Gear Design & Transmission Calculator (ISO 6336)

Design spur and helical gear trains. Calculate gear ratio, speed, torque, contact stress (pitting σH), and tooth root bending safety factor (σF).

Gear Design & Strength

ISO 6336 Spur, Helical & Multi-Gear Train

Standard tooth size parameter; increases bending strength.
Face width of the tooth; increases contact load capacity.
Pinion teeth count. Min 17 recommended to avoid undercut.
Driven gear teeth count; determines speed reduction ratio.
Değme açısı (Standart: 20°, Ops: 14.5°, 25°)
0° = Düz Dişli, >0° = Helis Dişli
DESIGN VERIFIED — SAFE
9.28
Tooth Root Bending Safety (SF)
/
4.42
Tooth Flank Contact Safety (SH)
Gear Ratio
3.00:1
Center Dist
120.0 mm
Pitch Velocity (v)
4.59 m/s
Contact Ratio (εα)
1.67
Circ. Pitch (p)
9.42 mm
DYNAMIC MESH BLUEPRINT
1.0x CW
a = 120.0 mm (i = 3.00:1)
Manufacturing Dimensions (mm)ISO 6336:2019
Parameter
Pinion (z₁) (z₁)
Gear (z₂)
Tip Dia (da)
66.00
186.00
Ref Dia (d)
60.00
180.00
Root Dia (df)
52.50
172.50
Profile Shift (x)
0.000
0.000
Pressure Angle (αn)
20°
20°
Helix Angle (β)
0° (spur)
0° (spur)
Wildhaber Span (W_k):
22.98 mm (k=3)
60.09 mm (k=7)
Over Pins (M)
75.470
197.398

ALUCALC OS · GEAR PAIR MANUFACTURING PASSPORT

Gear Pair (External): m=3 mm | z₁=20 | z₂=60 | a=120.0 mm

Standard: ISO 6336:2019 / DIN 3960
Date: 9/9/2026
ParameterPinion (z₁=20)Gear (z₂=60)
Pitch Diameter (d)60.00 mm180.00 mm
Tip Diameter (da)66.00 mm186.00 mm
Root Diameter (df)52.50 mm172.50 mm
Center Distance (a)120.00 mm
Root Stress σF (ISO 6336-3)46.3 MPa—
Contact Stress σH (ISO 6336-2)339.6 MPa—
Bending Safety (SF)9.2812.43
Contact Safety (SH)4.42
εα / εβ / εγ1.67 / 0.00 / 1.67
Ft / Fr / Fa872 / 317 / 0 N
AluCalc OS Engineering & Drive Train StudioPage 1 / 1
▸Formula · assumptions · worked example(ISO 6336-1/2/3:2019 · DIN 3960 / DIN 3990 · AGMA 2001-D04)

Formula

\sigma_H = Z_H Z_E \sqrt{\frac{F_t}{d_1 b} \frac{u+1}{u} K_A K_V K_H}, \quad \sigma_F = \frac{F_t}{b \cdot m_n} Y_F Y_S K_A K_V K_F

ISO 6336 Method B: contact stress σH = ZH ZE Zε √(Ft(u±1)/(d1 b u)) and root stress σF = Ft YF YS Yβ KA Kv / (b mn), with SH ≥ 1.0 and SF ≥ 1.4.

Assumptions

  • · Standard 20° pressure angle involute gear profile with standard addendum/dedendum coefficients
  • · Tooth contact pattern and elastohydrodynamic oil film prevent micro-pitting and scuffing
  • · Required safety factor margins: SH ≥ 1.20 against pitting, SF ≥ 1.40 against root bending fatigue
ISO 6336-1/2/3:2019 / DIN 3990 Method B

Cylindrical Spur Gear Contact & Bending Verification (16MnCr5)

STATUS: PASS(SH = 1.35 ≥ 1.20 | SF = 2.10 ≥ 1.40)

Design verification of case-hardened steel pinion driving 60-tooth gear with contact stress (pitting) and root bending fatigue evaluation.

1. Inputs & Boundary Parameters (Girdiler)
Normal module mn3.00 mm
Pinion tooth count z120 [-]
Wheel tooth count z260 [-]
Face width b40.0 mm
Pinion input torque T1120.0 N·m
Pinion speed n11450 rpm
Pinion material16MnCr5 Case-hardened ISO 683-3
Contact fatigue limit σHlim1500.0 MPa
Bending fatigue limit σFlim430.0 MPa
Application factor KA1.25 [-]
2. Applied Governing Equations & Standard Clauses (Bağıntılar & Norm Maddesi)
Tangential Load Ft: Ft = (2000 · T1) / d1
ISO 6336-1:2019 Clause 4
Contact Stress (Pitting) σH: σH = ZH · ZE · √( (Ft · KA · KV · 1.5) / (d1 · b) )
ISO 6336-2:2019 Clause 5
Tooth Root Bending σF: σF = (Ft · KA · KV · YF · YS) / (b · mn)
ISO 6336-3:2019 Clause 5
Safety Factor Bounds: SH = σHP / σH ≥ 1.20, SF = σFP / σF ≥ 1.40
DIN 3990 / ISO 6336
3. Intermediate Calculation Stages (Ara Değerler)
Pitch diameter d1d1 = z1 · mn
60.0 mm
Tangential driving load FtFt = 2000·120 / 60
4000.0 N
Contact stress (pitting) σHAllowable limit σHP = 925.0 MPa
685.0 MPa
Root bending stress σFAllowable limit σFP = 386.4 MPa
184.0 MPa
4. Engineering Verification Result & Limit Threshold (Sonuç + Sınır)PASS
Pitting & Root Fatigue Safety: σH = 685.0 MPa (SH = 1.35) | σF = 184.0 MPa (SF = 2.10)
Acceptance limit: SH ≥ 1.20 (Pitting) & SF ≥ 1.40 (Bending)