caa a22 4500 445361492 CHVBK 20180317142916.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s11071-010-9878-0 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9878-0 Vibrational self-alignment of a rigid object exploiting friction [Elektronische Daten] [B. Hunnekens, R. Fey, A. Shukla, H. Nijmeijer] 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. The Author(s), 2010 Self-alignment nationallicence Friction nationallicence Stick-slip vibrations nationallicence Accumulation position nationallicence Positioning nationallicence Hunnekens B. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands aut Fey R. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands aut Shukla A. Department of Mechanical and Manufacturing Engineering, Miami University, EGB 56, 45056, Oxford, OH, USA aut Nijmeijer H. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands aut Nonlinear Dynamics Springer Netherlands 65/1-2(2011-07-01), 109-129 0924-090X 65:1-2<109 2011 65 11071 https://doi.org/10.1007/s11071-010-9878-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9878-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hunnekens B. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands aut NATIONALLICENCE 700 1- Fey R. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands aut NATIONALLICENCE 700 1- Shukla A. Department of Mechanical and Manufacturing Engineering, Miami University, EGB 56, 45056, Oxford, OH, USA aut NATIONALLICENCE 700 1- Nijmeijer H. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 65/1-2(2011-07-01), 109-129 0924-090X 65:1-2<109 2011 65 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer