TORQUE CALCULATION OF HYSTERESIS MOTOR USING FEM WITH ASSYMERTIC 2D

PERMEABILITY TENSOR

RISHIKESH CHOUDHARYELECTRICAL MACHINES AND DRIVES

12304EN005

Introduction of hysteresis motors. Finite element formulation. Torque computation. Analysis and experiment. Analyzed model. Simulation results. Conclusion References

CONTENTS

Despite of it’s low power output per unit volume , low power factor , low efficiency; the hysteresis motor is extensively used in fractional kw applications due to it’s following advantages-

self starting asynchronous acceleration self synchronization constant steady state speed low noise figure

Introduction

To estimate the machine behavior Need of hysteresis modeling Electromagnetic field distribution be

analyzed Modeling of semi hard PM material Hysteresis loop approximation

If we neglect higher order harmonics, the hysteresis ring rotating at synchronous speed undergoes static magnetic field.

Then, why we need hysteresis modeling of the material despite of knowing that it is undergoing static field.

sometime it is said that broader the hysteresis loop greater the torque but if a magnetic material experiences hysteresis loop, the area of the loop results not in torque but in loss !

Material modeling is motivated by following questions -

The necessary and sufficient conditions required for the production of steady state alignment torque are to have two fields one of which be produced by stationary member and other by rotating member having no relative speed in between so as to have constant space angular difference between them.

Hysteresis motor exploits the principle of the hysteretic phenomena due to which the induced time varying magnetic flux at any point lags in time behind the applied mmf to that point .

When balanced stator windings are energized by balanced set of currents , it produces rotating sinusoidal mmf wave in the air-gap sliding over the rotor surface at synchronous speed hence the mmf exposed to each individual elemental surface (parallel to rotor axis) becomes time varying.

Due to hysteresis, the magnetization in an elemental portion lags in time behind the applied mmf and when these time lagging induced magnetization of all individual elemental portions be unified together, a rotating flux density pattern results, lagging in space behind the stator produced mmf wave.

The angle of lag is shown by the fig-1,When flux density wave travels in Counterclockwise direction

Fig-1

The lag angle is well expressed by the two dimensional magnetic permeability tensor with asymmetric off diagonal components.

Hence the generated torque can be analyzed by employing finite element analysis using asymmetric permeability tenor.

The result is compared with experimental ones.

Finite element analysis has been developed by using the two dimensional permeability tensor. If the fields are varying two dimensionally, the constitutive equation between magnetic flux density and magnetic filed intensity is eqn (1).

-----(1)

Finite element formulation

If we assume the off-diagonal terms to be zero, H sometime leads B and sometime lags behind B

For the given condition we can have non zero torque-------------

Maxwell’s equation for magnetoquasistatic problems

-------- 2

------ 3

Torque per unit volume can be given

If we use constitutive equation ,

The torque per unit volume can be expressed as

By using analyzed field distribution , this

torque can be calculated in each element and sum of this torque over the hysteresis ring region is the total instantaneous torque generated in the rotor

Total torque at each step can be calculated by

the equation,

Where the subscript ‘e’ means an element , and represents the area of each element,

and represents axial length and E represents the entire region of ring.

And the time averaged torque is calculated as follows -

θ is the phase

angle of the input current.

Analyzed model – The analyzed model is a 5[W], 4 pole and

phase hysteresis motor. It was originally designed as single phase capacitance-run hysteresis motor, but the stator windings are changed into 2 phase ones. The specification of the analyzed motor is shown in Table. I. The cross section of the analysis and experiment model is presented in the Fig. 4.

The finite element mesh is shown in Fig. 5. The number of the node is 2094 and that of the element is 5738.

A quarter of the entire region has been analyzed by applying periodic condition.

In the analysis, Permeability of the stator part is assumed to be constant scalar and the permeability of the hysteresis ring is considered to be a tensor.

The values are-

Fig- 4 Cross section Fig-5Of analyzed motor finite element

mesh used in analysis

Specification of analysis motor -

There is comparison between experimental and analytical result -- fig-6

There is a comparison between simulation and experimental result in Fig. 6. The two results are in quite a good agreement. The cause of little differences between the two results may lie in following assumptions. The permeability in the stator core and the values of the tensor in the hysteresis ring are assumed to be constant and three dimensional end effect is neglected.

The effect of current harmonics on torque Almost 25% of torque ripple exists when there

exist 10% of 7‘th harmonics current component. This result implies that the output torque ripple is strongly affected by harmonics in the input current.

Fig-7

Finite element analysis of hysteresis motor has been investigated.

The torque in the hysteresis motor is assumed to be due to the fact that H leads B in the hysteresis ring.

Asymmetric two dimensional magnetic permeability tensor is used to represent the lag angle between 2 and E . By use of the tensor, torque under static magnetic field can be analyzed.

The Maxwell stress tensor-like method or full hysteresis modeling to compute toque requires much time consuming cost or produces mesh dependent result.

But the proposed method is very effective to compute the torque and has clear meaning of the origin of the torque in the hysteresis motor. The analysis results are in quite a good agreement with experimental ones.

concluion

M. A. Rahman, M. A. Copeland, and G. R. Slemon, "An analysis of the hysteresis motor, part 111 parasitic losses," IEEE Trans. on Power App. Syst., Vol. 88, No.6, pp.954-961, June 1969

P. H. Trickey, "Test analysis and calculation of polyphase hysteresis motors," IEEE Trans. on Power App. Syst., Vol. 91, No.5, pp.1855-62, 1972

G. R. Slemon, R. D. Jackson, and M. A. Rahman, "Performance predictions for large hysteresis motors," IEEE Trans. on Power App. Syst., Vol. 96,No.6, pp.1915-1919, Nov./Dec. 1977

G. Wakui, K. Kurihara, and T. Kubota, "Radial flux type hysteresis motor with reaction torque-numerical analysis of hysteresis motor using finite element method," IEEE Trans. Magn., vol. 23, No. 5, pp.m 3845-3852, September 1987

N. Galan, "The hysteresis motor with an anisotropic rotor," IEEE Trans. on Energy Conversion, vol. 2, No. 4, pp. 605-614, December 1987

Farouk A. A. Zaher, "An analytical solution for the field of a hysteresis motor based on complex permeability," IEEE Trans. Energy Conversion, vol. 5, No. 1, pp. 156-163, March 1990

H. Y. Lee, H. K. Jung, S. Y. Hahn, G.S. Park, "Finite element analysis of rotational hysteresis loss using two dimensional permeability tensor,“ Journal of Korean Magnetics Society, Vol. 5, No. 5, October 1995

J. D. Jackson, Classical Electrodynamics. pp. 168-169, John Wiley & Sons, 1975