A worm gear set is designed to have pressure angle of 30° which is equal to the helix angle. The efficiency of the worm gear set at an interface friction of 0.05 is

Concept:

Interface friction, μ

Efficiency, \(\eta = \frac{{\tan \lambda \left( {\cos \phi - \mu \tan \lambda } \right)}}{{\cos \phi \tan \lambda \; + \;\mu }}\)

\(\tan \lambda = - \mu + \sqrt {1 - {\mu ^2}} \)

Calculation:

Given, μ = 0.05, ϕ = 30°

\(\tan \lambda = - \mu + \sqrt {1 - {\mu ^2}} = - 0.05 + \sqrt {1 - {{0.05}^2}} = 0.948{\rm{\;}}\)

tan λ = 0.948

cos ϕ = 0.866

Therefore, 

\(\eta = \frac{{0.948\;\left( {0.866 - 0.05 \times 0.948} \right)}}{{0.866 \times 0.948 + 0.05}} = 0.8910\;\)