| name | gear-rating-agma |
| description | AGMA gear rating — bending stress (J factor), contact stress (I factor), load distribution factor K_H, dynamic factor K_v, reliability factor, power rating, AGMA 2101/ISO 6336. |
| metadata | {"priority":7,"promptSignals":{"phrases":["AGMA gear rating","AGMA 2101","gear bending stress","gear contact stress","J factor gear","I factor gear","gear power rating"],"minScore":3}} |
AGMA Gear Rating — Complete Skill
AGMA 2101-D04 / 2001-D04 (Metric/Inch)
Bending Stress (AGMA)
σ_t = W_t K_o K_v K_s (P_d/F) × (K_H K_B / J)
W_t = tangential load [lb]; P_d = diametral pitch [1/in]; F = face width [in]
Or in metric: σ_F = W_t K_o K_v K_s (K_H K_B) / (b m_t J)
Allowable bending stress:
σ_all = (S_at / S_F) × Y_N / (K_T K_R)
S_at = allowable bending stress number (AGMA Table 3 by grade and material)
S_F = safety factor (≥ 1.2 typical; ≥ 2.0 for critical)
Y_N = stress cycle factor for bending life; K_T = temperature factor; K_R = reliability factor
Contact Stress (AGMA)
σ_c = C_p × √(W_t K_o K_v K_s × K_H C_f / (d_w F I))
C_p = elastic coefficient [√psi] = √(1/(π(1/E₁×ν₁ + 1/E₂×ν₂)... )) ≈ 2300 psi^(1/2) for steel
C_f = surface condition factor (= 1.0 for cut gears)
Allowable contact stress:
σ_c,all = (S_ac / S_H²) × Z_N × C_H / (K_T K_R)
S_ac = allowable contact stress number; S_H = safety factor (≥ 1.0–1.2)
Z_N = stress cycle factor for contact life; C_H = hardness ratio factor
Correction Factors
Dynamic Factor K_v
Accounts for internally generated dynamic loads from tooth-to-tooth accuracy
AGMA Quality Grade (Q_v or AGMA Class):
Q_v 5: commercial quality (hobbed/shaped, no finishing)
Q_v 9: high precision (ground)
Q_v 12: precision (ground + lapped)
K_v formula (AGMA 2001):
K_v = (B + √(200 V))^A / B^A (for V in ft/min)
A, B = functions of Q_v
Or use published charts
Higher quality number → lower K_v → better dynamic behavior
Load Distribution Factor K_H (K_m in older AGMA)
K_H = 1 + C_mc(C_pf C_pm + C_ma C_e)
C_mc = lead correction factor (1.0 for straight spur; 0.8 for crowned)
C_pf = pinion proportion factor (depends on F/d₁ ratio)
C_pm = pinion proportion modifier (shaft offset)
C_ma = mesh alignment factor (depends on F and application)
C_e = mesh alignment correction (1.0 for enclosed gear; 0.80 for precision)
Typical K_H range: 1.1–1.8 (wider = worse, more misalignment)
Size Factor K_s (AGMA)
K_s = 1.192 (F √(Y / P_d))^0.0535 [per AGMA; accounts for non-uniform stress in large gears]
K_s ≥ 1.0; increases for large module gears
Overload Factor K_o (AGMA)
Application factor; depends on prime mover and driven machine:
| Prime mover | Driven machine | K_o |
|---|
| Uniform (electric motor) | Uniform | 1.00 |
| Uniform | Moderate shock | 1.25–1.50 |
| Moderate shock | Heavy shock | 1.75–2.00 |
Reliability Factor K_R
K_R = 0.658 - 0.0759 ln(1-R) for R > 0.99
K_R = 0.50 - 0.109 ln(1-R) for R ≤ 0.99
R = 0.90 → K_R = 0.85; R = 0.99 → K_R = 1.00; R = 0.999 → K_R = 1.25
Geometry Factors J and I
Bending Geometry Factor J
J accounts for tooth profile, loading angle, stress correction
For standard spur (no corrections):
J ≈ 0.24–0.48 depending on number of teeth and pressure angle
From AGMA Table 1 (20° pressure angle, full depth, standard center distance)
More teeth → higher J (more gradual stress rise)
Contact Geometry Factor I (also called C_c or Z_I)
I = sin(φ) cos(φ) / (2 m_N) × m_g/(m_g + 1) (for external spur gears)
φ = pressure angle; m_N = load sharing ratio (≈ 1 for spur, < 1 for helical)
m_g = gear ratio N_G/N_P
For helical: I modified by helical geometry (higher than spur; better contact ratio)
Stress Cycle Factors Y_N, Z_N
From AGMA Figures 14 and 15 (S-N based):
Y_N = bending life factor; Z_N = contact life factor
For infinite life (> 3×10⁶ cycles for bending; > 10⁸ for contact): Y_N = Z_N = 1.0
For short life: Y_N and Z_N can be > 1.0 (lower stress requirement for fewer cycles)
Material Allowables (AGMA 2101 Table 3)
Grade 1 steel (commercial heat treatment):
Bending: S_at = 55,000 psi (379 MPa); Contact: S_ac = 150,000 psi (1034 MPa)
Grade 2 (controlled hardening, HRC 55+):
S_at = 65,000 psi (448 MPa); S_ac = 175,000 psi (1207 MPa)
Grade 3 (case carburized, HRC 60):
S_at = 75,000 psi (517 MPa); S_ac = 200,000 psi (1380 MPa)
ISO 6336 Comparison
AGMA and ISO 6336 produce similar results but different factor names:
ISO K_H → AGMA K_H; ISO Y_F (form factor) → AGMA 1/J; ISO Z_H (Hertz factor) → affects I
ISO safety factor definition differs (applied to stress vs. capacity)
Design Procedure
- Determine W_t from power and pitch radius
- Select material and grade → get S_at, S_ac
- Estimate K_o, K_v (from quality), K_s, K_H
- Calculate σ_t and σ_c
- Compare σ_t ≤ σ_all,bending and σ_c ≤ σ_all,contact
- If not satisfied: increase face width F, increase module m, better material/grade, higher quality
Output
Provide: W_t [N], σ_t [MPa] vs. S_at/S_F, σ_c [MPa] vs. S_ac/S_H, all correction factors (K_o, K_v, K_s, K_H, K_B), J and I factors, safety factors S_F and S_H, dominant failure mode (bending or contact), required module and face width.
