[1] Chen Long, Zhang Jianrun,. Stability analysis of the rotating tribological pair systemon circular-disc end faces [J]. Journal of Southeast University (English Edition), 2020, 36 (1): 24-31. [doi:10.3969/j.issn.1003-7985.2020.01.004]

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Stability analysis of the rotating tribological pair systemon circular-disc end faces()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

36

Issue:

2020 1

Page:

24-31

Research Field:

Mechanical Engineering

Publishing date:

2020-03-20

Info

Title:

Stability analysis of the rotating tribological pair systemon circular-disc end faces

Author(s):

Chen Long;  Zhang Jianrun

School of Mechanical Engineering, Southeast University, Nanjing 211189, China

Keywords:

rotating tribological pair system;  contact stiffness;  Stribeck effect;  dynamic model;  stability

PACS:

TH113;TH117

DOI:

10.3969/j.issn.1003-7985.2020.01.004

Abstract:

In order to study the stability of friction and contact of the rotating tribological pair system, considering the influence of the changeable factors on the stability, the system dynamics analysis model based on the Lagrange equation is firstly established. The surface contact stiffness model is determined on the basis of the fractal theory. The model of the friction torque with velocities is created by using the Stribeck friction effect. The Lyapunov indirect method is employed to explore the eigenvalue problem of the system state equation. The effects of the applied load, the fractal dimension, the fractal scaling coefficient and the Stribeck coefficient on the system stability are investigated in detail. The numerical simulation results demonstrate that the tribological pair system is prone to causing system instability at low speed, and the system instability boundary value decreases when the Stribeck coefficient decreases. The fractal dimension and the fractal scaling coefficient impact the system stability slightly when fractal dimensions are large, and the system instability can be reduced by properly increasing the surface smoothness. Moreover, the system instability evidently increases with the increase in the applied load and the Stribeck coefficient. These achievements can provide a reference and theoretical support for the analysis of the dynamic performance of the tribological pair system.

References:

