gear-fatigue

name	gear-fatigue
description	Gear fatigue — bending fatigue (AGMA 2101/ISO 6336), contact (pitting) fatigue, allowable bending stress, allowable contact stress, life factors, material factors, lubrication correction, micropitting, scuffing, gear fatigue test methods.
metadata	{"priority":7,"promptSignals":{"phrases":["gear fatigue","gear bending fatigue","gear pitting","AGMA 2101 fatigue","ISO 6336 fatigue","gear tooth fatigue"],"minScore":3}}

Gear Fatigue — Complete Skill

Gear Fatigue Fundamentals

Two primary failure modes:

1. Bending fatigue (tooth root cracking): stress concentration at tooth root; cyclic bending from contact force; crack initiates at root fillet → propagates through tooth → tooth fracture
2. Contact (pitting) fatigue: Hertzian contact stress at tooth flank; subsurface crack initiation → surface pitting; progressive destruction of tooth surface

Fatigue loading: Gear tooth experiences one bending stress cycle per revolution (unidirectional loading for most gears) Contact stress cycle: reciprocating (for idler gears); unidirectional (for drive/driven gears) Number of cycles: N_L = 60 × n [RPM] × t [hours] × L_H [design life in hours]

AGMA 2101-D04 (SI) — Allowable Stresses

Bending Stress Number

Fundamental formula: σ_F = W_t × K_o × K_v × K_s × (P_d/F) × (K_H × K_B / J) [AGMA English units; or per AGMA 2101 SI] σ_F = F_t × K_A × K_v × K_Hα / (b × m_t × Y_J) [SI; F_t = tangential force; b = face width; m_t = transverse module; Y_J = geometry factor]

Allowable bending stress number: σ_F_allow = (S_t × Y_N) / (K_T × K_R × SF_F) [MPa; S_t = allowable bending stress at 10⁷ cycles; Y_N = stress cycle factor for bending]

Life factor for bending (Y_N): N_L < 3×10⁶: Y_N > 1.0 (more than endurance limit life → use curve) N_L = 10⁷: Y_N = 1.0 (reference point) N_L > 10⁷: Y_N = 1.3405 × N_L^(-0.0178) [life reduction for long life; material dependent]

Reliability factor K_R: R = 0.99: K_R = 1.50; R = 0.99: 1.00; R = 0.90: 0.80; R = 0.50: 0.70 (varies by material scatter)

Allowable Bending Stress (S_t — AGMA Grade)

Material	Grade	S_t [MPa]
Steel, normalized	Grade 1	170
Steel, through-hardened HRC 25–55	Grade 1	0.533 × HB + 88.3
Carburized & case-hardened, HRC 55–64	Grade 2	380 (typical)
Carburized & case-hardened, Grade 3	Grade 3	450 (clean steel)
Nitrided steel (Nitralloy 135M)	Grade 2	380

Formula for through-hardened: S_t = 0.533 × HB + 88.3 [MPa] (AGMA 2101)

Contact Stress Number (Pitting)

Fundamental contact stress: σ_H = Z_E × √(F_t × K_A × K_v × K_Hβ × Z_R / (b × d₁ × Z_H² × Z_ε² × Z_β²)) [ISO 6336 notation] σ_H = W_t × C_o × C_v × C_s × C_m × C_f / (d_p × F × I) × C_p^0.5 [AGMA; C_p = elastic coefficient]

Allowable contact stress: σ_H_allow = (S_c × Z_N × C_H) / (K_T × K_R × SF_H) [MPa; S_c = allowable contact stress; Z_N = contact life factor; C_H = hardness ratio factor]

Life factor for contact (Z_N): Z_N = 1.0 at N_L = 10⁷; Z_N = 1.4488 × N_L^(-0.023) for N_L < 10⁷ (stronger material for fewer cycles) Z_N = 1.1695 × N_L^(-0.016) for N_L > 10⁷ (conservative; assumes no endurance limit for pitting)

Allowable Contact Stress (S_c — AGMA Grade)

Material	Grade	S_c [MPa]
Steel, through-hardened	Grade 1	2.22 × HB + 200
Carburized, case-hardened HRC 60	Grade 2	1,380
Carburized, Grade 3	Grade 3	1,550
Nitrided (Nitralloy 135M)	Grade 2	1,170
Cast iron	Grade 1	380

ISO 6336 Method B — Bending and Contact Fatigue

Bending (ISO 6336-3)

Tooth root stress: σ_F = F_t / (b × m) × K_A × K_v × K_Fα × K_Fβ × Y_F × Y_S × Y_β × Y_B [MPa] Y_F = form factor (tooth geometry — from ISO 6336-3 tables); Y_S = stress correction factor; Y_β = helix angle factor

