Waclaw Maciolek and Tadeusz J. Sobczyk, Member, IEEE Cracow University of Technology, Poland
Abstract - Induction motor rotor cage diagnostics bases on additional components in stator phase current with (1-2s)fo and modeled by using the equivalent magnetizing currents and a cage asymmetry is modeled by specialfactors.
effect of the cage asymmetry whereas the (1+2s)fo component is a secondary effect. It is commonly known, that it arises due to speed ripples, which are generated by alternating component of electromagnetic torque in a motor with faulty cage. This paper shows that magnetic saturation of a main magnetic circuit also generates the (1+2s)fo component in stator currents. A specialmathematical model accounting for saturation is used to prove this thesis. Results of quantitative analysis of an influence of inertia and saturation on the (1+2s)fo component is shown.
(1+2s)fo frequencies. The (1-2s)fo component arises as the main
II. MODEL FOR STUDY OF THE SATURATION
Basic phenomena in induction motors with faulty cage can
Index Terms-Inductionmachines, cage fault diagnostics,
be predicted from a mono-harmonic model. However a full model, allowig calculatig all currents i cage elements, iS a rather complicated and has to have 3+N+l equations. When concentrating on stator currents, a simplified model can be used, in which cage asymmetry is modeled by some
A. Simplified model assumingmagnetic linearity
monitor or to diagnose an induction motor rotor cage Montor induction cge ) bynd MotpornCurents Aasisf(MC respect to bands components (1-2s)f0 and (1+ 2s)f0 with residethe main components of the supply frequency fo are used. In fact, the component of the (1- 2s)fo frequency is a main effect of a cage asymmetry at a constant rotor speed. However, a motor with faulty cage produces analternating component of the electromagnetic torque with a 2sf 2 frequency. For normal operation, the slip of the motor is small and the frequency of this alternating component is so small that the rotor speed, answering to this torque, becomes not constant and also has some fluctuations of the 2sfo frequency. It generates additional components of the (1+2s)f. frequency in the stator currents. The speed fluctuations disappear for greater slips because of the rotor inertia and the right hand side-band (1+ 2s)fo component also disappears. The component of the (1-2s)fo frequency can be relatively easy analytically predicted from algebraic equations of a mono-harmonic induction cage motor model for constant speed. To calculate the (1 + 2s)f. component the motion equation has to be addedand solutions can only be found numerically. However, the (1+ 2s)f. component arises also due to the non-linearity of the main magnetic circuit, even at a constant rotor speed . This paper tries to answer how these two phenomena interacting on the right hand side-band (1 + 2s)f0 component using the mathematical model, in which magnetic nonlinearity is
In this paper such a model proposed in  has been It reduces the problem to an analysis of a 3-phase wound-rotor motor with unsymmetrical resistances in the rotor phases. The asymmetry of equivalent rotor resistances is modeled by two factors ks and kas, which have been calculated for any individual cage fault  . This model
is valid forsmall slip only, but MCSA deals just for such operation. The side-band stator current components obtained from such simplified model are very close to those obtained from the full model of rotor cage . E uations of model have tfli o
CLs +Lt 0 d dt L eCip' 0 R 0
L +L 0 L ejpp 0
LIetiP 0 L'P +L 0
, i0 p L'P +L iN-p
Rs 0 0...