Topology optimization considering multi-axis machining constraints using projection methods

Abstract

Topology optimization under manufacturing constraints is an important and active area of research. The primary goal is to ensure optimized designs are manufacturable, and more specifically, are optimized considering the geometric restrictions associated with the considered manufacturing process. Herein we consider the manufacturing process of machining, which imposes a challenging set of geometric restrictions compared to free-form topology optimization. We consider the case of 2.5 axis machining, as well as more general 5-axis machining, and use a projection-based approach for ensuring designed voids have a direct path to the boundary of the design domain along a candidate machining axis, and at a minimum feature size of the machining tool. As with other projection approaches, these manufacturing constraints are achieved through the projection operations and explicit constraints are not needed. Intermediate volume fractions are prevented through SIMP penalization and sensitivities are computed by the adjoint method for use in a typical gradient-based optimizer. Various 2D and 3D minimum compliance examples are presented, and solutions are shown to respect the imposed 2.5 axis and 5 axis machining constraints with near 0/1 (void/solid) final distributions of material.