0
RESEARCH PAPERS

An Improved Tool Path Model Including Periodic Delay for Chatter Prediction in Milling

[+] Author and Article Information
R. P. Faassen1

Department of Mechanical Engineering,  Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlandsr.p.h.faassen@tue.nl

N. van de Wouw, H. Nijmeijer

Department of Mechanical Engineering,  Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

J. A. Oosterling

Division of Design and Manufacturing, TNO Science and Industry, P.O. Box 6235, 5600 HE Eindhoven, The Netherlands

1

Corresponding author.

J. Comput. Nonlinear Dynam 2(2), 167-179 (Dec 11, 2006) (13 pages) doi:10.1115/1.2447465 History: Received August 22, 2006; Revised December 11, 2006

The efficiency of the high-speed milling process is often limited by the occurrence of chatter. In order to predict the occurrence of chatter, accurate models are necessary. In most models regarding milling, the cutter is assumed to follow a circular tooth path. However, the real tool path is trochoidal in the ideal case, i.e., without vibrations of the tool. Therefore, models using a circular tool path lead to errors, especially when the cutting angle is close to 0 or π radians. An updated model for the milling process is presented which features a model of the undeformed chip thickness and a time-periodic delay. In combination with this tool path model, a nonlinear cutting force model is used, to include the dependency of the chatter boundary on the feed rate. The stability of the milling system, and hence the occurrence of chatter, is investigated using both the traditional and the trochoidal model by means of the semi-discretization method. Due to the combination of this updated tool path model with a nonlinear cutting force model, the periodic solution of this system, representing a chatter-free process, needs to be computed before the stability can be investigated. This periodic solution is computed using a finite difference method for delay-differential equations. Especially for low immersion cuts, the stability lobes diagram (SLD) using the updated model shows significant differences compared to the SLD using the traditional model. Also the use of the nonlinear cutting force model results in significant differences in the SLD compared to the linear cutting force model.

Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic representation of the milling process; (a) side view, (b) top view

Grahic Jump Location
Figure 4

The circular tooth path approximation of a mill with three teeth

Grahic Jump Location
Figure 5

Chip thickness as a function of rotation angle for various models: r=5mm, z=2, fz=2mm/tooth

Grahic Jump Location
Figure 6

Relative error in chip thickness as a function of rotation angle for various models: r=5mm, z=2, fz=0.2mm/tooth

Grahic Jump Location
Figure 8

Normalized delay as a function of rotation angle: r=5mm, z=2, fz=0.2mm/tooth

Grahic Jump Location
Figure 9

Graphical interpretation of the finite difference method for ODEs

Grahic Jump Location
Figure 10

Graphical interpretation of period time and the delay. In this case τi≠mih.

Grahic Jump Location
Figure 11

Displacement of the tool. Periodic solution using the finite difference method and numerical simulation of 20 revolutions (axis directions as in Fig. 3). (a) ap=1mm; stable cut. (b) ap=2mm; unstable cut.

Grahic Jump Location
Figure 2

Block diagram of the milling process

Grahic Jump Location
Figure 3

The tooth path of a mill with three teeth

Grahic Jump Location
Figure 7

Entry (left) and exit (right) angles. The values from Eqs. 30,31 are plotted as circles; r=5mm, z=2, fz=0.2mm/tooth. For legend, see Fig. 5.

Grahic Jump Location
Figure 12

Stability lobes for upmilling using the traditional and the trochoidal model for several immersion levels. (a) 100% immersion; (b) 50% immersion; (c) 10% immersion; (d) 5% immersion.

Grahic Jump Location
Figure 13

Stability lobes for downmilling using the traditional and the trochoidal model for several immersion levels. (a) 100% immersion; (b) 50% immersion; (c) 10% immersion; (d) 5% immersion.

Grahic Jump Location
Figure 14

Chip thickness including periodic vibrations for a 5% downmilling cut at 23,650rpm and ap=33mm

Grahic Jump Location
Figure 15

Effect of the frequency change f1→f2 and the delay change τ1→τ2 on the fraction of waves ϵ1 and ϵ2=ϵ3

Grahic Jump Location
Figure 16

Stability lobe with some possible values for the number of waves M+ϵ

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