The mathematical model and a case study of the cosine face gear drive that has a predesigned fourth order function of transmission errors and a localized bearing contact

Traditionally, a face gear drive uses an involute pinion. If the number of teeth of pinion is smaller than the minimum number of teeth without undercutting, the pinion will be undercut. To avoid undercutting, it is necessary to quit using involute pinion. This paper proposes a new face gear drive called cosine face gear drive. The cosine face gear drive has a predesigned fourth order function of transmission errors and a localized bearing contact. Therefore, it has a smoother motion curve and no edge contact problem. According to coordinate transformation theory, the theory of gearing, and differential geometry, the mathematical model of the cosine face gear drive is created, including position vectors, unit normal vectors, principal curvatures, principal directions, the condition of contact, and the condition for producing the predesigned fourth order function of transmission errors. A numerical case is studied to verify the mathematical model. The geometric solid model of the case is created. The actual form of the function of transmission error is analyzed. Contact paths and contact ellipses are analyzed. The effects of assembly errors on contact paths and on the function of transmission errors are analyzed. Contact and fillet stresses are analyzed using finite element analysis.