Dynamics of milling processes with variable time delays

Long, Xinhua; Balachandran, Balakumar; Mann, Brian P.

doi:10.1007/s11071-006-9058-4

Cited by 72 publications

(50 citation statements)

References 21 publications

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“…For the method proposed here, the main sources of error in the stability diagram calculation come from the modelling of the process, the tool-path discretization and the input parameters. The hypotheses assumed in the model for simplicity's sake introduce an error: the simplified non-trochoidal kinematic of the tool edges [39], the linear forces model or the relation between dynamic forces and dynamic displacements [40][41][42]. The stability algorithm can introduce an error in the solution, particularly if the single-frequency solution is used in interrupted milling.…”

Section: Discussionmentioning

confidence: 99%

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

Campa

Lacalle

Celaya

2011

International Journal of Machine Tools and Manufacture

122

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The milling of thin parts is a high added value operation where the machinist has to face the chatter problem. The study of the stability of these operations is a complex task due to the changing modal parameters as the part losses mass during the machining and the complex shape of the tools that are used. The present work proposes a methodology for chatter avoidance in the milling of flexible thin floors with a bull-nose end mill. First, a stability model for the milling of compliant systems in the tool axis direction with bullnose end mills is presented. The contribution is the averaging method used to be able to use a linear model to predict the stability of the operation. Then, the procedure for the calculation of stability diagrams for the milling of thin floors is presented. The method is based on the estimation of the modal parameters of the part and the corresponding stability lobes during the machining. As in thin floor milling the depth of cut is already defined by the floor thickness previous to milling, it is proposed the use of stability diagrams that relate the tool position along the tool-path with the spindle speed. Hence, the sequence of spindle speeds that the tool must have during the milling can be selected. Finally, this methodology has been validated by means of experimental tests.

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Section: Discussionmentioning

confidence: 99%

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

Campa

Lacalle

Celaya

2011

International Journal of Machine Tools and Manufacture

122

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“…Some of this behavior is also confirmed by the work of Long and Balachandran (107) , who have also studied the influence of the feed rate on nonlinear dynamics of a milling operation. In related recent work (108) , it has been pointed out that the feed rate leads to a variable delay term in the governing equations and period-doubling and Neimark-Sacker bifurcations are also possible in these systems. Systems with variable time delays and multiple time delays still remain a topic of active research.…”

Section: Journal Of System Design and Dynamicsmentioning

confidence: 99%

A Review of Nonlinear Dynamics of Mechanical Systems in Year 2008

Shaw

Balachandran

2008

JSDD

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In this article, we provide an overview of a selection of topics of current interest in nonlinear dynamics and vibrations of mechanical systems. Specifically, we cover the traditional topics of structural dynamics, rotating systems, vibration control, vehicle dynamics, and machining, as well as some topics that have emerged more recently, namely micro-and nano-electromechanical systems, piecewise smooth systems, and structural health monitoring and system identification. In the introductory and closing sections, we offer our perspective on the state of affairs in nonlinear dynamics and its utility in the study of mechanical systems.

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“…Isolated islands of instability due to the periodicity of the process [22] or nonzero helix angles [23,24] have recently been discovered. Most recently, the milling process has been investigated for the special cases of variable timedelays [25], variable pitch [26], and state-dependent regenerative delay [27].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels

Butcher

Bobrenkov

Bueler

et al. 2009

Journal of Computational and Nonlinear Dynamics

114

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In this paper the dynamic stability of the milling process is investigated through a single degree-of-freedom model by determining the regions where chatter (unstable) vibrations occur in the two-parameter space of spindle speed and depth of cut. Dynamic systems like milling are modeled by delay-differential equations (DDEs) with timeperiodic coefficients. A new approximation technique for studying the stability properties of such systems is presented. The approach is based on the properties of Chebyshev polynomials and a collocation expansion of the solution. The collocation points are the extreme points of a Chebyshev polynomial of high degree. Specific cutting force profiles and stability charts are presented for the up-and down-milling cases of one or two cutting teeth and various immersion levels with linear and nonlinear regenerative cutting forces.The unstable regions due to both secondary Hopf and flip (period-doubling) bifurcations CND-08-1016, Butcher 2 are found, and an in-depth investigation of the optimal stable immersion levels for downmilling in the vicinity of where the average cutting force changes sign is presented.

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Dynamics of milling processes with variable time delays

Cited by 72 publications

References 21 publications

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams

A Review of Nonlinear Dynamics of Mechanical Systems in Year 2008

Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels

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