Abstract
In this paper, a PZT (lead zirconate titanate)-based absorber and energy harvester (PAEH) is used for passive control of friction-induced stick-slip vibration in a friction system. Its stability condition coupled with PAEH is analytically derived, whose efficiency is then demonstrated by numerical simulation. The results show that the structural parameters of the PAEH can significantly affect the system stability, which increases with the mass ratio between the PAEH and the primary system, but first increases and then decreases with the natural frequency ratio between the PAEH and the primary system. The impacts of the electric parameters of the PAEH on the system stability are found to be insignificant. In addition, the PAEH can effectively suppress the stick-slip limit cycle magnitude in a wide working parameter range; however, it does not function well for friction systems in all the working conditions. The stick-slip vibration amplitude can be increased in the case of a large loading (normal) force. Finally, an experiment on a tribo-dynamometer validates the findings of the theoretical study, in which the vibration reduction and energy harvesting performance of the PAEH is fully demonstrated.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Data availability
The data used in this research work are available from the authors on reasonable request.
References
Feeny B, Guran A, Hinrichs N, Popp K. A historical review on dry friction and stick-slip phenomena. Appl Mech Rev 51(5): 321–341 (1998)
Berger E J. Friction modeling for dynamic system simulation. Appl Mech Rev 55(6): 535–577 (2002)
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)
Hetzler H, Schwarzer D, Seemann W. Analytical investigation of steady-state stability and Hopf-bifurcations occurring in sliding friction oscillators with application to low-frequency disc brake noise. Commun Nonlinear Sci Numer Simul 12(1): 83–99 (2007)
Chen F, Ouyang H J, Wang X C. A new mechanism for friction-induced vibration and noise. Friction 11(2): 302–315 (2023)
Kendrick J E, Lavallée Y, Hirose T, Di Toro G, Hornby A J, De Angelis S, Dingwell D B. Volcanic drumbeat seismicity caused by stick-slip motion and magmatic frictional melting. Nat Geosci 7(6): 438–442 (2014)
Kim S S, Hwang H J, Shin M W, Jang H. Friction and vibration of automotive brake pads containing different abrasive particles. Wear 271(7–8): 1194–1202 (2011)
Behrendt J, Weiss C, Hoffmann N P. A numerical study on stick-slip motion of a brake pad in steady sliding. J Sound Vib 330(4): 636–651 (2011)
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)
Lu X D, Zhao J, Mo J L, Wu Y K, Xu J W, Zhang Y F, Zhou Z R. Suppression of friction-induced stick-slip behavior and improvement of tribological characteristics of sliding systems by introducing damping materials. Tribol Trans 63(2): 222–234 (2020)
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 Process 164: 108222 (2022)
Saha A, Wahi P. Delayed feedback for controlling the nature of bifurcations in friction-induced vibrations. J Sound Vib 330(25): 6070–6087 (2011)
Von Wagner U, Hochlenert D, Jearsiripongkul T, Hagedorn P. Active control of brake squeal via “smart pads”. In Proceedings of the 22nd Annual Brake Colloquium & Exhibition, Warrendale, PA, USA, 2004.
