Abstract
In the experiment, we observed such a phenomenon: the alternating normal force changes the vibration state of a friction system. A single-degree-of-freedom mathematical model was used in this paper to discuss the effects of a constant and alternating normal force on the stick–slip vibration characteristics for different dynamic and static friction coefficients. Under the condition that the applied constant normal force continues to increase, the vibration amplitude of the system, the amplitude of the limit cycle, and the adhesion time of the system increase. When the difference between the dynamic and static friction coefficients (DSFCs) is small, the system has a complete and clear limit cycle. When the dynamic friction coefficient is reduced, the difference between DSFCs increases, and the limit cycle of the system is deformed. The friction system has more abundant dynamic vibration characteristics under an alternating normal force than a constant normal force. The vibration state of the system presents a single-cycle stick–slip vibration when the alternating normal force excites the multi-order harmonic response of the friction system, and the excitation frequency of the alternating normal force is the same as the main response frequency of the system with the highest energy or the low-order even-order main frequency. In contrast, the system exhibits various vibration modes when the excitation frequency of the alternating normal force is dissimilar to the main frequency of the system's highest energy response or is consistent with the odd-order main frequency. In addition, increasing the difference between DSFCs or using very high excitation frequencies and excitation amplitudes increases the likelihood of the system entering a chaotic vibration state.
Similar content being viewed by others
Data availability
The data used in this research work are available from the authors by reasonably request.
References
Ibrahim, R.A.: Friction-induced vibration, chatter, squeal, and chaos, Part I: mechanics of contact and friction. Appl. Mech. Rev. 47, 209–226 (1994)
Akay, A.: Acoustics of friction. J. Acoust. Soc. Am. 111, 1525–1548 (2002)
Lima, R., Sampaio, R.: Parametric analysis of the statistical model of the stick-slip process. J. Sound Vib. 397, 141–151 (2017)
Lima, R., Sampaio, R.: Construction of a statistical model for the dynamics of a base-driven stick-slip oscillator. Mech. Syst. Signal Proc. 91, 157–166 (2017)
Du, Z.W., Fang, H.B., Zhan, X., Xu, J.: Experiments on vibration-driven stick-slip locomotion: a sliding bifurcation perspective. Mech. Syst. Signal Proc. 105, 261–275 (2018)
Woodhouse, J.: The acoustics of the violin: a review. Rep. Prog. Phys. 77, 115901 (2014)
He, B.B., Ouyang, H.J., He, S.W., Ren, X.M.: Dynamic analysis of integrally shrouded group blades with rubbing and impact. Nonlinear Dyn. 92, 2159–2175 (2018)
Bettella, M., Harrison, M.F., Sharp, R.S.: Investigation of automotive creep groan noise with a distributed-source excitation technique. J. Sound Vib. 255, 531–547 (2002)
Jearsiripongkul, T., Hochlenert, D.: Disk brake squeal: modeling and active control. 2006 IEEE Conference on Robotics, Automation and Mechatronics. (2006)
Popp, K., Stelter, P.: Stick-slip vibrations and chaos. Philos. Trans. R. Soc. A 332, 89–105 (1990)
VanDeVelde, F., DeBaets, P.: Mathematical approach of the influencing factors on stick-slip induced by decelerative motion. Wear 201, 80–93 (1996)
Li, Z.L., Ouyang, H., Guan, Z.Q.: Friction-induced vibration of an elastic disc and a moving slider with separation and reattachment. Nonlinear Dyn. 87, 1045–1067 (2017)
Lisowski, B., Retiere, C., Moreno, J.P.G., Olejnik, P.: Semiempirical identification of nonlinear dynamics of a two-degree-of-freedom real torsion pendulum with a nonuniform planar stick–slip friction and elastic barriers. Nonlinear Dyn. 100, 3215–3234 (2020)
Pascal, M.: Sticking and nonsticking orbits for a two-degree-of-freedom oscillator excited by dry friction and harmonic loading. Nonlinear Dyn. 77, 267–276 (2014)
Wang, X.C., Mo, J.L., Ouyang, H., Huang, B., Lu, X.D., Zhou, Z.R.: An investigation of stick-slip oscillation of Mn-Cu damping alloy as a friction material. Tribol. Int. 146, 106024 (2020)
Nakano, K.: Two dimensionless parameters controlling the occurrence of stick-slip motion in a 1-DOF system with Coulomb friction. Tribol. Lett. 24, 91–98 (2006)
McMillan, A.J.: A non-linear friction model for self-excited vibrations. J. Sound Vib. 205, 323–335 (1997)
Marin, F., Alhama, F., Moreno, J.A.: Modelling of stick-slip behaviour with different hypotheses on friction forces. Int. J. Eng. Sci. 60, 13–24 (2012)
Oestreich, M., Hinrichs, N., Popp, K.: Bifurcation and stability analysis for a non-smooth friction oscillator. Arch. Appl. Mech. 66, 301–314 (1996)
