Gearbox Design

Deterministic engineering intelligence platform for mechanical, structural, and electrical designers. 91 modules validated solvers, 3D CAD workspace, and ISO/DIN standards compliance.

Loading...
▸Formula · assumptions · 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)