*3.1. The LcVL Product*

As shown in Figure 4, the LcVL product was fabricated by stacking and bonding wood veneers in a layer-upon-layer manner. The product demonstrated that the LcVL procedure was able to take advantage of the qualities of additive manufacturing, specifically, the ability to manufacture complex geometries, such as internal voids, that are nigh impossible to accomplish using SM techniques, such as CNC. However, since LcVL is based on LOM characteristics, although the overall product formation is additive in nature, the production of each layer via cutting is a subtractive process. These subtractive drawbacks should be marginal in comparison to the technical simplicity of the LcVL process. Residual materials could be repurposed as raw materials for 3D printing. For example, leftover veneers could be used to produce wood powder for wood/polylactic acid filaments.

**Figure 4.** Comparison between the laser-cut veneer lamination (LcVL) product and its 3D model. (**a**) Orthographic view of the LcVL product; (**b**) Orthographic view of the 3D model of the product; (**c**) Top view of the LcVL product; (**d**) Top view of the 3D model of the product; (**e**) Tubular voids present in the 3D model of the product postrotation; (**f**) Tubular voids present in the 3D model of the product prerotation.

Furthermore, the surface area of tubular voids present in Figure 4e is 1.27 times the surface area of SM possible tubular voids in Figure 4f. The increased surface area in products with intricate geometrical structures, such as the product presented in Figure 4, could prove beneficial for the development of special-purpose, wood-based products. For example, the spacious tubular voids of complex LcVL-printed structures contain larger void surfaces and enable greater convenience for architecting desired tortuosity, which could improve sound absorption compared to standard SM possible structures [20]. Overall, as demonstrated by the printed product in Figure 4, LcVL was able to properly realize the 3D model of the desired product to a satisfactory degree. However, the LcVL method is not ideal for fabricating products with high angle overhangs without additional external support to ensure uniform pressure on each layer.

Notably, comparing the printed models present in Figure 4a (LcVL) and Figure 2a,d (FDM) revealed visible distinctions in processing resolution. As will be discussed in detail in the following section, the fabricating resolution of LcVL-printed products is primarily dependent on the layer parameters.

#### *3.2. Effects of Layer Parameters on Processing Resolution*

As depicted in Figure 5a, LcVL is unable to replicate the modeling curve line (MCL) with perfect precision. The resulting step-like contour along the Z-axis comprises a theoretical manufacturing error (TME) between the 3D model and the fabricated product. Using the region circled in green in Figure 5a as an example, the relation between layer (veneer) height and TME could be described as follows:

**Figure 5.** (**a**) Theoretical manufacturing error between contours of the modeling curve line and LcVL layer stacking; (**b**) Calculation parameters for the theoretical manufacturing error from LcVL layer stacking; (**c**) Theoretical manufacturing error between contours of the modeling curve line and postrotation LcVL layer stacking; (**d**) Calculation parameters for the theoretical manufacturing error from postrotation layer stacking.

As shown in Figure 5b, when *s* is the arc length of a MCL, *r* the radius of the MCL, *θ* the central angle of the MCL, *α* the angle of the MCL to horizontal, *h* the layer height, and *e<sup>s</sup>* the TME from layer height, then

$$s = 2r\sin\frac{\theta}{2} \tag{1}$$

$$l = \sqrt{s^2 - h^2} \tag{2}$$

$$\frac{1}{2}s \cdot e = \frac{1}{2}h \cdot l \tag{3}$$

$$e\_s = \frac{h \cdot \sqrt{s^2 - h^2}}{s} \tag{4}$$

The relation between layer height and TME from each step/layer of a quarter circle MCL with radius 1 was calculated and plotted in Figure 6a. The quarter circle was divided into five and ten layers to obtain proportional layer heights of 0.2 and 0.1, respectively. As can be seen in Figure 6a, the proportional layer height of 0.2 consistently exhibited greater TME compared to the smaller layer height of 0.1. Therefore, TME is positively associated with layer height.

In addition to the TME caused by layer height, the fabrication accuracy of the LcVL product in Figure 4 suffered further TME from layer rotation. As shown in Figure 5c, the apparent discrepancy between the MCL (highlighted in blue) and the printed product contributed to additional TME (highlighted in red). The TME from layer rotation could be described as follows:

**Figure 6.** (**a**) Relation between layer height and theoretical manufacturing error (TME) from layer height, where total angle is the sum of *α* and *θ*; (**b**) Relation between layer number and TME from layer rotation.

