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To reconstruct the tooth surface of a circular arc tooth trace cylindrical gear (CATT gear), one needs to create an accurate 3D model and investigate geometric features of the tooth profile. According to the processing principle of the rotating knife dish milling, and using the space meshing theory and differential geometry, the tooth surface equation and the tooth profile of CATT gears have been deduced. Then, the tooth surface reconstruction of CATT gears was done and a 3D model was created. Next, based on theoretical deduction, it was proven that the profile of the middle section was involute, and the other section was hyperbolic. Finally, the influences of the design parameters on the tooth profile were investigated. The general tendency is that the gear tooth thickness becomes thinner as the gear width increases and the tooth line radius decreases, and the tooth profiles of the concave and the convex tooth surface may intersect. The influences of the module need to be discussed separately. The tooth thickness deviation increases as the module increases. But the relative tooth thickness deviation is opposite. Therefore, it is suggested that RT  (3-4)b and the module should be large to improve the bearing capacity. The results of the investigation provide a reference for the design, profile modification, lubrication, and measuring of CATT gears.

Tooth Surface Reconstruction and Tooth Profile Geometric Analysis of Circular Arc Tooth Trace Cylindrical Gears