The technique of equivalent linearization is presented in this paper as a powerful technique to perform nonlinear dynamic analysis of squeeze film damper (SFD) supported rotors using linear rotor-dynamic methods. Historically, it is customary to design SFDs for rotor-dynamic analysis by assuming circular-centered orbits, which is convenient in making the nonlinear damper coefficients time independent and thus can be used in an iterative approach to determine the rotor-dynamic characteristics. However, the general synchronous orbit is elliptic in nature due to possible asymmetry in the rotor support. This renders the nonlinear damper coefficients time dependent, which would require extensive numerical computation using numerical integration to determine the rotor dynamic characteristics. Alternatively, it is shown that the equivalent linearization, which is based on a least-squares approach, can be used to obtain time-independent damper coefficients for SFDs executing eccentric elliptic orbits, which are nonlinear in the orbit parameters. The resulting equivalent linear forces are then used in an iterative procedure to obtain the unbalance response of a rigid rotor-SFD system. Huge savings over numerical integration are reported for this simple rotor. The technique can be extended to be used in conjunction with currently available linear rotor-dynamic programs to determine the rotor-dynamic characteristics through iteration. It is expected that for multirotor multibearing systems this technique will result in even more economical computation.
Dynamic analysis of an elastic ring squeeze film damper supported rotor using a semi-analytic method
