Chaotic and stochastic dynamics of orthogonal metal cutting

Wiercigroch, Marian; Cheng, Alexander H.‐D.

doi:10.1016/s0960-0779(96)00111-7

Cited by 50 publications

(32 citation statements)

References 8 publications

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“…Such a type of dynamic noise may not be the most realistic in the case of cutting dynamics. Correlated multiplicative noise in the driving term, i.e., the cutting force, would probably match the conditions of real cutting better [15,20]. However, for the dynamics of stochastic processes described by the Langevin equation with uncorrelated Gaussian noise, some interesting analytical results are available which have recently led to new methods for analysis of noisy time series [19,21].…”

Section: Discussionmentioning

confidence: 99%

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Chatter Onset in Non-Regenerative Cutting: A Numerical Study

Gradišek

Govekar

Grabec

2001

Journal of Sound and Vibration

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Section: Discussionmentioning

confidence: 99%

“…The present study extends previous studies by considering non-zero damping, and by introducing additive dynamic noise into the system. In reference [15], the e!ect of multiplicative dynamic noise on cutting dynamics is also investigated, but in a di!erent context.…”

Section: Chatter In Non-regenerative Cuttingmentioning

confidence: 99%

Chatter Onset in Non-Regenerative Cutting: A Numerical Study

Gradišek

Govekar

Grabec

2001

Journal of Sound and Vibration

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“…Finally, the role of the dry friction and the stick-and-slip motion [10][11][12] was indicated and studied extensively. Recently, apart from the widely studied conditions of regular chatter vibrations, noise like chaotic oscillations caused by various system nonlinearities were predicted and detected [13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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

Litak

Rusinek

2012

Meccanica

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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.

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“…Chaotic motions have been observed in the responses of chattering machine-tool systems by Grabec [4,5] and Wiercigroch [22,23], Wiercigroch and Cheng [24], Warmi ! n nski et al [25], Kalmar-Nagy and Pratt [26], and Wiercigroch and Krivtsov [27].…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solutions for Primary Chatter in the Non-Linear Metal Cutting Model

Warmiński

Litak

Cartmell³

et al. 2003

Journal of Sound and Vibration

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This paper considers an accepted model of the metal cutting process dynamics in the context of an approximate analysis of the resulting non-linear differential equations of motion. The process model is based upon the established mechanics of orthogonal cutting and results in a pair of non-linear ordinary differential equations which are then restated in a form suitable for approximate analytical solution. The chosen solution technique is the perturbation method of multiple time scales and approximate closed-form solutions are generated for the most important non-resonant case. Numerical data are then substituted into the analytical solutions and key results are obtained and presented. Some comparisons between the exact numerical calculations for the forces involved and their reduced and simplified analytical counterparts are given. It is shown that there is almost no discernible difference between the two thus confirming the validity of the excitation functions adopted in the analysis for the data sets used, these being chosen to represent a real orthogonal cutting process. In an attempt to provide guidance for the selection of technological parameters for the avoidance of primary chatter, this paper determines for the first time the stability regions in terms of the depth of cut and the cutting speed co-ordinates. #

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Chaotic and stochastic dynamics of orthogonal metal cutting

Cited by 50 publications

References 8 publications

Chatter Onset in Non-Regenerative Cutting: A Numerical Study

Chatter Onset in Non-Regenerative Cutting: A Numerical Study

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

Approximate Analytical Solutions for Primary Chatter in the Non-Linear Metal Cutting Model

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