On Set-oriented Numerical Methods for Global Analysis of Non-smooth Mechanical Systems

Abstract

A large number of engineering systems include non-linear or even non-smooth behaviour. During development and optimisation of mechanical systems, a comprehensive dynamical analysis may be essential. Set-oriented Numerical Methods offer a new and efficient approach to global dynamical analysis without the requirement for a detailed a priori knowledge of the system dynamics. This paper shows the basic concepts behind this method and presents its application to a simple model of a vibro-impact device for ultrasonic/sonic drilling. In this drilling device an impacting mass transmits vibrational energy from a piezoelectric actuator as shock waves into a drill stem. Relative global attractors will be derived which show statistical distributions for the occurrence of all possible states. Periodic solutions can be identified parallel to the evaluation of chaotic behaviour. Thus a global understanding of the system performance can be obtained, offering new ways for model verification and system design.