0
TECHNICAL PAPERS

Nonlinear Dynamics of High-Speed Milling—Analyses, Numerics, and Experiments

[+] Author and Article Information
Gabor Stepan1

Department of Applied Mechanics,  Budapest University of Technology and Economics, Budapest, H-1521, Hungarystepan@mm.bme.hu

Robert Szalai

Department of Applied Mechanics,  Budapest University of Technology and Economics, Budapest, H-1521, Hungaryszalai@mm.bme.hu

Brian P. Mann

bmann@mae.ufl.eduDepartment of Mechanical and Aerospace Engineering,  University of Florida, Gainesville, FL 32611

Philip V. Bayly

pvb@mecf.wustl.eduDepartment of Mechanical Engineering, Washington University, St. Louis, MO 63130

Tamas Insperger

inspi@mm.bme.huDepartment of Applied Mechanics,  Budapest University of Technology and Economics, Budapest, H-1521, Hungary

Janez Gradisek

Laboratory of Synergetics,  University of Ljubljana, Ljubljana, SI-1000, Sloveniajanez.gradisek@fs.uni-lj.si

Edvard Govekar

Laboratory of Synergetics,  University of Ljubljana, Ljubljana, SI-1000, Slovenia̱edvard.govekar@fs.uni-lj.si

1

Address for correspondence: Budapest University of Technology and Economics, Department of Applied Mechanics, Budapest, 1521, Hungary.

J. Vib. Acoust 127(2), 197-203 (Jun 10, 2004) (7 pages) doi:10.1115/1.1891818 History: Received December 23, 2003; Revised June 10, 2004

High-speed milling is often modeled as a kind of highly interrupted machining, when the ratio of time spent cutting to not cutting can be considered as a small parameter. In these cases, the classical regenerative vibration model, playing an essential role in machine tool vibrations, breaks down to a simplified discrete mathematical model. The linear analysis of this discrete model leads to the recognition of the doubling of the so-called instability lobes in the stability charts of the machining parameters. This kind of lobe-doubling is related to the appearance of period doubling vibrations originated in a flip bifurcation. This is a new phenomenon occurring primarily in low-immersion high-speed milling along with the Neimark-Sacker bifurcations related to the classical self-excited vibrations or Hopf bifurcations. The present work investigates the nonlinear vibrations in the case of period doubling and compares this to the well-known subcritical nature of the Hopf bifurcations in turning processes. The identification of the global attractor in the case of unstable cutting leads to contradiction between experiments and theory. This contradiction draws the attention to the limitations of the small parameter approach related to the highly interrupted cutting condition.

FIGURES IN THIS ARTICLE
<>
Copyright © 2005 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Mechanical model of highly interrupted cutting

Grahic Jump Location
Figure 2

Stability chart (stable region shaded)

Grahic Jump Location
Figure 3

Iteration (xj,vj), stable period-1 (P1) and unstable period-2 (P2) solutions, and center manifold (CM)

Grahic Jump Location
Figure 4

Bifurcation diagram

Grahic Jump Location
Figure 5

Experimental stability chart (엯—stable cutting, ×—unstable cutting)

Grahic Jump Location
Figure 6

Reconstructed experimental trajectories at parameter points A, B, and C (gray—experimental trajectories, black—filtered trajectory; dots refer to tool/workpiece contact, continuous black lines refer to tool free-flight above workpiece)

Grahic Jump Location
Figure 7

Numerically determined stable period-2 oscillation of tool (trajectory and time-history) (continuous line means contact, “엯” means tool above possible contact, dashed line means-free-flight)

Grahic Jump Location
Figure 8

Tooth path during period-2 oscillation

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In