Allowable tooth root stress: σ_FP = (σ_Flim × Y_ST × Y_NT) / (S_F,min × Y_δrel × Y_Rrel × Y_X) [σ_Flim = material endurance limit; Y_ST = stress correction for test; SF_min ≥ 1.25]

σ_Flim (ISO 6336): Carburized, case-hardened: 350–450 MPa (Mlq material quality); nitrided: 290–350 MPa; through-hardened: 200–290 MPa

Contact Fatigue (ISO 6336-2)

Hertzian stress at pitch point: σ_H = Z_H × Z_E × Z_ε × Z_β × √(F_t / (b × d₁) × K_A × K_v × K_Hα × K_Hβ × u+1/u) [MPa] Z_H = zone factor (function of helix angle and pressure angle); Z_E = elastic coefficient; Z_ε = contact ratio factor; u = gear ratio

Allowable contact stress: σ_HP = σ_Hlim × Z_NT × Z_L × Z_V × Z_R × Z_W × Z_X / S_H,min [S_H,min ≥ 1.0 typically]

σ_Hlim (ISO 6336): Carburized, case-hardened: 1,250–1,550 MPa; nitrided: 950–1,200 MPa; through-hardened HRC 55: 1,000–1,200 MPa

Advanced Gear Failure Modes

Micropitting (Frosted Surface)

Mechanism: surface fatigue in EHD lubrication regime; micro-cracks at Ra-scale asperities; shallow pitting < 10 μm deep Condition: specific film thickness Λ = h_min / (Ra₁² + Ra₂²)^0.5 < 0.4–0.8 → risk of micropitting Prevention: Λ > 2.0 (full film) by using: smoother surface finish; higher viscosity oil; EP additives; shot peen (+ lapping for smooth finish) AGMA 925: specific methodology for Λ calculation and micropitting assessment

Scuffing (Adhesive Wear)

Flash temperature criterion (Blok): T_flash = T_bulk + μ × F_n × v_slip × B_M / (4 × b_H × √(v_1² + v_2²)) [°C; B_M = thermal contact coefficient] Scuffing when T_flash > T_scuff [T_scuff from FZG or ASTM D5182 test data]

FZG test (DIN 51354): standardized gear test; 12 load stages → scuffing at specific load stage; lubricant rated by failure load stage API GL-4/GL-5: gear oil additive requirements for scuffing protection (sulfur-phosphorus EP additives)

Case Depth and Core Hardness

Carburized gear case depth: Effective case depth (550 HV): CHD = 0.1–0.3 × module (for small modules); 0.5–1.5 mm typical Total case depth: 1.3–1.8 × CHD

Core hardness: HRC 28–38 (for carburized steel 8620, 9310); provides toughness for impact

Nitrided gear case depth: 0.2–0.5 mm total case; 0.15–0.35 mm effective; softer core

Shot peening benefit: Induces -400 to -800 MPa surface compressive residual stress → reduces mean stress → S_t and S_c increase 10–30% Mandatory for high-cycle aerospace gears (AGMA 923)

Gear Fatigue Testing

FZG test rig (DIN 51354): power recirculating; 12 load stages; scuffing and pitting resistance Pitting test (ISO 14635): standard conditions; time to first pitting; compare lubricant or material Single tooth fatigue test (STF): isolates bending fatigue; high cycle to failure; develops S-N curve for root Back-to-back test rig (AGMA 923): complete gear pair under realistic loading; preferred for certification

Standards

Standard	Scope
AGMA 2101-D04	Fundamental rating factors for involute spur/helical gears (SI)
ISO 6336 (Parts 1–5)	Load capacity calculation of spur and helical gears
AGMA 923-B05	Metallurgical specifications for gear steels
AGMA 925-A03	Effect of lubrication on gear surface distress
DIN 51354	FZG gear test machine procedure
AGMA 2000	Gear classification and inspection handbook

Output

Provide: gear geometry (module, face width, number of teeth), material and heat treatment (grade per AGMA 2101 or ISO 6336), hardness [HRC or HB], case depth [mm] (if case-hardened), tangential force F_t [kN], bending stress σ_F [MPa] vs. allowable σ_F_allow [MPa] (safety factor SF_F), contact stress σ_H [MPa] vs. allowable σ_H_allow [MPa] (safety factor SF_H), design life N_L [cycles], life factor Y_N and Z_N applied, specific film thickness Λ (micropitting check), shot peening requirement, FZG scuffing load stage (if applicable), and applicable standard (AGMA 2101, ISO 6336, AGMA 925).