Abstract: This puper incorporated and developed the method originated by A/DA. TERAUCHI. and NAGAMUYA. to which a high value is set presently at home and abroad, in which the stress and deflection of tooth on spurgears are calculated by means of the method of complex variables in plane elasticity. In this paper, their approximate solution was developed to become exact solution. The accuracy of the mapping shape of tooth was increased. It was mentioned that the mapping junction was expressed by five fractional terms, with the mapping error being less than 1% m. A calculating principle was proposed to find out the displacement of contact point in relation to central line of the ndiacent gear tooth affecting the quality of mesh of gears directly. The computer program was made, and according to the computed results, the figures were given so that the displacement of the contact point in the normal direction can be calculated conveniemly for engineering calculation.

Key words: Lagrange multiplier, BEM, Sobolev space