# The Impact of Design Complexity on Additive Manufacturing Performance

Kyudong Kim, Kijung Park, Hyun Woo Jeon

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Kyudong Kim, Kijung Park, Hyun Woo Jeon. The Impact of Design Complexity on Additive Manufacturing Performance. IFIP International Conference on Advances in Production Management Systems (APMS), Sep 2022, Gyeongju, South Korea. pp.227-234, 10.1007/978-3-031-16407-1_27 hal-05386061

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# The Impact of Design Complexity on Additive Manufacturing Performance

Kyudong Kim<fnref n="1" /> Ⓒ, Kijung Park<fnref n="1" />(✉) Ⓒ, and Hyun Woo Jeon<fnref n="2" /> Ⓒ

**Abstract.** Complexity in a manufacturing system can lead to unnecessary costs due to an increase in manufacturing uncertainty that negatively affects the reliability and controllability of the system. Despite the importance of understanding complexity in manufacturing, the conceptualization of complexity for an additive manufacturing (AM) system and its impact on operational performance have not been clearly articulated in the literature. As a response, this study characterizes a complexity measure relevant to AM and identifies the impact of the complexity on operational performance in an AM system. For this, design complexity for AM is defined by considering both the volume ratio and area ratio of a part design. Then, a virtual AM plant for aircraft parts is built by a discrete event simulation to derive the average order lead time of each part design. A linear regression analysis is performed to understand the impact of the calculated design complexity on the AM performance. As a result, this study shows that design complexity negatively affects the average order lead time of the AM system. The findings from this study indicate that the design aspects of complexity for an AM based system should be properly managed to improve its operational performance.

**Keywords:** Additive manufacturing · Design complexity · Discrete event simulation · Regression analysis

## 1 Introduction

Many concepts and metrics of complexity for a manufacturing system have been widely discussed in previous studies [1–3]. Complexity is related to an increase in uncertainty that negatively affects the reliability and controllability of a manufacturing process [1, 3]. Despite a consensus of the negative impact of complexity on operational performance [2], the complexity of additive manufacturing (AM) has not been fully discussed in the literature. Moreover, existing studies relevant to AM have not sufficiently investigated how AM complexity affects the operational performance of an AM system that handles multiple AM machines for various part designs.

<footnote n="1">¹ Department of Industrial and Management Engineering, Incheon National University, Incheon, Republic of Korea
{sooe07,kjpark}@inu.ac.kr</footnote>

<footnote n="2">² Department of Industrial and Management Systems Engineering, Kyung Hee University, Yongin-si, Republic of Korea
hwjeon@khu.ac.kr</footnote>
Focusing on the above issues, this paper aims not only to propose a complexity measure for AM but also to investigate the impact of AM complexity on the operational performance of an AM system. First, this study proposes a design complexity measure to quantify the complexity underlying in a part design for AM. Next, a virtual AM plant for aircraft parts, which handles multiple fused filament fabrication (FFF) machines for carbon fiber reinforced polyether-ether-ketone (CFR-PEEK), is modeled for discrete event simulation to estimate the average order lead time of each part design. Then, a regression analysis is performed to identify whether the proposed design complexity measure has a statistically significant impact on the operational performance obtained from the simulation model.

## 2 Literature Review

Design complexity for AM has been addressed based on the computer-aided design (CAD) of a part because a CAD model contains geometric information for digital manufacturing [4, 5]. Conner et al. [6] evaluated design complexity by considering three geometric parameters: (1) the volume ratio of a part to its bounding box, (2) the surface area ratio of a sphere with equivalent volume to a part, (3) the number of holes in a part. Pradel et al. [7] proposed a design complexity measure through the ratio between the surface area of a part and the volume of a design space between functional surfaces. Valentan et al. [8] used three design parameters for a part (i.e., the number of triangle in the standard tessellation language (STL), the surface area of a part, and the volume of a part) to represent design complexity. Johnson et al. [9] addressed five design complexity metrics: (1) the number of surface of a part, (2) the number of triangle in STL of a part, (3) the volume ratio of a part to the volume of a bounding box, (4) the area ratio to the surface area of a cube, and (5) the area ratio to the surface area of a sphere. Fera et al. [10] proposed a design complexity metric, which is defined as a ratio between part volume and envelope convex volume. Joshi and Anand [11] calculated a complexity score for measuring design complexity based on AM parameters (i.e., sharp corners, thin regions and thin gaps, support structure volume, and part volume and height) and subtractive manufacturing parameters (i.e., internal corners, number of free form surfaces, tool inaccessibility, and machining volume of stock).

