Fold bifurcation in the state-dependent delay model of milling - Analytical and numerical solutions

Daniel Bachrathy, G. Stépán

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The standard models of the milling process describe the surface regeneration effect by a delay-differential equation with constant time delay. In this study, an improved two degree of freedom model is presented for milling process where the regenerative effect is described by an improved state dependent time delay model. The model contains exact nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool. This model is valid in case of large amplitude forced vibrations close to the near-resonant spindle speeds. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization of the state-dependent delay differential equation around these periodic solutions by means of the semi-discretization method. The results are validated by an advanced numerical time domain simulation where the chip thickness is calculated by means of Boolean algebra.

Original languageEnglish
Title of host publicationProceedings of the ASME Design Engineering Technical Conference
Pages521-527
Number of pages7
Volume4
EditionPARTS A AND B
DOIs
Publication statusPublished - 2011
EventASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 - Washington, DC, United States
Duration: Aug 28 2011Aug 31 2011

Other

OtherASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
CountryUnited States
CityWashington, DC
Period8/28/118/31/11

Fingerprint

State-dependent Delay
Analytical Solution
Fold
Bifurcation
Numerical Solution
Delay Differential Equations
Time Delay
Time delay
Differential equations
Describing Function
Forced Vibration
Semidiscretization
Shooting Method
Periodic Motion
Discretization Method
Boolean algebra
Regeneration
Describing functions
Model
Milling (machining)

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modelling and Simulation

Cite this

Bachrathy, D., & Stépán, G. (2011). Fold bifurcation in the state-dependent delay model of milling - Analytical and numerical solutions. In Proceedings of the ASME Design Engineering Technical Conference (PARTS A AND B ed., Vol. 4, pp. 521-527) https://doi.org/10.1115/DETC2011-48300

Fold bifurcation in the state-dependent delay model of milling - Analytical and numerical solutions. / Bachrathy, Daniel; Stépán, G.

Proceedings of the ASME Design Engineering Technical Conference. Vol. 4 PARTS A AND B. ed. 2011. p. 521-527.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bachrathy, D & Stépán, G 2011, Fold bifurcation in the state-dependent delay model of milling - Analytical and numerical solutions. in Proceedings of the ASME Design Engineering Technical Conference. PARTS A AND B edn, vol. 4, pp. 521-527, ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011, Washington, DC, United States, 8/28/11. https://doi.org/10.1115/DETC2011-48300
Bachrathy D, Stépán G. Fold bifurcation in the state-dependent delay model of milling - Analytical and numerical solutions. In Proceedings of the ASME Design Engineering Technical Conference. PARTS A AND B ed. Vol. 4. 2011. p. 521-527 https://doi.org/10.1115/DETC2011-48300
Bachrathy, Daniel ; Stépán, G. / Fold bifurcation in the state-dependent delay model of milling - Analytical and numerical solutions. Proceedings of the ASME Design Engineering Technical Conference. Vol. 4 PARTS A AND B. ed. 2011. pp. 521-527
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