Chatter suppression by parametric excitation: Model and experiments

Abstract Chatter vibration leads to challenges in precise machining due to its harmful effect on productivity and surface quality. In this study, a chatter suppression method based on parametric excitation was developed. The effect of parametric excitation on self-excited vibration was investigated based on a model of a van der Pol–Mathieu–Duffing oscillator with a time delay. It reveals that there can be a zero solution for the oscillator under the effect of parametric excitation, while it is impossible to have a stable zero equation without parametric excitation. The stability of a parametrically excited vibration system regarding the regenerative effect in the cutting processes was studied by the averaging method. The stability analysis shows that parametric excitation with an appropriate frequency and large amplitude has a chatter suppression effect no matter whether the waveform is a sinusoidal wave, square wave or triangular wave. To validate the effect of parametric excitation for chatter suppression, experiments were conducted based on a magnetorheological (MR) fluid-controlled boring bar, which can generate high-frequency parametric excitation based on the quick response of the MR fluid. Cutting experiments with an excitation current of different waveforms and diverse frequencies show that chatter can be significantly suppressed by the effect of parametric excitation.

[1]  Ozden Turan,et al.  A passive adaptor to enhance chatter stability for end mills , 2007 .

[2]  Renyuan Fei,et al.  Improvement of machining stability using a tunable-stiffness boring bar containing an electrorheological fluid , 1999 .

[3]  Jokin Munoa,et al.  Stability of milling processes with continuous spindle speed variation: Analysis in the frequency and time domains, and experimental correlation , 2008 .

[4]  Fatihcan M. Atay,et al.  VAN DER POL'S OSCILLATOR UNDER DELAYED FEEDBACK , 1998 .

[5]  I. Garitaonandia,et al.  An active system of reduction of vibrations in a centerless grinding machine using piezoelectric actuators , 2007 .

[6]  Sanjiv G. Tewani,et al.  A study of cutting process stability of a boring bar with active dynamic absorber , 1995 .

[7]  Zichen Chen,et al.  Parameter optimization of time-varying stiffness method for chatter suppression based on magnetorheological fluid-controlled boring bar , 2010 .

[8]  Philip K. Chan,et al.  In-process detection and suppression of chatter in milling , 1992 .

[9]  Soo Hun Lee,et al.  Programming spindle speed variation for machine tool chatter suppression , 2003 .

[10]  Jerzy Warminski,et al.  Parametric self-excited non-linear system vibrations analysis with inertial excitation , 1995 .

[11]  Christian Brecher,et al.  Electrohydraulic Active Damping System , 2005 .

[12]  Jerzy Warminski,et al.  Vibrations of a non-ideal parametrically and self-excited model , 2001 .

[13]  Zhongkui Sun,et al.  Chaotic motion of Van der Pol–Mathieu–Duffing system under bounded noise parametric excitation , 2008 .

[14]  R. Nabergoj,et al.  The Effect of Parametric Excitation on a Self-Excited Three-Mass System , 2004 .

[15]  A. Maccari,et al.  Vibration amplitude control for a van der Pol–Duffing oscillator with time delay , 2008 .

[16]  Natarajan Shankar,et al.  Mitigation of chatter instabilities in milling by active structural control , 2001 .

[17]  A. Tusset,et al.  An Intelligent Controller Design for Magnetorheological Damper Based on a Quarter-car Model , 2009 .

[18]  Chen Zichen.  Measurement and analysis of dynamic characteristics of magnetorheological intelligent boring bar , 2009 .

[19]  Fadi Dohnal,et al.  Averaging in vibration suppression by parametric stiffness excitation , 2008 .

[20]  Zichen Chen,et al.  On-line chatter detection and identification based on wavelet and support vector machine , 2010 .

[21]  Min Chen,et al.  Control Approaches to the Suppression of Machining Chatter Using Active Magnetic Bearings , 2007, IEEE Transactions on Control Systems Technology.

[22]  M. Belhaq,et al.  Effect of vertical high-frequency parametric excitation on self-excited motion in a delayed van der Pol oscillator , 2008 .

[23]  Jerzy Warminski,et al.  SELF-EXCITED SYSTEM VIBRATIONS WITH PARAMETRIC AND EXTERNAL EXCITATIONS , 1995 .

[24]  Horizontal fast excitation in delayed van der Pol oscillator , 2008 .

[25]  Colin H. Hansen,et al.  The response of a Duffing-van der Pol oscillator under delayed feedback control , 2006 .

[26]  Satish Nagarajaiah,et al.  Semi‐active control of sliding isolated bridges using MR dampers: an experimental and numerical study , 2005 .

[27]  B. J. Stone.  The Effect of Time Varying Parameters on the Build-Up of Chatter in Turning , 1985 .

[28]  Zichen Chen,et al.  Magnetorheological fluid-controlled boring bar for chatter suppression , 2009 .