With the efforts to define and quantify design complexity for AM, there also have been attempts to examine the impact of design complexity on AM performance in the literature. Johnson et al. [9] addressed that design complexity metrics have no significant effects on processing time for CAD modeling. Baumers et al. [12] showed that design complexity has a weak impact on energy consumption for an AM machine. Pradel et al. [7] revealed that an increase in the surface area of a part negatively affects printing time and material cost for an AM machine. Chen et al. [13] stated that a higher level of design complexity significantly negative impacts on the build quality of AM.

Although a relationship between design complexity and AM performance for a single AM machine has been explained in the literature, the impact of design complexity on an entire AM system has not been sufficiently discussed so far. As a response, this study proposes a design complexity measure for AM. Then, a discrete event simulation model is built to identify the impact of design complexity on operational performance in an AM system that handles multiple AM machines and multiple part orders.
# 3 Methodology

## 3.1 Development of Design Complexity for AM

A design complexity measure for AM is proposed in this section. This study employed the volume ratio and the area ratio defined in [14] to quantify design complexity for AM because they comprehensively characterize the geometric features of a part design. The volume ratio ($V_R$) is expressed as:

$$V_R = V_P/V_B(0 < V_R \le 1), \qquad (1)$$

where $V_P$ is the volume of a part design, and $V_B$ is the volume of a bounding box for the part design. A bounding box is defined as a box given by the maximum length, width, and height of the part design [14]. The volume ratio becomes 1 (i.e., the lowest complexity level) if the volume of the part is the same as the volume of its bounding box. Similarly, the area ratio ($A_R$) is defined as:

$$A_R = A_S/A_P(0 < A_R \le 1), \qquad (2)$$

where $A_P$ is the surface area of a part design, and $A_S$ is the surface area of a sphere that has the same volume as its part design.

A design complexity measured for AM is proposed by combining the above two elements in Eq. (1) and Eq. (2). The design complexity (DC) measure for AM is expressed as:

$$DC = 1/(V_R A_R) \qquad (3)$$

If an AM machine fabricates a simple part design such as a cube or a sphere, the value of the proposed measure becomes close to 1, which indicates a low complexity level. On the other hand, the proposed measure has a large value if a part design includes various design features (e.g., holes and complex shapes).

## 3.2 Impact of Design Complexity on AM Performance

In order to estimate the operational performance of an AM system, a virtual AM plant, which handles 15 part designs for aircraft part type (i.e., bracket, door hinge, engine cover, fork fitting, and seat buckle) (see Fig. 1), is modeled for discrete event simulation. The part designs are collected from Thingiverse [15], which is an open source platform for CAD models. The CAD model of each part design is resized by the Simplify3D [16] slicing software to have the same part volume (= 10 cm³) to identify the impact of design complexity on operational performance at the same condition.

A virtual AM plant is created based on a simulation model in Kim et al. [17] with the following assumptions and conditions. AM machines are assumed to be Apium P220 [18], which is an industrial FFF based 3D printer and compatible with CFR-PEEK. The AM plant consists of 20 parallel FFF machines for CFR-PEEK, and only uses CFR-PEEK as a material to produce aircraft parts. The plant employs a make-to-order strategy, which allows orders to immediately start manufacturing when they arrive at
the AM system. If all AM machines are processing to fabricate parts, an incoming order waits in a centralized queue until any FFF machine is available within the AM system. Each order type consists of multiple parts of the same part design, and the inter-arrival time of each order is assumed to follow a normal distribution: N (μ = 4.0 h, σ = 0.5 h). In addition, one of 15 aircraft part designs is randomly assigned to an order type with an equal chance. The part quantity of each order follows a uniform distribution: u[15units, 25units]. The printing time of each aircraft part is assumed to follow a normal distribution: N (μ = t in Fig. 1, σ = 100 s). The estimated printing time (t) of each aircraft part design is obtained by Simplify3D [16]; the default process parameter settings of Apium P220 for CFR-PEEK are used to derive the estimated printing time information provided by Simplify3D [16] (see Fig. 1).

