Topology Optimization with Accessibility Constraint for Multi-Axis Machining

John MelonakosCase Studies, Computer Vision Leave a Comment

Researchers from the Palo Alto Research Center (PARC) credit ArrayFire in a paper published in the Journal of Computer-Aided Design. The paper is titled “Topology Optimization with Accessibility Constraint for Multi-Axis Machining” and showcases ArrayFire accelerating the workload.


In this post, a topology optimization (TO) framework is presented to enable the 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. The 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.

An inaccessibility measure field (IMF) is defined 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 the formation of inaccessible regions. Unlike existing discrete formulations, the IMF provides a continuous spatial field that is desirable for TO convergence. The approach applies to the arbitrary geometric complexity of the part, tools, and fixtures and is highly parallelizable on multi-core architectures.

The effectiveness of the framework is demonstrated on benchmark and realistic examples in 2D and 3D. It is shown that it is possible to directly construct manufacturing plans for the optimized designs based on the accessibility information.

The Approach

In Figure 1, we see the overall approach to the problem described above. A 5-axis milling machine can manufacture parts but has constraints preventing arbitrary designs. The approach of this paper applies those constraints resulting in an optimized design that is guaranteed to be accessible everywhere to the machine.

In Figures 11-13, we see an example of the approach applied to a GE bracket for tool orientations along 3 different axes in both positive and negative directions. Figure 13 shows the difference between unconstrained accessibility (a) and constrained accessibility (b) which is machineable in the 3-axis mill.

The Results

ArrayFire was used to accelerate the speed of computational design. In Table 3, speedups are shown for varying part and tool resolutions, comparing traditional “finite element analysis (FEA)” with the approach of the paper named “inaccessibility measure field (IMF)” which uses ArrayFire.

Speedups range from 8X at lower sizes to 33X at higher sizes.

Thanks to these researchers for sharing their great work with us!

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