Damir Zarko

Analytical calculation of magnetic field distribution in the slotted air gap of a surface permanent-magnet motor using complex relative air-gap permeance

We present an analytical method for calculation of no-load magnetic field distribution in the slotted air gap of a surface permanent-magnet (PM) motor with radial or parallel magnetization. The method introduces the notion of complex relative air-gap permeance, calculated from the conformal transformation of the slot geometry, to take into account the effect of slotting. As a result, an accurate solution of both radial and tangential components of the flux density can be obtained which shows excellent agreement with the results of finite-element simulations. As an example of the effectiveness of the model, we present calculations of the back electromotive force and the cogging torque waveforms in a surface PM motor.

Analytical Solution for Cogging Torque in Surface Permanent-Magnet Motors Using Conformal Mapping

We present an analytical method for the calculation of cogging torque in surface permanent-magnet (PM) motors. The cogging torque is calculated by integrating the Maxwell stress tensor inside the air gap. The principle of complex relative air-gap permeance derived from conformal transformation of the slot geometry is used to take into account the effect of slotting and to calculate the radial and tangential components of the air-gap flux density required for integration of the tangential component of the Maxwell stress tensor. We implemented the proposed analytical solution on a 7-kW four-pole surface PM motor and compared the results with finite-element solutions. We present an example of finding the optimal magnet angular span to yield minimum cogging torque as an example of the effectiveness of the method.

Design of a linear bulk superconductor magnet synchronous motor for electromagnetic aircraft launch systems

High-temperature superconducting (HTS) material in bulk form is used to design a linear synchronous motor for an electromagnetic aircraft launch system. The motor is designed without an iron core. Stator coils are placed in the air while the permanent magnets used in conventional design of linear permanent magnet synchronous motors are replaced by the HTS bulk magnets. The physical, operational, and equivalent circuit parameters of the linear motor with HTS bulk magnets are compared with those of a linear permanent magnet synchronous motor and linear induction motor designed for the same application. Results show that utilizing superconducting magnets is only superior at temperatures below 40 K.

Turbogenerator end-winding leakage inductance calculation using a 3-D analytical approach based on the solution of Neumann Integrals

An analytical technique that can be effectively used for the calculation of the end-winding leakage inductance of a turbogenerator has been presented. It is based on a three-dimensional geometric model of the end-winding region in which each coil is modeled as a set of serially connected straight filaments. The calculation of the mutual inductance of the end coils is based on the multiple solutions of the Neumann integral. The method also accounts for the influence of stator core iron on the end-winding leakage inductance by using the method of images. The results of the calculations have been compared with the measured values of the leakage inductance for 247-MVA turbogenerator manufactured by KONCAR Generators and Motors Inc., Zagreb, Croatia. The principle of the end-winding leakage inductance calculation described herein can be effectively used for other types of machines and windings as well.

Magnetic Field Analysis of Inset and Surface-Mounted Permanent-Magnet Synchronous Motors Using Schwarz–Christoffel Transformation

In this paper, we apply an original numerical Schwarz-Christoffel (SC) transformation to analyze magnetic field originating from permanent magnets and the armature winding currents in a slotted air gap of an inset permanent-magnet synchronous motor. We obtained the solution of the SC integral numerically using Matlab SC Toolbox. We used this field solution to calculate both cogging torque and electromagnetic torque by integrating the Maxwell stress tensor inside the air gap. The case without inter-polar piece, which is equivalent to a surface-mounted permanent-magnet motor, is also treated. The accuracy of the developed method is verified by comparing its results with those obtained from the developed numerical finite-element models.

Analytical Model of Slotted Air-Gap Surface Mounted Permanent-Magnet Synchronous Motor With Magnet Bars Magnetized in the Shifting Direction

An analytical model is presented, which uses two-dimensional field theory in polar coordinates to determine the flux density distribution, cogging torque, back EMF and electromagnetic torque in the slotted air gap of permanent-magnet motors with surface mounted magnet bars which are magnetized in shifting direction. The magnet arc to pole pitch ratio in the motor is not necessarily equal to unity like in the case of Halbach array magnetization. The effect of stator slots is introduced by modulating the magnetic field distribution in the slotless stator by the complex relative air-gap permeance. With this complex permeance, the radial and tangential components of flux density are calculated. In the analytical and numerical study a finite number of magnet bars, which is considered sufficient to get a sinusoidal magnetization, is used. The influence of the number of magnet bars on magnetization is also investigated. The accuracy of the developed model is verified by comparing its results with those obtained from experimental measurement and previously validated linear and nonlinear numerical finite element code.

Design and comparison of linear synchronous motor and linear induction motor for electromagnetic aircraft launch system

Two basic linear motor designs suitable for an electromagnetic aircraft launch system (EMALS) have been presented in the paper. The motors have been designed with an emphasis on easy assembly and replacement even at the cost of slightly reduced performances. Both, linear permanent magnet synchronous motor (LPMSM) and linear induction motor (LIM) are assembled from modular stator segments which can be quickly and easily replaced. Performances and equivalent circuit parameters of the LPMSM and LIM designs are compared at the end of the paper.

Permanent Magnet Machine Design Practice and Optimization

The complexity of the permanent magnet (PM) machine structure makes the optimal design of the PM machine always a difficult task. The multiple objectives of an optimal design make most classic optimization algorithms inapplicable, due to the nonlinearity and some discontinous variables. In this paper, two interior permanent magnet (IPM) machine design practices with modular stator structure and conventional stator structure are discussed. The design process is directly coupled with finite-element analysis (FEA) with the machine design guidelines embedded in the optimization process. Multivariable optimization methods based on Monte Carlo and differential evolution algorithms are applied in the design phase and the results are compared in this paper

Analytical Solution for Electromagnetic Torque in Surface Permanent-Magnet Motors Using Conformal Mapping

We present an analytical method for the calculation of electromagnetic torque in surface permanent-magnet (PM) motors. Our method uses conformal mapping to calculate the electromagnetic torque by integrating the Maxwell stress tensor inside the air gap. It uses the radial and tangential components of the flux density in the slotted air-gap produced by the currents flowing in the three-phase armature winding. We demonstrate our analytical solution on a 7-kW four-pole surface PM motor and compare the results with finite-element solutions. We present the results for various angular spans of permanent magnets and various sizes of the slot opening to confirm the validity of the analytical approach.

Calculation of Unbalanced Magnetic Pull in a Salient-Pole Synchronous Generator Using Finite-Element Method and Measured Shaft Orbit

In this paper, the unbalanced magnetic forces which act upon the rotor of a salient-pole synchronous generator due to eccentric motion of the rotor shaft in the presence of magnetic field in no-load and loaded condition are calculated using the finite-element method. The displacement of the rotor is modeled using the actual shaft orbit measured on a 5-MVA salient-pole generator driven by a gas turbine in a cogeneration plant. The influences of the stator winding parallel paths and the rotor damper winding on attenuation of unbalanced magnetic pull are analyzed using the finite-element method. It is shown that under linear conditions the correlations between separate harmonic components of the shaft orbit, the resulting harmonic components of the unbalanced magnetic pull and the induced stator winding currents can be established in both the no-load and loaded condition.