The influence of asymmetry in centralizing spring of squeeze film damper on stability and bifurcation of rigid rotor response

One of the main challenges in the design of rotating machinery is the occurrence of undesirable vibration. In this paper, stability and bifurcation of the unbalance response of a rigid rotor supported by squeeze film damper with asymmetry in centralizing spring are investigated. The unbalanced rotor response is determined by the shooting method and the stability of these solutions is examined by using the Floquet theorem. Numerical examples are given for both symmetric (Kx=Ky) and asymmetry (Kx≠Ky) centralizing springs in x or y direction. Jump phenomenon and subharmonic and quasi-periodic vibrations are predicted for a range of design and operating parameters such as the unbalancing (U), gravity (W), bearing (B) and spring (K). The results show that increasing the spring stiffness asymmetry parameter in y direction has no influence on the nature of system response and occurrence of bifurcation. But, examining the effect of increase in stiffness parameter in x direction leads to occurrence instability and period-doubling bifurcation in response to the system. Our findings show that this phenomena are due to the weight force in the y direction. Finally, it is shown that the unsymmetrical stiffness of squeeze film dampers in the presence of cavitation promoting the chance of undesirable nonsynchronous vibrations.