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TECHNICAL PAPERS

# Mathematical Model and Surface Deviation of Cylindrical Gears With Curvilinear Shaped Teeth Cut by a Hob Cutter

[+] Author and Article Information
Jui-Tang Tseng

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30010, Republic of China

Chung-Biau Tsay1

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30010, Republic of China

1

Author to whom correspondence should be addressed.

J. Mech. Des 127(5), 982-987 (Oct 07, 2004) (6 pages) doi:10.1115/1.1876437 History: Received June 07, 2004; Revised October 07, 2004

## Abstract

The generating motion of a cylindrical gear with curvilinear shaped teeth cut by a CNC hobbing machine is proposed. On the basis of the cutting mechanism and the gear theory, the surface equation of this type of gear is developed as a function of hob cutter design parameters. Computer graphs of the curvilinear-tooth gear are presented based on the developed gear’s mathematical model, and the tooth surface deviations due to machine-tool settings with nominal radius of circular tooth traces are also investigated.

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Topics: Gears , Equations

## Figures

Figure 1

A schematic drawing of a 6-axis CNC hobbing machine

Figure 2

Generating method of a curvilinear-tooth gear cut by hob cutters

Figure 3

Geometry of the straight-edged cutting blade and worm-type hob cutter

Figure 4

Relations between the hob cutter and cutting blade coordinate systems. (a) Relationship between coordinate systems Sc and Sf . (b) Relationship between coordinate systems S1 and Sf .

Figure 5

Coordinate systems of the hob cutter and CNC hobbing machine

Figure 6

Computer graph of the curvilinear-tooth gear

Figure 7

Different tooth profiles of the curvilinear-tooth gear generated by R=100mm, 120mm, and 200mm

Figure 8

Transverse chordal thickness on a different cross section

Figure 9

Thickness of tooth at addendum circle on a different cross section

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