Vibrational self-alignment of a rigid object exploiting friction
| Autor: | Henk Nijmeijer, Bgb Bram Hunnekens, Amit Shukla, Rhb Rob Fey |
|---|---|
| Přispěvatelé: | Department of Mechanical Engineering [Eindhoven], Technische Universiteit Eindhoven (TU/e)-Eindhoven University of Technology [Eindhoven] (TU/e), Department of Mechanical and Manufacturing Engineering, Miami University [Ohio] (MU), Dynamics and Control, Mechanical Engineering |
| Jazyk: | angličtina |
| Předmět: |
0209 industrial biotechnology
Dynamical systems theory Friction Aerospace Engineering Ocean Engineering 02 engineering and technology Surface finish Stick-slip vibrations 01 natural sciences Self-alignment Acceleration Skin friction line 020901 industrial engineering & automation Position (vector) Accumulation position 0103 physical sciences Electrical and Electronic Engineering 010301 acoustics Physics Mechanical Engineering Applied Mathematics Mathematical analysis Vibration Classical mechanics Control and Systems Engineering Collision response Constant (mathematics) Positioning |
| Zdroj: | Nonlinear Dynamics Nonlinear Dynamics, Springer Verlag, 2010, 65 (1-2), pp.109-129. ⟨10.1007/s11071-010-9878-0⟩ Nonlinear Dynamics, 65(1-2), 109-129. Springer |
| ISSN: | 0924-090X 1573-269X |
| DOI: | 10.1007/s11071-010-9878-0 |
| Popis: | International audience; In this paper, one-dimensional self-alignment of a rigid object via stick-slip vibrations is studied. The object is situated on a table, which has a prescribed periodic motion. Friction is exploited as the mechanism to move the object in a desired direction and to stop and self-align the mass at a desired end position with the smallest possible positioning error. In the modeling and analysis of the system, theory of discontinuous dynamical systems is used. Analytic solutions can be derived for a model based on Coulomb friction and an intuitively chosen table acceleration profile, which allows for a classification of different possible types of motion. Local stability and convergence is proven for the solutions of the system, if a constant Coulomb friction coefficient is used. Next, near the desired end position, the Coulomb friction coefficient is increased (e.g. by changing the roughness of the table surface) in order to stop the object. In the transition region from low friction to high friction coefficient, it is shown that, under certain conditions, accumulation of the object to a unique end position occurs. This behavior can be studied analytically and a mapping is given for subsequent stick positions. |
| Databáze: | OpenAIRE |
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