Abstract: The tooth deflection of spur gear was calculated by the conformal mapping method which is the complex potentials approach in two dimensional elasticity theory. The analytic solution was deritived for determining the displacement, at force active point. The mapping function was expressed by ten fractional terms, the accuracy of the mapping shape of tooth was increased and the exact solution of tooth deflections was obstained. The compution results of tooth deflections under Hertz contact given by this method were contrasted to those by Terauchi’s concentrated load method, the accuracy of the results by this method was greatly increased, and compared with those Weber's and Lunderg's formuls, this method was confirmed to be reliable.

Key words: Deflection, Involute gear, Spur gear tooth