Theory of finite amplitude machine tool instability

Shi, Haijian; Tobias, S. A.

doi:10.1016/0020-7357(84)90045-3

Cited by 147 publications

(120 citation statements)

References 4 publications

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“…This decreasing characteristic does not mean that the small amplitude periodic forced vibration of the machining process is stable; it is still linearly unstable. The decreasing amplitude does not converge to the periodic forced vibration, but it converges to a chatter vibration [38,39], which corresponds to a stable chaotic attractor (see Fig. 9).…”

Section: Poincare Sectionmentioning

confidence: 99%

“…At the left and right side, where the periodic motion is linearly stable or linearly unstable, respectively, the Floquet multipliers can be identified by means of the proposed method. The parameter domain in between is called unsafe or bistable zone since two attractive motions coexist: stable cutting and (mathematically stable) chatter, which are separated by an unstable periodic motion [39,38]. In this range, the vibration can jump from the linear attraction zone to the chatter motion due to a large-enough perturbation.…”

Section: Case Studymentioning

confidence: 99%

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Operational stability prediction in milling based on impact tests

Kiss

Hajdu

Bachrathy

et al. 2018

Mechanical Systems and Signal Processing

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Chatter detection is usually based on the analysis of measured signals captured during cutting processes. These techniques, however, often give ambiguous results close to the stability boundaries, which is a major limitation in industrial applications. In this paper, an experimental chatter detection method is proposed based on the system's response for perturbations during the machining process, and no system parameter identification is required. The proposed method identifies the dominant characteristic multiplier of the periodic dynamical system that models the milling process. The variation of the modulus of the largest characteristic multiplier can also be monitored, the stability boundary can precisely be extrapolated, while the manufacturing parameters are still kept in the chatter-free region. The method is derived in details, and also verified experimentally in laboratory environment.

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Section: Poincare Sectionmentioning

confidence: 99%

Section: Case Studymentioning

confidence: 99%

Operational stability prediction in milling based on impact tests

Kiss

Hajdu

Bachrathy

et al. 2018

Mechanical Systems and Signal Processing

View full text Add to dashboard Cite

show abstract

“…In other words, while machining in chatter free conditions, it is possible that perturbations cause the system to jump towards another attractor which involves large chatter oscillations. Cutting force model according to [19] with nominal depth of cut h = 0.07 mm.…”

Section: Bifurcation Analysis and Nonlinear Tuning Of The Absorbermentioning

confidence: 99%

Enforcing Linear Dynamics Through the Addition of Nonlinearity

Habib

Grappasonni

Kerschen

2016

Nonlinear Dynamics, Volume 1

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A passive vibration absorber, termed the nonlinear tuned vibration absorber (NLTVA), is designed for the suppression of chatter vibrations. Unlike most passive vibration absorbers proposed in the literature, the NLTVA comprises both a linear and a nonlinear restoring force. Its linear characteristics are tuned in order to optimize the stability properties of the machining operation, while its nonlinear properties are chosen in order to control the bifurcation behavior of the system and guarantee robustness of stable operation. In this study, the NLTVA is applied to turning machining.

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“…His formulation was latter adopted by many investigators and led to major advances towards the understanding and prediction of the chatter phenomenon. Hanna [4], Shi and Tobias [5], Tlusty [6] and others carried out theoretical and experimental researches on cutting chatter, explained the mechanism of stabilization of chatter amplitudes and the phenomenon of finite amplitude instability, and presented a non-linear theory of machine tool chatter. Chaos cutting is an important phenomenon which is related to the non-linear theory of machine tool chatter.…”

Section: Introductionmentioning

confidence: 99%

Experimental Investigation of Evolution Process of Nonlinear Characteristics from Chatter Free to Chatter

Kong¹,

Liu²,

Wang³

2011

JMP

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The vibration acceleration time history of the cutter holder was separated into three parts; namely, chatter free, transition and chatter processes. The reconstructed attractor and probability distribution of vibration acceleration time series were studied in order to observe the system's behavior. The Lyapunov exponent andKolmogorov entropy were used to help judge the cutting state. Meanwhile, the relation curves of the Lyapunov exponent and entropy versus machining parameters were plotted and discussed. The research shows that Lyapunov exponent and Kolmogorov entropy are toned up when vibration acceleration time history goes from chatter free, transition to chatter. When cutting state transited from chatter free to chatter, the Lyapunov exponent and Kolmogorov entropy increase with increasing amplitude. In addition, the relation curves looks like stability lobes. The experimental study allow us to select optimal machining parameters for decreasing the uncertainty of cutting vibration.

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Theory of finite amplitude machine tool instability

Cited by 147 publications

References 4 publications

Operational stability prediction in milling based on impact tests

Operational stability prediction in milling based on impact tests

Enforcing Linear Dynamics Through the Addition of Nonlinearity

Experimental Investigation of Evolution Process of Nonlinear Characteristics from Chatter Free to Chatter

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