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Diagonal shaving of an involute pinion: optimization of the geometric and kinematic parameters for the pinion finishing operation

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Abstract

Investigation of diagonal shaving of an involute pinion and optimization of parameters for the pinion finishing operation and of the shaving cutter design are the objectives of the current research. The paper covers the following topics: (1) analysis of the local topology of the pinion tooth surface and shaving cutter; (2) exploration of the parameters of geometry of contact between the involute tooth surfaces of the pinion and the shaving cutter; (3) determination of the optimum parameters of the shaving cutter design and of the kinematics of the diagonal shaving operation. An approach for the computation of the optimum parameters for the diagonal shaving operation of an involute pinion is developed. The approach is based on fundamental results in the theory of gearing obtained by Buckingham (Analytical mechanics of gears, Dover Publications, New York). The developed approach enables the computation of the optimum parameters for the gear finishing operation. Its application can be easily extended to and employed for the optimization of parameters for other methods of rotary shaving operations of involute and non-involute pinions, i.e., axial (transverse or conventional) shaving, tangential (or underpass) shaving, and plunge shaving operations. Computer simulation of the diagonal shaving operation proves that application of the developed approach enables shaving time reduction or reduction of the actual pinion tooth surface deviation from the true involute tooth surface.

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Abbreviations

C :

Center distance

C s :

Machining surface of a shaving cutter

K :

Point of contact of a pinion tooth surface P p and the shaving cutter tooth surface C s

N c :

Number of shaving cutter teeth

N p :

Number of pinion teeth to be machined

P p :

Tooth surface of the pinion to be machined

R :

Auxiliary (phantom) rack

d b,p :

Pinion base diameter

d b,c :

Shaving cutter base diameter

m :

Modulus

P b :

Base pitch

u :

Tooth ratio

Σ:

Crossed-axes angle

λ b,p :

Pinion base lead angle (λ b,p=90°−ψ b,p)

φ n :

Normal pressure angle

ψ c :

Shaving cutter pitch helix angle

ψ b,c :

Shaving cutter base helix angle

ψ b,p :

Pinion base helix angle

ψ p :

Pinion pitch helix angle

ω c :

Shaving cutter rotation

ω p :

Pinion rotation

c:

Shaving cutter to be applied

p:

Pinion to be machined

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Authors and Affiliations

  1. Innovation Center, Eaton Corporation, 26201 Northwestern Highway, Southfield, MI, 48037, USA

    Stephen P. Radzevich

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  1. Stephen P. Radzevich
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Correspondence to Stephen P. Radzevich.

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Radzevich, S.P. Diagonal shaving of an involute pinion: optimization of the geometric and kinematic parameters for the pinion finishing operation. Int J Adv Manuf Technol 32, 1170–1187 (2007). https://doi.org/10.1007/s00170-006-0439-0

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  • DOI: https://doi.org/10.1007/s00170-006-0439-0

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