Design of Machine Elements
From transcript: 20ME510 DME 1 (D) · 20ME610 DME 2 (C) · 20ME68L Design & CAMA Lab (A)
Cheat sheet
Formulas
Shaft ASME elliptic (approx): (32n/(π d³)) √((Km M)²+(Kt T)²) ≤ σ_allow (forms vary by code)
Combined: σx = 32 M /(π d³) ; τ = 16 T /(π d³) ; then von Mises / max shear
Key shear: τ = F /(w L) ; crushing σ = F /(t/2 · L) (approx geometries)
Bolt preload Fi ; external load share C = kb/(kb+km) ; Fb = Fi + C P ; Fm = Fi − (1−C)P
Weld throat t = 0.707 h (fillet); τ = P /(0.707 h L)
Helical spring: τ = K_w (8 F D)/(π d³) ; K_w Wahl ≈ (4C−1)/(4C−4)+0.615/C ; C=D/d
Spring rate k = G d⁴ /(8 D³ N_a)
Lewis gear bending: σ = W_t /(m b Y) (Y Lewis form factor)
AGMA adds dynamic Kv, geometry J, overload Ko, etc.
Bearing L10 life: L10 = (C/P)^p × 10^6 rev ; p=3 ball, 10/3 roller
Equivalent P = X Fr + Y Fa (catalog X,Y)
Fatigue design: σa/Se + σm/Sut ≤ 1/n (Goodman)
Column/shaft whirling / critical speed awareness for long shafts
σ_all = Sut / n or Sy / n (static)
Fatigue: 1/σa / Se + σm / Sut = 1/n (Goodman approx.)
Shaft ASME elliptic (common form): d³ ∝ √( (Km M)² + (Kt T)² ) / τ_all
Bolt: Fi + C P (preload + load factor sharing)
Spring: τ = Ks (8 F D)/(π d³) ; Ks Wahl factor
Lewis gear: σb = Wt / (b π m y)
Definitions
- Design process
- Specs → concepts → analysis → iterate → drawings/DFM
- Yield vs ultimate based design
- Ductile often Sy/n ; brittle Sut/n
- Endurance Se'
- Polished rotating beam baseline then Marin factors
- Stress concentration Kt / Kf
- Geometric / fatigue stress concentration
- Preload
- Initial bolt tension after tightening
- Joint constant C
- Fraction of external load taken by bolt
- Wahl factor
- Curvature + shear correction in spring wire
- L10 life
- Life 90% of bearings reach at given load
- Module / diametral pitch
- Gear tooth size metrics
- Factor of safety
- Accounts uncertainty — not a substitute for analysis
- Endurance limit Se
- Fatigue strength amplitude as N→∞ (steels approx.)
- Stress concentration Kt
- σ_max / σ_nom at notches, holes, keyways
- Preferred fits
- Hole/shaft basis — clearance, transition, interference
Topic-wise short notes
Shafts, keys, fasteners
- Shafts transmit T and often M — size from fatigue at seats/shoulders.
- Shoulder fillets, snap rings, keyways create Kt — use charts.
- Couplings: rigid vs flexible; alignment sensitivity.
- Bolted joints: separation when Fm→0 — maintain preload.
- Power screws: self-locking if lead angle < friction angle.
Gears, bearings, springs
- Spur first-pass Lewis; refine AGMA; helical quieter higher capacity.
- Idlers change direction not ratio magnitude (ideal).
- Deep-groove ball vs cylindrical/taper roller — load direction.
- Spring surge/buckling for long compression springs.
- Clutches/brakes: torque capacity μ R F ; heat dissipation duty cycle.
Shafts, keys, couplings
- ASME code elliptical vs max-shear — know which syllabus uses.
- Hollow shafts: better stiffness/mass for same OD sometimes.
Fasteners, welds, springs, gears, bearings
- Weld design: primary shear + secondary from moment about CG of group.
- Eccentric loads on bolt groups — vector sum of primary/secondary.
Design for fatigue workflow
- Find alternating/mean at hot spot → apply Kt/Kf → Marin Se → Goodman/n.
- Infinite life if below Se; else Basquin/S–N finite life.
- Surface treatments (shot peen, carburize) raise fatigue strength.
Exam traps & quick notes
- Iterate: load → failure mode → material → size → check deflection/buckling.
- DFMA: reduce parts, design for machining/fixture access.
- Project: BAJA steering/brakes; Fleurette jigs — load paths & tolerances.
- State theory of failure and loading (static/fatigue) every design.
- Units: N·mm vs N·m — classic exam trap.
- Keys/set screws sized for torque with shock factors.
- Bearings: check C catalog dynamic rating; static Co for shock.
- Gears: check bending AND wear (contact) stresses.
- DFM: fillets for Kt, standard sizes, grind allowances.
Comprehensive notes
Shafts, keys, fasteners
Combined bending+torsion; key shear/crushing; bolted joints under eccentric load; welded throat size.
Gears, bearings, springs
Spur/helical strength & wear; L10 bearing life; helical spring surge & buckling.
External: SKF bearing calculator ↗ AGMA gear standards intro ↗
Shafts, keys, couplings
Combined bending+torsion criteria; ASME elliptic forms; key shear/crushing; fatigue stress concentration at seats/shoulders.
External: NPTEL ↗ Engineering Toolbox ↗
Fasteners, welds, springs, gears, bearings
Bolt preload and load factor C; weld throat; helical spring Wahl factor; Lewis/AGMA gear bending; L10 bearing life. Iterate size ↔ deflection ↔ package.
External: NPTEL ↗ Engineering Toolbox ↗
Interview Q&A for this subject
Q: Why preload bolts?
A: Increases fatigue life of bolts under cyclic external load by sharing via joint stiffness; prevents separation.
External: ASQ / quality ↗ MIT OCW ↗