Accurate Tooth Stiffness of Spiral Bevel Gear Teeth by the Finite Strip Method

A Finite Strip element is presented for the analysis of variable height and thickness gear teeth, curved along a spiral wound on a cone. The formulation, based on Mindlin's plate theory, accounts for transverse shear deformation and uses localized functions series in the tooth facewidth direction combined with numerical integration in all directions. The formulation is applied to the clamped-free boundary condition, usual in gearing, and supports any type of transverse loads and moments. The precision of the calculated tooth deflection is ascertained through equivalent numerical tests using Finite Element Analysis. Results agree within 5% of bending displacement at the point of load application.