Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts
Question Statement:
A spur gear pair has a velocity ratio of $3.5$. The pinion has 20 teeth and transmits power at a module of $4\text{ mm}$. Calculate the center-to-center distance between the pinion and gear shafts in $\text{mm}$.
Answer Key:
180
Step-by-Step Solution & Explanation
Given:
- Number of teeth on pinion $T_p = 20$
- Velocity ratio $i = 3.5$
- Teeth on gear $T_g = i \times T_p = 3.5 \times 20 = 70$
- Module $m = 4\text{ mm}$
Pitch circle diameter of pinion:
$d_p = m \times T_p = 4 \times 20 = 80\text{ mm}$
Pitch circle diameter of gear:
$d_g = m \times T_g = 4 \times 70 = 280\text{ mm}$
Center-to-center distance $C$:
$C = \frac{d_p + d_g}{2} = \frac{80 + 280}{2} = \frac{360}{2} = 180\text{ mm}$