Mechanical Design of Machine Elements
Domain scope
Mechanical Design of Machine Elements covers shafts, gears, bearings, fasteners, keys, springs, belts, and fits. The exam tests whether you can select a component size from static or fatigue strength, apply standards, and recognize combined loading.
Core rules
- Static design compares working stress with yield strength divided by a safety factor.
- Torsion in a solid round shaft: τ = 16T/(πd³). Bending: σ = 32M/(πd³).
- Combined von Mises equivalent stress: σ_eq = √(σ² + 3τ²).
- Fatigue uses the endurance limit and stress concentration: Goodman gives 1/n = σ_a/S_e + σ_m/S_ut.
- Gear ratio = N₂/N₁ = d₂/d₁; module m = d/N.
- Bearing rating life L₁₀ = (C/P)^p, with p = 3 for ball bearings and 10/3 for roller bearings.
Worked example
A solid shaft transmits 500 N·m with allowable shear stress 40 MPa and negligible bending. Convert torque to N·mm: 500,000 N·mm. Then d = [16T/(πτ)]^(1/3) = [16×500,000/(π×40)]^(1/3) = (63,662)^(1/3) ≈ 39.9 mm. Select 40 mm or the next standard size. Note that MPa = N/mm², so the units are consistent.
Traps
- Forgetting to convert N·m to N·mm before using the torsion formula.
- Using ultimate strength as the allowable stress instead of yield or endurance data.
- Ignoring keyway, shoulder, or thread stress concentrations.
- Mixing bearing life in revolutions with life in hours.
- Applying the wrong exponent p for the bearing type.