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An approach for design optimization of helical gear pair with balanced specific sliding and modified tooth profile

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Abstract

A unique perspective in design optimization of helical gear pair has been emerged and presented in this article. Specific sliding needs to be balanced for enhancing wear and scuffing resistance of helical gears. Optimized modification in tooth profile has immense benefits in gear operations. Effect of profile shift and specific sliding on design optimization of helical gear pair have been studied and found to be beneficial of great importance. Preventing undercutting, balancing of wear and bending fatigue strength and centre distance adjustment are some of the advantages of profile tooth modifications. Real-coded genetic algorithm (RCGA) has been used to attain minimum volume of helical gear pair. Profile shift coefficients for gear and pinion have been included as design variables along with mostly used generic design variables, module, face width and number of teeth on pinion. Specific sliding, transverse contact ratio and face width constraint along with other strength requirements are the design constraints. The optimal design solutions obtained with and without profile shift are recorded and compared with commercially used software for validation. 3D computer-aided design (CAD) models have been developed by using the optimized results obtained from RCGA and commercially used software. These CAD models are used for performing finite element analysis (FEA) on the helical gear set for analyzing the stress developed in the gear pair. The developed stress in the helical gear pair is found to be well within the allowable stress limits for the gear pair.

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Abbreviations

b :

Facewidth

\(d_{a_{1}}\) :

Pinion tip diameter

\(d_{a_{2}}\) :

Gear tip diameter

i :

Transmission ratio

F t :

Tangential load

K A :

Application factor

K F α :

Transverse load factor (bending stress)

K F β :

Face load factor (bending stress)

K H α :

Transverse load factor (contact stress)

K H β :

Face load factor (contact stress)

K V :

Dynamic factor

m :

Normal module

m t :

Transverse module

N 1 :

Pinion rotational speed

r b :

Base diameter

T :

Torque

t s t :

Starting time

V :

Volume of helical gear pair

x 1 :

Pinion profile shift

x 2 :

Gear profile shift

Y F :

Form factor

Y N T :

Life factor

Y S T :

Stress concentration factor

Y β :

Helix angle factor

Z B :

Single pair tooth contact factor (Pinion)

Z D :

Single pair tooth contact factor(Gear)

Z E :

Elasticity factor

Z H :

Zone factor

Z L :

Lubrication factor

z 1/z 2 :

Number of teeth on pinion/gear

Z 𝜖 :

Contact ratio factor

Z β :

Helix angle factor

ρ :

Density

σ F P :

Nominal permissible bending stress

σ H P :

Nominal permissible contact stress

σ F l i m :

Allowable bending stress

σ H l i m :

Allowable contact stress

α t :

Transverse pressure angle

𝜖 α :

Transverse contact ratio

1:

Pinion

2:

Gear

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Acknowledgements

The authors would like to thank Mr. Chinmay Joddar, Manager - Design and Development, New Allenberry Works, Kolkata, India, for helping in validation part with commercially used software.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Patna, Patna, India

    Paridhi Rai & Asim Gopal Barman

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  1. Paridhi Rai
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  2. Asim Gopal Barman
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Correspondence to Asim Gopal Barman.

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Rai, P., Barman, A.G. An approach for design optimization of helical gear pair with balanced specific sliding and modified tooth profile. Struct Multidisc Optim 60, 331–341 (2019). https://doi.org/10.1007/s00158-019-02198-7

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