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Stiff and soft active control of friction by vibrations and their energy efficiency
J. Benad (1), M. Popov (1,2,3), K. Nakano (4), V. L. Popov (1,2)
1 Technische Universität Berlin, Berlin 10623, Germany
2 National Research Tomsk Polytechnic University, Tomsk 634050, Russia
3 National Research Tomsk State University, Tomsk 634050, Russia
4 Yokohama National University, Yokohama 240-8501, Japan
This work builds upon the results of two recent theoretical studies on the influence of friction by normal and sideways oscillations. The findings are in part rewritten to a more compact and dimensionless form so as to present the results for both oscillation modes side by side in a consistent manner. Thereby, it is shown that for the considered system the macroscopic coefficient of friction is only a function of a dimensionless sliding velocity and a dimensionless oscillation amplitude. Furthermore, the energy efficiency is characterized for both modes for the first time by comparing the total energy needed for a sliding motion which includes the superimposed oscillations with the energy needed for the same sliding motion without the additional oscillations. It is shown that this ratio is also only a function of the two dimensionless system parameters. We consider a simple one-spring model in a displacement-controlled setting. Any system-dynamical feedback is neglected. The lower end of the spring either slides, sticks or jumps on a rigid plane. In the case of normal oscillations, the macroscopic coefficient of friction can be reduced only when the contact point undergoes a stick-slip motion (“stiff control of friction”) whereas with sideways oscillations the macroscopic coefficient of friction can be reduced also when the contact point is continuously sliding (“soft control of friction”). It is found that the motion with superimposed sideways oscillations requires more energy for any combination of system parameters, than the corresponding motion without the oscillations. For the case of normal oscillations however, there are combinations of system parameters for which the motion with the superimposed oscillations requires less, the same, or more energy than for the reference case without the oscillations.