Extension of Tlusty׳s law for the identification of chatter stability lobes in multi-dimensional cutting processes

Otto, Andreas; Rauh, Stefan; Kolouch, Martin; Radons, Günter

doi:10.1016/j.ijmachtools.2014.03.007

Cited by 37 publications

(31 citation statements)

References 19 publications

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“…The dynamic components are considered to be small perturbations of the static or quasi-static displacements and forces; therefore, a linearized model was used in the stability analysis [17]. The dynamic cutting force in the machine tool coordinates can be given by the following equation:…”

Section: Computation Of Open Loop Transfer Functionmentioning

confidence: 99%

“…The Chatter prediction for uncertain parameters 321 matrix B(t) contains the cutting force coefficients and the directional factors related to the transformation between the machine tool and process coordinates (for details see Refs. [17,19]). For the milling processes, these coefficients, and therefore the matrix B(t), are time periodic with a tooth passing period s. Note that the force F(t) in Eq.…”

Section: Computation Of Open Loop Transfer Functionmentioning

confidence: 99%

“…(6) holds, is determined by the eigenvalue with the largest real part, namely, K R (x crit ) [17]. This corresponds to the critical frequencies close to the eigenfrequency of one of the structure's dominant modes.…”

Section: Stability Lobes and Modal Assurance Criterionmentioning

confidence: 99%

“…(6) is equivalent to the ZOA. In this case an analytical expression for the eigenvalues K(x) can be obtained [17]. However, for the MFS, the number of the higher harmonics and the dimension of the matrices increase.…”

Section: Stability Lobes and Modal Assurance Criterionmentioning

confidence: 99%

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Chatter prediction for uncertain parameters

et al. 2018

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The occurrence of chatter in milling processes was investigated in this study. The prediction of the stability lobes of metal cutting processes requires a model of the cutting force and a model of the dynamic machine tool behavior. Parameter uncertainties in the models may lead to significant differences between the predicted and measured stability behavior. One approach towards robust stability consists of running a large number of simulations with a random sample of uncertain parameters and determining the confidence levels for the chatter vibrations, which is a time-consuming task. In this paper, an efficient implementation of the multi frequency solution and the construction of an approximate solution is presented. The approximate solution requires the explicit calculation of the multi frequency solution only at a few parameter points, and the approximation error can be kept small. This study found that the calculation of the robust stability lobe diagram, which is based on the approximate solution, is significantly more efficient than an explicit calculation at all random parameter points. The numerically determined robust stability diagrams were in good agreement with the experimentally determined stability lobes.

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Section: Computation Of Open Loop Transfer Functionmentioning

confidence: 99%

Section: Computation Of Open Loop Transfer Functionmentioning

confidence: 99%

Section: Stability Lobes and Modal Assurance Criterionmentioning

confidence: 99%

Section: Stability Lobes and Modal Assurance Criterionmentioning

confidence: 99%

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Chatter prediction for uncertain parameters

et al. 2018

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“…Stability analysis of these systems requires the application of the Floquet theory of DDEs. In the recent years, several numerical techniques have been developed in order to determine stability lobe diagrams for milling operations, such as the semi-discretization method Stepan, 2002a, 2011), the temporal finite element method (Bayly et al, 2003); the multi-frequency solution (Altintas and Budak, 1995;Budak and Altintas, 1998;Bachrathy and Stepan, 2013;Otto et al, 2014), just to mention a few. This paper aims to give a brief overview on the main issues of machine tool chatter.…”

Section: Introductionmentioning

confidence: 99%

Regenerative delay, parametric forcing and machine tool chatter: A review

2015

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Two intrinsic component of machine tool chatter modeling is regenerative time delay and parametric forcing. The corresponding governing equations are therefore given in the form of delay-differential equations with time-periodic coefficients. In this paper, a brief review is given on the mechanism of these two effects, and recent numerical techniques from the literature are categorized and discussed.

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Position-dependent stability analysis of turning with tool and workpiece compliance

Otto

Khasawneh

Radons

2015

Int J Adv Manuf Technol

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A universal frequency domain approach for studying the dynamics of metal cutting with a flexible workpiece and a compliant tool is derived. The method is used for the identification of the position-dependent stability lobes in turning. It enables a fast, accurate, and systematic stability analysis of turning processes in the parameter space, which is not restricted to simple dynamic models with only a specific number of modes in one spatial direction. In particular, a combination of experimental data for the tool tip dynamics with analytical or numerical data for the workpiece dynamics is possible, which is demonstrated by a concrete example. The effect of the mode interaction between tool and workpiece modes via the cutting process is illustrated. Counterintuitively, the possibility of a process destabilization for an increased workpiece stiffness was observed, which can be explained by the mode interaction. The presented methods and results can be efficiently used for optimizing machine tool development and process planning.

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Extension of Tlusty׳s law for the identification of chatter stability lobes in multi-dimensional cutting processes

Cited by 37 publications

References 19 publications

Chatter prediction for uncertain parameters

Chatter prediction for uncertain parameters

Regenerative delay, parametric forcing and machine tool chatter: A review

Position-dependent stability analysis of turning with tool and workpiece compliance

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