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An integro-differential equation with variable delay arising in machine tool vibration

Wang, Feng-Bin, Gourley, Stephen A. and Xiao, Yanyu (2018) An integro-differential equation with variable delay arising in machine tool vibration SIAM Journal on Applied Mathematics.

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Abstract

We rigorously derive an integro-differential equation as a model for the possible onset of regenerative chatter during a turning process using a lathe. The cut is made parallel to the axis of rotation of the spindle. The model allows the spindle speed to continuously vary with time, which results in the presence of a variable time delay determined from a threshold condition. We present a number of conditions sufficient for the elimination of chatter, these emphasize sufficiently low feed rate or sufficiently high spindle speed. Numerical simulations cast light on the effect of a sinusoidally varying spindle speed, a feature of some modern lathes. Spindle speed variation can cure chatter but does not necessarily do so, and can fail at higher values of the tool feed rate.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
NameEmailORCID
Wang, Feng-Bin
Gourley, Stephen A.S.Gourley@surrey.ac.uk
Xiao, Yanyu
Date : 2018
DOI : 10.1137/18M1190239
Copyright Disclaimer : © 2017, Society for Industrial and Applied Mathematics
Uncontrolled Keywords : Delay differential equation; Threshold delay; Chatter; Spindle speed variation
Related URLs :
Depositing User : Clive Harris
Date Deposited : 13 Nov 2018 14:39
Last Modified : 05 Jul 2019 16:11
URI: http://epubs.surrey.ac.uk/id/eprint/849869

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