Abstract
The present paper is devoted to a theoretical analysis of sliding friction under the influence of oscillations perpendicular to the sliding plane. In contrast to previous works we analyze the influence of the stiffness of the tribological contact in detail and also consider the case of large oscillation amplitudes at which the contact is lost during a part of the oscillation period, so that the sample starts to “jump”. It is shown that the macroscopic coefficient of friction is a function of only two dimensionless parameters—a dimensionless sliding velocity and dimensionless oscillation amplitude. This function in turn depends on the shape of the contacting bodies. In the present paper, analysis is carried out for two shapes: a flat cylindrical punch and a parabolic shape. Here we consider “stiff systems”, where the contact stiffness is small compared with the stiffness of the system. The role of the system stiffness will be studied in more detail in a separate paper.
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Eaves A, Smith A, Waterhouse W, Sansome D. Review of the application of ultrasonic vibrations to deforming metals. Ultrasonics 13(4): 162–170 (1975)
Siegert K, Ulmer J. Superimposing ultrasonic waves on the dies in tube and wire drawing. J Eng Mater Technol 123(4): 517 (2001)
Murakawa M. The utility of radially and ultrasonically vibrated dies in the wire drawing process. J Mater Process Technol 113(1–3): 81–86 (2001)
Ashida Y, Aoyama H. Press forming using ultrasonic vibration. J Mater Process Technol 187–188: 118–122 (2007)
Fridman H D, Levesque P. Reduction of static friction by sonic vibrations. J Appl Phys 30(10): 1572 (1959)
Pohlman R. Influence of ultrasonic vibration on metallic friction. Ultrasonics 4: 178–185 (1966)
Godfrey D. Vibration reduces metal to metal contact and causes an apparent reduction in friction. Tribol Trans 10(2): 183–192 (1967)
Lenkiewicz W. The sliding friction process—Effect of external vibrations. Wear 13(2): 99–108 (1969)
Tolstoi D M. Significance of the normal degree of freedom and natural normal vibrations in contact friction Wear 10(3): 199–213 (1967)
Schmidt J. A note on the contact problem in an ultrasonic travelling wave motor. Int J Non-Linear Mech 31(6): 915–924 (1996)
Storck H, Littmann W, Wallaschek J, Mracek M. The effect of friction reduction in presence of ultrasonic vibrations and its relevance to travelling wave ultrasonic motors. Ultrasonics 40(1–8): 379–383 (2002)
Socoliuc A, Gnecco E, Maier S, Pfeiffer O, Baratoff A, Bennewitz R, Meyer E. Atomic-scale control of friction by actuation of nanometer-sized contacts. Science 313(5784): 207–210 (2006)
Guo W, Yin J, Qiu H, Guo Y, Wu H, Xue M. Friction of lowdimensional nanomaterial systems. Friction 2(3): 209–225 (2014)
Chowdhury M, Helali M. The effect of amplitude of vibration on the coefficient of friction for different materials. Tribol Int 41 (4): 307–314 (2008)
Popov V L, Starcevic J, Filippov A E. Influence of ultrasonic in-plane oscillations on static and sliding friction and intrinsic length scale of dry friction processes. Tribol Lett 39: 25–30 (2010)
Teidelt E, Starcevic J, Popov V L. Influence of ultrasonic oscillation on static and sliding friction. Tribol Lett 48: 51–62 (2012)
Teidelt E, Willert E, Filippov A E, Popov V L. Modeling of the dynamic contact in stick-slip microdrives using the method of reduction of dimensionality. Phys Mesomech 15(5–6): 287–292 (2012)
Nguyen H X, Teidelt E, Popov V L, Fatikow S. Dynamical tangential contact of rough surfaces in stick-slip microdrives: modeling and validation using the method of dimensionality reduction. Phys Mesomech 17(4): 304–310 (2014)
Starcevic J, Filippov A E. Simulation of the influence of ultrasonic in-plane oscillations on dry friction accounting for stick and creep. Phys Mesomech 15(5–6): 330–332 (2012)
Grzemba B, Pohrt R, Teidelt E, Popov V L. Maximum micro-slip in tangential contact of randomly rough self-affine surfaces. Wear 309(1): 256–258 (2014)
Milahin N, Starcevic J. Influence of the normal force and contact geometry on the static force of friction of an oscillating sample. Phys Mesomech 17(3): 228–231 (2014)
Milahin N, Li Q, Starcevic J. Influence of the normal force on the sliding friction under ultrasonic oscillations. Facta Universitatis. Series: Mechanical Engineering 13(1): 27–32 (2015)
Popov V L, Dimaki A, Psakhie S, Popov M. On the role of scales in contact mechanics and friction between elastomers and randomly rough self-affine surfaces. Sci Rep 5: 11139 (2015)
Popov V L. What does friction really depend on–Robust governing parameters in contact mechanics and friction. Phys Mesomech 19 (2): 115–122 (2016)
Popov V L, Heß M. Method of Dimensionality Reduction in Contact Mechanics and Friction. Berlin-Heidelberg (Germany): Springer, 2015.
