Research Papers

Dynamics and Stability of Five-Axis Ball-End Milling

[+] Author and Article Information
Erdem Ozturk

Manufacturing Research Laboratory, Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul 34956, Turkey

Erhan Budak1

Manufacturing Research Laboratory, Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul 34956, Turkeyebudak@sabanciuniv.edu


Corresponding author.

J. Manuf. Sci. Eng 132(2), 021003 (Mar 26, 2010) (13 pages) doi:10.1115/1.4001038 History: Received June 24, 2009; Revised January 13, 2010; Published March 26, 2010; Online March 26, 2010

Being one of the most important problems in machining, chatter vibrations must be avoided as they result in high cutting forces, poor surface finish, and unacceptable part quality. Using stability diagrams is an effective method to predict chatter free cutting conditions. Although there have been numerous works in milling dynamics, the stability of five-axis ball-end milling has not been studied in detail. In this paper, the stability of the five-axis ball-end milling is analyzed using analytical (frequency domain), numerical (time-domain), and experimental methods. The models presented consider 3D dynamics of the five-axis ball-end milling process including the effects of all important process parameters such as the lead and tilt angles. Both single- and multi-frequency solutions are presented. Unlike other standard milling cases, it is observed that adding multi-frequency effects in the solution has marginal influence on the stability diagrams for five-axis ball-end milling operations due to effects of the ball-end milling geometry on the engagement region, thus, on the directional coefficients. The stability limits predicted by single- and multi-frequency methods are compared with time-domain simulations and experiments. Using the models and experimental results, the effects of the lead and tilt angles on the stability diagrams are also shown. The presented models can be used in analysis of five-axis ball-end milling dynamics as well as in the selection of the milling conditions for increased stability.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Geometry of the ball-end mill: (a) 3D view; (b) top view

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Figure 2

(a) Coordinate systems (b) lead and tilt angles, and cutting types: (c) first cut, (d) following cut, and (e) slotting

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Figure 3

The dynamic chip thickness

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Figure 4

Variations in the (a) static chip thickness and (b) radial cutting force coefficient

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Figure 5

(a) A representative engagement boundary in five-axis ball-end milling; (b) variations in the start and exit angles along the tool axis

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Figure 6

(a) Dynamic cutting forces in x-, y-, and z-directions on the jth flute on the disk element l; (b) discrete heights (Δz), (Δa), and (ΔA)

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Figure 7

Change in the feed direction with respect to the MCS due to the lead and tilt angles on a machine tool, where the rotary axes are on the table side: (a) before the lead and tilt angles are applied; (b) after the lead and tilt angles are applied

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Figure 8

Golden section search algorithm: (1−g) is the golden ratio, which is equal to 0.6180340

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Figure 9

Variation in an element of the directional coefficient matrix in (a) flat-end milling and (b) ball-end milling operations

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Figure 10

Stability diagrams: (a) three-axis flat-end milling case, where the radial depth is 4.515 mm (start and exit angles are 0 deg and 58.265 deg); (b) a following cut ball-end milling case, where the stepover is 4.515 mm; (c) a fictitious ball-end milling case, where the start and exit angles are fixed as 0 deg and 58.265 deg, respectively

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Figure 11

Stability diagrams of example 1; time-domain solutions of two cutting depths at 17,800 rpm

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Figure 12

Sound spectrums and surface photos at unstable and stable points

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Figure 13

Stability diagrams for the second example; sound spectrum and spectrum of the tool displacement in the feed direction (calculated by the time-domain) at 14,650 rpm and 1 mm

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Figure 14

The displacement of the cutting tool at 14,650 rpm: (a) 0.5 mm cutting depth (stable), (b) 0.9 mm cutting depth (marginally stable), and (c) 1.25 mm cutting depth (unstable)

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Figure 15

Effect of the lead and tilt angles on the absolute stability




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