Subtopic: Power transmission systems – gear trains, differential, final drives and power take-off
Question Statement:
In a tractor differential gear unit, the ring gear (crown wheel) rotates at $50\text{ rpm}$. While taking a turn, the inner drive wheel slows down to $30\text{ rpm}$. The rotational speed of the outer drive wheel in $\text{rpm}$ is ________ (answer in integer).
Answer Key:
70
Step-by-Step Solution & Explanation
In a standard bevel gear differential mechanism, the crown wheel speed is the arithmetic mean of the two axle shaft speeds:
$N_{\text{crown}} = \frac{N_1 + N_2}{2}$
Given $N_{\text{crown}} = 50\text{ rpm}$ and $N_1 = 30\text{ rpm}$:
$50 = \frac{30 + N_2}{2} \implies 100 = 30 + N_2 \implies N_2 = 70\text{ rpm}$