Abstract
This study investigates the vibration transmission and power dissipation behaviour of a mass-spring-damper system mounted on a conveyor belt. Coulomb friction exists between the mass and the belt moving at a constant velocity and acts as the external force for the mass. The steady-state power flow characteristics are obtained based on numerical integrations. The vibration energy dissipation at the contact interface and by the viscous damper is evaluated and quantified. The vibration transmission is measured by force transmissibility. For the system without the viscous damper, the instantaneous friction power can be positive or negative, depending on the motion characteristics of the mass. For the system with the viscous damper, in the steady-state motion, the vibration energy input caused by the friction can be dissipated by the viscous damper and also by the friction. Furthermore, effects of the magnitude of conveyor belt speed, damping ratio and friction force on the dynamic behaviour of systems are examined, and the power dissipation ratio of the system is analyzed. The results are expected to provide insights into the vibration transmission and suppression design of systems with friction.
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Ibrahim, R.A.: Friction-induced vibration, chatter, squeal, and chaos, Part II: dynamic and modeling. Appl. Mech. Rev. 47(7), 227–253 (1994)
McMillan, A.J.: A non-linear friction model for self-excited vibrations. J. Sound Vib. 205(3), 323–335 (1997)
Popp, K., Hinrichs, N., Oestreich, M.: Dynamical behaviour of a friction oscillator with simultaneous self and external excitation. Sadhana 20(2), 627–654 (1995)
Popp, K., Stelter, P.: Stick-slip vibrations and chaos. Philos. Trans. Phys. Sci. Eng. 332, 89–105 (1990)
Kruse, S., Tiedemann, M., Zeumer, B., Reuss, P., Hetzler, H., Hoffmann, N.: The influence of joints on friction induced vibration in brake squeal. J. Sound Vib. 340, 239–252 (2015)
Wang, X.C., Huang, B., Wang, R.L., Mo, J.L., Ouyang, H.: Friction-induced stick-slip vibration and its experimental validation. Mech. Syst. Signal Process. 142, 106705 (2020)
Saha, A., Wiercigroch, M., Jankowski, K., Wahi, P., Stefański, A.: Investigation of two different friction models from the perspective of friction-induced vibrations. Tribol. Int. 90, 185–197 (2015)
Marques, F., Flores, P., Pimenta Claro, J.C., Lankarani, H.M.: A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dyn. 86(3), 1407–1443 (2016). https://doi.org/10.1007/s11071-016-2999-3
Saha, A., Wahi, P., Wiercigroch, M., Stefański, A.: A modified LuGre friction model for an accurate prediction of friction force in the pure sliding regime. Int. J. Non Linear Mech. 80, 122–131 (2016)
Do, N., Ferri, A.A.: Energy transfer and dissipation in a three-degree-of-freedom system with stribeck friction. In: Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Orlando, pp. 195–204. ASME (2005)
Goyder, H.G.D., White, R.G.: Vibrational power flow from machines into built-up structures, Part I: introduction and approximate analyses of beam and plate-like foundations. J. Sound Vib. 68(1), 59–75 (1980)
Royston, T.J., Singh, R.: Vibratory power flow through a nonlinear path into a resonant receiver. J. Acoust. Soc. Am. 101(4), 2059–2069 (1997)
Vakakis, A.F., Gendelman, O.V., Bergman, L.A., McFarland, D.M., Kerschen, G., Lee, Y.S.: Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems. Springer, New York (2008). https://doi.org/10.1007/978-1-4020-9130-8
Yang, J.: Power flow analysis of nonlinear dynamical systems. University of Southampton (2013)
Yang, J., Xiong, Y.P., Xing, J.T.: Dynamics and power flow behaviour of a nonlinear vibration isolation system with a negative stiffness mechanism. J. Sound Vib. 332(1), 167–183 (2013)
Yang, J., Shi, B., Rudd, C.: On vibration transmission between interactive oscillators with nonlinear coupling interface. Int. J. Mech. Sci. 137, 238–251 (2018)
Yang, J., Jiang, J.Z., Neild, S.A.: Dynamic analysis and performance evaluation of nonlinear inerter-based vibration isolators. Nonlinear Dyn. 99(3), 1823–1839 (2019). https://doi.org/10.1007/s11071-019-05391-x
Shi, B., Yang, J., Rudd, C.: On vibration transmission in oscillating systems incorporating bilinear stiffness and damping elements. Int. J. Mech. Sci. 150, 458–470 (2019)
Dai, W., Yang, J., Shi, B.: Vibration transmission and power flow in impact oscillators with linear and nonlinear constraints. Int. J. Mech. Sci. 168, 105234 (2020)
Dong, Z., Shi, B., Yang, J., Li, T.: Suppression of vibration transmission in coupled systems with an inerter-based nonlinear joint. Nonlinear Dyn. 107(2), 1637–1662 (2021)
Dai, W., Yang, J.: Vibration transmission and energy flow of impact oscillators with nonlinear motion constraints created by diamond-shaped linkage mechanism. Int. J. Mech. Sci. 194, 106212 (2021)
Karnopp, D.: Computer simulation of stick-slip friction in mechanical dynamic systems. J. Dyn. Syst. Meas. Contr. 107(1), 100–103 (1985)
Olsson, H.M.: Control systems with friction. Department of Automatic Control, Lund Institute of Technology (LTH), Sweden (1997)
Dai, W., Yang, J., Wiercigroch, M.: Vibration energy flow transmission in systems with Coulomb friction. Int. J. Mech. Sci. 214, 106932 (2022)
Xiong, Y.P., Xing, J.T., Price, W.G.: A general linear mathematical model of power flow analysis and control for integrated structure-control systems. J. Sound Vib. 267(2), 301–334 (2003)
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This work was supported by National Natural Science Foundation of China under Grant number 12172185 and by the Zhejiang Provincial Natural Science Foundation under Grant number LY22A020006.
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Chao, C., Shi, B., Yang, J., Wiercigroch, M. (2023). Vibration Power Dissipation in a Spring-Damper-Mass System Excited by Dry Friction. In: Dimitrovová, Z., Biswas, P., Gonçalves, R., Silva, T. (eds) Recent Trends in Wave Mechanics and Vibrations. WMVC 2022. Mechanisms and Machine Science, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-031-15758-5_99
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