A design optimisation procedure to minimize fillet bending stresses in an epicyclic gear system

This paper presents the development of a design algorithm for epicyclic gear systems. The criterion on which the design performance is assessed is the maximum tensile stress induced in the fillets of the sun, planet and annulus gears. From an initial set of prescribed real and integer design parameters the finite element method is used to determine the maximum tensile fillet stresses in each gear. An objective function is formulated to represent the total stress in the system by combining the maximum fillet stresses in each component. A sequential procedure is then used to minimize the objective function subject to equality, inequality and integer function constraints. The finite element method is used to evaluate the stresses in the gear teeth and iterative application of the analysis and optimization stages converges to produce a design vector such that the maximum stress produced in all components of the system is minimized. Since the effectiveness of each design is assessed using the finite element method, the factorized stiffness matrix is reused to calculate the design derivatives. This makes the processes very efficient in its use of computer resources.