Abstract
A method of calculating nonlinear vibrational oscillations in mechanical contact systems with amplitude-dependent forces of hysteresis type is considered. The method is based on the representation of solutions of forced oscillation equation as nonlinear shapes corresponding to a model conservative system. Two-and three-dimensional dynamic characteristics of the principal and subharmonic modes of symmetrical tangential oscillations are obtained. Conditions under which friction contact oversteps the limits of the pre-sliding at force and kinematic vibrational loadings are specified. The results are compared to the Coulomb model of the friction force and this model is shown to be unsuitable for calculating contact oscillations with small amplitudes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Vibratsii v tekhnike (Vibrations in Engineering), Tom 2. Kolebaniya nelineinykh mekhanicheskikh sistem (Vol. 2. Oscillations of Nonlinear Mechanical Systems), Blekhman, I.I., Ed., Moscow: Mashinostroenie, 1979.
Kragelskii, I.V., Dobychin, M.N., and Kombalov, V.S., Friction and Wear Calculation Methods, Oxford: Pergamon, 1982.
Johnson, K.L., Contact Mechanics, Cambridge: Cambridge Univ. Press, 1987.
Kostogryz, S.G., Mechanics of Vibrational Friction in Nominally Static Friction Contact, Doctoral (Eng.) Dissertation, Khmelnitskii: Techn. Univ. of Podolye, 1995.
Plakhtienko, N.P., Methods of Identification of Nonlinear Mechanical Oscillatory Systems, Prikl. Mekh., 2000, vol. 36, no. 12, pp. 38–68.
Gekker, F.R., Generalized Dynamic Model of “Dry” Friction Units, J. of Friction and Wear, 1998, vol. 19, no. 2, pp. 10–15.
Chen, J.J., Yang, B.D., and Menq, C.H., Periodic Force Response of Structures Having Tree-Dimensional Frictional Constraints, J. of Sound and Vibration, 2000, vol. 229, no. 4, pp. 775–792.
Xia, F., Modelling of Two-Dimensional Coulomb Friction Oscillator, J. of Sound and Vibration, 2003, vol. 265, no. 5, pp. 1063–1074.
Liu, C.-S., Hong, H.-K., and Liou, D.-Y., Two-Dimensional Friction Oscillator: Group-Preserving Scheme and Handy Formulae, J. of Sound and Vibration, 2003, vol. 266, no. 1, pp. 49–74.
Mindlin, R.D., Compliance of Elastic Bodies in Contact, Trans. ASME. J. Appl. Mech., 1949, vol. 16, no. 3, pp. 259–268.
Mindlin, R.D., Mason, W.P., Osmer, J.F., and Deresiewicz, H., Effects of an Oscillating Tangential Force on the Contact Surfaces of Elastic Spheres, Proc. 1 st US National Congress of Appl. Mech., New York, 1952, pp. 203–208.
Mindlin, R.D. and Deresiewicz, H., Elastic Spheres in Contact under Varying Oblique Forces, Trans. ASME. J. Appl. Mech., 1953, vol. 20, no. 3, pp. 327–332.
Maksak, V.I., Predvaritel’noe smeshchenie i zhestkost’ mekhanicheskogo kontakta (Pre-Displacement and Rigidity of Mechanical Contact), Moscow: Nauka, 1975.
Maksak, V.I., Tritenko, A.N., Druzhinin, N.V., Kun, Ya.I., and Maksimenko, A.A., Contact Oscillations of Solids at Impact Loading, in Rasseyanie energii pri kolebaniyakh mekhanicheskikh system (Energy Dissipation in Oscillations of Mechanical Systems), Kiev: Naukova Dumka, 1989, pp. 145–152.
Maksimenko, A.A., Perfil’eva, N.V., and Koteneva, N.V., Dynamic Contacts at Complex Loading in Static Friction, Izv. vuzov. Mashinostroenie, 2002, nos. 2–3, pp. 28–37.
Perfil’eva, N.V., Dinamicheskaya model’ uprugogo mekhanicheskogo kontakta v predelakh treniya pokoya (Dynamic Model of Elastic Mechanical Contact at Static Friction), Novosibirsk: Nauka, 2003.
Zaspa, Yu.P., Contact Resonance in a Nominally Stationary Friction Couple under Forced Tangential Vibrations, J. of Friction and Wear, 2004, vol. 25, no. 2, pp. 43–52.
Zaspa, Yu.P., Contact Resonance in a Nominally Stationary Friction Couple under Inertial Vibrations, J. of Friction and Wear, 2004, vol. 25, no. 3, pp. 13–19.
Zaspa, Yu.P., Dynamics of Forced Tangential Oscillations of Elastic Friction Contact in Transition from Predisplacement to Sliding, J. of Friction and Wear, 2004, vol. 25, no. 4, pp. 88–98.
Zaspa, Yu.P., Contact Resonance in Joints of Parts at Vibration. One-Dimensional Model of Nonlinear Oscillations and Method for Calculating It, Trenie i iznos, 2006, vol. 27, no. 6, pp. 592–611.
Kononenko, V.O. and Plakhtienko, N.P., Determination of Loop-Like Characteristics of Nonlinear Oscillatory Systems Based on Oscillation Analysis, Prikl. Mekh., 1970, vol. 6, no. 9, pp. 9–15.
Prokhorov, G.V., Kolbeev, V.V., Zhelnov, K.I., and Ledenev, M.A., Matematicheskii paket Maple V Release 4. Rukovodstvo pol’zovatelya (Maple V Mathematical Package, Release 4. User Manual), Kaluga: Oblizdat, 1998.
Biderman, V.L., Teoriya mekhanicheskikh kolebanii (Theory of Mechanical Oscillations), Moscow: Vysshaya Shkola, 1980.
Timoshenko, S.P., Yang, D.H., and Wiver, W., Kolebaniya v inzhenernom dele (Oscillations in Engineering), Moscow: Mashinostroenie, 1985.
Hinkle, J.D., Peterson, L.D., and Warren, P.A., Component Level Evaluation of a Friction Damper for Submicron Vibrations, Proc. 43 d Structures, Structural Dynamics and Mat. Conf., Denver, 2002, pp. 1–8.
Domber, J.L., Hinkle, J.D., Peterson, L.D., and Warren, P.A., Dimensional Repeatability of an Elastically Folded Composite Hinge for Deployed Spacecraft Optics, J. of Spacecraft and Rockets, 2002, vol. 39, no. 5, pp. 646–652.
Author information
Authors and Affiliations
Additional information
Original Russian Text © Yu.P. Zaspa, 2007, published in Trenie i Iznos, 2007, Vol. 28, No. 1, pp. 85–100.
About this article
Cite this article
Zaspa, Y.P. Nonlinear shapes of steady-state vibrational oscillations of mechanical contact. Symmetrical tangential oscillations. J. Frict. Wear 28, 87–104 (2007). https://doi.org/10.3103/S1068366607010102
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3103/S1068366607010102