Machine Elements and Design
Machine elements and design questions test selection and sizing of gears, bearings, shafts, belts, fasteners, springs and fits, plus failure theories and design factors. The emphasis is on load paths, ratings and units rather than catalogue recall.
Core rules
- Gear ratio i=N2/N1=ω1/ω2; ideal torque multiplies by i while speed divides by i. Power is conserved apart from losses.
- For a ball bearing, L10=(C/P)^p million revolutions, with p=3 for ball bearings and 10/3 for roller bearings; C and P must use the same units.
- Shaft design under combined bending and torsion uses equivalent stress; use a fatigue factor and stress-concentration factor at shoulders.
- A key resists torque by shear: τ=F/(Lw), with F=T/r. Check bearing pressure on the side, not only shear.
- Interference fits and tolerances must specify hole and shaft limits; a clearance fit has positive minimum clearance.
Worked example
A 20-tooth pinion drives a 60-tooth gear. Input torque is 10 N·m at 1500 rpm. Ratio i=60/20=3. Ideal output torque is 30 N·m and output speed is 500 rpm. Input power P=Tω=10×(1500×2π/60)=1571 W; the output power is also about 1571 W before losses, confirming consistency.
Traps
- Multiplying torque by the speed ratio instead of the gear ratio.
- Using bearing life with C in kN and P in N without converting.
- Designing a key for torque divided by radius but forgetting the key length.
- Treating a nominal diameter as sufficient without tolerance class.
- Ignoring service factors for shock or reversing loads.