| name | contact-fatigue |
| description | Contact fatigue — Hertz contact, pitting life, Lundberg-Palmgren subsurface fatigue model, RCF, spalling, gear pitting, bearing life rating, surface vs. subsurface initiation, ISO 6336 pitting resistance. |
| metadata | {"priority":7,"promptSignals":{"phrases":["contact fatigue","rolling contact fatigue","pitting","spalling","surface fatigue","gear pitting"],"minScore":3}} |
Contact Fatigue (Rolling Contact Fatigue) — Complete Skill
Contact Fatigue Mechanisms
Rolling Contact Fatigue (RCF): cyclic Hertzian stress at rolling contact → fatigue crack initiation and propagation
Two main modes:
- Subsurface initiation: at depth of max shear stress z_max (Lundberg-Palmgren); inclusions act as stress raisers
- Surface initiation: at asperity contacts, lubricant film breakdown; micro-pitting precursor
Failure modes:
- Pitting: small craters (mm scale); surface-initiated; lubricant entrapment in cracks
- Spalling: large area shallow craters; subsurface-initiated; hardened case cracking
- Micro-pitting: surface roughness scale (< 10 μm deep); thin EHL film (Λ < 0.7)
- Delamination: ductile materials; subsurface crack parallel to surface → platelets
Hertz Contact Stress
Sphere on Flat (or Ball on Raceway)
Maximum contact pressure:
p₀ = (3P / (2πa²)) [Pa; a = contact radius]
a = (3PR_eff / 4E')^(1/3) [m; P = normal force; R_eff = effective radius; E' = reduced modulus]
Reduced modulus:
1/E' = (1-ν₁²)/E₁ + (1-ν₂²)/E₂
Effective radius:
1/R_eff = 1/R₁ + 1/R₂ [for same-sign curvatures]
Cylinder on Cylinder (Line Contact)
Half-width of contact:
b = √(4PR_eff / (πLE')) [m; L = contact length]
Maximum Hertz pressure:
p₀ = 2P / (πbL) [Pa]
Subsurface stresses (line contact):
Max shear stress τ_max ≈ 0.30 p₀ at depth z = 0.786b
Max orthogonal shear stress τ_orth = 0.25 p₀ at z = 0.5b (first fatigue crack-relevant quantity)
Lundberg-Palmgren Life Model
Basic life theory (bearing pitting life):
ln(1/S) ∝ N_cycles^c × τ_orth^h × V / z_max^e
where S = survival probability; V = stressed volume; τ_orth = orthogonal shear stress; z_max = depth
Simplified bearing L10 life formula:
L₁₀ = (C/P)^p [million revolutions]
C = dynamic load capacity [N]; P = equivalent dynamic load [N]
p = 3 (ball bearings); p = 10/3 (roller bearings)
Modified life (ISO 281):
L_nm = a₁ × a_ISO × L₁₀
a₁ = reliability factor (a₁=1 for 90% survival; a₁=0.21 for 99%)
a_ISO = life modification factor (accounts for lubrication, contamination)
a_ISO:
a_ISO = f(κ, e_C) [tabulated function]
κ = viscosity ratio = ν_actual / ν_required; e_C = contamination factor (0=clean, 1=heavily contaminated)
κ ≥ 1 → a_ISO = 1.0–10 depending on cleanliness
κ < 0.4 → a_ISO < 1.0 (film breakdown)
Gear Surface Fatigue (Pitting) — ISO 6336
Contact stress (AGMA/ISO):
σ_H = Z_E × Z_H × Z_ε × Z_β × √(F_t/(b × d_w1) × (u+1)/u × K_A × K_v × K_Hβ × K_Hα)
where:
Z_E = elasticity factor [√MPa]; Z_H = zone factor (tooth geometry); Z_ε = contact ratio factor
Z_β = helix factor; F_t = tangential force; b = face width; d_w1 = pitch diameter; u = gear ratio
Allowable contact stress:
σ_H,lim = σ_H,lim_basic × Z_NT × Z_L × Z_v × Z_R × Z_W × Z_X
σ_H,lim_basic = material pitting fatigue limit (from ISO 6336-5 material tables):
| Material | σ_H,lim [MPa] |
|---|
| Through-hardened 300 HB | 500–600 |
| Case hardened 55–64 HRC | 1300–1500 |
| Nitrided 700–900 HV | 1000–1200 |
Safety factor for pitting:
S_H = σ_H,lim / σ_H ≥ 1.0 (ISO 6336; practical ≥ 1.1–1.2)
EHL Film Thickness and Λ Ratio
Specific film thickness:
Λ = h_min / √(Ra₁² + Ra₂²) [h_min = minimum EHL film thickness; Ra = surface roughness]
Pitting susceptibility:
| Λ | Risk |
|---|
| > 3 | Full film; negligible surface fatigue |
| 1–3 | Mixed; some surface fatigue risk |
| 0.7–1.0 | Micro-pitting likely |
| < 0.7 | Severe micro-pitting; rapid wear |
EHL minimum film thickness (Dowson-Higginson, line contact):
h_min = 2.65 × R × G^0.54 × U^0.70 / W^0.13
G = αE' (material parameter); U = η₀u_s/(E'R) (speed parameter); W = P/(E'RL) (load parameter)
α = pressure-viscosity coefficient [Pa⁻¹]; η₀ = dynamic viscosity at ambient P; u_s = sum velocity
Surface Fatigue Life Prediction (Zaretsky Model)
Alternative to Lundberg-Palmgren:
L₁₀ ∝ τ₀^(-n) × V^(-1/e) × N_max^(1-n)
n = fatigue exponent (9 for steel); τ₀ = critical shear stress range
Accounts for stressed volume more explicitly
Contact Fatigue Testing Standards
ASTM E2509: standard for contact fatigue test — disc-on-disc configuration
NASA/ISO: rolling contact fatigue test with test rig at controlled Hertz stress
FZG pitting test: ISO 14635-1; gear test rig; failure load stage for pitting
S-N curve for contact fatigue:
σ_H,lim at 10⁷ cycles (endurance limit for pitting); slope b_H ≈ -1/8 (shallower than bending fatigue)
For N < 10⁷: σ_H,N = σ_H,lim × (N_ref/N)^(1/b_H)
Influence of Residual Stress
Compressive residual stress (shot peening, case hardening):
Reduces effective R ratio at crack tip → delays subsurface crack initiation
σ_H,lim improvement: +10–20% with shot peening (case-hardened gears)
Optimal depth of compressive zone: 0.5–2× depth of max shear stress z_max
Tensile residual stress (grinding burns):
Accelerates surface fatigue; look for grinding pattern in thermographic inspection
Standards
| Standard | Scope |
|---|
| ISO 6336 | Gear strength — pitting resistance (Part 2) |
| ISO 281 | Rolling bearing life rating |
| AGMA 2101 | Gear rating pitting and bending |
| ASTM E2509 | Contact fatigue test standard |
| ISO 14635-1 | FZG gear lubricant test |
| DIN 3990 | Gear calculation (equivalent to ISO 6336) |
Output
Provide: contact configuration (point/line/elliptical), Hertz pressure p₀ [MPa], contact half-width a or b [mm], depth of max shear stress z_max [mm], τ_orth [MPa], L10 life [million cycles or hours] with ISO 281 modification factors (a₁, a_ISO, κ), specific film thickness Λ ratio vs. threshold, pitting safety factor S_H (ISO 6336), material pitting limit σ_H,lim [MPa], residual stress effect [%], failure mode prediction (pitting/spalling/micro-pitting), and applicable standard (ISO 6336, ISO 281, AGMA 2101).
