Subtopic: Power transmission systems – gear trains, differential, final drives and power take-off
Question Statement:
In a tractor power transmission, the input pinion (24 teeth) is in mesh with a gear (46 teeth) on counter shaft and another gear (20 teeth) of counter shaft is in mesh with main shaft gear (50 teeth). The engine is running at 1800 rpm, differential gear ratio is 3.5:1 and final drive ratio is 4:1. If the tractor is fitted with 1.2 m diameter rear wheels, the forward speed of the tractor in km h⁻¹ is _____.
Official Answer Key:
5.5 to 6.5
Step-by-Step Solution & Explanation
• Gearbox reduction = (46/24) × (50/20) = 1.9167 × 2.5 = 4.7917.
• Main-shaft speed = 1800/4.7917 = 375.65 rpm.
• Total further reduction through differential × final drive = 3.5 × 4 = 14.
• Wheel speed = 375.65/14 = 26.83 rpm.
• Wheel circumference = πD = π × 1.2 = 3.7699 m.
• Linear speed = 26.83 rev/min × 3.7699 m/rev = 101.15 m/min = 1.686 m/s = 1.686 × 3.6 ≈ 6.07 km/h, inside the accepted range 5.5–6.5.
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