As shown in Figure 5d, when *R* is the radius of rotation, *n* is the number of layers (layer number), *β* is the angle of rotation between the top and bottom layers, *δ* is the angle of rotation between successive layers, and *e<sup>r</sup>* is the TME from layer rotation, then

$$
\delta = \frac{\beta}{n-1} \tag{5}
$$

$$e\_I = 2R\sin\frac{\delta}{2}\tag{6}$$

$$e\_I = 2R\sin\frac{\beta}{2(n-1)}\tag{7}$$

The relation between layer numbers (5–25) and TME from layer rotation for a height-1 hypothetical model with 45◦ of rotation between the top and bottom layers was calculated and plotted in Figure 6b. As can be seen in Figure 6b, the corresponding TME from layer rotation underwent reduction with larger layer numbers. Therefore, for the same product

height, larger layer (veneer) numbers could result in decreased TME not only from layer rotation, but also from layer height as a result of the smaller layer height. Notably, for the product presented in this study (Figure 4), calculations showed that a 100% increase in layer number could increase the bonding area by 225%, which could increase production costs. The lower the layer height, the smaller the veneer thickness, which also increases the difficulty of veneer manufacturing. Notably, although the sample created for this study was a small object in the centimeter scale, the core characteristics of the LcVL method could be scaled up to manufacture structures in the meter scale, in theory. Naturally, corresponding parameters, such as the product height, layer height, and layer number should be adjusted accordingly to optimize the TME.

## *3.3. Wood Texture Direction and LcVL-Product Structure*

The structural directionality of LcVL products could be designed through wood texture directions. The sample presented in Figure 4 was created by stacking identical layers with each layer rotated by 2.25◦ . As shown in Figure 7a, a pair of identically-cut layers share the same wood texture direction. Thus, since all layers are 2.25◦ offset from their adjacent layers, the wood texture directions of all layers are 2.25◦ apart in this sample. However, as shown in Figure 7b, if layer 2 was cut with a counterclockwise 2.25◦ rotation from layer 1, then the wood texture direction of layer 2 would be 2.25◦ clockwise from layer 1. Thus, if such layer pairs were laminated together with a 2.25◦ counterclockwise layerto-layer increment, the resulting product would have consistent wood texture direction. Alternatively, if layer 2 was cut with a 90◦ counterclockwise plus 2.25◦ counterclockwise rotation, as shown in Figure 7c, then the wood texture directions of layers 1 and 2 would be orthogonal in a product with 2.25◦ counterclockwise-rotated layers. The directionality of such a product could be analyzed with the orthogonal principle of plywood technology. The designability of LcVL-product structures is essential for creating material templates and matrices for composites of varying properties with LcVL.

**Figure 7.** Wood-texture direction (indicated by red arrows) and distinct layer-cutting solutions (**a**) Cutting solution with identically cut layer 1 and layer 2. The resulting wood texture directions of the structure are 2.25◦ between each layer. (**b**) Cutting solution that produces a product with a consistent wood texture direction. (**c**) Cutting solution that produces a product with orthogonal wood texture directions between layers.

#### **4. Conclusions**

LcVL is a relatively simple procedure for constructing customized and geometrically complex wood products which would otherwise be impossible, difficult, and/or costly using SM. Aside from raw material costs, costs of material waste and time consumption are optimizable factors of efficiency. In addition, the LcVL produce should be fairly adoptable, as its core technologies, laser-cutting and plywood, are already widely used in the wood industry.

From the above findings, the following conclusions could be made:


**Author Contributions:** Conceptualization, Y.T. and P.L.; methodology, P.L.; investigation, Y.T. and Q.Y.; writing—original draft preparation, Y.T.; writing—review and editing, Y.T. and P.L.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This project was supported by the PROGRAM FOR NEW CENTURY EXCELLENT TAL-ENTS IN UNIVERSITY OF CHINA, grant number NCET-13-0711 and the START-UP FUNDING FROM QILU UNIVERSITY OF TECHNOLOGY, SHANDONG ACADEMY OF SCIENCES.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Acknowledgments:** The authors would like to thank Zelong Li (University of British Columbia) for his help.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

