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Technical Briefs

Tooth Root Strength of Spur and Helical Gears Manufactured With Gear-Shaper Cutters

[+] Author and Article Information
Andrzej Kawalec1

Department of Mechanical and Aerospace Engineering,  Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Polandak@prz.edu.pl

Jerzy Wiktor

Department of Mechanical and Aerospace Engineering,  Rzeszów University of Technology, W. Pola 2, 35-959 Rzeszów, Polandjwiktor@prz.edu.pl

1

Corresponding author.

J. Mech. Des 130(3), 034502 (Feb 05, 2008) (5 pages) doi:10.1115/1.2829909 History: Received July 06, 2006; Revised August 11, 2007; Published February 05, 2008

At the beginning of gear transmission design, mainly simplified methods of gear strength analysis based on ISO or AGMA standards are used. However, they allow for calculation of approximate and sometimes biased stresses. Moreover, ISO standard is generally focused on using racks for gear manufacturing. A method proposed in this paper allows for computation of the parameters of critical section, strength coefficients YF, YS, and tooth root stress σF according to the procedure from ISO standard also in the case of machining gears with gear type tools. The proposed improvement of ISO standard leads to replacement of real gear tool with rack with substitute tip radius ρa0*. The developed method maintains basic assumptions and advantages of ISO standard, including its simplicity. Simultaneously, it allows for computing the maximum tooth root stresses σF: (i) very close to results of accurate geometric analysis and finite element analysis, and (ii) much closer, compared to conventional ISO procedure, to results obtained using AGMA standard.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometric relations in manufacturing transmission manufactured gear-gear tool, the determination of the critical section F‐F according to the ISO standard (3) and the parameters of critical section: sFn, hFe, ρF

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Figure 2

The FE model of a helical gear segment for β1=30deg with boundary conditions: B1, all DOF fixed; B2 and B3, all DOF fixed except radial movements defined in their own local coordinate systems

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Figure 3

The distribution of the effective stresses at tooth root of loaded tooth in the FE model shown in Fig. 2

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Figure 4

The influence of z1 on the maximum tooth root stresses σF for spur gears (β1=0deg) machined with gear tools (G) and racks (R). Symbols are explained in Nomenclature.

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Figure 5

The influence of z1 on parameters of critical section for spur gears (β1=0deg) generated with gear and rack tools

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Figure 6

The influence of the number of teeth z0 of gear tool on the maximum tooth root stresses σF for spur gears (z1=45) machined with gear tools (G) and racks (R)

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Figure 7

The influence of the helix angle β1 on the maximum principal stresses at tooth root σF; z1=45; (enlarged view for β1∊⟨10deg,20deg⟩, σF∊⟨320MPa,420MPa⟩ — right)

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