gear-rating-agma

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

1. Determine W_t from power and pitch radius
2. Select material and grade → get S_at, S_ac
3. Estimate K_o, K_v (from quality), K_s, K_H
4. Calculate σ_t and σ_c
5. Compare σ_t ≤ σ_all,bending and σ_c ≤ σ_all,contact
6. 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.