Perturbation Analysis of Spindle Speed Variation in Machine Tool Chatter

The mathematical models representing machine tool chatter dynamics have been cast as differential equations with delay. The suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which models the machine tool chatter with continuously modulated spindle speed. The explicit time-dependent delay terms, due to spindle speed modulation, are replaced by state dependent delay terms by augmenting the original equations. The augmented system of equations is autonomous and has two pairs of pure imaginary eigenvalues without resonance. We make use of Lyapunov-Schmidt Reduction method to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.

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Machine-Tool Chatter Suppression by Multi-Level Random Spindle Speed Variation

10.1115/imece1999-0755 ◽

1999 ◽

Author(s):

Alpay Yilmaz ◽

Emad AL-Regib ◽

Jun Ni

Keyword(s):

Spindle Speed ◽

New Method ◽

Spindle System ◽

Speed Variation ◽

Chatter Suppression ◽

Random Fashion ◽

Spindle Speed Variation ◽

Machine Tool Chatter ◽

Multi Level ◽

The Stability

Abstract This paper presents a new method for varying the spindle speed to suppress chatter in machining. The spindle speed is varied in pseudo-random fashion within the bandwidth of the spindle system. Both implementation issues and spindle system responses to such signals are investigated. A new method to analyze the stability of machining systems with varying spindle speed is also introduced. The effectiveness and advantages of the random spindle speed variation in chatter suppression is verified using numerical simulations and experiments.

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Machine Tool Chatter Suppression by Multi-Level Random Spindle Speed Variation

Journal of Manufacturing Science and Engineering ◽

10.1115/1.1378794 ◽

2002 ◽

Vol 124 (2) ◽

pp. 208-216 ◽

Cited By ~ 56

Author(s):

Alpay Yilmaz ◽

Emad AL-Regib ◽

Jun Ni

Keyword(s):

Spindle Speed ◽

New Method ◽

Spindle System ◽

Speed Variation ◽

Chatter Suppression ◽

Random Fashion ◽

Spindle Speed Variation ◽

Machine Tool Chatter ◽

Multi Level ◽

The Stability

This paper presents a new method for varying the spindle speed to suppress chatter in machining. The spindle speed is varied in a pseudo-random fashion within the bandwidth of the spindle system. Both implementation issues and spindle system responses to such signals are investigated. A new method to analyze the stability of machining systems with varying spindle speed is also introduced. The effectiveness and advantages of the random spindle speed variation in chatter suppression is verified using numerical simulations and experiments.

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Simulation for Sinusoidal Spindle Speed Variation Cutting in Time Domain Based on Simulink

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.188.549 ◽

2011 ◽

Vol 188 ◽

pp. 549-554

Author(s):

Kuan Min Mao ◽

Min Zhang ◽

Ming Zhu ◽

Ling Yin

Keyword(s):

Time Domain ◽

Amplitude Ratio ◽

Block Diagram ◽

Spindle Speed ◽

Chatter Vibration ◽

Speed Variation ◽

Chatter Suppression ◽

Spindle Speed Variation ◽

Machine Tool Chatter ◽

Nonlinear Mechanical

This paper presents a simulink block diagram which is constructed on the basis of a classical nonlinear mechanical model of machine tool chatter vibration. With varying amplitude ratio and frequency ,sinusoidal spindle speed variation (S3V) cutting process is investigated in time domain, which tests and verifies the feasibility of chatter suppression by S3V method.

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Control of Chatter by Spindle Speed Variation in High-Speed Milling

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.112.179 ◽

2010 ◽

Vol 112 ◽

pp. 179-186 ◽

Cited By ~ 8

Author(s):

Sébastien Seguy ◽

Gilles Dessein ◽

Lionel Arnaud ◽

Tamás Insperger

Keyword(s):

High Speed ◽

Spindle Speed ◽

High Speed Milling ◽

Speed Variation ◽

Milling Operations ◽

Spindle Speed Variation ◽

Machine Tool Chatter ◽

Parametric Studies ◽

Sinusoidal Shape ◽

The Stability

High-speed milling operations are often limited by regenerative vibrations. The aim of this paper is to analyze the effect of spindle speed variation on machine tool chatter in high-speed milling. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. Parametric studies show also the influence of the frequency and amplitude variation parameters. This modeling is validated experimentally by variable spindle speed cutting tests with a triangular shape. Stable and unstable tests are analyzed in term of amplitude vibration and surface roughness degradation. This work reveals that stability must be considered at period variation scale. It is also shown that spindle speed variation can be efficiently used to suppress chatter in the flip lobe area.

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