The effect of bifurcation and chaos on the functioning of mechanical systems with clearance

Many rotor systems are subjected to complex response patterns due to various nonlinearities in the system. These nonlinearities are in the form of clearance and or friction. A comprehensive dynamic behavior characterization of such systems becomes increasingly important such that a practicing engineer or a designer is well aware of all the possible motions that the system can exhibit during the course of their operation. This research is aimed at developing a problem independent analysis tool for identifying regimes of complex nonlinear behavior that strongly nonlinear problems are capable of displaying. The three systems that are studied in this research are (1) Single degree of freedom clearance type nonlinear oscillator that is a representation of the generic model of a gear pair interaction; (2) Rolling element bearing system with combined parametric excitation, clearance type nonlinearity and nonlinear Hertzian type contact forces; and (3) Rotor with unbalance mass mounted on supports with clearance. The presence of complex behavior like chaos in a clearance type nonlinear system is demonstrated through an experimental investigation of a rack/pinion system.