ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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Bifurcations and Chaos in High-Speed Milling

Róbert Szalai
Budapest University of Technology and Economics, Department of Applied Mechanics

Wednesday, June 1, 2005 15:00-16:00,
NIST North (820), Room 145
Wednesday, June 1, 2005 13:00-14:00,
Room 4550

Abstract: High-speed milling is a common manufacturing technology in industry, which is used to produce complicated parts with high accuracy. However, at some parameters this process shows instabilities, resulting in inaccuracies in the machined part. Traditionally, stability charts are computed to determine parameter regions where vibrations do not occur. For computing these charts one uses a linear approximation of the mathematical model, leaving nonlinear vibrations unrevealed. However, investigating local bifurcations, it turns out that nonlinear vibrations coexist with linearly stable stationary motions. By using numerical continuation techniques, we find that stable, high-amplitude oscillations cover quite large parameter regions, explaining the presence of undesired vibrations in the stable part of the stability chart. To illustrate the accuracy of our model, experimental data are compared with our findings. Chaotic motions also arise in high-speed milling due to the piecewise smooth dynamics of the tool's motion when it leaves and enters the workpiece. We model these phenomena by a two-dimensional, discrete-time map and find that the dynamics itself is conjugate to a modified version of Smale's horseshoe map.

Speaker Bio: Róbert Szalai is a PhD student of Professor Gábor Stépán in the Department of Applied Mechanics at the Budapest University of Technology and Economics (BUTE), working in the area of quasiperiodic and chaotic motions in dynamical systems. After finishing his undergraduate studies in Mechanical Engineering at BUTE in 2002, Mr. Szalai was a Visiting Fellow in the Department of Engineering Mathematics at the University of Bristol for five months on a Hungarian Eotvos Scholarship, and he completed a master's thesis, also in 2002, entitled Nonlinear Vibrations of Interrupted Cutting Processes, under the joint supervision of Professors S. John Hogan of Bristol and Gábor Stépán. Mr. Szalai is currently a Fulbright Fellow at MIT, working with Professor George Haller in the Department of Mechanical Engineering.

Presentation Slides: PDF

Contact: T. J. Burns

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.

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