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Parametric investigation of the combined effect of whole depth and cutter tip radius on the bending strength of 20° involute gear teeth

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Abstract

Standard 20° spur gears are typically generated with a whole depth of 2.2–2.25 times the module. At the nominal centre distance, this leaves a radial clearance, which is in itself redundant from a functional point of view. However, the intrinsic geometry of the cutting process always results in a non-involute root profile (the trochoid), which is even more pronounced in the case of using a rounded cutter tip in order to increase the strength of the cutting edge. Larger tip radii produce stronger tooth fillets, potentially increasing the bending strength, but reducing the involute part of the tooth. Thereby, they increase the risk of interference with mating gears. This paper performs a parametric investigation of the combined effect of the cutter radius and the dedendum on the clearance and the resulting tooth bending strength using analytical calculations, computerised generation and finite element simulations to determine the exact tooth geometry in search of stronger tooth forms. Non-dimensional modelling is used to obtain results applicable to entire gear families.

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Abbreviations

\({\alpha_o}\) :

Pressure angle

a 12 :

Centre distance

b :

Tooth width

c c :

Cutter tip radius coefficient

c f :

Dedendum coefficient

c k :

Addendum coefficient

c s :

Tooth thickness coefficient

r s :

Form circle radius

\({{t}^{\prime}}\) :

Trochoid tip thickness of the generating rack tooth (sharp tooth)

P N :

Normal force

m :

Module

r b :

Base circle radius (ref. to involute)

r o :

Radius of pitch circle

r g :

Involute base radius (ref. to involute)

r k :

Outside radius

\({\sigma }\) :

Bending stress at tooth critical cross-section

\({\varepsilon }\) :

Contact ratio

t b :

Base Pitch (ref. to involute)

u :

Ref. to non-dimensional gear

i :

Ref. to gear no. i

x :

Addendum modification coefficient

z :

Number of teeth

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Authors and Affiliations

  1. Faculty of Industrial Design Engineering, Delft University of Technology, Landbergstraat 15, 2628 CE, Delft, The Netherlands

    C. Spitas, A. Amani & M. Rajabalinejad

  2. School of Mechanical Engineering, National Technical University of Athens, Athens, Greece

    V. Spitas

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  1. C. Spitas
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Correspondence to C. Spitas.

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Spitas, C., Spitas, V., Amani, A. et al. Parametric investigation of the combined effect of whole depth and cutter tip radius on the bending strength of 20° involute gear teeth. Acta Mech 225, 361–371 (2014). https://doi.org/10.1007/s00707-013-0971-6

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  • DOI: https://doi.org/10.1007/s00707-013-0971-6

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