Delay dynamical systems and applications to nonlinear machine-tool chatter

Fofana, M. S.

doi:10.1016/s0960-0779(02)00407-1

Cited by 45 publications

(33 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Simple Hopf bifurcations arising in DDEs have also been studied using center manifold reductions [3,[11][12][13][14], normal-form theory (bypassing the center manifold reductions) [15][16][17], and the method of multiple scales or MMS (bypassing the normal forms as well) [4,18,19]. Fofana [20] used center manifold reductions to study double Hopf bifurcations in a DDE model for regenerative machine tool chatter, while Stépán and Haller [21] used the theory of normal forms along with a center manifold analysis for a DDE model for robot control. The application of the methods given in [20,21] is more difficult for the tool vibration DDE considered herein, primarily because of the non-symmetric nonlinearity and the complicated center manifold reduction.…”

Section: Introductionmentioning

confidence: 99%

Regenerative Tool Chatter Near a Codimension 2 Hopf Point Using Multiple Scales

Wahi

Chatterjee

2005

Nonlinear Dyn

View full text Add to dashboard Cite

We study a well-known regenerative machine tool vibration model (a delay differential equation) near a codimension 2 Hopf bifurcation point. The method of multiple scales is used directly, bypassing a center manifold reduction. We use a nonstandard choice of expansion parameter that helps understand practically relevant aspects of the dynamics for not-too-small amplitudes. Analytical expressions are then obtained for the double Hopf points. Both sub-and supercritical bifurcations are predicted to occur near the reference point; and analytical conditions on the parameter variations for each type of bifurcation to occur are obtained as well. Analytical approximations are supported by numerics.

show abstract

Section: Introductionmentioning

confidence: 99%

Regenerative Tool Chatter Near a Codimension 2 Hopf Point Using Multiple Scales

Wahi

Chatterjee

2005

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…The obtained signals were analyzed using statistical and recurrence methods. We claim for larger cutting force component the frictional stick-and-slip mechanism of self-sustained vibrations [12,37,38] can be more important than the regenerative effect [5,13,26]. However the main period of vibrations is caused by the rotational motion of an unbalanced workpiece shaft.…”

Section: Discussionmentioning

confidence: 86%

“…He analyzed the self-sustained mechanism of vibrations. The subsequent studies show the importance of regenerative effects [3][4][5][6], and structural dynamics [7][8][9]. Finally, the role of the dry friction and the stick-and-slip motion [10][11][12] was indicated and studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a stainless steel turning process by statistical and recurrence analyses

Litak

Rusinek

2012

Meccanica

View full text Add to dashboard Cite

This paper explores the cutting force oscillations. Forces have been measured during the stainless steel turning. We provide the results of standard statistical analysis of the corresponding time series together with their recurrence properties. We claim that the system, which initially exhibits regular vibrations, is unstable to chaotic oscillation for some fairly larger cutting depths. This characteristic transition in the cutting dynamics can be monitored by recurrences and could have the important implications to design a new control procedure.

show abstract

“…These problems are described by DDE which indeed are a type of differential equations where time derivatives at the current moment of time depend on the solution and possibly on its derivatives at previous moments. For instance, in cutting processes the effect of time delay generates harmful vibrations-a so called regenerative chatter [6,11,12,15,26,27,[30][31][32]. This one and another kind of chatter in real processes are very often investigated by means of various methods of nonlinear time series analysis [16][17][18][19][20][21]28].…”

Section: Introductionmentioning

confidence: 99%

Time delay Duffing’s systems: chaos and chatter control

2014

View full text Add to dashboard Cite

The effect of a delay feedback control (DFC), realized by displacement in the Duffing oscillator, for parameters which generate strange chaotic Ueda attractor is investigated in this paper. First, the classical Duffing system without time delay is analysed to find stable and especially unstable periodic orbits which can be stabilized by means of displacement delay feedback. The periodic orbits are found with help of the continuation method using the AUTO97 software. Next, the DFC is introduced with a time delay and a feedback gain parameters. The proper time delay and feedback gain are found in order to destroy the chaotic attractor and to stabilize the periodic orbit. Finally, chatter generated by time delay component is suppressed with help of an external excitation.

show abstract

Delay dynamical systems and applications to nonlinear machine-tool chatter

Cited by 45 publications

References 23 publications

Regenerative Tool Chatter Near a Codimension 2 Hopf Point Using Multiple Scales

Regenerative Tool Chatter Near a Codimension 2 Hopf Point Using Multiple Scales

Dynamics of a stainless steel turning process by statistical and recurrence analyses

Time delay Duffing’s systems: chaos and chatter control

Contact Info

Product

Resources

About