Journal of Applied Nonlinear Dynamics
Stick-Slip Instability in a Compliant Bistable Double-Slider Mechanism
Journal of Applied Nonlinear Dynamics 10(4) (2021) 775--789 | DOI:10.5890/JAND.2021.12.013
Alborz Niknam , Kambiz Farhang
Department of Mechanical Engineering and Energy Processes, Southern Illinois University Carbondale,\\ 1263 Lincoln Drive, Carbondale, IL 62901-6899, USA
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Abstract
A This paper investigates friction-induced instability in a Single Degree-of-Freedom, pseudo-rigid-body representation of a bistable compliant mechanism composed of two sliders connected with a massless rigid link. The friction force is a function of the state variables through Stribeck effect and variable contact force due to the structural nonlinearity of the mechanism. A Constant normal force ensures the mass-belt contact during oscillation. It is shown that the steady-state response of the vibrating mechanism depends on the belt velocity, applied normal load, and stiffness. The applied normal force and belt velocity, as bifurcation parameters, are used to define the number and location of equilibrium points and their corresponding stability.
References
-
[1]  | Howell, L.L. (2001), Compliant mechanisms, John Wiley & Sons.
|
-
[2]  | Kota, S., Lu, K.-J., Kreiner, Z., Trease, B., Arenas, J., and Geiger, J. (2005), Design
and application of compliant mechanisms for surgical tools,
J. Biomech. Eng.,
127, 981-989.
|
-
[3]  | Kota, S., Hetrick, J.A., Osborn, R., Paul, D., Pendleton, E., Flick, P., and
Tilmann, C. (2003), Design and application of compliant mechanisms for morphing
aircraft structures, in: Industrial and Commercial Applications of Smart
Structures Technologies, pp. 24-34.
https://doi.org/10.1117/12.483869.
|
-
[4]  | Jensen, B.D. and Howell, L.L. (2004), Bistable configurations of compliant
mechanisms modeled using four links and translational joints, J. Mech. Des.,
126, 657-666.
|
-
[5]  | Chen, G., Gou, Y., and Zhang, A. (2011), Synthesis of compliant multistable mechanisms
through use of a single bistable mechanism, J. Mech. Des.,
133,
81007-81009. http://dx.doi.org/10.1115/1.4004543.
|
-
[6]  | S\"{o}nmez, \"{U} and Tutum, C.C. (2008), A Compliant bistable mechanism design
incorporating elastica buckling beam theory and pseudo-rigid-body model, J.
Mech. Des., 130, 42304-42314. http://dx.doi.org/10.1115/1.2839009.
|
-
[7]  | Jensen, B.D., Howell, L.L., and Salmon, L.G. (1999), Design of two-link, in-plane,
bistable compliant micro-mechanisms, J. Mech. Des., 121, 416-423.
http://dx.doi.org/10.1115/1.2829477.
|
-
[8]  | Niknam, A. and Farhang, K. (2018), Vibration instability in a large motion bistable
compliant mechanism due to stribeck friction, J. Vib. Acoust.,
http://dx.doi.org/10.1115/1.4040513.
|
-
[9]  | Berger, E. (2002), Friction modeling for dynamic system simulation, Appl. Mech.
Rev., 55, 535. https://doi.org/10.1115/1.1501080.
|
-
[10]  | Ibrahim, R.A. (1994), Friction-induced vibration, chatter, squeal, and
chaos---Part II: dynamics and modeling, Appl. Mech. Rev., 47, 227-253.
http://dx.doi.org/10.1115/1.3111080.
|
-
[11]  | Ibrahim, R.A. (1994), Friction-induced vibration, chatter, squeal, and
chaos---Part I: mechanics of contact and friction, Appl. Mech. Rev.,
47,
209-226. http://dx.doi.org/10.1115/1.3111079.
|
-
[12]  | Kovalyshen, Y. (2015), Understanding root cause of stick-slip vibrations in
deep drilling with drag bits, Int. J. Non. Linear. Mech., 67, 331-341.
