Design of Machine Elements
What you must command
Design philosophy (factor of safety, allowable stress), failure theories (maximum principal stress, maximum shear, distortion energy), fatigue design (S–N curve, endurance limit, Goodman and Soderberg lines), and the design of shafts, keys, couplings, bearings, bolts, springs, belts, and clutches. Know standard thread and bearing designations.
Traps that appear in questions
- Factor of safety: define against yield or ultimate - the question usually specifies.
- Distortion energy (von Mises) is preferred for ductile materials; maximum shear theory is conservative.
- Fatigue: mean stress shifts the allowable alternating stress; Goodman is the common conservative line.
- Bearing life: L₁₀ = (C/P)^p million revolutions, with p = 3 for ball bearings and 10/3 for roller bearings.
- Springs: Wahl factor corrects for curvature and direct shear; ignore it and the answer is slightly off.
- Bolted joints: preload matters; do not assume the full applied load is carried by the bolt alone.
Worked rule of thumb
For a shaft transmitting power P at speed N, torque T = 60P/(2πN). Example: P = 15 kW at 1500 rpm gives T = 60 × 15 000/(2π × 1500) ≈ 95.5 N·m. For a solid shaft in pure torsion with allowable shear τ, d = (16T/(πτ))^(1/3). With τ = 40 MPa: d = (16 × 95.5/(π × 40×10⁶))^(1/3) ≈ (1.216×10⁻⁵)^(1/3) ≈ 0.023 m, or 23 mm - round up to a standard size.
For a ball bearing with C = 30 kN and P = 6 kN, L₁₀ = (30/6)³ = 125 million revolutions - a quick, reliable check.