State dependent regenerative effect in milling processes

Dániel Bachrathy, G. Stépán, János Turi

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

The governing equation of milling processes is generalized with the help of accurate chip thickness derivation resulting in a state dependent delay model. This model is valid for large amplitude machine tool vibrations and uses accurate nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool relative to the workpiece. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization around these periodic solutions by means of the semidiscretization method applied for the corresponding time-periodic delay system. Predictor-corrector method is developed to continue the periodic solutions as the bifurcation parameter, that is, the axial immersion is varied. It is observed that the influence of the state dependent delay on linear stability can be significant close to resonance where large amplitude forced vibrations occur. The existence of an unusual fold bifurcation is shown where a kind of hysteresis phenomenon appears between two different stable periodic motions.

Original languageEnglish
Article number041002
JournalJournal of Computational and Nonlinear Dynamics
Volume6
Issue number4
DOIs
Publication statusPublished - 2011

Fingerprint

State-dependent Delay
Periodic Motion
Periodic Solution
Bifurcation
Predictor-corrector Methods
Describing Function
Forced Vibration
Describing functions
Semidiscretization
Shooting Method
Dependent
Milling (machining)
Machine Tool
Delay Systems
Periodic Systems
Linear Stability
Immersion
Hysteresis
Machine tools
Linearization

Keywords

  • bistability
  • fold bifurcation
  • milling
  • stability
  • state dependent delay

ASJC Scopus subject areas

  • Mechanical Engineering
  • Applied Mathematics
  • Control and Systems Engineering

Cite this

State dependent regenerative effect in milling processes. / Bachrathy, Dániel; Stépán, G.; Turi, János.

In: Journal of Computational and Nonlinear Dynamics, Vol. 6, No. 4, 041002, 2011.

Research output: Contribution to journalArticle

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