Machine Design and Mechanical Components
Machine design items test whether you can pick a failure criterion, apply the right correction factors, and then read a catalogue value correctly. Shafts, bearings, gears, belts, keys and bolted joints dominate.
Core rules
- Static failure: von Mises σ′ = √(σ² + 3τ²) compared with S_y; Tresca is more conservative.
- Fatigue: fully reversed endurance limit S_e = k_a k_b k_c k_d k_e S_e′ with S_e′ ≈ 0.5 S_ut for steels.
- Modified Goodman: σ_a/S_e + σ_m/S_ut = 1/n. For combined loading, compute von Mises for both alternating and mean components first.
- Bearings: L₁₀ = (C/P)^p million revolutions, p = 3 for ball, 10/3 for roller.
- Bolted joints: preload F_i ≈ 0.75 F_p, where F_p = A_t S_p; the joint separates when external load exceeds the preload share.
Worked example
A deep-groove ball bearing with C = 30 kN carries P = 3 kN at 1500 rpm. L₁₀ = (30/3)³ = 1000 million revolutions = 1×10⁹ rev. Life in hours = 10⁹/(1500 × 60) = 11,111 h, comfortably beyond a typical 20,000 h target only if the load stays at 3 kN - so check the duty cycle.
Traps
- Using S_ut instead of S_e in the Goodman equation, or omitting the size factor k_b.
- Applying the alternating stress to the mean term when combining bending and torsion.
- Reading bearing C from the catalogue at the wrong speed rating.
- Forgetting that key length is sized on bearing (crushing) stress, not on the shaft diameter alone.