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Based on the cylindrical coordinates and the space engagement theory, which utilize a cylindrical coordinate system, an arbitrary curve equation was obtained and a method of curve expansion was established. This allows any order of pitch curve of non-circular curved face gear and normal equidistant curve parameter equations to be derived. The tooth profile points of the non-circular curved face gear can be solved using the numerical calculation method where the tooth profile intersects with the pitch curve and normal equidistant curves of non-circular curved face gear. Finally the numerical method used to solve the tooth profile of the non-circular curved face gear was proved to be accurate and correct from the small error between measured data and the data of theoretical calculation.

Numerical Calculation of Tooth Profile of a Non-circular Curved Face Gear