<table><caption>**Fig. 1.** Aircraft part designs and their information</caption><thead><tr><th>Aircraft part design</th><th>Bracket A</th><th>Bracket B</th><th>Bracket C</th><th>Door hinge A</th><th>Door hinge B</th></tr></thead><tbody><tr><td>t (sec)</td><td>10140</td><td>9480</td><td>11040</td><td>8940</td><td>9540</td></tr><tr><td>V<sub>R</sub></td><td>0.08</td><td>0.23</td><td>0.16</td><td>0.52</td><td>0.38</td></tr><tr><td>A<sub>R</sub></td><td>0.29</td><td>0.44</td><td>0.33</td><td>0.35</td><td>0.28</td></tr><tr><td>Aircraft part design</td><td>Door hinge C</td><td>Engine cover A</td><td>Engine cover B</td><td>Engine cover C</td><td>Fork fitting A</td></tr><tr><td>t (sec)</td><td>10440</td><td>15180</td><td>16380</td><td>13140</td><td>10140</td></tr><tr><td>V<sub>R</sub></td><td>0.18</td><td>0.23</td><td>0.06</td><td>0.13</td><td>0.25</td></tr><tr><td>A<sub>R</sub></td><td>0.37</td><td>0.10</td><td>0.27</td><td>0.24</td><td>0.28</td></tr><tr><td>Aircraft part design</td><td>Fork fitting B</td><td>Fork fitting C</td><td>Seat buckle A</td><td>Seat buckle B</td><td>Seat buckle C</td></tr><tr><td>t (sec)</td><td>12540</td><td>11460</td><td>14700</td><td>10740</td><td>11040</td></tr><tr><td>V<sub>R</sub></td><td>0.10</td><td>0.24</td><td>0.16</td><td>0.33</td><td>0.44</td></tr><tr><td>A<sub>R</sub></td><td>0.31</td><td>0.33</td><td>0.28</td><td>0.34</td><td>0.29</td></tr></tbody></table>

When the fabrication of an aircraft part for an order is completed, the part temporarily waits in the AM plant if the part quantity for the order is multiple; the order leaves the AM system only when the assigned part quantity is satisfied. The AM plant is assumed to be operated for one year (= 52 weeks). In addition, the simulation model runs 100 replications to obtain steady-state statistics. The simulation model is built using Simio 11 [19].

The average order lead time of each aircraft part design obtained by the simulation model is considered to evaluate the operational performance of the AM system. The average order lead time (LTᵢ) of each aircraft part design (i) is expressed by:

$$LT_i = \frac{\sum_{j=1}^{N_i} DT_i^j - AT_i^j}{N_i}, \quad (4)$$
where $AT_i^j$ denotes the arrival time of order $j$ for aircraft part design $i$, $DT_i^j$ is the departure time of order $j$ for aircraft part design $i$ for customer delivery, and $N_i$ indicates the total number of completed orders for aircraft part design $i$.

In order to calculate the design complexity of each aircraft part design, the design information for the volume, area, and bounding box of each part design is obtained from Makexyz [20], which is an online 3D printing service platform. Then, the volume ratio ($V_R$) and area ratio ($A_R$) of each part design are derived by Eqs. (1-2) (see Fig. 1). Based on the obtained the volume ratio ($V_R$) and area ratio ($A_R$) of each part design, the design complexity of each part design is calculated by Eq. (3). To identify the statistically significance of the proposed design complexity on the average order lead time for the AM system, the single linear regression analysis is performed using Minitab 20.3 [21].