Andreaus, U., Casini, P.: Dynamics of friction oscillators excited by a moving base and/or driving force. J. Sound Vib. 245, 685–699 (2001)
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)
Wei, D.G., Song, J.W., Nan, Y.H., Zhu, W.W.: Analysis of the stick-slip vibration of a new brake pad with double-layer structure in automobile brake system. Mech. Syst. Signal Proc. 118, 305–316 (2019)
Ozaki, S., Hashiguchi, K.: Numerical analysis of stick-slip instability by a rate-dependent elastoplastic formulation for friction. Tribol. Int. 43, 2120–2133 (2010)
Lee, S.M., Shin, M.W., Lee, W.K., Jang, H.: The correlation between contact stiffness and stick-slip of brake friction materials. Wear 302, 1414–1420 (2013)
Vadivuchezhian, K., Sundar, S., Murthy, H.: Effect of variable friction coefficient on contact tractions. Tribol. Int. 44, 1433–1442 (2011)
Fu, T., Wang, W.H., Ge, N., Wang, X.G., Zhang, X.Y.: Intelligent computing and simulation in seismic mitigation efficiency analysis for the variable friction coefficient RFPS structure system. Neural Comput. Appl. 33, 925–935 (2020)
Hashiguchi, K., Ozaki, S.: Constitutive equation for friction with transition from static to kinetic friction and recovery of static friction. Int. J. Plast. 24, 2102–2124 (2008)
Wei, D.G., Ruan, J.Y., Zhu, W.W., Kang, Z.H.: Properties of stability, bifurcation, and chaos of the tangential motion disk brake. J. Sound Vib. 375, 353–365 (2016)
Rusli, M., Fesa, M.H., Dahlan, H., Bur, M.: Squeal noise analysis using a combination of nonlinear friction contact model. Int. J. Automot. Mech. Eng. 17, 8160–8167 (2020)
Wang, X.C., Huang, B., Wang, R.L., Mo, J.L., Ouyang, H.J.: Friction-induced stick-slip vibration and its experimental validation. Mech. Syst. Signal Proc. 142, 106705 (2020)
Liu, N.Y., Ouyang, H.J.: Friction-induced vibration considering multiple types of nonlinearities. Nonlinear Dyn. 102, 2057–2075 (2020)
Hong, H.K., Liu, C.S.: Coulomb friction oscillator: modelling and responses to harmonic loads and base excitations. J. Sound Vib. 229, 1171–1192 (2000)
Hong, H.K., Liu, C.S.: Non-sticking oscillation formulae for Coulomb friction under harmonic loading. J. Sound Vib. 244, 883–898 (2001)
Jang, Y.H., Barber, J.R.: Effect of phase on the frictional dissipation in systems subjected to harmonically varying loads. Eur. J. Mech. A-Solids 30, 269–274 (2011)
Maegawa, S., Suzuki, A., Nakano, K.: Precursors of global slip in a longitudinal line contact under non-uniform normal loading. Tribol. Lett. 38, 313–323 (2010)
Pilipchuk, V., Olejnik, P., Awrejcewicz, J.: Transient friction-induced vibrations in a 2-DOF model of brakes. J. Sound Vib. 344, 297–312 (2015)
Liu, N.Y., Ouyang, H.J.: Friction-induced vibration of a slider-on-rotating-disc system considering uniform and non-uniform friction characteristics with bi-stability. Mech. Syst. Signal Proc. 164, 108222 (2022)
Krallis, M., Hess, D.P.: Stick-slip in the presence of a normal vibration. Lubr. Sci. 8, 205–219 (2002)
Papangelo, A., Ciavarella, M.: Effect of normal load variation on the frictional behavior of a simple Coulomb frictional oscillator. J. Sound Vib. 348, 282–293 (2015)
Pasternak, E., Dyskin, A., Karachevtseva, I.: Oscillations in sliding with dry friction. Friction reduction by imposing synchronised normal load oscillations. Int. J. Eng. Sci. 154, 103313 (2020)
Karnopp, D.: Computer simulation of stick-slip friction in mechanical dynamic systems. J. Dyn. Syst., Meas Control 107, 100–103 (1985)
Wang, X.C., Wang, R.L., Huang, B., Mo, J.L., Ouyang, H.J.: A study of effect of various normal force loading forms on frictional stick-slip vibration. J. Dyn. Monit. Diagn. 1, 46–55 (2022)
Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985)
Wei, D.G., Zhu, W.W., Wang, B., Ma, Q., Kang, Z.H.: Effects of brake pressures on stick-slip bifurcation and chaos of the vehicle brake system. J Vibroeng 17, 2718–2732 (2015)
Acknowledgements
The authors are grateful for the Independent Research Projects of State Key Laboratory of Traction Power (2020TPL-T06), the Financial Support of the National Natural Science Foundation of China (No. 51822508), and the Sichuan Province Science and Technology Support Program (No. 2020JDTD0012).
Funding
The Independent Research Projects of State Key Laboratory of Traction Power (2020TPL-T06), the Financial Support of the National Natural Science Foundation of China (No. 51822508), the Sichuan Province Science and Technology Support Program (No. 2020JDTD0012).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhu, Y.G., Wang, R.L., Xiang, Z.Y. et al. The effect of dynamic normal force on the stick–slip vibration characteristics. Nonlinear Dyn 110, 69–93 (2022). https://doi.org/10.1007/s11071-022-07614-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-022-07614-0