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Research Papers

A New and Accurate Mathematical Model for Computer Numerically Controlled Programming of 4Y1 Wheels in 2½-Axis Flute Grinding of Cylindrical End-Mills

[+] Author and Article Information
Silai Xiao

College of Mechanical and Vehicle Engineering,
Hunan University,
Changsha, Hunan 410082, China;
Zhuzhou Cemented Carbide Group Corp. Ltd,
Zhuzhou, Hunan 412003, China

Zezhong C. Chen

e-mail: zezhong.chen@concordia.ca
Department of Mechanical
and Industrial Engineering,
Concordia University,
Montreal, QC, H3G 1M8, Canada

Aiming Tan

Zhuzhou Cemented Carbide Group Corp. Ltd,
Zhuzhou, Hunan 412003, China

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received March 6, 2012; final manuscript received November 14, 2012; published online July 17, 2013. Editor: Robert Landers.

J. Manuf. Sci. Eng 135(4), 041008 (Jul 17, 2013) (11 pages) Paper No: MANU-12-1074; doi: 10.1115/1.4023379 History: Received March 06, 2012; Revised November 14, 2012

Solid carbide cylindrical end-mills are widely used in machining, and their helical flutes are crucial to their cutting performance. In industry, the flute is simply defined with four key parameters: the helical angle, the radial rake angle, the fluting angle, and the core radius, which are specified in an end-mill design. The flute shape is not fully defined, while it is often generated by a 1A1 or 1V1 diamond wheel in 2½-axis computer numerically controlled (CNC) grinding. Unfortunately, the two simple wheels cannot make largely different flute shapes, preventing further improvement of the end-mills. Although no research result on how the flute geometry affects the end-mill cutting attribute has come into public yet, it is now necessary to employ more complicated wheels to grind flutes with the specified parameter values but much different flute shapes. For this purpose, the 4Y1 diamond wheel is employed in this work. However, the commercial tool grinding software cannot determine the dimensions and the set-up angle for the 4Y1 wheel. To address this problem, a new mathematical model of the flute parameters in terms of the dimensions and the set-up angle of the 4Y1 wheel is formulated, thus, the 4Y1 wheel can be used in flute grinding. This work lays a foundation of using complex wheels to grind flutes with more shapes in order to improve the end-mill's cutting ability.

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Figures

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Fig. 1

Illustration of 1A1, 1V1, and 4Y1 diamond wheels in (a), (b), and (c), respectively

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Fig. 2

Illustration of the helical flute parameters of a cylindrical four-flute end-mill

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Fig. 3

Illustration of the dimensions of the 4Y1 grinding wheel and the wheel coordinate system XGYGZGOG

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Fig. 4

Illustration of the 2½-axis flute machining configuration

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Fig. 5

The equivalent kinematics of the 2½-axis fluting with a 4Y1 wheel

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Fig. 6

Illustration of the contact curve between the 4Y1 wheel and the flute

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Fig. 7

The segments of the flute profile on the cross section of zT as zero

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Fig. 8

Plots of rake angles in terms of the wheel set-up angle and its dimensions; (a) a plot of the rake angle versus the wheel set-up angle, (b) a plot of the rake angle versus the wheel radius, (c) a plot of the rake angle versus the wheel height H1, and (d) a plot of the rake angle versus the wheel angle

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Fig. 9

Plots of the fluting angles in terms of the wheel set-up angle and its dimensions; (a) a plot of the fluting angle versus the wheel set-up angle, (b) a plot of the fluting angle versus the wheel radius, (c) a plot of the fluting angle versus the wheel height H1, and (d) a plot of the fluting angle versus the wheel angle

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Fig. 10

The plot of the fluting angles of the flute in terms of the 4Y1 wheel dimensions, H1 and α

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Fig. 11

The CAD solid models (a)–(e) of the flutes by using 4Y1 wheels 1–5, respectively

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