https://doi.org/10.1016/j.ijnonlinmec.2014.10.019.
|
-
[13]  | Sarker, M., Rideout, D.G., and Butt, S.D. (2017), Dynamic model for longitudinal and
torsional motions of a horizontal oilwell drillstring with wellbore
stick-slip friction, J. Pet. Sci. Eng., 150, 272-287.
https://doi.org/10.1016/j.petrol.2016.12.010.
|
-
[14]  | Mirzababaei, S. and Filip, P. (2017), Impact of humidity on wear of automotive
friction materials, Wear., 376-377, 717-726.
https://doi.org/https://doi.org/10.1016/j.wear.2017.02.020.
|
-
[15]  | 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,
563-572. https://doi.org/10.1007/s11249-012-0100-z.
|
-
[16]  | 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, 83-99.
https://doi.org/10.1016/j.cnsns.2006.01.007.
|
-
[17]  | Juel Thomsen, J. and Fidlin, A. (2003), Analytical approximations for stick-slip
vibration amplitudes, Int. J. Non. Linear. Mech., 38, 389-403.
https://doi.org/10.1016/S0020-7462(01)00073-7.
|
-
[18]  | Niknam, A. and Farhang, K. (2019), Friction-induced vibration due to mode-coupling
and intermittent contact loss, J. Vib. Acoust. 141, 021012 (10 pages).
https://doi.org/10.1115/1.4041671.
|
-
[19]  | Hoffmann, N. and Gaul, L. (2004), A sufficient criterion for the onset of
sprag-slip oscillations, Arch. Appl. Mech., 73, 650-660.
https://doi.org/10.1007/s00419-003-0315-4.
|
-
[20]  | Sinou, J.-J., Thouverez, F., and Jezequel, L. (2003), Analysis of friction and
instability by the centre manifold theory for a non-linear sprag-slip model,
J. Sound Vib., 265, 527-559.
https://doi.org/10.1016/S0022-460X(02)01453-0.
|
-
[21]  | Dupont, P.E. and Bapna, D. (1996), Perturbation stability of frictional sliding
with varying normal force, J. Vib. Acoust., 118, 491-497.
http://dx.doi.org/10.1115/1.2888211.
|
-
[22]  | Dupont, P.E. and Bapna, D. (1994), Stability of sliding frictional surfaces with
varying normal force, J. Vib. Acoust., 116, 237-242.
|
-
[23]  | Luo, A.C.J. and Gegg, B.C. (2006), On the mechanism of stick and nonstick, periodic
motions in a periodically forced, linear oscillator with dry friction, J. Vib. Acoust., 128, 97-105.
|
-
[24]  | Luo, A.C.J. and Huang, J. (2012), Discontinuous dynamics of a non-linear,
self-excited, friction-induced, periodically forced oscillator, Nonlinear
Anal. Real World Appl., 13, 241-257.
|
-
[25]  | Luo, A.C.J. and Gegg, B.C. (2006), Dynamics of a harmonically excited oscillator
with dry-friction on a sinusoidally time-varying, traveling surface, Int. J.
Bifurc. Chaos., 16, 3539-3566.
|
-
[26]  | Luo, A.C.J. and Gegg, B.C. (2006), Periodic motions in a periodically forced
oscillator moving on an oscillating belt with dry friction, ASME Journal of Computational and Nonlinear Dynamics, 1, 212-220.
|
-
[27]  | Luo, A.C.J. and Zwiegart Jr, P. (2008), Existence and analytical predictions of
periodic motions in a periodically forced, nonlinear friction oscillator, J.
Sound Vib., 309, 129-149.
|
-
[28]  | Won, H.I. and Chung, J. (2016), Stick--slip vibration of an oscillator with
damping, Nonlinear Dyn., 86, 257-267.
https://doi.org/10.1007/s11071-016-2887-x.
|