Design, dynamics, and dissipation of a torsional-magnetic spring mechanism

Ali Kanj, Rhinithaa P. Thanalakshme, Chengzhang Li, John Kulikowski, Gaurav Bahl, Sameh Tawfick

Research output: Contribution to journalArticlepeer-review


We present an analytical and experimental study of a torsional magnetic spring where the restoring torque results from magnetic field interactions between rotating and fixed permanent magnets (PMs). The rotating cylindrical PM, called the rotor, is supported on ball bearings between two fixed permanent magnets, called the stators. Perturbing the rotor from its equilibrium angle induces a restoring magnetic torque whose effect ressembles a torsional spring. Along with this restoring effect, dissipation mechanisms arise from structural viscoelasticity, air, electromagnetic damping, and friction in the ball bearings. To investigate dynamic effect of these restoring and dissipation mechanisms, we construct an experimental setup capable of mechanical, electrical, and magnetic measurements. For various rotor–stator gaps in this setup, we validate an analytical model that assumes viscous and dry (Coulomb) damping during the rotor's free response. Moreover, we force the rotor by an electromagnetic coil into high amplitude oscillations. We observe unusual resonator's nonlinearity: at large rotorstator gaps, the oscillations are softening; at reduced gaps, the oscillations stiffen-then-soften. The developed reduced-order models capture the nonlinear effects of the rotor-to-stator and the rotor-to-coil distances. These magnetic oscillators are promising for low-frequency electromagnetic signal transmission and for designing magneto-elastic metamaterials with tailorable nonlinearity.

Original languageEnglish (US)
Article number109307
JournalMechanical Systems and Signal Processing
StatePublished - Nov 1 2022


  • Ball bearings
  • Coil electromechanical actuation
  • Coulomb/dry damping
  • Nonlinear oscillations
  • Permanent magnets
  • System-identification
  • Torsional spring

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications


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