Using nonlinear springs to reduce the whirling of a rotating shaft

Vibrations in rotating machinery cause many problems such as fatigue of the rotating components, excessive noise, or transmission of vibration to the supporting structure. A major source of this vibration is out-of-balance forces and this paper proposes that the rotor response is reduced by suspending the machine on nonlinear springs. In the field of vibration isolation, nonlinear mounts have been proposed which have the same static stiffness as an equivalent linear support, i.e. load bearing capability, but at the same time offer a low dynamic stiffness, i.e. a lower natural frequency. Thus the isolator is effective over an increased frequency range. These mounts are known in the literature as high-static-low-dynamic-stiffness (HSLDS) mechanisms. In this paper, the rotor is suspended on a hardening HSLDS spring to considerably reduce the critical speeds to values far away from the operating speed. The advantages of the nonlinear supports are demonstrated using a simple two degree of freedom rotating machine model consisting of a rigid disk, and shafts, bearings and supports that are flexible but have negligible mass. Following a linear analysis to highlight the benefits of a low dynamic stiffness, an approximate analytical solution of the nonlinear equation of motion is presented. A comparison between the linear and nonlinear response shows the effectiveness of the nonlinear supports. Finally, the problems that occur if the nonlinearity is too strong are highlighted.