Spiral bevel gears tooth geometry based on tooth trace and contact ellipse theory

This paper presents a novel procedure for spiral bevel gear design without classical gear machine cutting parameters considerations; it is based on favorable conditions of contact and interference avoidance constraints. In the first step, the work is focused on the tooth trace mathematical model; it is built on the pitch cone surface with its normalized parameters. In the second step, tooth surface geometry is generated by a kinematic procedure using the calculated tooth trace. Design parameters are calculated to satisfy favorable conditions of meshing and contact using relationships between principal curvatures and directions of pinion and gear surfaces and Tooth Contact Analysis (TCA) algorithm. Calculated tooth surface is evaluated using two tools TCA and Finite Element Analysis (FEA); function of transmission errors obtained from TCA tool has the same parabolic form and magnitude as the convensional geometry; FEA gives a potential contact locus on the mean pich line of the drive teeth without edge contact or stress concentration zones.