An optimal design technique for crowned teeth of helical gear is presented

which includes 3 D finit element method

flexibility matrix and mathematical programming.In the calculation the manufacturing and assembling errors

the deformations of gears and supporting structure are taken into account.For the objective function to uniform the load distribution under the two limited error conditions

a quadratic program is automatically formed and solved by computer.Thus an optimal longitudinal modification with crowning is obtained

which has a comprehensive effect on decreasing the sensitivity to the errors and uniforming the load distribution.Comparison of this modification with the traditional ones demonstrates the advantages of this method in accuracy and effectiveness.