Negative stiffness coefficients for magnetic actuators using Laplace's equation

L. S. Stephens, M. A. Casemore

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Magnetic bearings offer high speed and low power losses as compared to film riding and rolling element bearings. Significant efforts are underway to apply magnetic bearings to gas turbines and jet aircraft engines. Negative stiffness coefficients for magnetic actuators can have a significant impact on shaft rotordynamics. These coefficients are typically computed as the sensitivity of a magnetic force expression derived from a lumped parameter reluctance network. However, as the complexity of magnetic actuator designs increases, the reluctance network method may become impractical for, or even incapable of, coefficient determination. In this paper, an alternative method is presented for determination of negative stiffness coefficients for a large class of magnetic actuators. The method solves the Dirichlet boundary value problem for the magnetomotive force in the actuator air gap, subject to periodic boundary conditions that can be represented by Fourier series. A conformal transformation to bipolar coordinates is used that results in a boundary value problem that is solvable using separation of variables. Negative stiffness coefficients are presented and the method is benchmarked against well-known solutions using the reluctance network method.

Original languageEnglish
Pages (from-to)612-618
Number of pages7
JournalJournal of Engineering for Gas Turbines and Power
Issue number3
StatePublished - Jul 2001

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Fuel Technology
  • Aerospace Engineering
  • Energy Engineering and Power Technology
  • Mechanical Engineering


Dive into the research topics of 'Negative stiffness coefficients for magnetic actuators using Laplace's equation'. Together they form a unique fingerprint.

Cite this