Question Bank • QB_FP_ADV_046 NAT • 2 Marks

Section 3: Farm Power

Tractors and Power Tillers

Subtopic: Power transmission systems – gear trains, differential, final drives and power take-off

Question Statement:

The bevel crown wheel (differential cage) of a tractor drives the rear wheels through a bevel gear differential. The crown wheel rotates at $N_{\text{cage}} = 120\text{ rpm}$. While making a sharp turn in the field, the inner driving wheel is restrained so that it rotates at $N_{\text{inner}} = 40\text{ rpm}$. The rotational speed of the outer driving wheel ($N_{\text{outer}}$) in $\text{rpm}$ is ________ (answer in integer).

Answer Key:

200

Step-by-Step Solution & Explanation

``` Bevel Differential Kinematics: N_cage = (N_left + N_right) / 2 ``` **Step-by-step Calculation:** 1. Differential kinematic relation: $N_{\text{cage}} = \frac{N_{\text{inner}} + N_{\text{outer}}}{2}$ 2. Rearranging for outer wheel speed: $N_{\text{outer}} = 2 N_{\text{cage}} - N_{\text{inner}}$ 3. Substituting values: $N_{\text{cage}} = 120\text{ rpm}, \quad N_{\text{inner}} = 40\text{ rpm}$ $N_{\text{outer}} = (2 \times 120) - 40 = 240 - 40 = 200\text{ rpm}$
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