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.
Skip Nav Destination
e-mail: bachrathy@mm.bme.hu
e-mail: stepan@mm.bme.hu
e-mail: turi@utdallas.edu
Article navigation
October 2011
Research Papers
State Dependent Regenerative Effect in Milling Processes
Dániel Bachrathy,
Dániel Bachrathy
Research Group on Dynamics of Vehicles and Machines,
e-mail: bachrathy@mm.bme.hu
Hungarian Academy of Sciences
, Budapest H-1111, Hungary
Search for other works by this author on:
Gábor Stépán,
Gábor Stépán
Department of Applied Mechanics,
e-mail: stepan@mm.bme.hu
Budapest University of Technology and Economics
, Budapest H-1111, Hungary
Search for other works by this author on:
János Turi
János Turi
Programs in Mathematical Sciences,
e-mail: turi@utdallas.edu
University of Texas at Dallas
, Richardson, TX 75083-0688
Search for other works by this author on:
Dániel Bachrathy
Research Group on Dynamics of Vehicles and Machines,
Hungarian Academy of Sciences
, Budapest H-1111, Hungarye-mail: bachrathy@mm.bme.hu
Gábor Stépán
Department of Applied Mechanics,
Budapest University of Technology and Economics
, Budapest H-1111, Hungarye-mail: stepan@mm.bme.hu
János Turi
Programs in Mathematical Sciences,
University of Texas at Dallas
, Richardson, TX 75083-0688e-mail: turi@utdallas.edu
J. Comput. Nonlinear Dynam. Oct 2011, 6(4): 041002 (9 pages)
Published Online: March 22, 2011
Article history
Received:
December 31, 2009
Revised:
February 4, 2011
Online:
March 22, 2011
Published:
March 22, 2011
Citation
Bachrathy, D., Stépán, G., and Turi, J. (March 22, 2011). "State Dependent Regenerative Effect in Milling Processes." ASME. J. Comput. Nonlinear Dynam. October 2011; 6(4): 041002. https://doi.org/10.1115/1.4003624
Download citation file:
Get Email Alerts
Numerical Simulation Method for the Rain-Wind Induced Vibration of the Three-Dimensional Flexible Stay Cable
J. Comput. Nonlinear Dynam
An Investigation of Dynamic Behavior of Electric Vehicle Gear Trains
J. Comput. Nonlinear Dynam (March 2025)
Nonlinear Dynamic Analysis Framework for Slender Structures Using the Modal Rotation Method
J. Comput. Nonlinear Dynam (March 2025)
Related Articles
Nonlinear Dynamics of High-Speed Milling—Analyses, Numerics, and Experiments
J. Vib. Acoust (April,2005)
A Contribution to Improve the Accuracy of Chatter Prediction in Machine Tools Using the Stability Lobe Diagram
J. Manuf. Sci. Eng (April,2014)
Machine Tool Chatter and Surface Location Error in Milling Processes
J. Manuf. Sci. Eng (November,2006)
Vibration Frequencies in High-Speed Milling Processes or a Positive Answer to Davies, Pratt, Dutterer and Burns
J. Manuf. Sci. Eng (August,2004)
Related Proceedings Papers
Related Chapters
Accuracy of an Axis
Mechanics of Accuracy in Engineering Design of Machines and Robots Volume I: Nominal Functioning and Geometric Accuracy
Dynamic Behavior in a Singular Delayed Bioeconomic Model
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)
Research on Cutting-Tooth Outline Distortion of Internal Helical Gearing Machine Tool
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3