State Dependent Regenerative Effect in Milling Processes

Author:

Bachrathy Dániel1,Stépán Gábor2,Turi János3

Affiliation:

1. Research Group on Dynamics of Vehicles and Machines, Hungarian Academy of Sciences, Budapest H-1111, Hungary

2. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest H-1111, Hungary

3. Programs in Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75083-0688

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.

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Reference33 articles.

1. Vibration of machine tools

2. Surface Properties of the Machined Workpiece for Helical Mills;Bachrathy;Mach. Sci. Technol.

3. The Stability of Machine-Tool Against Self-Excited Vibration in Machining;Tlusty

4. Stability of High-Speed Milling;Insperger

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