A generalised technique for applying harmonic analysis to determine the steady-state performance of a cage induction motor with any stator winding connection and any excitation configuration, is described. Explicit formulas are given for all the impedances required. The method is verified by means of comparison between experimentally measured variations of input power, input current, and electromagnetic torque and those calculated using the technique.

Generalised harmonic analysis for the steady-state performance of sinusoidally-excited cage induction motors

Condition monitoring can diagnose the inception of fault mechanisms in induction motors, thus avoiding failure and expensive repairs. Therefore, there is a strong need to develop an efficient condition monitoring approach. The main aim is to achieve a relatively low cost and non-invasive system which is still powerful in terms of monitoring for online detection of developing faults. The paper addresses rotor eccentricity faults and studies conventional monitoring techniques for induction motors. The eccentricity-generated additional air-gap flux waves should be reduced in order to reduce the unbalanced magnetic pull (UMP) when there is an eccentric rotor. The radial forces in an induction motor are calculated, and the characteristics of UMP are described.

A Review of the Monitoring and Damping Unbalanced Magnetic Pull in Induction Machines Due to Rotor Eccentricity

A new method is given to study the performances of squirrel cage motors of complex design (non uniform air gap, windings with high space harmonic content). It is based on the analysis of electric circuits with time varying coefficients, rather than on consideration of air gap fluxes. It is shown that this method provides good results. It is the basis of a companion paper devoted to the motor which has been the object of the 1975-1976 IEEE single phase motor calculation and test project.

General Rotating mmf Theory of Squirrel Cage Induction Machines with Non Uniform Air Gap and Several Non Sinusoidally Distributed Windings

Numerical methods are generally applied to induction devices by assuming 2-dimensional geometry, and are difficult to extend to 3 dimensional eddy currents because the field relationships require vector functions, each with 3 interdependent components. A simpler description is sought by replacing the field quantities by two coupled networks, one electric and one magnetic. These provide an insight into the behaviour of the device, since they combine a terminal equivalent circuit with a topological description, and they are suitable for numerical solution. Their key property is their interlinkage. It is shown that this can be manipulated to provide a scalar-potential description of the 3-dimensional eddy-current problem, corresponding to the dynamic equivalent of a magnetic shell. The same approach can be used to derive a variety of equivalent circuits for induction devices and, when applied to a transformer, shows that the magnetising, and not the leakage reactance, should be split into two components. The scalar-potential formulation is particularly simple when applied to thin plates, backed by unsaturated iron, and its validity has been demonstrated by comparing calculated and measured flux distributions around a square copper plate. It is here applied to conductors of large cross-section, and the results compared with the customary vector-potential formulation in 2 dimensions.

A network approach to the numerical solution of Eddy-current problems

Electromagnetic forces act between the rotor and stator when the rotor is performing eccentric motions with respect to the stator. The aim of this research was to study the charactarestics of the forces and develop the tools to calculate these forces accurately and as quickly as possible. A new method, called the impulse method, is developed into the finite element analysis of the electromagnetic field to calculate the forces for a wide whirling frequency range by one simulation. The idea of the impulse method is to move the rotor from its central position for a short period of time. This displacement excitation disturbs the magnetic field and, by doing this, produces forces between the rotor and stator. Using spectral analysis techniques, the frequency response function of the forces is calculated using the excitation and response signals. The impulse method is based on the assumption of the spatial linearity of the force. The impulse method is utilised in the analysis of the rotor eccentricity. The spatial linearity of the force and the effects of the circulating currents and saturation on the forces are studied herein. The field of investigation is enlarged from the cylindrical whirling motion to the conical motions of the rotor. The modelling of the conical motion requires that the axial variations of the magnetic field be taken into account. This is done by multislice finite element analysis.

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Electromagnetic forces acting between the stator and eccentric cage rotor

The paper develops an analysis of induction machines with any number and configuration of stator windings, and a general nonconstant airgap. The analysis involves resolution into harmonic series, together with matrix inversions. It is ideally suited to solution by digital computer. The work is supported by experimental evidence from a variable-gap shaded-pole motor.

J.F. Eastham

Papers

Generalised theory of induction motors with asymmetrical airgaps and primary windings