Uncertainty Quantification for a Permanent Magnet Synchronous Machine with Dynamic Rotor Eccentricity

  • Zeger Bontinck
  • Oliver Lass
  • Herbert De Gersem
  • Sebastian Schöps
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


The influence of dynamic eccentricity on the harmonic spectrum of the torque of a permanent magnet synchronous machine is studied. The spectrum is calculated by an energy balance method. Uncertainty quantification is applied by using generalized Polynomial Chaos and Monte Carlo. It is found that the displacement of the rotor impacts the spectrum of the torque the most.



This work is supported by the German BMBF in the context of the SIMUROM project (grant number 05M2013), by the ‘Excellence Initiative’ of the German Federal and State Governments and the Graduate School of Computational Engineering at TU Darmstadt.


  1. 1.
    Belmans, R., Vandenput, A., Geysen, W.: Calculation of the flux density and the unbalanced pull in two pole induction machines. Electr. Eng. 70, 151–161 (1987)Google Scholar
  2. 2.
    Bontinck, Z., De Gersem, H., Schöps, S.: Response surface models for the uncertainty quantification of eccentric permanent magnet synchronous machines. IEEE Trans. Magn. 52, (2016)Google Scholar
  3. 3.
    Coenen, I., Herranz Garcia, M., Hameyer, K.: Influence and evaluation of non-ideal manufacturing process on the cogging torque of a permanent magnet excited synchronous machine. COMPEL 30, 876–884 (2011)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dick, J., Kuo, F.Y., Sloan, I.H.: High-dimensional integration: the quasi-Monte Carlo way. Acta Numer. 22, 133–288 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Dorrell, D.G., Chindurza, I., Cossar, C.: Effects of rotor eccentricity on torque in switched reluctance machines. IEEE Trans. Magn. 41, 3961–3963 (2005)CrossRefGoogle Scholar
  6. 6.
    Frohne, H.: Über den einseitigen magnetischen Zug in Drehfeldmaschinen. Electr. Eng. 51, 300–308 (1968)Google Scholar
  7. 7.
    Mizia, J., Adamiak, K., Eastham, A.R., Dawson, G.E.: Finite element force calculation: comparison of methods for electric machines. IEEE Trans. Magn. 24, 447–450 (1988)CrossRefGoogle Scholar
  8. 8.
    Preston, T., Reece, A., Sangha, P.: Induction motor analysis by time-stepping techniques. IEEE Trans. Magn. 24, 471–474 (1988)CrossRefGoogle Scholar
  9. 9.
    Sadowski, N., Lefevre, Y., Lajoie-Mazenc, M., Cros, J.: Finite element torque calculation in electrical machines while considering the movement. IEEE Trans. Magn. 28, 1410–1413 (1992)CrossRefGoogle Scholar
  10. 10.
    Salon, S.J.: Finite Element Analysis of Electrical Machines. Kluwer, Boston (1995)CrossRefGoogle Scholar
  11. 11.
    Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., Tarantola, S.: Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity check. Comput. Phys. Commun. 181, 259–270 (2010)zbMATHGoogle Scholar
  12. 12.
    Schöps, S., De Gersem, H., Weiland, T.: Winding functions in transient magnetoquasistatic field-circuit coupled simulations. COMPEL 32, 2063–2083 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Silwal, B., Rasilo, P., Perkkiö, L., Oksman, M., Hannukainen, A., Eirola, T., Arkkio, A.: Computation of torque of an electrical machine with different types of finite element mesh in the air gap. IEEE Trans. Magn. 50, 1–9 (2014)CrossRefGoogle Scholar
  14. 14.
    Tärnhuvud, T., Reichert, K.: Accuracy problems of force and torque calculations in FE-systems. IEEE Trans. Magn. 24, 443–446 (1988)CrossRefGoogle Scholar
  15. 15.
    Xiu, D.: Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton (2010)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Zeger Bontinck
    • 1
  • Oliver Lass
    • 2
  • Herbert De Gersem
    • 3
  • Sebastian Schöps
    • 1
  1. 1.Graduate School of Computational EngineeringTechnische Universität Darmstadt64293 DarmstadtGermany
  2. 2.Department of Mathematics, Chair of Nonlinear OptimizationTechnische Universität DarmstadtDarmstadGermany
  3. 3.Institut für Theorie Elektromagnetischer FelderTechnische Universität DarmstadtDarmstadtGermany

Personalised recommendations