Frequency spectrum and vibration analysis of high speed gear-rotor system with tooth root crack considering transmission error excitation

• A finite element node dynamic model of gear-rotor-bearing system is proposed.
• The time-varying mesh stiffness is calculated with improved energy method.
• The different forms of transmission error excitations are introduced to the model.
• Influences of transmission error excitation on the dynamic responses are studied.
• Influences of crack length on the dynamic responses are investigated.
• The RMS value, kurtosis value and frequency spectrum of the response are analyzed.

A finite element node dynamic model of gear-rotor-bearing system with different lengths of crack by taking the time-varying mesh stiffness, backlash, transmission error excitation, flexible shaft and supporting bearing into account is proposed. The time-varying mesh stiffness of gear-pair with cracked tooth is obtained by applying the improved potential energy method. Due to the periodic features of the dynamic responses of the system when the tooth is cracked, the short term component (tooth profile error and tooth pitch error) and long term component (accumulative pitch error) transmission error excitations are introduced, the RMS values, kurtosis values, and frequency spectrum diagrams of the dynamic response with respect to input speed considering different forms of transmission error excitation are gained. The influences of transmission error excitation and crack length on the dynamic responses are investigated. The effectiveness of the RMS value, kurtosis value and frequency spectrum in the judgment of the crack length is analyzed.