High-frequency dither forces are often used to reduce unwanted vibration in frictional systems. This paper examines how the effectiveness of these dither-cancellation techniques is influenced by the type of periodic signal employed. The paper uses the method of averaging as well as numerical integration to study a single-degree-of-freedom (SDOF) system consisting of a mass in frictional contact with a translating surface. Recently, it was found that sinusoidal dither forces had the ability to stabilize or destabilize such a system, depending on the system and frictional characteristics as well as the amplitude and frequency of the dither signal [1]. This paper extends this analysis to general, periodic dither forces. In particular, the system response for sinusoidal dither waveforms is compared to that of triangular dither waveforms and square dither waveforms. It is found that, for a given amplitude and frequency of the dither signal, square waveforms are much more effective in canceling friction-induced oscillations than sinusoidal dither; likewise, sinusoidal waveforms are more effective than triangular waveforms for a given amplitude and frequency. A criterion is developed that relates the effectiveness of the waveform to the properties of the integral of the dither signal.

1.
Michaux, M.A., Ferri, A.A., and Cunefare, K.A., “Effect of tangential dither signal on friction induced oscillations in a SDOF model,” to appear, ASME 2005 International Design Engineering Technical Conferences, September 24–28, 2005, Long Beach, California, USA
2.
Cunefare
K. A.
and
Graf
A. J.
, “
Experimental active control of automotive disc brake rotor squeal using dither
,”
Journal of Sound and Vibration
,
2002
.
250
(
4
): p.
579
590
.
3.
Thomsen
J. J.
, “
Using fast vibrations to quench friction-induced oscillations
,”
Journal of Sound and Vibration
,
1999
.
228
(
5
): p.
1079
1102
.
4.
Thomsen
J. J.
and
Fidlin
A.
, “
Analytical Approximations For Stick-Slip Vibration Amplitude
,”
International Journal of Non-Linear Mechanics
,
2003
.
38
: p.
389
403
.
5.
Thomsen
J. J.
, “
Some general effects of strong high-frequency excitation: stiffening, biasing and smoothening
.”
Journal of Sound and Vibration
,
2002
.
253
(
4
): p.
807
831
.
6.
Dzirasa, Mawuli, 2002, “Experimental Investigation of Dither Control for the Supprression of Automotive Brake Squeal,” MS Thesis, G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0405.
7.
Oldenburger, R. and T. Nakada, Signal Stabilization of Self-Oscillating Systems. IRE Transactions on Automatic Control, 1961(September): p. 319–325.
8.
Gelb, A. and W. Vander Velde, Multiple-Input Describing Functions and Non-Linear System Design. 1968, New York: McGraw-Hill.
9.
Ibrahim
R. A.
, “
Friction-Induced Vibration, Chatter, Squeal, and Chaos- Part I: Mechanics of Contact and Friction; - Part II: Dynamics and Modeling
,”
Applied Mechanics Reviews
,
1994
.
47
(
7
): p.
209
253
.
10.
Armstrong-He´louvry
B.
,
Dupont
P.
, and
Canudas De Wit
C.
, “
A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines with Friction
,”
Automatica
,
1994
.
30
(
7
): p.
1083
1138
.
11.
Andreaus
U.
and
Casini
P.
, “
Dynamics of friction oscillators excited by a moving base and/or driving force
,”
Journal of Sound and Vibration
,
2001
.
245
(
4
): p.
685
699
.
12.
Michaux, M.A., 2005, “Suppression of Friction-Induced Oscillations through Use of High-Frequency Dither Signals,” Ph.D. Thesis, G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0405.
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