Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts
Question Statement:
A spur gear in a tractor gearbox has a module $m = 6\text{ mm}$, face width $b = 60\text{ mm}$, and $T = 25$ teeth. The allowable bending stress of the gear material is $\sigma_b = 140\text{ MPa}$. Using the Lewis equation with Lewis form factor $Y = 0.369$, the beam strength (Lewis bending load capacity $F_b = \sigma_b \cdot b \cdot m \cdot Y$) of the gear tooth in $\text{kN}$ is ________ (round off to 2 decimal places).
Answer Key:
18.60
Step-by-Step Solution & Explanation
The beam strength of a spur gear tooth according to the Lewis formula is:
$F_b = \sigma_b \cdot b \cdot m \cdot Y$
Where:
• $\sigma_b = 140\text{ MPa} = 140\text{ N/mm}^2$
• Face width $b = 60\text{ mm}$
• Module $m = 6\text{ mm}$
• Lewis form factor $Y = 0.369$
$F_b = 140 \times 60 \times 6 \times 0.369 = 18,597.6\text{ N} \approx 18.60\text{ kN}$