Question Bank • QB_FP_ADV_049 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 final drive of a farm tractor employs a spur pinion having $Z_p = 12$ teeth meshing with a bull gear having $Z_b = 66$ teeth. The differential shaft rotates at $N_d = 165\text{ rpm}$ and delivers a torque of $T_d = 400\text{ N}\cdot\text{m}$ to the pinion. Assuming a mechanical efficiency of $\eta = 95\%$ for the final drive gear pair, the torque delivered to the rear drive wheel axle in $\text{N}\cdot\text{m}$ is ________ (round off to integer).

Answer Key:

2090

Step-by-Step Solution & Explanation

``` Bull Gear Final Drive: Pinion: Z_p = 12 teeth, Input torque T_d = 400 N*m Bull Gear: Z_b = 66 teeth Efficiency: eta = 95% = 0.95 ``` **Step-by-step Calculation:** 1. Gear reduction ratio ($i$): $i = \frac{Z_b}{Z_p} = \frac{66}{12} = 5.5$ 2. Torque delivered to the wheel axle with efficiency $\eta = 0.95$: $T_{\text{wheel}} = T_d \times i \times \eta$ $T_{\text{wheel}} = 400\text{ N}\cdot\text{m} \times 5.5 \times 0.95 = 2200 \times 0.95 = 2090\text{ N}\cdot\text{m}$
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