Stick-slip vibration of a moving oscillator on an axially flexible beam

다국어 초록 (Multilingual Abstract)

This study investigates the stick-slip vibration between an axially flexible beam fixed at both ends and an oscillator moving on the beam. After deriving the equations of motion for the stick and slip states, the stick-slip vibrations between the oscillator and the beam are analyzed. In addition, to obtain the irregularly changed contact position due to the axial deformation of the beam and oscillator movement, a mathematical expression for the contact position is derived. It is found that the long-period stick-slip vibration is influenced mainly by the oscillator and the short-period vibration is influenced mainly by axial deformation of the beam.
Furthermore, the dynamic responses show that even if a high damping ratio is applied to the oscillator, stick-slip vibration due to axial deformation of the beam can occur. Finally, the analysis shows that a kind of the internal resonance occurs between the oscillator and the beam when the harmonics of the natural frequency of the oscillator match the natural frequencies of the beam.

참고문헌 (Reference)

1 C. Chevennement-Roux, "Wiper systems with flexible structures-instabilities analysis and correlation with a theoretical model" SAE 2005

2 A. Koenen, "Tribological and vibroacoustic behavior of a contact between rubber and glass(application to wiper blade)" 40 : 1484-1491, 2007

3 A. Papangelo, "Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening-strengthening friction law: Analytical results and comparison with experiments" 90 : 2037-2046, 2017

4 H. M. Sedighi, "Stick-slip vibrations of layered structures undergoing large deflection and dry friction at the interface" 135 : 061006-, 2013

5 H. I. Won, "Stick-slip vibration of an oscillator with damping" 86 : 257-267, 2016

6 J. Heilig, "Stability of a nonlinear brake system at high operating speeds" 34 : 235-247, 2003

7 J. M. Gibert, "On the stick-slip dynamics in ultrasonic additive manufacturing" 332 : 4680-4695, 2013

8 Fujie Xia, "On the Motion of the Structure Varying Multibody Systems with Two-Dimensional Dry Friction" 대한기계학회 19 (19): 927-935, 2005

9 Z. Veraszto, "Nonlinear dynamics of hardwarein-the-loop experiments on stick-slip phenomena" 94 : 380-391, 2017

10 S. Chatterjee, "Non-linear control of friction-induced selfexcited vibration" 42 : 459-469, 2007

11 M. Pascal, "New limit cycles of dry friction oscillators under harmonic load" 70 : 1435-1443, 2012

12 M. Pascal, "New events in stick-slip oscillators behaviour" 75 : 283-288, 2011

13 J. J. Sinou, "Mode coupling instability in friction-induced vibrations and its dependency on system parameters including damping" 26 : 106-122, 2007

14 A. Saha, "Investigation of two different friction models from the perspective of friction-induced vibrations" 90 : 185-197, 2015

15 A. Ammar, "Investigate stick-slip intervals with one equation of motion and analyse the effect of the friction noise" 2 : 96-111, 2013

16 D. Tonazzi, "Instability scenarios between elastic media under frictional contact" 40 : 754-766, 2013

17 H. Ouyang, "Friction-induced vibration of an elastic slider on a vibrating disc" 41 : 325-336, 1999

18 Z. Li, "Friction-induced vibration of an elastic disc and a moving slider with separation and reattachment" 87 : 1045-1067, 2017

19 H. Ouyang, "Friction-induced parametric resonances in discs : effect of a negative friction-velocity relationship" 209 : 251-264, 1998

20 S. Yamagishi, "Friction vibration modeling with detachment and adhesion by Cellular Automata" 11 : 226-232, 2015

21 J. Wojewoda, "Estimation of Lyapunov exponents for a system with sensitive friction model" 79 : 667-677, 2009

22 Liping Tang, "Effects of weight on bit on torsional stick-slip vibration of oilwell drill string" 대한기계학회 31 (31): 4589-4597, 2017

23 N. Hoffmann, "Effects of damping on mode-coupling instability in friction induced oscillations" 83 : 524-534, 2003

24 U. Galvanetto, "Dynamics of a simple damped oscillator undergoing stick-slip vibrations" 34 : 337-347, 1999

25 Jia-lin Tian, "Dynamic characteristics and test analysis of a new drilling downhole tool with anti-stick-slip features" 대한기계학회 32 (32): 4941-4949, 2018

26 V. N. Pilipchuk, "Disc brake ring-element modeling involving friction-induced vibration" 8 : 1085-1104, 2002

27 M. Sparham, "Cutting force analysis to estimate the friction force in linear guideways of CNC machine" 85 : 65-79, 2016

28 M. A. Heckl, "Curve squeal of train wheels, part 1: Mathematical model for its generation" 229 : 669-693, 2000

29 Z. Wang, "Control of chaotic vibration in automotive wiper systems" 39 : 168-181, 2009

30 S. C. Chang, "Chaos attitude motion and chaos control in an automotive wiper system" 41 : 3491-3504, 2004

31 A. Saha, "An analytical study of time-delayed control of friction-induced vibrations in a system with a dynamic friction model" 63 : 60-70, 2014

32 J. Chung, "A time integration algorithm for structural dynamics with improved numerical dissipation : The generalized-α method" 60 : 371-375, 1993

33 M. Pascal, "A new model of dry friction oscillator colliding with a rigid obstacle" 91 : 2541-2550, 2018

34 A. Saha, "A modified LuGre friction model for an accurate prediction of friction force in the pure sliding regime" 80 : 122-131, 2016