Zhao X W, Gräbner N, von Wagner U. Avoiding creep groan: Investigation on active suppression of stick-slip limit cycle vibrations in an automotive disk brake via piezoceramic actuators. J Sound Vib 441: 174–186 (2019)
Wang X, Wu H M, Yang B T. Nonlinear multi-modal energy harvester and vibration absorber using magnetic softening spring. J Sound Vib 476: 115332 (2020)
Kerschen G, Vakakis A F, Lee Y S, McFarland D M, Kowtko J J, Bergman L A. Energy transfers in a system of two coupled oscillators with essential nonlinearity: 1:1 resonance manifold and transient bridging orbits. Nonlinear Dyn 42(3): 283–303 (2005)
Yang K, Zhang Y W, Ding H, Yang T Z, Li Y, Chen L Q. Nonlinear energy sink for whole-spacecraft vibration reduction. J Vib Acoust 139(2): 021011 (2017)
Wang X, Yang B T. Transient vibration control using nonlinear convergence active vibration absorber for impulse excitation. Mech Syst Signal Process 117: 425–436 (2019)
Lin J, Liu W Z. Experimental evaluation of a piezoelectric vibration absorber using a simplified fuzzy controller in a cantilever beam. J Sound Vib 296(3): 567–582 (2006)
Ture Savadkoohi A, Lamarque C H, Dimitrijevic Z. Vibratory energy exchange between a linear and a nonsmooth system in the presence of the gravity. Nonlinear Dyn 70(2): 1473–1483 (2012)
Taleshi M, Dardel M, Pashaie M H. Passive targeted energy transfer in the steady state dynamics of a nonlinear plate with nonlinear absorber. Chaos Solitons Fractals 92: 56–72 (2016)
Maegawa S, Itoigawa F. Design method for suppressing stick-slip using dynamic vibration absorber. Tribol Int 140: 105866 (2019)
Popp K, Rudolph M. Vibration control to avoid stick-slip motion. J Vib Contr 10(11): 1585–1600 (2004)
Bergeot B, Berger S, Bellizzi S. Mode coupling instability mitigation in friction systems by means of nonlinear energy sinks: Numerical highlighting and local stability analysis. J Vib Contr 24(15): 3487–3511 (2018)
Zhang C L, Xu J C, Fang S T, Qiao Z J, Yurchenko D, Lai Z H. A pendulum-based absorber-harvester with an embedded hybrid vibro-impact electromagnetic-dielectric generator. Nano Energy 107: 108126 (2023)
Rezaei M, Talebitooti R, Liao W H. Investigations on magnetic bistable PZT-based absorber for concurrent energy harvesting and vibration mitigation: Numerical and analytical approaches. Energy 239: 122376 (2022)
Tang X D, Zuo L. Simultaneous energy harvesting and vibration control of structures with tuned mass dampers. J Intell Mater Syst Struct 23(18): 2117–2127 (2012)
Chen W, Xiang Z Y, Mo J L, Fan Z Y, Qian H H, Wang J Y. Energy harvesting and vibration reduction by sandwiching piezoelectric elements into elastic damping components with parallel-grooved structures. Compos Struct 241: 112105 (2020)
Wang X F, Mo J L, Ouyang H J, Xiang Z Y, Chen W, Zhou Z R. Simultaneous energy harvesting and tribological property improvement. Friction 9(5): 1275–1291 (2021)
Xiang Z Y, Mo J L, Qian H H, Chen W, Luo D B, Zhou Z R. Friction-induced vibration energy harvesting of a high-speed train brake system via a piezoelectric cantilever beam. Tribol Int 162: 107126 (2021)
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 Process 118: 305–316 (2019)
Stanton S C, McGehee C C, Mann B P. Nonlinear dynamics for broadband energy harvesting: Investigation of a bistable piezoelectric inertial generator. Phys D Nonlinear Phenom 239(10): 640–653 (2010)
Chen W, Mo J L, Xiang Z Y, Wang A Y, Liu Q A, Qian H H. A new concept of frequency-excitation-up conversion to improve the yield of linear piezoelectric generators. Sens Actuat A Phys 325: 112712 (2021)
Wang W, Cao J Y, Bowen C R, Zhou S X, Lin J. Optimum resistance analysis and experimental verification of nonlinear piezoelectric energy harvesting from human motions. Energy 118: 221–230 (2017)
Tonazzi D, Passafiume M, Papangelo A, Hoffmann N, Massi F. Numerical and experimental analysis of the bi-stable state for frictional continuous system. Nonlinear Dyn 102(3): 1361–1374 (2020)
Saha A, Wahi P, Bhattacharya B. Characterization of friction force and nature of bifurcation from experiments on a single-degree-of-freedom system with friction-induced vibrations. Tribol Int 98: 220–228 (2016)
Mei X T, Dong R H, Sun F, Zhou R, Zhou S X. Array piezoelectric energy harvester with frequency up-conversion in rotational motions: Theoretical analyses and experimental validations. Nonlinear Dyn 111(11): 9989–10009 (2023)
