The thesis can be downloaded for free here.

Popular science summary

Roughly speaking, vibro-impacts are characterized by repeated collisions between objects or internal machine components whose movement is constrained by physical barriers, such as stops and clearances. This phenomenon is very common in engineering applications, being useful in some cases and problematic in others. While vibro-impacts can improve the performance of some devices, like concrete breakers, hammering, riveting and drilling devices, it also produces noise and wear in loose-joints, heat-exchangers and gear-pairs.

The coefficient of restitution and contact forces are the most common ways to model vibro-impact systems. In this Ph.D. project, the advantages and disadvantages of those model approaches are discussed and compared against experimental observations. Different impact situations are tested experimentally, from hard unilateral impacts with tightened, neutral or loose gaps, to bilateral soft collisions. Common ground model comparisons are made by correlating analytical and numerical model predictions to experimental results. It is shown that both models are able to capture some important properties of vibro-impact systems, producing qualitative insight into their dynamic behavior.

Abstract

Vibro-impact phenomena are characterized by the occurrence of intermittent collisions between objects or internal machine components whose movement is constrained by physical barriers, such as stops and clearances. Vibro-impacts can enhance the effectiveness of hammering, riveting, and drilling applications, but are an undesirable phenomenon for loose joints, heat exchangers, and rotating machines, producing noise, wear and failure. Its applicability and relevance drive the continuous development of different model formulations and analytical/numerical solution schemes intended to reproduce specific experimental results or particular dynamic behavior.

This Ph.D. thesis presents a detailed discussion of the most common model formulations for vibro-impact problems: contact force models and the coefficient of restitution, (CoR). Common ground comparisons are made by correlating analytical and numerical model predictions to experimental results. Different impact situations are tested experimentally, from hard unilateral impacts with tightened, neutral or loose gaps, to bilateral soft collisions. The experimental setup consists of a lumped mass cantilever beam with base-excitation provided by an electrodynamic shaker.

To obtain qualitative insight, the experimental setup is represented by a single degree of freedom (SDOF) model, facilitating the use of different analytical tools like harmonic linearization, pointwise mapping, and averaging. The validity of approximated solutions is tested using numerical simulations. For hard impacts, non-smooth transformations are combined with standard averaging and also used as a pre and post-processing step for numerical simulations.

The frequency response of the experimental setup with bilateral soft impacts around its fundamental linear resonance is replicated using three contact force models consisting of a piecewise linear function, a high order power function, and a combination of the first two, combining their advantages. The influence of model parameters on the frequency response is also investigated numerically.

Experiments involving hard unilateral impacts reveal the existence of complex behavior, which could not be replicated by the SDOF model with CoR. However, it is still possible to confirm theoretical predictions about the influence of gap width on the location of the resonant peak. The effects of deviations of the gap width’s nominal value on the response amplitude are also investigated.

Equivalence relations between piecewise linear impact forces and the coefficient of restitution are presented and compared numerically. The transition from soft to hard impacts is investigated experimentally by changing the contact stiffness with different helical springs.

Comparison of analytical, numerical and experimental results revealed the wider application range of impact force modeling with respect to the CoR. Still, both model approaches are able to provide qualitative insights on some important characteristics of experimental vibro-impact systems.