0
Technical Brief

On the Passive Control of Friction-Induced Instability Due to Mode Coupling

[+] Author and Article Information
Alborz Niknam

Department of Mechanical Engineering
and Energy Processes,
Southern Illinois University Carbondale,
1263 Lincoln Drive,
Carbondale, IL 62901-6899
e-mail: alborz@siu.edu

Kambiz Farhang

Mem. ASME
Department of Mechanical Engineering
and Energy Processes,
Southern Illinois University Carbondale,
1263 Lincoln Drive,
Carbondale, IL 62901-6899
e-mail: farhang@siu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received March 12, 2018; final manuscript received March 5, 2019; published online April 9, 2019. Assoc. Editor: Tesheng Hsiao.

J. Dyn. Sys., Meas., Control 141(8), 084503 (Apr 09, 2019) (6 pages) Paper No: DS-18-1120; doi: 10.1115/1.4043121 History: Received March 12, 2018; Revised March 05, 2019

This study investigates a passive controller for a coupled two degrees-of-freedom (DOFs) oscillator to suppress friction-induced mode-coupling instability. The primary system is acted upon by a friction force of a moving belt and static coupling of the oscillator provided with an oblique spring. The combined system, original system plus absorber, response is governed by two sets of differential equations to include contact and loss of contact between the mass and the belt. Therefore, the model accounts for two sources of nonlinearity in the system: (1) discontinuity in the friction force and (2) intermittent loss of contact. Friction coefficient and absorber orientation are used to define planar parameter space for stability analysis. For various mass ratios, the parameter space is divided into stable and unstable zones by defining stability boundaries. In general, an absorber expands the stability region and provides a significant reduction in transient response overshoot and settling time. Incorporation of the absorber also prevents mass-belt separation, thereby suppressing the belt-speed-overtake by the primary mass.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Le Rouzic, J. , Le Bot, A. , Perret-Liaudet, J. , Guibert, M. , Rusanov, A. , Douminge, L. , Bretagnol, F. , and Mazuyer, D. , 2013, “ Friction-Induced Vibration by Stribeck's Law: Application to Wiper Blade Squeal Noise,” Tribol. Lett., 49(3), pp. 563–572. [CrossRef]
Daei, A. R. , Davoudzadeh, N. , and Filip, P. , 2016, “ Optimization of Brake Friction Materials Using Mathematical Methods and Testing,” SAE Int. J. Mater. Manuf., 9(1), pp. 118–122. [CrossRef]
Daei, A. R. , Majumdar, D. , and Filip, P. , 2015, “ Performance of Low-Metallic Cu-Free Brake Pads With Two Different Graphite Types,” SAE Paper No. 2015-01-2677.
Monteiro, H. L. S. , and Trindade, M. A. , 2017, “ Performance Analysis of Proportional-Integral Feedback Control for the Reduction of Stick-Slip-Induced Torsional Vibrations in Oil Well Drill strings,” J. Sound Vib., 398, pp. 28–38. [CrossRef]
Ibrahim, R. A. , 1994, “ Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part I: Mechanics of Contact and Friction,” ASME Appl. Mech. Rev., 47(7), pp. 209–226. [CrossRef]
Ibrahim, R. A. , 1994, “ Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part II: Dynamics and Modeling,” ASME Appl. Mech. Rev., 47(7), pp. 227–253. [CrossRef]
Akay, A. , 2002, “ Acoustics of Friction,” J. Acoust. Soc. Am., 111(4), pp. 1525–1548. [CrossRef] [PubMed]
Hoffmann, N. , Fischer, M. , Allgaier, R. , and Gaul, L. , 2002, “ A Minimal Model for Studying Properties of the Mode-Coupling Type Instability in Friction Induced Oscillations,” Mech. Res. Commun., 29(4), pp. 197–205. [CrossRef]
Hetzler, H. , Schwarzer, D. , and Seemann, W. , 2007, “ 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), pp. 83–99. [CrossRef]
Juel, J. , and Fidlin, A. , 2003, “ Analytical Approximations for Stick–Slip Vibration Amplitudes,” Int. J. Non-Linear Mech., 38(3), pp. 389–403. [CrossRef]
Armstrong-Hélouvry, B. , Dupont, P. , and De Wit, C. C. , 1994, “ A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction,” Automatica, 30(7), pp. 1083–1138. [CrossRef]
Won, H. I. , and Chung, J. , 2016, “ Stick–Slip Vibration of an Oscillator With Damping,” Nonlinear Dyn., 86(1), pp. 257–267. [CrossRef]
Niknam, A. , and Farhang, K. , 2018, “ Vibration Instability in a Large Motion Bistable Compliant Mechanism Due to Stribeck Friction,” ASME J. Vib. Acoust., 140(6), p. 061017.
Al-Bender, F. , Symens, W. , Swevers, J. , and Van Brussel, H. , 2004, “ Theoretical Analysis of the Dynamic Behavior of Hysteresis Elements in Mechanical Systems,” Int. J. Non-Linear Mech., 39(10), pp. 1721–1735. [CrossRef]
Ruderman, M. , and Iwasaki, M. , 2016, “ On Damping Characteristics of Frictional Hysteresis in Pre-Sliding Range,” J. Phys.: Conf. Ser., 727, p. 12014. https://iopscience.iop.org/article/10.1088/1742-6596/727/1/012014
Hoffmann, N. , and Gaul, L. , 2003, “ Effects of Damping on Mode-Coupling Instability in Friction Induced Oscillations,” Z. Angew. Math. Mech., 83(8), pp. 524–534. [CrossRef]
Hoffmann, N. , Bieser, S. , and Gaul, L. , 2004, “ Harmonic Balance and Averaging Techniques for Stick-Slip Limit-Cycle Determination in Mode-Coupling Friction Self-Excited Systems,” Tech. Mech., 24(3–4), pp. 185–197. http://www.ovgu.de/ifme/zeitschrift_tm/2004_Heft3_4/Hoffmann.pdf
Li, Z. , Ouyang, H. , and Guan, Z. , 2016, “ Nonlinear Friction-Induced Vibration of a Slider–Belt System,” ASME J. Vib. Acoust., 138(4), p. 041006. [CrossRef]
Sinou, J. J. , and Jézéquel, L. , 2007, “ Mode Coupling Instability in Friction-Induced Vibrations and Its Dependency on System Parameters Including Damping,” Eur. J. Mech., A, 26(1), pp. 106–122. [CrossRef]
Niknam, A. , and Farhang, K. , “ Friction-Induced Vibration Due to Mode-Coupling and Intermittent Contact Loss,” ASME J. Vib. Acoust., 141(2), p. 021012. [CrossRef]
Niknam, A. , 2018, “Vibration Instability in Frictionally Driven Elastic Mechanical System,” Southern Illinois University, Carbondale, IL.
Armstrong, B. , and Amin, B. , 1996, “ PID Control in the Presence of Static Friction: A Comparison of Algebraic and Describing Function Analysis,” Automatica, 32(5), pp. 679–692. [CrossRef]
Dupont, P. E. , 1994, “ Avoiding Stick-Slip Through PD Control,” IEEE Trans. Autom. Control, 39(5), pp. 1094–1097. [CrossRef]
Nath, J. , and Chatterjee, S. , 2016, “ Tangential Acceleration Feedback Control of Friction Induced Vibration,” J. Sound Vib., 377, pp. 22–37. [CrossRef]
Nath, J. , and Chatterjee, S. , 2016, “ Nonlinear Control of Stick-Slip Oscillations by Normal Force Modulation,” J. Vib. Control, 24(8), pp. 1427–1439. [CrossRef]
Popp, K. , 2005, “ Modelling and Control of Friction-Induced Vibrations,” Math. Comput. Modell. Dyn. Syst., 11(3), pp. 345–369. [CrossRef]
Leine, R. I. , and Nijmeijer, H. , 2004, Dynamics and Bifurcations of Non-Smooth Mechanical Systems, Springer-Verlag, Berlin.

