An automatic design optimization procedure to minimize fillet bending stresses in involute spur gears

This paper presents the development of an automatic design algorithm for gears. The criterion on which the design performance is assessed is the maximum tensile stress induced in the gear tooth fillet under service conditions. Starting from an initial set of design parameters the stresses in the gear tooth fillet are calculated. The maximum value of the stress is then expressed as a function of the design variables. By minimizing this function, the objective function, subject to both equality and inequality constraints a new set of design parameters, is produced. Iterative application of the analysis and minimization stages forms a sequence of non-linear optimization problems which converges to yield the optimal design. Finite element techniques employed to calculate accurately the stresses in the gear tooth are again used to compute the design derivatives. This process is very economical, owing to its efficient reuse of the factorized stiffness matrix. The algorithm is illustrated by its application to a spur gear tooth of involute profile. Both linear and non-linear forms of the objective function are used and a comparison made between the solutions obtained.