1. Introduction
A wide range of technologies have been applied to the construction of free-form buildings elements, but these newly built structures have required vast capital, and technologies are lacking to economically produce high-quality free-form members [
1,
2,
3,
4,
5,
6]. In addition, disposable molds used for free-form panels are not sustainable. For instance, the expected initial construction cost of the Sydney Opera House was USD 7 million, but it increased to USD 1.02 hundred million, about 15 times the initial cost [
1], and the total construction cost of the Bilbao Guggenheim Museum was USD 1.27 hundred million, which is about 14 times the initially expected construction cost [
2]. Similarly, the recently built Dongdaemun Design Plaza required twice the original budget, and the equivalent of more than USD 200 million was spent on the frequent design and service change orders [
7]. Many other free-form buildings, including the MIT Stata Center and the Walt Disney Concert Hall, have exceeded their planned budgets [
8]. Such increased costs result from the great amounts of manpower and time required to ensure the quality of curved surfaces. Time and manpower needs vary according to the materials and technology used to produce the free-form members. The most common materials used to produce free-form components are metal and concrete [
9,
10,
11,
12]. Metal may corrode or deform due to a slight impact, making it difficult to maintain, and it takes the maintenance costs for the insulation and corrosion protection. Concrete is superior to metal in terms of its formability and strength, it being easy to maintain, and it being able to solve the problems of metal [
13]. However, the cost and construction time can be higher for concrete than metal when producing free-form members using the existing technology. In particular, the molds for free-form structures cannot be reused, which creates great burdens on the environment and cost [
14]. In addition, shape accuracy is inconsistent, varying according to workers’ skills and competence in producing free-form concrete panels or segments. In particular, when different workers plaster and surface panels, the panel thickness may change depending on the worker. Moreover, panels of differing quality may be produced by the same worker, resulting in a quality control problem. For managers to interpret the designs of differently shaped panels, prepare shop drawings, and produce such panels is a fairly difficult job. Moreover, 3D printers can also make concrete panels. However, many technologies need to be developed in order to use 3D printers for manufacturing 3D panels. Such problems can be solved by developing a suitable computerized numeric control (CNC) machine that can produce accurately shaped molds for free-form concrete materials in a short period of time. This paper presents a production technology of high-quality free-form concrete panels using the CNC machine developed in this project, and the shape quality is experimentally verified.
The present project included the following four steps:
- (1)
A CNC machine suitable for producing variable molds was developed, and a prototype was manufactured;
- (2)
Concrete panels were designed based on the curvature and size of existing free-form buildings;
- (3)
A variable mold was produced using the CNC machine, and concrete panels were produced;
- (4)
The error in the shape produced by the CNC machine was analyzed to verify the performance.
2. Consideration of Previous Studies
Making a new formwork every time is very time-consuming and costly. Construction engineers can easily implement 3D designs through CNC machines. In preceding studies, Mandl et al. and Lindsey and Gehry used CNC processing technology to fabricate an expandable polystyrene (EPS) formwork [
3,
15], whereas Ito Toyo and associates processed wood with a CNC machine to produce molds and used them to fabricate free-form concrete members [
16]. CNC-processed molds can ensure accuracy in the concrete shape, but they are not reusable, pointing to the need for improvement. Franken and ABB implemented free-form concrete based on a digital formwork using CNC and acrylic glass to render the surface tension of a water droplet [
17]. However, these studies merely introduced the production and superiority of free-form concrete, failing to secure its economic viability. Thus, a variable formwork is needed that is reusable and capable of enabling mass production. Latorre studied technology utilized to build a free-form dorm using a pneumatic system [
18]. This technology was limited in terms of the implementable shape, requiring separate fabrication for the construction. In addition, Verhaegh studied the use of fabric for a formwork to implement free-form concrete [
19]. However, additional study was needed to achieve accurate shapes using fabric and develop a reinforcement approach. Accordingly, this approach required time for fabricating molds in large quantities used to restrain the shape of the fabric. EPS formwork is designed with 3D-CAD (Computer Aided Design), processed with a CNC system, and installed. Installed EPS blocks are utilized as formwork for concrete placement [
2,
20].
