Vibro-Impacts of a Piecewise-Linear System With a Clearance

Abstract Vibro-impacts are commonly observed in various engineering systems as a consequence of clearances they possess. Such motions are known to cause excessive noise issues posing a challenge in the design of such systems. Many of these systems can be formulated into a single-degree-of-freedom piecewise-linear system excited by force fluctuations. In this study, starting from a rattling gear pair example, such an equivalent piecewise-linear system will be defined and non-dimensionalized. A computationally efficient piecewise-linear solution technique will then be employed to solve the non-smooth dynamic equation. Parameter sensitivity studies will be conducted to map the overall dynamic response. Bifurcation diagrams will characterize P(m,n) type periodic and chaotic vibro-impact motions, demonstrating systematic bifurcations between P(m,n) and P(m,n+1) type periodic vibro-impact motions. A gear pair test setup will be utilized to demonstrate some of the predicted vibro-impact motions revealed by their bifurcation diagrams.