Combination resonances of rotor systems with asymmetric residual preloads in bolted joints

For highly-loaded rotor systems of aero-engines, residual preloads in the same row of bolts are generally asymmetric after multiple operational cycles. The asymmetry in residual bolt preloads could lead to time-varying stiffness of rotors, which become parametrically excited systems. This paper investigates the combination resonances of bolted rotor systems with asymmetric preloads under multi-frequency excitation. A new breathing model induced by asymmetric bolt preloads is proposed, which takes the rotor whirling position into account, instead of using the assumption of weight dominance. Theoretical studies are conducted on a Jeffcott rotor with asymmetric bolt preloads under two-frequency excitation, whose approximate analytical solution is obtained through the Harmonic Balance Method. Results show that combination tones arise in the vibration spectra, whose frequencies are the combinations of two excitation frequencies. The amplitude of a combination tone reaches the maximum value when its frequency is in the vicinity of natural frequencies, which correspond to the combination resonance. To extend these results to practical rotors with more complex structures, the finite element modeling method of bolted joints with asymmetric preloads is presented based on the Euler-Bernoulli beam theory. Experimental validations are performed on a practical aero-engine dual rotor system with an inter-shaft bearing. Good agreement is shown in the comparison between numerical and experimental results, which indicate that combination resonances of practical dual rotor systems could occur in the vicinity of dual-rotor coupled vibration mode.