Dynamic behaviour of the Laval rotor with a transverse crack

This paper presents an introduction to the dynamic behaviour of a one disc rotor (Laval rotor) having a transverse crack in the elastic shaft. With the aid of a simple crack model the non-linear equations of motion are derived. Due to the weight dominance in the elastic deflection of the horizontal shaft the equations can be simplified to linear but time-variant equations.The stability analysis is carried out with Floquet's method and the results are presented in an overview diagram. The forced vibrations due to crack and unbalance are discussed in much detail. The orbit decomposition into forward and backward whirls (two-sided spectral order analysis) turns out to be a helpful tool for the understanding the complicated dynamic phenomena. Some hints for crack detection are given.