Toolpath Generation for High Density Spatial Fiber Printing Guided by Principal Stresses

Abstract

While multi-axis 3D printing can align continuous fibers along principal stresses in continuous fiber-reinforced thermoplastic (CFRTP) composites to enhance mechanical strength, existing methods have difficulty generating toolpaths with high fiber coverage. This is mainly due to the orientation consistency constraints imposed by vector-field-based methods and the turbulent stress fields around stress concentration regions. This paper addresses these challenges by introducing a 2-RoSy representation for computing the direction field, which is then converted into a periodic scalar field to generate partial iso-curves for fiber toolpaths with nearly equal hatching distance. To improve fiber coverage in stress-concentrated regions, such as around holes, we extend the quaternion-based method for curved slicing by incorporating winding compatibility considerations. Our proposed method can achieve toolpaths coverage between 87.5% and 90.6% by continuous fibers with 1.1mm width. Models fabricated using our toolpaths show up to 84.6% improvement in failure load and 54.4% increase in stiffness when compared to the results obtained from multi-axis 3D printing with sparser fibers.

Figures (22)

• Figure 1: Challenges associated with stress-aware fiber placement in prior methods. (a1) The stress tensors and (a2) the maximal principal stresses obtained by eigenvalue decomposition. The toolpath generated based on the field which exhibits directional ambiguity Fang_SIGA20, as depicted in (b2), deviates from the actual stress field, particularly in regions with significant directional changes -- see the region highlighted by red dash lines. (a3) Even when the direction of the stress field is corrected to obtain a vector field with uniform orientation, the generated path (b3) fails to fully cover the surface layer Fang_ADDMA24 -- see those regions covered by the gray shadows. By contrast, our proposed method directly generates a periodic scalar field (b1), enabling the computation of fiber paths with near-constant hatching distance and achieving a dense, uniform fiber arrangement.
• Figure 2: The impact of turbulent region in the stress field on toolpath generation: (a) Stress concentration near the load-bearing holes induces turbulence in the stress field; (b & c) Periodic parameterization results obtained using the original stress field as input, with the corresponding toolpaths extracted from the strip patterns.
• Figure 3: An illustration to explain the deformation-based $S^3$-Slicer Zhang_SIGA22: (a) The initial input volume model $\mathcal{M}$ under applied force $F$, where the maximal principal stress $\sigma_{\text{max}}$ in an element and the normal vector $n_f$ at a vertex on the boundary surface are also illustrated; Tetrahedral elements are applied with local rotation for enhancing mechanical strength (SR) and improving surface quality (SQ). The local printing directions $\mathbf{d}_p$ (as $z$-axis in the deformed shape) are made to be perpendicular to the maximal stress (b1) or be parallel to the surface normal (b2) by rotating every element. (c) The deformed model $\mathcal{M}^d$ is obtained through a scale-controlled deformation algorithm that stitches locally rotated elements together. The resulting field meets both the SR and the SQ requirements. (d) The height field of a deformed model is mapped back to the original model $\mathcal{M}$ as a scalar field so that the curved layers can be extracted as the iso-surfaces of the scalar field.
• Figure 4: The computational pipeline with steps as a diagram explanation of our method for generating high density toolpaths for fiber placement: (a) the input T-bracket model is represented as a volumetric mesh $\mathcal{M}$ and the field of maximal principal stresses can be obtained from FEA by using the given loads as boundary conditions; (b) the deformed model $\mathcal{M}^d$ and (c) the curved layers are generated by the extension version of $S^3$-Slicer Zhang_SIGA22; (d) the field of maximal principal stresses $\sigma_{max}$ is projected from elements onto the curved layers (represented as triangular mesh surfaces); (e) the direction field $\mathbf{d}(\cdot)$ generated by our method following the stress field by using the 2-Rotational Symmetry (2-RoSy) representation, which means that there are two equivalent directions that are $180^{\circ}$ apart at every point; (f) the strip pattern obtained from the optimized periodic scalar field, which uses the $\mathbf{d}(\cdot)$ as input; (g) the toolpath generated from strip pattern by using the marching square algorithm Maple_ICGMG03; (h) the final toolpath for fiber placement after tracing connected toolpaths and removing the toolpaths shorter than a hardware-constrained length $\bar{L}$ that cannot be physically realized. Note that corresponding sections for different steps of the pipeline have been indicated on the flow chart.
• Figure 5: The definition and application illustration of the local frame on a 2D manifold. (a) Polar coordinates defined at each vertex $v_i \in \mathcal{V}$. (b) Illustration of the method for measuring the angle between two adjacent vectors on the manifold. Note that the unit vector $\mathbf{d}_{v_i}$ and the angle $\phi_i$ are equivalent here, representing the same quantity in different coordinate systems.