Simple Stress Formulae for a Thin-Rimmed Spur Gear. Part 1: Derivation of Approximation Formulae for Tooth Fillet and Root Stresses

Using the finite element method, influences of chordal tooth thickness at the critical section of tooth, radius of curvature of fillet, rim thickness, and supporting condition of a thin-rimmed spur gear on the tooth fillet and root stresses are investigated. Summing up a lot of FEM calculated results, a set of approximate formulae is derived for the calculation of tooth fillet and root stresses of a thin-rimmed spur gear. A comparison between the FEM calculated stress values and the values from these approximation formulae has shown good agreement.