Study on Practical Application of Fluctuating Speed Cutting for Regenerative Chatter Control

Hoshi, Tetsutaro; Sakisaka, Naruo; Moriyama, I. M.; Sato, Makoto; Higashimoto, Akemi; Tokunaga, Takashi

doi:10.1299/kikai1938.44.1085

Cited by 19 publications

(19 citation statements)

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“…The so-called spindle speed variation (SSV), where the spindle speed is varied continuously to improve chatter performance is attracting increasing attention because of its simplicity and effectiveness in chatter suppression. It has been found in experiments conducted by Inamura and Sata [5], Hosi and Sato [6] and Sexton and Stone [7] when the amplitude and the frequency of SSV are within some range, the chatter can be greatly suppressed or eliminated. By adapting existing mathematical techniques, a perturbative method was developed in [8] to obtain finite-dimensional equations in order to systematically study the mechanism of spindle speed variation for chatter suppression.…”

Section: Introductionmentioning

confidence: 98%

Delay equations with fluctuating delay related to the regenerative chatter

Demir

Hasanov

Namachchivaya

2006

International Journal of Non-Linear Mechanics

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Section: Introductionmentioning

confidence: 98%

Delay equations with fluctuating delay related to the regenerative chatter

Demir

Hasanov

Namachchivaya

2006

International Journal of Non-Linear Mechanics

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“…The so-called Spindle Speed Variation (SSV), where the spindle speed is varied continuously to improve chatter performance is attracting increasing attention because of its simplicity and effectiveness in chatter suppression. It has been found in experiments conducted by Inamura and Sata [10], Hosi and Sato [9] and Sexton and Stone [15] when the amplitude and the frequency of SSV are within some range, the chatter can be greatly suppressed or eliminated. By adapting existing mathematical techniques, a perturbative method was developed in [11] to obtain finite dimensional equations in order to systematically study the mechanism of spindle speed variation for chatter suppression.…”

Section: Introductionmentioning

confidence: 98%

Delay equations with fluctuating delay related to the regenerative chatter I: reduced bifurcation equation

Demir

Hasanov

Namachchivaya

2005

Applicable Analysis

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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. The reduced bifurcation equation is obtained by making use of Lyapunov-Schmidt Reduction method.

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“…The study of time-periodic delays gained popularity in the 1970s when several researchers [1][2][3][4] started focussing on the suppression of tool-chatter using continuous modulation of the spindle speed. The governing mathematical model for machining with periodic spindle speed modulation is a DDE with a variable delay as opposed to a DDE with constant delay for machining with a constant spindle speed.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation studies of delayed systems with variable delays using Galerkin projections

Wahi

2014

Int. J. Dynam. Control

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In this paper, we use finite dimensional ordinary differential equation (ODE) approximations of delay differential equations (DDEs) with variable delays for stability and bifurcation studies. Two different approaches to handle variable delays in these systems have been presented. The first one involves embedding the variable time-delay in a fixed delay interval and is suitable for variable delays whose variation with time is explicitly defined and an upper-bound is known apriori. The efficacy of this procedure is demonstrated for the practical example of turning operation where periodic or random variation of spindle speed is employed for chatter control. For the practical application of a statedependent delayed model for turning, this approach leads to a system of differential algebraic equations which are not easily amenable to stability and bifurcation studies. Hence, an alternate approach based on mapping the variable delay to a fixed delay using a dynamic scaling of the delayed variable is presented which results in system of ODEs facilitating the stability and bifurcation analysis. In all the cases, an excellent agreement has been achieved between the stability results from the approximation and the analytical/full numerical simulation studies. Bifurcation diagrams have been presented only for the state-dependent delay case where they match the existing results reported in the literature using DDE-biftool.

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Study on Practical Application of Fluctuating Speed Cutting for Regenerative Chatter Control

Cited by 19 publications

References 0 publications

Delay equations with fluctuating delay related to the regenerative chatter

Delay equations with fluctuating delay related to the regenerative chatter

Delay equations with fluctuating delay related to the regenerative chatter I: reduced bifurcation equation

Stability and bifurcation studies of delayed systems with variable delays using Galerkin projections

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