Stability Analysis of a Linear Friction-Induced Vibration Model and Its Prevention Using Active Force Control

This paper presents friction-induced vibration (FIV) caused by combined mode-coupling and negative damping effects in a simple FIV model. In doing so, a new four-degree-of-freedom linear model which consists of a slider and a block is proposed and then simulated using MATLAB/Simulink. Stability or instability of the FIV model is defined by the convergence or divergence of time domain responses of the slider and the block. Having found critical slope of friction-velocity characteristics that generate instabilities in the model, a conventional closed loop proportional-integral-derivative (PID) controller is first introduced into the main model in order to attenuate the vibration level and subsequently to suppress it. Later, the model is integrated with the active force control (AFC) element to effectively reject the disturbance and reduce the vibrations. It is found that the integrated PID-AFC scheme is effective in reducing vibration compared to the pure PID controller alone. Thus, the proposed control scheme can be one of the potential solutions to suppress vibration in a friction-induced vibration system.

[1]  Musa Mailah,et al.  Intelligent active force control of a robot arm using fuzzy logic , 2000, 2000 TENCON Proceedings. Intelligent Systems and Technologies for the New Millennium (Cat. No.00CH37119).

[2]  S. M. Hashemi-Dehkordi,et al.  Intelligent active force control with piezoelectric actuators to reduce friction induced vibration due to negative damping , 2010 .

[3]  John E. Mottershead,et al.  Parametric resonances in an annular disc, with a rotating system of distributed mass and elasticity; and the effects of friction and damping , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[4]  Utz von Wagner,et al.  Minimal models for disk brake squeal , 2007 .

[5]  Joseph C. S. Lai,et al.  Brake squeal: a literature review , 2002 .

[6]  Aaron John Graf.  Active control of automotive disc bake rotor squeal using dither , 2000 .

[7]  S. Chatterjee,et al.  Time-delayed absorber for controlling friction-driven vibration , 2009 .

[8]  Ken Nakano,et al.  Safety-design criteria of sliding systems for preventing friction-induced vibration , 2009 .

[9]  Michael J. Brennan,et al.  SIMPLE MODELS TO INVESTIGATE THE EFFECT OF VELOCITY DEPENDENT FRICTION ON THE DISC BRAKE SQUEAL NOISE , 2004 .

[10]  Huajiang Ouyang,et al.  Numerical analysis of automotive disc brake squeal: a review , 2005 .

[11]  L. Gaul,et al.  Quenching mode-coupling friction-induced instability using high-frequency dither , 2005 .

[12]  Yu-Kan Hu,et al.  Vehicle Disc Brake Squeal Simulations and Experiences , 1999 .

[13]  C. A. Tan,et al.  Suppression of Self-Excited Vibration by Dither Technique with Potential Application to Reduce Brake Squeal , 2004 .

[14]  L. Gaul,et al.  A minimal model for studying properties of the mode-coupling type instability in friction induced oscillations , 2002 .

[15]  J. R Hewit,et al.  Fast dynamic decoupled control for robotics, using active force control , 1981 .

[16]  John D. Fieldhouse,et al.  The Application of Holographic Interferometry to the Study of Disc Brake Noise , 1993 .

[17]  Kenneth A. Cunefare,et al.  EXPERIMENTAL ACTIVE CONTROL OF AUTOMOTIVE DISC BRAKE ROTOR SQUEAL USING DITHER , 2002 .

[18]  Musa Mailah,et al.  Control of mobile manipulator using resolved acceleration with iterative-learning-proportional-integral active force control , 2007 .

[19]  Chin An Tan,et al.  Disc Brake Squeal: Mechanism, Analysis, Evaluation, and Reduction/Prevention , 2006 .

[20]  M. A.J..  A NON-LINEAR FRICTION MODEL FOR SELF-EXCITED VIBRATIONS , 1997 .

[21]  Michael J. Brennan,et al.  Analysis of disc brake noise using a two-degree-of-freedom model , 2002 .

[22]  Huajiang Ouyang,et al.  Prediction and assignment of latent roots of damped asymmetric systems by structural modifications , 2009 .

[23]  Musa Mailah,et al.  Vehicle active suspension system using skyhook adaptive neuro active force control , 2009 .

[24]  John E. Mottershead,et al.  Friction-induced parametric resonances in discs: Effect of a negative friction-velocity relationship , 1998 .

[25]  S. W. E. Earles,et al.  Instabilities Arising From the Frictional Interaction of a Pin-Disk System Resulting in Noise Generation , 1976 .

[26]  J. R Hewit,et al.  An active method for the control of mechanical systems in the presence of unmeasurable forcing , 1986 .

[27]  Wei Zhang,et al.  Sliding bifurcations and chaos induced by dry friction in a braking system , 2009 .

[28]  Gregory D. Liles.  Analysis of Disc Brake Squeal Using Finite Element Methods , 1989 .

[29]  Norbert Hoffmann,et al.  Harmonic Balance and Averaging Techniques for Stick-Slip Limit-Cycle Determination in Mode-Coupling Friction Self-Excited Systems , 2004 .

[30]  Huajiang Ouyang,et al.  A receptance-based method for predicting latent roots and critical points in friction-induced vibration problems of asymmetric systems , 2009 .

[31]  John D. Fieldhouse.  An Investigation Into Disc Brake Noise Using Holographic Interferometry , 1991 .

[32]  John E. Mottershead,et al.  Dynamic instabilities in a simple model of a car disc brake , 1999 .

[33]  Guan Dihua,et al.  A Study on Disc Brake Squeal Using Finite Element Methods , 1998 .

[34]  S. M. Hashemi-Dehkordi,et al.  Implementation of active force control to disc brake for noise-free performance , 2009 .

[35]  Oliver M. O’Reilly,et al.  Automotive disc brake squeal , 2003 .

[36]  S. M. Hashemi-Dehkordi,et al.  Suppressing Friction-Induced Vibration Due To Negative Damping and Mode Coupling Effects Using Active Force Control , 2010 .

[37]  Kenneth A. Cunefare,et al.  Disc Brake Rotor Squeal Suppression Using Dither Control , 2001 .

[38]  S M HASHEMI-DEHKORDI,et al.  Reducing friction-induced vibration using intelligent active force control (AFC) with piezoelectric actuators , 2012 .