Calculation of conformal mapping function of the tooth profile on evolvent gear by computer

The exact solution of the stress and the displacement on spur gear can be gained by the method of conformal mapping of complex variables in plane elasticity. But it is difficult to get the comformal mapping function for the tooth profile with different parameters. They used to be obtained through trial method. This is time-consuming and expensive. In this paper a computer program is drawn up for the conformal mapping function. A large amount of calculation has given proof of its success and of the precision of the mapping function: thereby the main obstacle has been removed for the practical application of the conformal mapping method to the stress and displacement of tooth on evolvent gear.