A Comparative Study between a Pair of Cosine Gears and a Pair of Involute Gears: Contact Stress, Root Fillet Stress, and Contact Ratio

Cheng-Kang Lee


Contact stresses, root fillet stresses, and contact ratios of a pair of cosine gears and a pair of involute gears are analyzed and compared in this paper. The mathematical models of pinions and gears are created based on the coordinate transformation theory and the theory of gearing. Static structural finite element analysis is performed by using ANSYS. The assumption of contact of one tooth is not adopted in order to comply with the real situation of meshing. Numerical results have shown that maximum contact stress and maximum root fillet stress of cosine pinion are smaller than those of involute pinion, maximum contact stress of cosine gear is approximately equal to that of involute gear, and maximum fillet stress of cosine gear is smaller than that of involute gear. The pair of cosine gears has a higher strength but a lower contact ratio in comparison with the pair of involute gears. Maximum contact and root fillet stresses can be reduced largely when the number of teeth in contact is increased from 1 to 2.


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