Machine Design
Machine Design
The paper tests static failure theories, fatigue design, shaft–key–bolt joints, bearings, springs, and design for manufacture. Candidates lose marks by choosing the wrong failure criterion.
Core rules
- Static yielding: von Mises equivalent stress σ′ = √(σ_x² − σ_xσ_y + σ_y² + 3τ_xy²); Tresca uses maximum shear. Compare with yield strength divided by the design factor.
- Fatigue: modified Goodman line σ_a/S_e + σ_m/S_ut = 1/n; Soderberg uses S_y in place of S_ut and is more conservative. Include size, surface, load, and reliability factors when adjusting S_e.
- Bolted joints: preload controls joint separation; check bolt and member stiffness. Eccentric loading adds shear and moment.
- Keys: check shear τ = F/(wL) and bearing σ_b = F/((t/2)L), where F = 2T/d for a shaft of diameter d.
Worked example
A 50 mm diameter shaft transmits 200 N·m through a key 10 mm wide, 8 mm high, and 50 mm long. Tangential force F = 2T/d = 2 × 200/0.05 = 8000 N. Shear stress = F/(wL) = 8000/(0.010 × 0.050) = 16 MPa. Bearing stress uses half the key height: 8000/(0.004 × 0.050) = 40 MPa. Compare these with the key material's allowable shear and bearing stresses, not with the shaft stress.
Traps
Using S_y in Goodman instead of S_ut; using the full key height for bearing; ignoring stress concentration at a shoulder; applying a static factor of safety to a fatigue load without an endurance limit; and forgetting that a longer key does not help if bearing governs.