Topology optimization with accessibility constraint for multi-axis machining

Abstract

In this paper, we present a topology optimization (TO) framework to enable automated design of mechanical components while ensuring the result can be manufactured using multi-axis machining. Although TO improves the part's performance, the as-designed model is often geometrically too complex to be machined and the as-manufactured model can significantly vary due to machining constraints that are not accounted for during TO. In other words, many of the optimized design features cannot be accessed by a machine tool without colliding with the part (or fixtures). The subsequent post-processing to make the part machinable with the given setup requires trial-and-error without guarantees on preserving the optimized performance. Our proposed approach is based on the well-established accessibility analysis formulation using convolutions in configuration space that is extensively used in spatial planning and robotics. We define an inaccessibility measure field (IMF) over the design domain to identify non-manufacturable features and quantify their contribution to non-manufacturability. The IMF is used to penalize the sensitivity field of performance objectives and constraints to prevent formation of inaccessible regions. Unlike existing discrete formulations, our IMF provides a continuous spatial field that is desirable for TO convergence. Our approach applies to arbitrary geometric complexity of the part, tools, and fixtures, and is highly parallelizable on multi-core architecture. We demonstrate the effectiveness of our framework on benchmark and realistic examples in 2D and 3D. We also show that it is possible to directly construct manufacturing plans for the optimized designs based on the accessibility information.

Optimizing Build Orientation for Support Removal using Multi-Axis Machining

“…The objective is to find regions of the support structure S ⊂ R 3 that can be accessed by a cutting tool T ⊂ R 3 without colliding with the workpiece Ω, the platform P ⊂ R 3 , fixturing device F ⊂ R 3 . Our approach is a generalization of the IMF proposed in [2] for multiple fixturing devices. Let the tool assembly be T = (H ∪ K), where H and K are the tool holder and the cutter, respectively.…”

“…We define the IMF, f IMF : R 3 → R, over the 3D design domain for each given tool assembly T as the minimum collision volume between the stationary and moving objects over all sampled rotations in Θ T ⊂ SO(3) and sharp points K ⊆ T , where SO(3) is the group of different choices of sharp points and available tool orientations Θ ⊆ SO(3) [2]:…”

“…However, the nonzero numerical values of the IMF over the secluded support regions are useful to quantify the degree of their inaccessibility. Such measures are useful to define continuous penalty functions for design optimization [2], which is beyond the scope of this paper. Algorithm 1 describes the procedure for computing IMF for multiple tools and fixtures using convolutions by FFT.…”

“…Next, let us consider the 3D example of Fig. 7, which is a topologically optimized support bracket [2]. We aim to find an optimized build orientation for the support bracket given the 4 fixturing configurations of Fig.…”

“…In particular, we extend the inaccessibility measure field (IMF) introduced in [1,2] to hybrid AM-then-SM processes. Previous work on topology optimization for multi-axis machining [2] demonstrated the effectiveness of IMF as a continuous field in the Euclidean space that quantifies the collisions occurring between the part, fixture, and tool geometries to provide a penalty function to enforce accessibility by collision avoidance. We will briefly review the accessibility analysis and extend it to multiple fixtures in Section 2.…”