Question Bank • QB_FM_018 NAT • 2 Marks

Section 2: Farm Machinery

Machine Design

Subtopic: Overload safety devices used in farm machinery

Question Statement:

A PTO-driven rotary mower driveline incorporates a shear bolt safety device situated on an input flange at a radial distance of $r = 60\text{ mm}$ from the shaft centerline. The shear bolt is made of steel with an ultimate shear strength of $\tau_{ult} = 320\text{ MPa}$. If the driveline is designed to safely trip when the transmitted torque reaches $T = 900\text{ N}\cdot\text{m}$, the required nominal diameter of the shear bolt in $\text{mm}$ is ________ (round off to 2 decimal places). Take $\pi = 3.1416$.

Answer Key:

7.73

Step-by-Step Solution & Explanation

1. Tangential shearing force on the bolt ($F$): $F = \frac{T}{r} = \frac{900\text{ N}\cdot\text{m}}{0.060\text{ m}} = 15,000\text{ N}$ 2. Shear stress relationship at failure: $\tau_{ult} = \frac{F}{A} = \frac{F}{\frac{\pi}{4} d^2}$ $d^2 = \frac{4 F}{\pi \tau_{ult}} = \frac{4 \times 15,000}{\pi \times (320 \times 10^6\text{ N/m}^2)} = \frac{60,000}{1.0053 \times 10^9} \approx 5.9683 \times 10^{-5}\text{ m}^2$ $d = \sqrt{5.9683 \times 10^{-5}} = 0.007725\text{ m} \approx 7.73\text{ mm}$
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