines

Numerical method and analytical method are combined to compute two-dimensional magnetic fields of rotational electric machines in the dissertation. In the numerical and analytical combined method the magnetic fields in stator and rotor regions are dealt with by the finite element method while the magnetic field in air gap region is expressed by the analytical expressions. The analytical expression for air gap magnetic field of rotational electric machines is derived, in which the number of equivalent pole pairs is taken into account so that period conditions can be dealt with in the computation. When the mathematical model is established, the correct connection of two kinds of equations becomes a sticking point for the finite element equations and the analytical expressions to be integrated as a whole equation. The circumference components of magnetic intensity on the common boundary will be automatically equal by using of the natural boundary conditions on air gap surfaces of the stator and rotor, that is if only vector magnetism potentials on the common boundary are continued. Therefore the natural common boundary condition of equal vector magnetism potentials is applied to connect the finite element equations and the analytical expressions in the dissertation. The process is simple and convenient, from which no error connection is realized. The precision of the numerical and analytical combined method in the dissertation is fully affirmed by comparing the computation results with those of the finite element method in which a very fine spatial discretisation is created by an adaptive meshing algorithm. The numerical and analytical combined method in the dissertation is valid by the examples of the magnetic field computation for three special electrical machines.The accurate computation of magnetic fields is more and more important for modern electric machine design and meanwhile the modern design and analysis for electric machines bring forward higher request for magnetic field computation. The rotor rotation during magnetic field computation is necessary for many important calculations. Because of good applicability and high precision the finite element analysis method has become the preferred method for numerical magnetic field computation of machines. How to avoid aberration of grid shapes in the air gap region when rotor rotates, however, is the trickiness problem for the finite element method.With the numerical and analytical combined method the rotor can be freely rotated during magnetic field computation, which provides great convenience for computing machine induced electromotive force, electromagnetic torque and dynamic process etc., and higher computation precision will be obtained that is very important for modern machine design and analysis.The rotor rotation is needed for many calculations such as induced electromotive force, electromagnetism torque, inductance parameters etc. The agile rotor rotation is more needed for dynamic computations. The fundamental obstacle to rotor arbitrary rotation in finite element method is finite element mesh in air gap region. When the magnetic field in air gap is expressed by analytic expressions there exists no finite element meshes in the air gap region. Therefore the magnitude breakthrough is obtained in realization of rotor free rotation by application of the numerical and analytical combined method.Maxwell stress method is an available one to calculate electromagnetism torque of machines. Since the magnetic field in air gap is expressed by analytical model there is no finite element meshes in air gap region so that the precision of integral calculation in air gap will not be affected from mesh shapes. At the same time the expression of electromagnetic torque does not include the variable of integral radius in air gap region. It is correct in the theory that the result of electromagnetic torque calculation is surely independent of the circle radius of the line integral. The more accurate electromagnetic torque will be obtained.The magnetic fields of three different type machines, wheel drum permanent magnet brushless DC motor, phase-decoupled permanent magnet synchronous motor, novel stator doubly-fed doubly-salient permanent-magnet machine, are computed by the numerical and analytical combined method in the dissertation. Induced electromotive force waveforms of three kinds of machines calculated by the method are quite accordant to the experiment results, which prove the validity and adaptability of the method in the dissertation.Dynamic process of the wheel drum permanent magnet brushless DC motor is computed in the dissertation. Different from existing dynamic computation methods,...