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Research Papers: Design of Direct Contact Systems

A Novel Lengthwise Crowning Method for Face-Hobbed Straight Bevel Gears

[+] Author and Article Information
Yi-Pei Shih

Department of Mechanical Engineering,
National Taiwan University
of Science and Technology,
No. 43, Section 4, Keelung Road,
Taipei 106, Taiwan
e-mail: shihyipei@mail.ntust.edu.tw

1Corresponding author.

Contributed by the Power Transmission and Gearing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 7, 2016; final manuscript received March 1, 2017; published online April 24, 2017. Assoc. Editor: Qi Fan.

J. Mech. Des 139(6), 063301 (Apr 24, 2017) (9 pages) Paper No: MD-16-1561; doi: 10.1115/1.4036353 History: Received August 07, 2016; Revised March 01, 2017

A recent addition to the many milling processes used in manufacturing to cut straight bevel gears (SBGs) is a new face-hobbing (FH) method that uses a virtual hypocycloid straight-lined mechanism to produce straight-lined teeth. Despite earning much attention because of its high productivity, however, this method is unable to handle lengthwise crowning on tooth surfaces, which results in poor contact performance. This paper therefore proposes a novel lengthwise crowning method, applicable on a modern six-axis computer numerical control (CNC) bevel gear cutting machine, in which the gear blank performs a swinging motion during machining. This swinging motion is enabled by machine setting modifications, which here are derived from a mathematical model of a double (profile and lengthwise) crowned gear. After the model's correctness is confirmed using ease-off and tooth contact analyses, a final investigation examines the effect of two key parameters related to contact performance indexes whose interrelations are graphed to provide a designer reference.

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References

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Shih, Y.-P. , 2012, “ Mathematical Model for Face-Hobbed Straight Bevel Gears,” ASME J. Mech. Des., 134(9), p. 091006. [CrossRef]
Shih, Y.-P. , Huang, Y.-C. , Lee, Y.-H. , and Wu, J.-M. , 2013, “ Manufacture of Face-Hobbed Straight Bevel Gears Using a Six-Axis CNC Bevel Gear Cutting Machine,” Int. J. Adv. Manuf. Technol., 68(9), pp. 2499–2515. [CrossRef]
Shih, Y.-P. , 2013, “ A Lengthwise Modification for Face-Hobbed Straight Bevel Gears,” ASME Paper No. DETC2013-12233.
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Shih, Y.-P. , 2010, “ A Novel Ease-Off Flank Modification Methodology for Spiral Bevel and Hypoid Gears,” Mech. Mach. Theory, 45(8), pp. 1108–1124. [CrossRef]
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Figures

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Fig. 1

Hypocycloid straight-lined mechanism

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Fig. 2

Generation of a face-hobbed SBG using an IGG

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Fig. 3

Coordinate systems for a left-handed cutter head

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Fig. 4

Coordinate systems for the two types of blade edge: (a) straight-lined blade edge and (b) circular blade edge

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Fig. 5

Coordinate systems of the universal cradle-type bevel gear generator [11]: 1—cutter spindle, 2—tilt drum, 3—swivel drum, 4—eccentric drum, 5—cradle, 6—sliding base, 7—machine root angle, 8—blank offset, 9—machine center to back, and 10—work spindle

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Fig. 6

Cutting positions of the IGG and gear

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Fig. 7

Swinging motion of the gear blank for lengthwise crowning

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Fig. 8

Corrective machine settings for the swinging motion

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Fig. 17

Maximum major radius of the contact ellipses corresponding to the radius of the swing's circular arc

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Fig. 16

Maximum transmission error corresponding to the radius of the circular cutting edge

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Fig. 15

Tooth contact analysis: (a) contact pattern (contact ellipses) and (b) transmission errors

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Fig. 14

Ease-off topography

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Fig. 13

Flank deviations between the crowning and theoretical gears: (a) pinion and (b) ring gear

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Fig. 12

Three-dimensional SolidWork models of an FH SBG pair

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Fig. 11

Kinematic relations of the modified machine settings for the swinging motion

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Fig. 10

Gear blanks for the gear pair

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Fig. 9

Positions of the cutting edge for the gear pair

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