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Involute Spur Gear Pair in Tooth Contact
Tooth contact pressure and root bending stress evaluation under 18 kN tangential driving load with penalty contact along mating flanks.
In heavy industrial drivetrains and speed reducers, tooth mesh compliance and peak contact stress dictate pitting resistance and fatigue life according to ISO 6336. Excessive contact pressures cause surface micro-pitting and scuffing, while high tensile stresses at the root fillet can initiate catastrophic tooth breakage. This multi-body B-Rep assembly resolves normal contact pressure along the involute flank mating line and computes fillet bending stress under an 18 kN tangential driving load using a penalty-based contact formulation.
1. Geometry & FEA Mesh
- •2 distinct solid B-Rep bodies: 19-tooth driving pinion (module m = 5 mm, face width b = 45 mm) and 37-tooth driven gear wheel.
- •Materials: 18CrNiMo7-6 case-hardened carburized steel (E = 210 GPa, ν = 0.30, yield 850 MPa) for pinion; 42CrMo4 tempered steel (E = 210 GPa, ν = 0.29, yield 650 MPa) for gear wheel.
- •Conformal tetrahedral volume mesh across both bodies comprising 42,630 elements and 9,780 nodes (29,340 active DOFs), refined along mating tooth flanks and root fillets.
- •Penalty contact interface defined along mating active involute profile flanks with normal stiffness parameter tuned for penetration-free equilibrium.
2. Loads & Boundary Conditions
- •Driven gear bore internal cylindrical surface fully fixed (Ux = Uy = Uz = 0) to simulate rigid keyed shaft support.
- •Pinion bore mounted on cylindrical kinematic constraint allowing rotational freedom around the gear center axis.
- •18.0 kN tangential driving force applied along the pitch circle of the pinion, generating mating normal contact forces across the active tooth pair.
3. Simulation Results & Findings
- ✓Localized contact pressure along the mating contact line reaches a peak of 1,234.4 MPa, correlating within 4.2% of classical Hertzian cylinder contact theory.
- ✓Maximum tensile tooth root bending stress σ_vm = 385 MPa localized in the transition fillet of the pinion tooth flank, providing a safety factor SF = 2.21 against yield.
- ✓Maximum total displacement vector magnitude |u| = 0.806 mm at the tip radius of the driving tooth under full torsional deflection.
- ✓Zero global force imbalance: reaction balance error is 0.00% with solve runtime of 0.16 s.
WebCAE's multi-body contact solver allows gearbox designers to verify tooth contact patterns, root stresses, and flank contact pressures directly in the browser in under 0.2 seconds. Rapid penalty contact setup eliminates tedious manual meshing transitions and enables instant evaluation of profile shift modifications without external multi-body licenses.
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- ✓Nonlinear Contact & Buckling (Kσ, MITC4, RBE2/RBE3)
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