Nonlinear Dynamics

, Volume 47, Issue 1, pp 49–63

Dynamics of milling processes with variable time delays

Original Article

DOI: 10.1007/s11071-006-9058-4

Cite this article as:
Long, XH., Balachandran, B. & Mann, B.P. Nonlinear Dyn (2007) 47: 49. doi:10.1007/s11071-006-9058-4


A milling-process model with a variable time delay associated with each cutting tooth is presented in this article. The source of this variable time delay is the feed rate. The effect of the feed motion on the entry cutting angle, the exit cutting angle, and the amplitude of feed mark is also discussed. Loss-of-contact effects are also considered. The system dynamics is described by a set of delay differential equations with periodic coefficients and variable time delays. A semi-discretization scheme is presented for analyzing the stability of periodic orbits of this system. The analysis provides evidence of period-doubling bifurcations and secondary Hopf bifurcations. Good agreement is found between the numerical results obtained from this work and the results of related experimental studies.


StabilityMilling processTime delayChatterFeed rate

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.The State Key Lab of Vibration, Shock & NoiseShanghai Jiao Tong UniversityShanghaiPR China
  2. 2.Department of Mechanical EngineeringUniversity of MarylandCollege ParkU.S.A
  3. 3.Department of Mechanical and Aerospace EngineeringUniversity of MissouriColumbiaU.S.A