Parametric instability analysis of a rotating shaft subjected to a periodic axial force by using discrete singular convolution method

Abstract

Parametric instability problem of a rotating shaft subjected to a periodically varying axial force has been studied by using a numerical simulation method—discrete singular convolution. External viscous damping and internal material damping (Voigt–Kelvin model) have been considered. Parametric instability regions have been presented to illustrate the influence of spinning speed and damping. Numerical results reveal that for rotating shafts with no damping, parametric instability regions under different spinning speeds are ‘V’ shapes, and do not vary obviously with spinning speed increasing. While, for rotating shafts with damping, parametric instability regions are enlarged significantly as spinning speed increases. It may be considered that spinning speed has a great effect on parametric instability of rotating shafts with damping, but little influence on that of rotating shafts with no damping. Moreover, the increase of damping results in reduction of parametric instability regions, which is helpful to improve dynamic stability of systems. And it is also found that effects of internal material damping and external viscous damping on parametric instability regions are similar. Compared to the results by using theoretical methods of Floquet and Bolotin, it is observed that the numerical results support Floquet’s method, disagree with Bolotin’s method for parametrically excited rotating shafts. In consideration of Bolotin’s method leading to enlargement of instability regions, it is strongly recommended that Bolotin’s should not be applied to parametric instability analysis of rotating systems.