Advantages and drawbacks of applying periodic time-variant modal analysis to spur gear dynamics

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.