Set-oriented numerical analysis of a vibro-impact drilling system with several contact interfaces

Abstract

The dynamics of a novel piezoelectric device for drilling of brittle materials is investigated. This device consists of a resonantly driven piezoelectric actuator, a drill stem, as well as a free-flying mass oscillating and impacting between the tip of the piezoelectric actuator and the end of the drill stem. Contact interfaces exist between the actuator and the mass, the mass and the drill stem as well as between the drill stem and the machined material. Basic understanding of the device's dynamic behaviour is crucial, for example to enhance the drilling performance or to redesign the system for different corer or drill stem geometries. However, such a basic understanding is still missing. Experiments with a prototype device as well as simulations with simple models show irregular motion of the impacting mass. To investigate the complicated temporal behaviour of this system, so-called set-oriented numerical methods are applied. These methods are based on an adaptive subdivision technique for cell-mapping to approximate attractors and invariant measures. A model for the drilling device is proposed consisting of several degrees of freedom. The motion of the piezoelectric actuator tip follows a prescribed harmonic vibration; the free-flying mass is represented as a point mass. The drill stem is modelled as a rod structure to account for longitudinal wave propagation. The contact conditions between the different subsystems are described by complementary kinematics and force relations and Newton's impact law, respectively. Using the set-oriented methods, periodic and chaotic orbits are detected and parameter ranges for the occurrence of different types of solutions are determined. Additionally, basins of attraction for the corresponding attractors are computed. Information on the probability of attaining a particular attractor is obtained by quantifying its connected basin of attraction. An invariant measure is chosen which represents the drilling performance. For most important model parameters, for example the mass of the free-flying body or the actuator excitation frequency, drilling performance is evaluated by computing this invariant measure for each attractor. The computational results lead to a deeper understanding of the vibro-impact dynamics of this drilling device, reveal the global behaviour of the system dynamics and show the influence of different design parameters on the drilling performance.