Vibro-Impact Mechanics: Analytical, Numerical and Experimental Investigations

Geraldo Francisco de Souza Reboucas

Research output: Book/ReportPh.D. thesis

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Vibro-impact phenomena are characterized by the occurrence of intermittent colli-sions between objects or internal machine components whose movement is constrained by physical barriers, such as stops and clearances. Vibro-impacts can enhance the ef-fectiveness 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 re-produce specific experimental results or particular dynamic behavior.
This Ph.D. thesis presents a detailed discussion of the most common model formula-tions 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 experi-mentally, 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 be-havior, 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.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages141
ISBN (Electronic)978-87-7475-526-5
Publication statusPublished - 2018
SeriesDCAMM Special Report

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