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RESEARCH PAPERS

# On Satisfaction of the Fifth Necessary Condition of Proper Part Surface Generation in Design of Plunge Shaving Cutter for Finishing of Precision Involute Gears

[+] Author and Article Information

Eaton Automotive, Innovation Center, 26201 Northwestern Highway, Southfield, MI 48076stephenpradzevich@eaton.com

However, a principal difference is observed. While tooth flanks of helical gears with crossed axis make point contact, the gear tooth surface makes line contact with the plunge shaving cutter tooth surface.

To the best of the author’s knowledge, a mapping similar to the $c$-mapping is used by Gleason. This mapping is a particular case of the $c$-mapping. It is featuring the mapping plane $M$ through the axis of rotation of the helical gear. The simplified $c$-mapping is used for the analysis of gear tooth flank geometry and for some other purposes. The simplified $c$-mapping cannot be implemented for the analysis of meshing of gears with crossed axis; e.g., for the analysis of plunge shaving operation.

J. Mech. Des 129(9), 969-980 (Aug 21, 2006) (12 pages) doi:10.1115/1.2748452 History: Received June 05, 2006; Revised August 21, 2006

## Abstract

In this paper, a novel modified scheme and effective computer representation for design of a plunge shaving cutter is presented. The paper aims to develop a novel design of shaving cutter for plunge shaving of precision involute gears. The study is carried out on the premise of satisfaction of the fifth necessary condition of proper part surface generation (PSG) when designing the plunge shaving cutter. In the current study, the author’s earlier developed DG/K method of surface generation is used together with the principal elements of analytical mechanics of gears. (The DG/K method is based on fundamental results obtained in differential geometry of surfaces, and on kinematics of multi-parametric motion of a rigid body in the $E3$ space. The interested reader may wish to go for details to the monograph: Radzevich, S.P., Fundamentals of Surface Generation, Monograph, Kiev, Rastan, 2001, 592 pp., and to: Radzevich, S.P., Sculptured Surface Machining on Multi-Axis NC Machine, Monograph, Kiev, Vishcha Schola, 1991, 192 pp.) In the particular case under consideration, the method employs (a) an analytical description of the gear tooth surface to be machined, (b) configuration of the plunge shaving cutter relative to the involute gear, (c) analytical representation of the coordinate systems transformations, and (d) the fifth condition of proper PSG that is adapted to finishing of precision involute gears. The fifth condition of proper PSG is investigated in the paper. On the premise of the obtained results of the investigation, a novel design of plunge shaving cutter for finishing of precision involute gears is proposed. The developed novel design of plunge shaving cutter can be used on shaving machines available on the market, e.g. on Gleason’s new Genesis$™$ 130SV computer numerical control (CNC) shaving machine.

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## Figures

Figure 3

The applied coordinate systems

Figure 4

An example of violation of the fifth necessary condition of proper PSG in gear shaving operation

Figure 5

Mapping of the gear tooth flank G onto the common plane M through the pitch point P (the plane M is at the pitch lead angle λg to the gear axis of rotation Og)

Figure 6

The shape and parameters of the normalized c-map of the SAP boundary curve of the gear tooth (the gear module m=10mm, teeth number Ng=53, the pitch helix angle ψg=30deg, helix hand—right hand, face width Fg=50mm)

Figure 7

To the analysis of distortions when mapping the gear tooth surface G onto the plunge shaving cutter tooth flank T (1 – not shaved portions of the gear tooth flank)

Figure 8

The analysis of tooth flank distortion when mapping the gear flank G onto the plunge shaving cutter flank T

Figure 9

Modified tooth of a plunge shaving cutter of the proposed design

Figure 10

The major design parameters of the developed design of plunge shaving cutter tooth

Figure 11

Use of c-mapping for determining of axial profile of the plunge shaving cutter outer surface TLm

Figure 12

Example of the determining of parameters of the plunge shaving cutter outer surface TLm

Figure 13

Pointing of the shaving cutter bottomland

Figure 14

The shaving cutter serrations

Figure 15

The modified serrations of the plunge shaving cutter tooth

Figure 16

Serrations offset in design of conventional shaving cutter (a), and in the design of plunge shaving cutter (b)

Figure 1

The principal kinematics of plunge shaving operation

Figure 2

The analytical description of screw involute tooth surface G of a gear

## Errata

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