Research Papers

The Undercut Criterion of Pinion Shaper Cutters: And an Improvement by Modifying the Basic Rack Profile

[+] Author and Article Information
Mattias Svahn

Division of Machine Elements,
Department of Mechanical Engineering,
Lund University,
P.O. Box 118,
Lund SE-221 00, Sweden
e-mail: mattias.svahn@mel.lth.se

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received October 14, 2014; final manuscript received April 2, 2015; published online September 9, 2015. Assoc. Editor: Xiaoping Qian.

J. Manuf. Sci. Eng 138(1), 011011 (Sep 09, 2015) (8 pages) Paper No: MANU-14-1529; doi: 10.1115/1.4030375 History: Received October 14, 2014

The fillet of the gear tooth is highly stressed in operation; so for heavily loaded gears, the fillet geometry must be controlled. The manufacturer's task is to, within acceptable tolerances, produce the gear to the designer's specifications regardless of the manufacturing method. Most often gear cutting tools are used that work under generating conditions. The tool will form the gear tooth; so to produce the specified gear geometry and, especially, the fillet geometry, this tool must be conjugated to the same basic rack as the gear to cut. However, this gives a risk that the tooth tip of the tool will be undercut, and if this occurs the tool will not cut the intended gear fillet. In this report, novel analytical equations are derived, which predict the limit when the tool tip will be undercut. It is shown that if the gear tooth should be conjugated to the standard basic rack with a circular fillet, which is the normal case, very large tool-tooth numbers are needed for pinion shaper cutters and gear skiving cutters to avoid this type of undercut. However, the minimum tooth number to achieve a smooth continuous tool-tooth profile is reduced by modifications to the fillet of the basic rack profile.

Copyright © 2016 by ASME
Topics: Gears , Gear teeth , Geometry
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Grahic Jump Location
Fig. 1

Pinion shaper cutter cuts an internal gear, external gear, or rack

Grahic Jump Location
Fig. 2

Geometry of a pinion shaper cutter with circular tip rounding

Grahic Jump Location
Fig. 3

Pinion shaper cutter and basic rack profile

Grahic Jump Location
Fig. 4

Calculated basic rack profile conjugated to the pinion shaper cutter with circular tip rounding

Grahic Jump Location
Fig. 5

The radial distance R0,if where the tip rounding and the involute profile interconnect, transverse plane view

Grahic Jump Location
Fig. 6

The radial distance R0 from the center of the shaper cutter to the fillet of the basic rack, transverse plane view

Grahic Jump Location
Fig. 7

R0(ϕn), z = 40, β = 0 deg,αn = 20 deg,h0,t = 1.25,r0,t = 0.35, and x = 0

Grahic Jump Location
Fig. 8

The calculated tooth profile from data in Fig. 7

Grahic Jump Location
Fig. 10

Basic rack profile with elliptical fillet

Grahic Jump Location
Fig. 11

Calculated tooth profile of pinion shaper cutter with 18 teeth conjugated to basic rack with r0,t,η = 0.9 and r0,t,ξ = 0.45

Grahic Jump Location
Fig. 12

Radius of curvature of pinion shaper cutters with 15, 16, 17, and 18 teeth conjugated to a basic rack with elliptical fillet, r0,t,η = 0.9 and r0,t,ξ = 0.45

Grahic Jump Location
Fig. 13

Radius of curvature of cut external gears with 12, 13, 14, and 15 teeth conjugated to a rack with elliptical fillet, r0,t,η = 0.9 and r0,t,ξ = 0.45




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