Hybrid optimization for build orientation in fused filament fabrication using low- and high-fidelity build time estimation models

Abstract

Build time is one of the crucial aspects of the fused filament fabrication (FFF) process. A reliable estimate of build time is vital, as it is the basis for estimating production cost, process planning, and build orientation optimization (BOO). In the last two decades, many researchers have developed methods to estimate the build time of FFF processes. However, the efficient applicability of these methods as low-fidelity models in lieu of high-fidelity model like G-code generation software in the context of BOO considering their correlation and computational cost has not been well researched. This paper thus initially evaluates the correlation coefficient and computational cost of different build time estimate models proposed in literature and benchmarks them with a high-fidelity model which itself is validated with experiments. Then, the work proposes a hybrid optimization framework that uses multifidelity models to obtain optimum build orientation with improved computational performance. First, we do a multi-modal build orientation optimization by a Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations (RS-CMSA) algorithm using a low-fidelity model and use these as the initial points in a gradient-based optimization method using a high-fidelity model. The proposed hybrid method has been illustrated with example case studies as well as compared and evaluated to a standard optimization algorithm using a single fidelity model to demonstrate the overall methodology and its effectiveness.

Appendices

Appendix A. Calculation of support volume

Calculating the support volume is an essential step as most build-time models require the support volume information to calculate the build time. Support structures are used in FDM whenever there are overhanging features. This paper proposes a simple and efficient method using a ray-tracing algorithm for calculating the support volume, which can be used in optimization frameworks. Starting from the 3D CAD model, we identify the triangles which require support structure and project it onto the x-y plane (Fig.

Fig. 17

Support volume calculation

17a), then these triangles are discretized into points based on the size of the triangle (Fig. 17b). The cloud of points is then rounded to integer values, and then unique points are selected (Fig. 17c). This ensures that the distance between any two points in coordinate directions will be 1 unit. These points are then used as the source for the ray-tracing algorithm (Fig. 17d). For each ray, the Möller–Trumbore algorithm [31] is applied to find the intersections with mesh triangles.

Once the support length is obtained for all the points, the support volume can be calculated by the equation below. It is assumed that each ray has a square base of ∆x =1 unit and ∆y = 1 unit dimension, and the support volume is approximated as the sum of the volume of square prisms of base area 1 unit² and height r. To take into account the infill density, a term ID (percentage infill used for support structures) is multiplied by.

$${V}_{support}=ID\times {\Delta }_{x}\times {\Delta }_{y}\times \sum r$$

Appendix B. Optimization data

Please see Tables 3 and 4 here.

Table 3 Data from the optimization run for engineering geometries

Table 4 Optimization data run for free-form geometries