Parametric instability of a rotating shaft containing an elliptical front crack

Abstract

Compared with the widely used straight front crack model, an elliptical front crack has been found to be more accurate and realistic for modeling the transverse surface crack in rotating machinery. When the shaft rotates, the elliptical crack opens and closes alternatively, due to gravity, and thus a "breathing effect" occurs. This variance in shaft stiffness is time-periodic, and hence a parametrically excited system is expected. Thus, the parametric instability of a rotating shaft containing an elliptical front crack is studied in the paper. The local flexibility due to the crack is derived, and the governing equations of the crack shaft system are established using the assumed modes method. In virtue of discrete state transition matrix (DSTM) method, three typical instability regions of a practical used rotating shaft are determined numerically. The effects of crack parameters (depth, shape factor, position) and damping on the instability regions are respectively considered and discussed.