Figures

Grahic Jump Location
Fig. 1

Mechanical model of a 2DOF coupled oscillator

Grahic Jump Location
Fig. 2

Eigenvalue analysis for a system without vibration absorber: (a) real part of eigenvalue and (b) imaginary part of eigenvalue

Grahic Jump Location
Fig. 3

Critical coefficient of friction for different tilted angle and dimensionless mass at Γ3=0.8. Below each curve is stable region. The horizontal thick line shows μcr for a system without absorber.

Grahic Jump Location
Fig. 4

Critical coefficient of friction for different tilted angle and dimensionless mass at Γ3=0.4. Below each curve is stable region. The horizontal thick line shows μcr for a system without absorber.

Grahic Jump Location
Fig. 5

Loci of the dominant eigenvalues at different tilting angles. Dash line shows the imaginary axis. Γ3=0.4: (a) real part of the eigenvalue and (b) imaginary part of eigenvalue.

Grahic Jump Location
Fig. 6

Critical normal force (ncr) versus velocity of the belt for primary oscillator. Dots shows the ncr at corresponding belt velocity. Line shows fitted data. Γ2=0.8,Γc=0.2.

Grahic Jump Location
Fig. 7

Phase plane for the system in the x1-direction (case 1) μ=0.3, V=0.2: (a) without absorber and (b) with absorber

Grahic Jump Location
Fig. 8

Phase plane for the system (case 2) μ=0.3, V=0.5: (a) without absorber; (b) with absorber (in the x1-direction); (c) without absorber; and (d) with absorber (in the x2-direction)

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In