Scan Pattern–Mesh Intersection

Some additive manufacturing processes are characterized by a tool trajectory that follows a repetitive pattern in space; for example, powder bed fusion with the laser beam following a predefined island scanning strategy. In such cases, instead of describing individual trajectories of a toolpath, it is more effective to define a scan pattern that represents the idealized motion of a tool inside a part. The part being printed is divided into equally spaced (uniform thickness, $h$) slices or cutting planes that are perpendicular to the build axis, $K$ (see Figure 1(a) and Figure 1(b)). The build axis system I–J–K is a user-defined coordinate system that indicates the printing direction, K.

Figure 1. A scan pattern with four pattern patches.

The scan pattern consists of a rectangular unit cell (see Figure 2). The rectangular unit cell is repeated to cover the cutting plane. The rectangular unit cell consists of a number of smaller rectangular patches. Each patch can define a local angle, $\phi$, between the direction of the scanning motion of the tool and the I-axis. You can assign an eigenstrain tensor to each of the pattern patches representing the inelastic deformation induced by the process. You can define a scan pattern by defining extents of individual patches (x_min, y_min) and (x_max, y_max). All patches together must form a rectangular unit cell that must be situated entirely in the first quadrant of the I–J plane, and one corner of the cell must be at (0, 0).

Figure 2. A scan pattern with four patches with local orientations rotated by 90°, 0°, 135°, and 45° with respect to the I-axis of the build axis system.

A scan pattern is active inside a scanning region. A scanning region is a build axis–oriented bounding box defined by its extent (x_min, y_min, z_min) and (x_max, y_max, z_max) (see Figure 1(a)). The height of a scanning region (z_max–z_min) must be an integral multiple of the thickness, h, of a slice. Multiple nonoverlapping scanning regions can be defined to cover the entire part. A different scan pattern can be active inside each scanning region. All scanning regions share the same build axis system. A layer-to-layer or slice-to-slice rotation angle, $\theta$, can be defined. The scan pattern is rotated by $(i-1)\theta$ on the $i^{th}$ slice for layer $i>1$ (see Figure 1(c)).

For a given element, the toolpath-mesh intersection module computes the number of slices, m, inside the element in a given increment (see Figure 3). It finds which pattern patch contains the center of each slice in that element and the local orientation of that patch considering the layer-to-layer rotation, $\theta$, and the local rotation, $\phi$, of the scanning direction in that patch. The module also computes the partial volumes, $v_f$, of the element below each slice.

Figure 3. Scan pattern overlaid on an element.