Vibro-impact dynamics of fretting wear

Abstract: The dynamics and wear of non-linear impact oscillators, comprising a single-degree of freedom system as well as continuous beam systems are analysed. The considered beams are of cantilever type with the lateral motion of the free end constrained by elastic supports. They are modelled as Bernoulli beams with Rayleigh damping. A finite-element method is used for discretisation in space and Newmark's method for time integration. Wear is quantified using the work-rate concept. The model calculations are compared with measurements of contact forces and displacements made on a loosely supported nuclear fuel rod span subject to both harmonic and random excitation. Details of the vibro-impact dynamics in the time domain are well reproduced in the digital simulations. Work-rates computed from measured and simulated quantities are also in good agreement. Furthermore, the dynamics of vibro-impacts are characterised through global and local stability and bifurcation analysis. Global analysis is made by extensive time integration for both harmonic and stochastic excitation. The local analysis is made by way of a Poincaré mapping method relating the states at subsequent impacts at the elastic supports for harmonically excited systems. The domains of stability are mapped out and the work-rate at stable periodic orbits is examined.