Electromagnetic fields in the air gap of an electric machine produce electromagnetic forces between the rotor and stator. The total force exerted on the rotor due to the eccentric rotor position is called the unbalanced magnetic pull. This eccentricity force is directed roughly over the shortest air gap. At low frequencies, the vibration amplitudes of flexural modes may be large enough to couple the electromagnetic system to the mechanical one. This electromechanical interaction changes the vibration behaviour of the system.The main purpose of this dissertation is to reveal the main rotordynamic consequences induced by the electromechanical interaction in cage induction motors. Another goal is to achieve this by deriving a simple and representative electromechanical rotor model with physical variables and parameters.In this study, a new parametric model was derived for the unbalanced magnetic pull induced by an arbitrary rotor motion in transient operation. The parameters of this model can be determined analytically from the basis of the machine characteristics or estimated numerically as in this study. To estimate the parameters, an efficient numerical method was developed from the analysis of impulse response. The numerical results showed that the simple electromagnetic force model, together with the estimated parameters, predicts the unbalanced magnetic pull fairly accurately.An electromechanical rotor model was derived by combining the Jeffcott rotor model with the simple electromagnetic force model, including two additional variables for the harmonic currents of the rotor cage. Applying this model, the rotordynamic effects of electromechanical interaction were studied. Three induction motors were used in the numerical examples. The results obtained show that the electromechanical interaction may decrease the flexural frequen-4 cies of the rotor, induce additional damping or cause rotordynamic instability. These interaction effects are most significant in motors operating at, or near, the first flexural critical speed. Excluding the potential rotordynamic instability, the numerical results indicate that the electromechanical interaction effectively reduces the unbalance response close to the first flexural critical speed. 5 PrefaceThis work was carried out during the period 2001-2003 as a part of the research project "Electromechanical interaction in vibration control of electric machines". The aim of this project was to enhance our understanding of the effects of electromechanical interaction in general, and electromagnetic damping in particular, on the vibration control of electrical machines. The research partners were the
The paper presents an impulse method to calculate the frequency response of the electromagnetic forces acting between the rotor and stator of a cage induction motor when the rotor is in whirling motion. Time-stepping finite element analysis is used for solving the magnetic field and the forces are calculated from the air gap field based on the principle of the virtual work. The impulse response method is applied to the finite element analysis by moving 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 is calculated using the excitation and response signals. The forces are calculated from the frequency response function. The forces calculated by impulse response method are compared with the forces calculated by a conventional computation. The results show very good agreement. The use of impulse method to calculate the forces in electrical machines is also discussed.
1-The paper deals with the electromagnetic forces in induction machines when the rotor is performing eccentric motion with respect to the stator. The studied eccentric motions of the rigid cage rotor are cylindrical circular whirling motion, symmetric conical whirling motion and the combination of these two basic modes of eccentric motions. The multi-slice, time stepping finite element analysis is used for solving the magnetic field, and the forces are calculated from the air gap by a method based on the principle of virtual work. The forces are measured for a test motor equipped with active magnetic bearings. The active magnetic bearings are used to generate the eccentric rotor motions and also to measure the electromagnetic forces. The measured and calculated forces show relatively good agreement. The results show that superposition is valid when determining forces. This means that the calculated forces of different motions can be combined and the result is the force of the combined motion.
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