The method of D-partition is used to analyse the stability of a two-degree-of-freedom system subjected to a delayed restoring force of the kind which causes chatter in certain types of machine tool. The central feature of the analysis is the reduction of a stabliity problem involving a transcendental characteristic equation to a much simpler problem concerning the roots of a related algebraic equation. The results of the exact analysis are compared with approximate results obtained by assuming that the normal modes of the two-degree-of-freedom system can be decoupled.
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References
1.
TobiasS. A.Machine-tool vibration1965 (Blackie).
2.
PorterB.‘Chatter analysis by the method of D-partition’, Jl mech. Engng Sci.19657 (No. 3), 348.
3.
PontryaginL. S.‘On the zeros of some elementary transcendental functions’, Izv. Akad. Nauk. S.S.S.R.19426, 115.
4.
AizermanM. A.Theory of automatic control1963 (Pergamon Press).
5.
PorterB.BaillieM. A.‘Analogue computer simulation of machine-tool chatter’, Engineer, Lond.1966222, 971.
6.
CaugheyT. K.O'KellyM. E. J.‘General theory of vibration of damped linear dynamic systems’, California Institute of Technology Dynamics Laboratory Report, 1963 (June).
