# Dynamics of electric machines rotors with unbalanced magnetic pull

### Аuthors

Davydov A. V.1*, Degtiarev S. A.2**, Kutakov M. N.1***, Leontiev M. K.1****

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. Scientific and technical centre of rotor dynamic Alfa-Tranzit Co., Ltd, 1, Leningradskaya street, Khimky, Moscow region, 141400, Russia

*e-mail: davidovarc@gmail.com
**e-mail: degs@alfatran.com
***e-mail: maxim.kutakov@alfatran.com
****e-mail: lemk@alfatran.com

### Abstract

Object and purpose of the study

Object of the study is Unbalanced Magnetic Pull (UMP) which arises in electric motors and generators and must be taken into account in rotor dynamics tasks. Review of existing methods of UMP determination noted its nonlinear nature. The algorithm to solve the task of rotor dynamics behavior with UMP in nonlinear transient analysis was created. Hydraulic turbine generator with UMP was analyzed.

Methodology

UMP value in electric machines depends on the eccentricity of rotor, the geometric size of the machine, the value of magnetic field in the air gap, the magnetic properties of rotor material, presence of the stator winding parallel turns. In nonlinear definition the matrix

equation describing the nonlinear dynamic model of the rotor system is given by:

[M]{ü}+ [C]{ù}+ [K]{u} {F(t)}+{R},

where [M] inertial matrix; [C] damping matrix; [K] stiffness matrix; {ü} {ù} {u} respectively columns of vibration acceleration, velocity and displacement; {F(t)} dynamic loading of any types internal or external; {R} the nonlinear reaction, taking into account a magnetic force between rotor and stator. The equation can be integrated in accordance with the scheme shown in figure.

Findings

It is shown that the UMP has a major influence on the rotors vibrations of electric machines. It reduces the critical speed, changes the position of resonances and vibration amplitudes. The main advantage provided by the method and developed algorithm is its relative simplicity and minimum of input data. Application UMP model to the studied rotor showed that the significant difference between linear and nonlinear statements appears when the air gap is more than 40%.

Originality/value

The presented method and the algorithm was implemented in the software system Dynamics R4 which allows you to carry out quickly and accurately the design and analysis dynamical structures of electrical machines in nonlinear statement with the UMP, as well as other nonlinear properties.

### Keywords:

rotor dynamics, unbalanced magnetic pull, electric machines, rotor eccentricity, Dynamics R4

### References

1. Dimentberg F.M., Kolesnikov K.S. Kolebaniya mashin, konstruktsii i ikh elementov (Fluctuations of the machines, structures and their elements), Moscow, Mashinostroenie, 1980, 544 p.
2. Pennacchi P. Nonlinear effects due to electromechanical interaction in generators with smooth poles. Nonlinear Dyn, 2009, 57, pp. 607-622.
3. Gustavsson Rolf K.The influence of magnetic pull on the stability of generators rotors. The 10th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery Honolulu, Hawaii, March 07-11, 2004, p. 9.
4. Z Song and Z Ma. Nonlinear vibration analysis of an eccentric rotor with unbalance magnetic pull, 2010 IOP Conf. Ser.: Earth Environ. Sci. 12 012110, available at: http://iopscience.iop.org/1755-1315/12/1/012110
5. Nasselqvist Mattias. Simulation and Characterization of Rotordynamic Properties for Vertical Machines. Doctors thesis, Department of Engineering Sciences and Mathematics, Division of Mechanics of Solid Materials. Lulea University of Technology, SE-97187, Lulea. 2009.
6. Arkkio A. Analysis of induction motors based on the numerical solution of the magnetic field and circuit equations, Acta Polytechn. Scand. Electr. Eng. Ser., 1987, 59, 97 p.
7. Holopainen T.P., Tenhunen A., Arkkio A. Electromagnetic circulatory forces and rotordynamic instability in electric machines. Proceedings of the 6th International Conference on Rotor Dynamics. Sydney, Australia, 30.9-4.10.2002, vol. 1, pp. 446-463.
8. Burakov A. Modeling the unbalanced magnetic pull in eccentric-rotor electrical machines with parallel windings. Doctoral Dissertation. Helsinki University of Technology. Department of Electrical and Communications Engineering. Laboratory of Electromechanics. TKK Dissertations 93. Espoo 2007, 154 p.
9. Zarko Damir, Ban Drago, Vazdar Ivan and Jaric Vladimir. Calculation of unbalanced magnetic pull in a salient-pole synchronous generator. 14th International Power Electronics and Motion Control Conference, EPE-PEMC 2010, pp.116-122, available at: http://bib.irb.hr/datoteka/481623.555.pdf
10. Shubov I.G. Shum i vibratsiya elektricheskikh mashin (Noise and vibration of electric machines), Leningrad, Energiya, 1973, 200 p.
11. Holopainen Timo P. Electromechanical interaction in rotordynamics of cage induction motors. Espoo 2004, VTT Publications 543, p. 64 + app. p.81.
12. Wiak S. and Napieralska-Juszezak E. Computed field models of electromagnetic devices, IOS Press, 2010, ch.4 pp. 103-329 (951 p.).
13. Gustavsson Rolf. Modelling and analysis of hydropower generator rotors. Licentiate thesis. The Polhem Laboratory, Division of Computer Aided Design Department of Applied Physics and Mechanical Engineering Lulea University of Technology SE-97187, Lulea, 2005, 32p.
14. Pyrhonen Juha, Jokinen Tapani and Hrabovcova Valeria. Design of Rotating Electrical Machines. 2008 John Wiley & Sons, Ltd. ISBN: 978-0-470-69516-6, 512 p.