Steady-state response of a geared rotor system with slant cracked shaft and time-varying mesh stiffness

•Steady-state response of geared rotor system with slant cracked shaft is studied.•Both slant crack breathing and time-varying mesh stiffness are considered.•Effects of crack types and crack depth on forced response spectra are discussed.•The slant cracked geared system has some unique response spectral features.•Sub-critical resonances are also found in the frequency response curves. The dynamic behavior of geared rotor system with defects is helpful for the failure diagnosis and state detecting of the system. Extensive efforts have been devoted to study the dynamic behaviors of geared systems with tooth root cracks. When surface cracks (especially for slant cracks) appear on the transmission shaft, the dynamic characteristics of the system have not gained sufficient attentions. Due to the parametric excitations induced by slant crack breathing and time-varying mesh stiffness, the steady-state response of the cracked geared rotor system differs distinctly from that of the uncracked system. Thus, utilizing the direct spectral method (DSM), the forced response spectra of a geared rotor system with slant cracked shaft and time-varying mesh stiffness under transmission error, unbalance force and torsional excitations are, respectively, obtained and discussed in detail. The effects of crack types (straight or slant crack) and crack depth on the forced response spectra of the system without and with torsional excitation are considered in the analysis. In addition, how the frequency response characteristics change after considering the crack is also investigated. It is shown that the torsional excitations have significant influence on the forced response spectra of slant cracked system. Sub-critical resonances are also found in the frequency response curves. The results could be used for shaft crack detection in geared rotor system.