Continuation analysis of overhung rotor bouncing cycles with smooth and contact nonlinearities

Abstract

Time simulation has been widely used when investigating the nonlinear response of rotating machines, due to its relative simplicity. However, this approach is computationally inefficient due to large transient decay times and the need to repeat the analysis for multiple drive speeds and initial conditions, and is incomplete because of its inability to give information about unstable responses. Alternatively, the numerical continuation method can be used to explore the nonlinear behaviour of such systems in a more systematic and efficient way. In rotating machinery, tighter tolerances are valued for efficiency, making the rotor–stator contact phenomenon a priority for research. Various cases including rigid and very compliant contact stiffness models have been investigated in the literature, in many cases showing responses similar to that of smooth nonlinearities such as cubic stiffness. This knowledge has been used in the present study to transform the bifurcation diagram of a simpler nonlinearity (cubic) to a more complex one (contact represented by bilinear stiffness approximated using a tanh formulation) through a homotopy of the nonlinear restoring forces present in the system definition. A 2-dof overhung rotor with gyroscopic effects is used in the investigation of quasiperiodic bouncing cycles that appear periodic in the rotating frame. This work not only provides more insight into the behaviour of nonlinear rotor–stator contact responses, but also demonstrates the numerical continuation method as a potential tool to explore the nonlinear rotating system’s response in a more structured manner.