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Research Papers

The Effect of Helix Angle Variation on Milling Stability

[+] Author and Article Information
Zoltan Dombovari1

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

Gabor Stepan

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

1

Corresponding author.

J. Manuf. Sci. Eng 134(5), 051015 (Sep 28, 2012) (6 pages) doi:10.1115/1.4007466 History: Received February 24, 2012; Revised August 09, 2012; Published September 25, 2012; Online September 28, 2012

Helical milling tools of nonuniform helix angles are widely used in manufacturing industry. While the milling tools with these special cutting edges are already available in the market, their cutting dynamics has not been fully explored. Also, there have been several attempts to introduce complex harmonically varied helix tools, but the manufacturing of harmonic edges is extremely difficult, and their effect on cutting dynamics is not clear either. In this study, a general mechanical model is introduced to predict the linear stability of these special cutters with optional continuous variation of the helix angle. It is shown that these milling tools cause distribution in regeneration. The corresponding time-periodic distributed delay differential equations are investigated by semi-discretization. This work points out how the nonuniform and harmonically varied helix cutters behave in case of high and low cutting speed applications.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 5

Linear stability of machining process performed by harmonically varied helix milling tools with symmetric engagement defined by Δϕ (thick continuous line) besides the linear stability of processes performed by a conventional milling tool (thin dashed lines)

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Figure 6

The dominant (chatter) frequencies along the linear stability in the case of nonuniform constant helix tools Fig. 4 (dashed lines represents the dominant vibration frequencies of the same operation with conventional tool)

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Figure 1

A real implementation (a) and the sketch (b) of the milling cutter with harmonically varied helix. (The real tool was provided by Prof. Gy. Matyasi: see Acknowledgment.)

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Figure 2

Edge pattern of nonuniform and harmonically varied helix tools (left panels) and the corresponding weight distributions (right panels). Minimum, zero level, and maximum values are denoted by black, middle gray (see top part of panel (b)), and white in panels (b) and (d).

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Figure 3

Occurrence density of delays (black is zero, while white is four occurrences)

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Figure 4

Linear stability of machining process performed by milling tools with nonuniform helices with symmetric engagement defined by Δϕ (thick continuous line) besides the linear stability of processes performed by a conventional milling tool (thin dashed lines)

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