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


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.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Mechanical model of highly interrupted cutting

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Figure 2

Stability chart (stable region shaded)

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Figure 3

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

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Figure 4

Bifurcation diagram

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Figure 5

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

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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)

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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)

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Figure 8

Tooth path during period-2 oscillation



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