Abstract
This paper examines the stability of the steady-state periodic response of a gear pair system supported by squeeze-film dampers. The steady-state response of the system is obtained by using the hybrid technique of Harmonic Balance Method and Time Collocation. The Fioquet-Liapunov theory is used to perform the stability analysis of the first variation equations with periodic coefficients, which is generated by the perturbation technique. The stability charts on gear mesh stiffness, spin ratio, disk unbalance, gravity, and squeeze-film damper are used to perform parameter studies. The numerical results show that the unstable region always occurs when the spin ratio is near the second coupled mode of the gear pair system. Furthermore, the mesh stiffness has a significant influence on the coupled critical speeds. Therefore, it plays an important role in determining the spin ratio stability range.
Highlights
Gear rotor-bearing systems are one of the most common mechanisms for modern power transmission
Shiau and Hwang (1993) studied the stability of a nonlinear rotor supported by squeeze-film dampers by using Floquet-Liapunov theory
A stability analysis is performed by using the hybrid method to obtain the steady-state periodic response and solving the eigenvalues of the Floquet transition matrix for the perturbed response
Summary
Gear rotor-bearing systems are one of the most common mechanisms for modern power transmission. Hwang and Shiau (1991) developed a Generalized Polynomial Expansion method to study the nonlinear effects of squeeze-film forces on flexible rotors. They applied the Harmonic Balance Method (HBM) and the Collocation Method to determine the system. Chen et al (1993) considered the application of squeeze-film dampers to control lateral vibrations of a gear pair system. Shiau and Hwang (1993) studied the stability of a nonlinear rotor supported by squeeze-film dampers by using Floquet-Liapunov theory. The equations of motion can be expressed as [M]{/} + (Ch[Sh] + [C]){O} + (kh[S] + [K]){q}
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
