Analysis of permanent magnet brushless AC motor using Fourier transform approach

Abstract

The paper presents an analytical model for determining performance characteristics of surface mounted permanent magnet brushless motor using Fourier transform technique. The proposed scheme assumes a simplified geometric model of surface mounted PM (SMPM) motor with dual current sheets using layer theory to analyse electrical machines. The layer theory considers regions of PMBLAC motor to be replaced by layers of respective homogeneous material properties. Isotropic model assumes stator to be sloltless while anisotropic model is also considered to account for stator slotting effect on the motor performance. The Fourier transform applicable to linear induction motor and introduced by S. Yamamura is modified and adapted for analysing PMBLAC motor. The primary stator winding and permanent magnets on rotor are replaced by their respective equivalent linear current densities. The proposed model is validated using experimental results from a 12-slot surface mounted PMBLAC motor. The proposed method is capable of calculating the effect of design parameters on the performance of the SMPM motor, thus making it suitable for design and optimisation at initial stage. Moreover, analytical validation is also presented to prove the effectiveness of the proposed method. Nomenclature A magnetic vector potential (A/m) D diameter of stator bore of original machine (m) H magnetic field intensity M magnetisation vector N number of conductors in primary winding T torque (Nm) H c coercivity of PM (kA/m) J p peak stator or primary linear current density (A/m) J s peak rotor or secondary linear current density corresponding to the dimensions, disposition and strengths of magnets in use (A/m) m ratio of two current densities (J p /J s ) I p stator coil current (A) p number of poles f frequency of stator supply (Hz) v peripheral speed of rotor (m/s) g actual air gap (mm) g e effective air gap length (mm) k pole pitch (mm) k e back-EMF constant h m thickness of magnet (mm) l layer number (subscript) σ l conductivity of respective layers (S/m) t pole pitch of original motor (m) t m pole pitch of the PM (m) j phase difference between primary and secondary current sheets k w1 winding factor j, χ, g Fourier indices of respective layers w o width of stator slot opening (mm) μ 1 permeability of rotor back iron (H/m) μ o absolute permeability of air (H/m) µ r = µ 2 relative permeability of PMs (H/m) t t stator tooth width (mm) t c stator coil width (mm)t w stator tooth-tip width (mm) t s stator slot-opening width (mm) ω angular speed (rad/s)

Memory Efficient Method for Electromagnetic Multi-Region Models Using Scattering Matrices

“…Therefore, semi-analytical models have been proposed over the years for increasingly complex structures in both 2D and 3D. One of the semi-analytical models is the harmonic modeling technique [4][5][6][7], which uses a Fourier basis to describe the solutions to the electromagnetic field quantities. By including position dependent material properties, such as the electrical conductivity [8] and the permeability [9][10][11], into the solutions, the spatial distribution of electromagnetic fields can also be accurately modeled for complex devices.…”

Parabola‐trapezoid and staircase current supply methods for PMBLM with full inverter utility and reduced torque ripple

“…The same analysis can be applied to other intervals, thus we can derive the mathematical expression of current waveform for phase A as (17). The expressions of phases B, C and D can be obtained by shifting phase A with π/4, π/2 and 3π/4 electrical radians, respectively, which are shown in (18)-(20)…”

“…The square-wave current is always used to drive the trapezoidal back-EMF motor, which is called as PM BLDCM in general [11][12][13][14][15][16]. And the sinusoidal-wave current is always used to drive the sinusoidal back-EMF motor, which is called as PM BLACM in general [17][18][19][20]. These two current waveforms and their improvements have been used for several different motors [21][22][23][24][25][26][27][28].…”

Design and analysis of a new down‐the‐hole electromagnetic hammer driven by tube linear motor

“…Although the permanent magnet motor has outstanding advantages, they are susceptible to the service temperature. It is well documented that the remanence of permanent magnetic materials will reduce significantly with increasing temperature, leading to the reduction of magnetic flux density of the air gap magnetic field of the motor and declining electromagnetic thrust [22–24]. Therefore, the theoretical calculation is needed to investigate the influence of high temperature on electromagnetic impact of motor.…”