Argatov I, Heß M, Pohrt R, Popov V L. The extension of the method of dimensionality reduction to non-compact and non-axisymmetric contacts. ZAMM-J Appl Math Mech 96(10): 1144–1155 (2016)
Popov V L. Kontaktmechanik und Reibung. Von der Nanotribologie bis zur Erdbebendynamik. 3. überarbeitete Auflage. Berlin-Heidelberg (Germany): Springer Vieweg, 2015.
Popov V L, Pohrt R, Heß M. General procedure for solution of contact problems under dynamic normal and tangential loading based on the known solution of normal contact problem. J Strain Analysis 51(4): 247–255 (2016)
Milahin N. Robuste Einflussparameter für Reibung und Oberflächenmodifizierung unter Einfluss von Ultraschall. PhD thesis. Technische Universität Berlin, 2016.
Teidelt E. Oscillating contacts: Friction induced motion and control of friction. PhD thesis. Technische Universität Berlin, 2015.
Dudko O K, Popov V L, Putzar G. Tribospectroscopy of randomly rough surfaces. Tribol Int 39(5): 456–460 (2006)
Mao X, Popov V L, Starcevic J, Popov M. Reduction of friction by normal oscillations. II. In-plane system dynamics. Friction, accepted (2017)
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This work was supported in part by the Ministry of Education of the Russian Federation, by COST Action MP1303 and the Deutsche Forschungsgemeinschaft.
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Mikhail POPOV. He obtained a bachelor degree in computer science from the Freie Universität Berlin in 2011 and a master degree in engineering science from the Tomsk Polytechnic University and Berlin Technical University in 2016. Currently he is a research assistant at the Tomsk Polytechnic University and a PhD student at the Berlin University of Technology. His research interests include efficient numerical methods in tribology, rubber friction, as well as friction and damping under the influence of oscillations.
Valentin L. POPOV. He is full professor at the Berlin University of Technology, studied physics (1976—1982) and obtained his doctorate in 1985 from the Moscow State Lomonosov University. He worked at the Institute of Strength Physics of the Russian Academy of Sciences. After a guest professorship in the field of theoretical physics at the University of Paderborn (Germany) from 1999 to 2002, he has headed the Department of System Dynamics and the Physics of Friction of the Institute of Mechanics at the Berlin University of Technology. His areas of interest include tribology, nanotribology, tribology at low temperatures, biotribology, the influence of friction through ultrasound, numerical simulation of frictional processes, research regarding earthquakes, as well as topics related to materials science such as the mechanics of elastoplastic media with microstructures, strength of metals and alloys, and shape memory alloys. He has published over 100 papers in leading international journals during the past 5 years. He is the author of the book “Contact Mechanics and Friction: Physical Principles and Applications” which appeared in three German, two English, Chinese, and Russian editions and co-author of the book on “Method of dimensionality Reduction in Contact Mechanics and Friction” which appeared in German, English and Chinese editions. He is the joint editor of international journals and regularly organizes international conferences and workshops on diverse tribological themes. He is a member of the Scientific Council of the German Tribological Society. He has intensively collaborated with many industrial corporations and possesses experience in implementing the results of scientific research in industrial applications.
Nikita POPOV. Master student in two majors: (a) physics and (b) computer science at the Berlin University of Technology.
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Popov, M., Popov, V.L. & Popov, N.V. Reduction of friction by normal oscillations. I. Influence of contact stiffness. Friction 5, 45–55 (2017). https://doi.org/10.1007/s40544-016-0136-4
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DOI: https://doi.org/10.1007/s40544-016-0136-4