[1] Akay A. Acoustics of friction[J]. The Journal of the Acoustical Society of America, 2002, 111(4): 1525-1548. DOI:10.1121/1.1456514.
[2] Suzuki H, Miura R. The jerking motion in servomechanisms, considering negative slope of friction characteristics[J]. Transactions of the Institute of Electrical Engineers of Japan A, 1967, 87(Supp S1): 1321-1330.
[3] Spurr R T. A theory of brake squeal[J]. Proceedings of the Institution of Mechanical Engineers: Automobile Division, 1961, 15(1): 33-52. DOI:10.1243/pime_auto_1961_000_009_02.
[4] Popp K, Stelter P. Stick-slip vibrations and chaos[J]. Philosophical Transactions of the Royal Society of London Series A: Physical and Engineering Sciences, 1990, 332(1624): 89-105. DOI:10.1098/rsta.1990.0102.
[5] Hoffmann N, Gaul L. Effects of damping on mode-coupling instability in friction induced oscillations[J]. ZAMM, 2003, 83(8): 524-534. DOI:10.1002/zamm.200310022.
[6] Crowther A R, Singh R. Analytical investigation of stick-slip motions in coupled brake-driveline systems[J]. Nonlinear Dynamics, 2007, 50(3): 463-481. DOI:10.1007/s11071-006-9187-9.
[7] Giannini O, Massi F. Characterization of the high-frequency squeal on a laboratory brake setup[J]. Journal of Sound and Vibration, 2008, 310(1/2): 394-408. DOI:10.1016/j.jsv.2007.08.009.
[8] Devarajan K, Balaram B. Analytical approximations for stick-slip amplitudes and frequency of duffing oscillator[J]. Journal of Computational and Nonlinear Dynamics, 2017, 12(4): 044501. DOI:10.1115/1.4034734.
[9] Abdo J, Abouelsoud A A. Analytical approach to estimate amplitude of stick-slip oscillations[J]. Journal of Theoretical and Applied Mechanics, 2011, 49(4): 971-986.
[10] Niknam A, Farhang K. Vibration instability in a large motion bistable compliant mechanism due to stribeck friction[J]. Journal of Vibration and Acoustics, 2018, 140(6): 061017. DOI:10.1115/1.4040513.
[11] Xiang W, Yan S Z, Wu J N. Dynamic analysis of planar mechanical systems considering stick-slip and Stribeck effect in revolute clearance joints[J]. Nonlinear Dynamics, 2019, 95(1): 321-341. DOI:10.1007/s11071-018-4566-6.
[12] Ouyang H, Mottershead J E, Cartmell M P, et al. Friction-induced vibration of an elastic slider on a vibrating disc[J]. International Journal of Mechanical Sciences, 1999, 41(3): 325-336. DOI:10.1016/s0020-7403(98)00059-9.
[13] Ouyang H, Mottershead J E. Dynamic instability of an elastic disk under the action of a rotating friction couple[J]. Journal of Applied Mechanics, 2004, 71(6): 753-758. DOI:10.1115/1.1795815.
[14] Kang J. Theoretical model for friction-induced vibration of ball joint system under mode-coupling instability[J]. Tribology Transactions, 2015, 58(5): 807-814. DOI:10.1080/10402004.2015.1020121.
[15] Sui X, Ding Q. Instability and stochastic analyses of a pad-on-disc frictional system in moving interactions[J]. Nonlinear Dynamics, 2018, 93(3): 1619-1634. DOI:10.1007/s11071-018-4280-4.
[16] Pohrt R, Popov V L. Normal contact stiffness of elastic solids with fractal rough surfaces[J]. Physical Review Letters, 2012, 108(10): 104301. DOI:10.1103/physrevlett.108.104301.
[17] Guan D, Jing L, Hilton H H, et al. Tangential contact analysis of spherical pump based on fractal theory[J]. Tribology International, 2018, 119: 531-538. DOI:10.1016/j.triboint.2017.11.034.
[18] Sun Y Y, Xiao H F, Xu J W, et al. Study on the normal contact stiffness of the fractal rough surface in mixed lubrication[J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2018, 232(12): 1604-1617. DOI:10.1177/1350650118758741.
[19] Xiao H F, Sun Y Y, Chen Z G. Fractal modeling of normal contact stiffness for rough surface contact considering the elastic-plastic deformation[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2019, 41: No.11. DOI:10.1007/s40430-018-1513-x.
[20] Liu P, Zhao H, Huang K, et al. Research on normal contact stiffness of rough surface considering friction based on fractal theory[J]. Applied Surface Science, 2015, 349: 43-48. DOI:10.1016/j.apsusc.2015.04.174.
[21] Pan W J, Li X P, Wang L L, et al. A normal contact stiffness fractal prediction model of dry-friction rough surface and experimental verification[J]. European Journal of Mechanics-A, 2017, 66: 94-102. DOI:10.1016/j.euromechsol.2017.06.010.
[22] Awrejcewicz J, Olejnik P. Analysis of dynamic systems with various friction laws[J]. Applied Mechanics Reviews, 2005, 58(6): 389-411. DOI:10.1115/1.2048687.
[23] Armstrong-Hélouvry B, Soom A. Control of machines with friction[J]. Journal of Tribology, 1992, 114(3): 637. DOI:10.1115/1.2920929.
[24] Majumdar A, Bhushan B. Fractal model of elastic-plastic contact between rough surfaces[J]. Journal of Tribology, 1991, 113(1): 1-11. DOI:10.1115/1.2920588.
[25] Liu W J, Tang F S. Modeling a simplified regulatory system of blood glucose at molecular levels[J]. Journal of Theoretical Biology, 2008, 252(4): 608-620. DOI:10.1016/j.jtbi.2008.02.021.
[26] Guan Z Z, Ye M H, Yin X C, et al. Recognition of surface roughness based on fractal theory and the microscopic images[J]. Applied Mechanics and Materials, 2012, 241/242/243/244: 3030-3033. DOI:10.4028/www.scientific.net/amm.241-244.3030.
[27] Pan Y L, Wu L Q, Zhang Y D. Study of the relationship between fractal model parameters and roughness parameter r_a[J]. Engineering Science, 2004, 6(5): 49-51.(in Chinese)

Memo

Memo:

Biographies: Chen Long(1994—), male, graduate; Zhang Jianrun(corresponding author), male, doctor, professor, zhangjr@seu.edu.cn.
Foundation items: The Science and Technology Support Program of Jiangsu Province(No.BE2014133), the Transformation Program of Scientific and Technological Achievements of Jiangsu Province(No. 201701213).
Citation: Chen Long, Zhang Jianrun. Stability analysis of the rotating tribological pair system on circular-disc end faces[J].Journal of Southeast University(English Edition), 2020, 36(1):24-31.DOI:10.3969/j.issn.1003-7985.2020.01.004.

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