Wang D W, Mo J L, Wang X F, Ouyang H, Zhou Z R. Experimental and numerical investigations of the piezoelectric energy harvesting via friction-induced vibration. Energy Convers Manag 171: 1134–1149 (2018)
Ghayesh M H, Farokhi H. Nonlinear broadband performance of energy harvesters. Int J Eng Sci 147: 103202 (2020)
Pan J N, Qin W Y, Deng W Z, Zhang P T, Zhou Z Y. Harvesting weak vibration energy by integrating piezoelectric inverted beam and pendulum. Energy 227: 120374 (2021)
Li C, Wang D F, Yang X, Suzuki Y. An ultra-low frequency ball-impacted potential-variable nonlinear energy harvester. Mech Syst Signal Process 182: 109588 (2023)
Wu Y P, Li S, Fan K Q, Ji H L, Qiu J H. Investigation of an ultra-low frequency piezoelectric energy harvester with high frequency up-conversion factor caused by internal resonance mechanism. Mech Syst Signal Process 162: 108038 (2022)
Gu L, Livermore C. Impact-driven, frequency up-converting coupled vibration energy harvesting device for low frequency operation. Smart Mater Struct 20(4): 045004 (2011)
Erturk A, Inman D J. Broadband piezoelectric power generation on high-energy orbits of the bistable Duffing oscillator with electromechanical coupling. J Sound Vib 330(10): 2339–2353 (2011)
Chen J T, Bao B, Liu J L, Wu Y F, Wang Q. Piezoelectric energy harvester featuring a magnetic chaotic pendulum. Energy Convers Manag 269: 116155 (2022)
Zhou Z Y, Qin W Y, Du W F, Zhu P, Liu Q. Improving energy harvesting from random excitation by nonlinear flexible bi-stable energy harvester with a variable potential energy function. Mech Syst Signal Process 115: 162–172 (2019)
Acknowledgements
The authors are grateful for the financial support of the National Natural Science Foundation of China (U22A20181, 52275214, 12272324).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors have no competing interests to declare that are relevant to the content of this article.
Additional information
Wei CHEN. He received his M.S. degree in mechanical engineering in 2021 from Southwest Jiaotong University, China. Currently, he is a doctoral candidate in the Department of Mechanical Engineering, Southwest Jiaotong University. His research interests include friction-induced vibration (FIV) and vibration-based energy harvesting.
Jiliang MO. He received his M.S. and Ph.D. degrees in mechanical design and theory from Southwest Jiaotong University, China, in 2003 and 2008, respectively. His current position is a professor at Southwest Jiaotong University, China. His research interests include tribology/dynamic behaviour analysis, vibration and noise control, and fault diagnosis and intelligence.
Huajiang OUYANG. He received his B.E. degree in 1982, master’s degree in 1985, and Ph.D. degree in 1989 from Dalian University of Technology, China. He is a professor in the School of Engineering, University of Liverpool, UK. He is also a Changjiang Scholarship Professor. His research interests include friction-induced vibration, moving-load dynamics, vibration based structural identification and energy harvesting, and vibration control.
Jing ZHAO. She received her Ph.D. degree in mechanical design and theory from Southwest Jiaotong University, China, in 2009. Now, she is an associate professor at School of Mechanical Engineering, Southwest Jiaotong University. Her research interests include drag reduction/energy recovery, bionic manufacturing and mechanical design theory.
Zaiyu XIANG. He received his M.S. degree in mechanical engineering in 2016 from Kunming University of Science and Technology, China. After then, he was in the lecturer faculty of mechanical and electrical engineering, Liuzhou Vocational and Technical College, China. Later, he received his Ph.D. degree in 2022 from School of mechanical engineering, Southwest Jiaotong University, China. He is currently an assistant professor in School of Mechanical Engineering, Guangxi University, China. His research interests include friction-induced vibration and energy harvesting.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Chen, W., Mo, J., Ouyang, H. et al. Suppressing friction-induced stick-slip vibration through a linear PZT-based absorber and energy harvester. Friction 12, 1449–1468 (2024). https://doi.org/10.1007/s40544-023-0801-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40544-023-0801-3