Mathematical Modelling of an Arch Tooth Surface as an Envelope

N.R. Shcherbakov; А.M. Bubenchikov; S.M. Kazakavitschyus

doi:10.4028/www.scientific.net/AMM.756.442

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 756Mathematical Modelling of an Arch Tooth Surface as...

Mathematical Modelling of an Arch Tooth Surface as an Envelope

Abstract:

We consider a gear with parallel rotation axes of an input and output part (spur gear), the input part having so-called arch teeth. We found the equation of the surfaces family for the arch tooth, the envelope of which is the tooth surface of the output part. We obtained an analytical solution of the equation that results from the condition of enveloping, which allowed to record parametric equations of the envelope determining the tooth surfaces of the output part.

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Periodical:

Applied Mechanics and Materials (Volume 756)

Pages:

442-446

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.756.442

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Online since:

April 2015

Authors:

N.R. Shcherbakov*, А.M. Bubenchikov, S.M. Kazakavitschyus

Keywords:

Arch Teeth, Envelope of the Surfaces Family

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References

[1] Litvin F. L., Theory of Gearing., Washington, D.C.: NASA RP-1212 (AVSCOM 88-CC035), (1989).

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[2] Shcherbakov N.R., Zakharkin N.V., Geometrical simulation of the driving gear detail surface as an envelope, Tomsk State University. Journal of Mathematics and Mechanics. Tomsk: TSU, 4, 20 (2012) 50-55.

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