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Research Papers

Stick-Slip Effect in a Vibration-Driven System With Dry Friction: Sliding Bifurcations and Optimization

[+] Author and Article Information
Hongbin Fang

Graduate Research Assistant
School of Aerospace Engineering and
Applied Mechanics,
Tongji University,
Shanghai 200092, China
e-mail: fanghongbin@tongji.asia

Jian Xu

Professor
School of Aerospace Engineering and
Applied Mechanics,
Tongji University,
Shanghai 200092, China
e-mail: xujian@tongji.edu.cn

1Corresponding author.

Manuscript received October 28, 2012; final manuscript received October 2, 2013; accepted manuscript posted October 19, 2013; published online December 10, 2013. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 81(5), 051001 (Dec 10, 2013) (10 pages) Paper No: JAM-12-1502; doi: 10.1115/1.4025747 History: Received October 28, 2012; Revised October 02, 2013; Accepted October 19, 2013

Vibration-driven systems can move progressively in resistive media owing to periodic motions of internal masses. In consideration of the external dry friction forces, the system is piecewise smooth and has been shown to exhibit different types of stick-slip motions. In this paper, a vibration-driven system with Coulomb dry friction is investigated in terms of sliding bifurcation. A two-parameter bifurcation problem is theoretically analyzed and the corresponding bifurcation diagram is presented, where branches of the bifurcation are derived in view of classical mechanics. The results show that these sliding bifurcations organize different types of transitions between slip and sticking motions in this system. The bifurcation diagram and the predicted stick-slip transitions are verified through numerical simulations. Considering the effects of physical parameters on average steady-state velocity and utilizing the sticking feature of the system, optimization of the system is performed. Better performance of the system with no backward motion and higher average steady-state velocity can be achieved, based on the proposed optimization procedures.

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Figures

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Fig. 1

Dynamic model: (a) a vibration-driven system, and (b) the Coulomb dry friction model

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Fig. 2

Phase space topology of the system

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Fig. 3

Schematic illustration of the crossing-sliding scenarios in case I

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Fig. 4

Schematic illustration of different sliding scenarios in case II

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Fig. 5

The bifurcation diagram (top), and (a)–(d) schematic illustrations of motions in different zones of the bifurcation diagram

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Fig. 6

Time histories of the dimensionless velocity x2 corresponding to points O1 to O7 in Fig. 5 (top): (a) point O1, (b) point O2, (c) point O3, (d) point O4, (e) point O5, (f) point O6, and (g) point O7

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Fig. 7

Density plot of the average velocity (m/s) in the b-ω plane, with M = 0.5 kg, m = 0.3 kg, f+ = 0.2, and f- = 0.8

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Fig. 8

Density plot of the average velocity (m/s) in the f--f+ plane, with M = 0.5 kg, m = 0.3 kg, b = 0.15 m, and ω = 15 rad/s

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Fig. 9

The bifurcation diagram and the points Q1 to Q6 for numerical examples

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Fig. 10

Time histories of the dimensional velocity x2 corresponding to (a) point Q3, and (b) point Q6

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Fig. 11

With the parameters (38) and driving-frequency ω = 12.44 rad/s: (a) average velocities correspond to different values of f- from 0 to 0.8, and (b) time histories of the dimensional velocity x2 = y· when f+ = 0

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