Advantages and Drawbacks of Applying Periodic Time-Variant Modal Analysis to Spur Gear Dynamics

Rune Pedersen, Ilmar Santos, Ivan Arthur Hede

Research output: Contribution to journalJournal articleResearchpeer-review


A simplified torsional model with a reduced number of degrees-of-freedom is used in order to investigate the potential of the technique. A time-dependent gear mesh stiffness function is introduced and expanded in a Fourier series. The necessary number of Fourier terms is determined in order to ensure sufficient accuracy of the results. The method of time-variant modal analysis is applied, and the changes in the fundamental and the parametric resonance frequencies as a function of the rotational speed of the gears, are found. By obtaining the stationary and parametric parts of the time-dependent modes shapes, the importance of the time-varying component relative to the stationary component is investigated and quantified. The method used for calculation and subsequent sorting of the left and right eigenvectors based on a first order Taylor expansion is explained. The advantages and drawbacks of applying the methodology to wind turbine gearboxes are addressed and elucidated.
Original languageEnglish
JournalMechanical Systems and Signal Processing
Issue number5
Pages (from-to)1495-1508
Publication statusPublished - 2010


  • Parametric vibration
  • Modal analysis
  • Time-variant systems
  • Gear dynamics

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