## 4 Results

Table 1 summarizes the results of the design complexity ($DC_i$) and the average order lead time ($LT_i$) derived for each aircraft part design ($i$).

<table><caption>**Table 1.** Design complexity and average order lead time for each aircraft part design</caption><thead><tr><th>Part design (i)</th><th>Bracket A</th><th>Bracket B</th><th>Bracket C</th><th>Door hinge A</th><th>Door hinge B</th></tr></thead><tbody><tr><td>DC<sub>i</sub></td><td>43.33</td><td>9.99</td><td>19.15</td><td>5.47</td><td>9.48</td></tr><tr><td>LT<sub>i</sub> (hours)</td><td>4.46</td><td>4.17</td><td>4.79</td><td>3.98</td><td>4.21</td></tr><tr><td>Part design (i)</td><td>Door hinge C</td><td>Engine cover A</td><td>Engine cover B</td><td>Engine cover C</td><td>Fork fitting A</td></tr><tr><td>DC<sub>i</sub></td><td>14.94</td><td>44.61</td><td>61.87</td><td>31.90</td><td>14.06</td></tr><tr><td>LT<sub>i</sub> (hours)</td><td>4.58</td><td>6.40</td><td>6.89</td><td>5.59</td><td>4.45</td></tr><tr><td>Part design (i)</td><td>Fork fitting B</td><td>Fork fitting C</td><td>Seat buckle A</td><td>Seat buckle B</td><td>Seat buckle C</td></tr><tr><td>DC<sub>i</sub></td><td>33.29</td><td>12.59</td><td>22.58</td><td>8.87</td><td>7.67</td></tr><tr><td>LT<sub>i</sub> (hours)</td><td>5.39</td><td>4.96</td><td>6.20</td><td>4.71</td><td>4.81</td></tr></tbody></table>

Table 2 and Fig. 2 show that the design complexity measure is a statistically significant predictor of the average order lead time ($p < 0.05$). The positive coefficient of the design complexity in Table 2 indicates the negative impact of design complexity on the average order lead time; the average order lead time of the AM system increases as the design complexity associated with the AM system increases. Although the complexity measure itself cannot explain all variations in the average lead time (R-sq = 58.76%), the moderate prediction power indicates that the proposed design complexity measure can serve as a good input variable along with other operational input variables to predict the average order lead time of an AM system.
<table><caption>**Table 2.** Regression results ($a = 0.05^{**}$)</caption><thead><tr><th>Major statistics</th><th>Result</th></tr></thead><tbody><tr><td>Regression equation</td><td>LT = 4.13 + 0.04 · DC</td></tr><tr><td>R-sq</td><td>58.76%</td></tr><tr><td>Test for β<sub>0</sub></td><td>t = 15.94, p = 0.00**</td></tr><tr><td>Test for β<sub>1</sub></td><td>t = 4.30, p = 0.00**</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Linear regression plot for average order lead time on design complexity</figcaption></figure>

# 5 Conclusions

This study defined design complexity for AM to investigate its impact on operational performance from an entire AM system aspect. First, a design complexity measure for AM was proposed based on the volume ratio and the area ratio of a part design. Then, the discrete event simulation of an AM system that handles AM orders for 15 aircraft part designs was built to obtain the average order lead time of each part design. Then, a single linear regression analysis was performed to identify the statistically significant impact of the proposed design complexity on the average order lead time. The results of this study showed that design complexity associated with an AM system negatively affects the average order lead time of the AM system and is a critical source of causing inefficient AM operations.

The findings from this study support that complexity is may not be free for AM [7]. Although AM has design freedom to fabricate parts [22], complexity inherent in a part design should be properly managed to improve operational performance for an AM system. For the future work of this study, the original simulation model should be extended to reflect a large AM plant scale and other performance measures. Then, operational strategies for AM to mitigate the impact of complexity on an AM system will be investigated to provide guidelines for best AM operations.
**Acknowledgement.** This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2022R1C1C1012140) for Kijung Park.

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