## Stability of interrupted cutting by temporal finite element analysis

Publication ,  Journal Article
Bayly, PV; Mann, BP; Halley, JE; Davies, MA
Published in: Proceedings of the ASME Design Engineering Technical Conference
January 1, 2001

Chatter in milling and other interrupted cutting operations occurs at different combinations of speed and depth of cut from chatter in continuous cutting. Prediction of stability in interrupted cutting is complicated by two facts: (1) the equation of motion when cutting is not the same as the equation when the tool is free; (2) no exact analytical solution is known when the tool is in the cut. These problems are overcome by matching the free response with an approximate solution that is valid while the tool is cutting. This approximate solution is obtained by the application of finite elements in time. The complete, combined solution is cast in the form of a discrete map that relates position and velocity at the beginning and end of each element to the corresponding values one period earlier. The eigenvalues of the linearized map are used to determine stability. Predictions of stability are confirmed by experiment.

## Published In

Proceedings of the ASME Design Engineering Technical Conference

January 1, 2001

6 C

## Start / End Page

2361 / 2370

### Citation

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Bayly, P. V., Mann, B. P., Halley, J. E., & Davies, M. A. (2001). Stability of interrupted cutting by temporal finite element analysis. Proceedings of the ASME Design Engineering Technical Conference, 6 C, 2361–2370.
Bayly, P. V., B. P. Mann, J. E. Halley, and M. A. Davies. “Stability of interrupted cutting by temporal finite element analysis.” Proceedings of the ASME Design Engineering Technical Conference 6 C (January 1, 2001): 2361–70.
Bayly PV, Mann BP, Halley JE, Davies MA. Stability of interrupted cutting by temporal finite element analysis. Proceedings of the ASME Design Engineering Technical Conference. 2001 Jan 1;6 C:2361–70.
Bayly, P. V., et al. “Stability of interrupted cutting by temporal finite element analysis.” Proceedings of the ASME Design Engineering Technical Conference, vol. 6 C, Jan. 2001, pp. 2361–70.
Bayly PV, Mann BP, Halley JE, Davies MA. Stability of interrupted cutting by temporal finite element analysis. Proceedings of the ASME Design Engineering Technical Conference. 2001 Jan 1;6 C:2361–2370.

## Published In

Proceedings of the ASME Design Engineering Technical Conference

January 1, 2001

6 C

2361 / 2370