Texaco Petrol Stations embodied free form by covering EPS formwork with polyurea and Parking Amsterdam Oosterdokseiland used EPS formwork for placing concrete [
20]. The Spencer Dock Bridge was built as EPS formwork, fabricated, and installed and concrete was placed for about 6 months [
20]. Curing and formwork removal took about 2 months [
19]. The concrete surface quality was good, but the joint between EPS blocks left unnecessary lines on the concrete surface. In addition, huge amounts of EPS waste caused environmental problems and a cost increase. Molds of the free-form concrete members used for the Dongdaemun Design Plaza in the Dongdaemun History and Culture Park were built using a BIM (Building Information Modeling) program—Digital Project. Wood was cut to be 300 mm long and formwork was built with internal and external ribs using wood frames. The polygonal formwork technique installs uniquely shaped systemized form panels and can embody free forms similar to the segment type. This technology uses wood panels and cuts each panel with a cutting robot or CNC machine [
21].
The CRAFT (Center for Rapid Automated Fabrication Technologies) at the University of Southern California in the United States studied robot-enabled automation, construction processes, new materials, and computer-assisted design with the aim of automating free-form concrete placement and large machinery fabrication and utilization in building construction automation. The CRAFT proposed a concept for producing free-form members using a large 3D printing instrument. However, the CRAFT remains at an experimental level, producing small members about 1–2 m wide and incapable of producing large members wider than 2 m. In addition, the limitations of the plotting fabrication method result in a considerable production time, rendering mass production impossible [
22]. Researchers from the Innovative Manufacturing and Construction Research Centre of Loughborough University in England are studying 3D printing of free-form concrete [
23]. There are two types of molds used in this method: master and direct molds. The master mold produces free-form concrete panels using 3D printing, and the direct mold produces formed concrete shapes. These methods have the disadvantage that extra manpower is required to produce accurate shapes because a shape printed for the first time is severely rugged. In addition, because it is produced with a plotting method similar to the CRAFT, it is time-consuming to produce one panel, and mass production of panels is economically infeasibility [
7]. As seen above, international studies on free-form building have attempted to put free-form building technology to practical use by employing CNC-processed expandable polystyrene (EPS), wood, fabric, and other materials. However, it is difficult to use this technology in practical applications due to time and cost constraints. Further, many free-form buildings completed to date [
19,
20,
24,
25,
26] have used steel, wood, EPS, and plastic, among other materials, to produce free-form members, but such molds were not reusable, adding fabrication time, incurring significant costs, increasing total construction cost, and delaying the schedule. To address these issues, the CRAFT and IMCRC (Innovative Manufacturing and Construction Research Centre) are actively studying free-form building solutions through academic–industrial partnership initiatives, but they are still far from practical solutions due to the limitations of applicable technical concepts. Therefore, it is necessary to develop a cost-effective variable formwork and free-form concrete production technology with the aim to reuse formworks and minimize labor requirements [
4]. Recognizing this need, Gramazio et al. used wax to develop reusable molds to produce concrete panels [
27]. However, they did not provide analyses or solutions to problems such as those relating to the solidification time, crystallization, strength, solidification shrinkage, and cracking. They only proposed the concept of the equipment and technology to produce shapes with wax molds, without a specific explanation. Their study results are limited in not addressing critical problems such as shrinkage, the solidification time, and cracking caused by pure wax during their experiments with the composite phase change material (PCM) mold they developed. In addition, their study merely suggested the concept of utilizing the recently presented 3D display technology for the production of mold shapes, and it is greatly limited in that it provides no standards or dimensions of the equipment used for the production of free-form shapes. Pedersen and Lenau implemented a shape, using multiple pins [
28]. However, the greater number of pins causes the cost of the CNC equipment to increase and the thin rubber membrane to become slack, resulting in greater errors. In addition, the absence of error analysis further compromises its trustworthiness. The CNC equipment herein is highly efficient in implementing smooth architectural designs. There have been several of attempts to study metal-working equipment using pin-type tools. Munro and Walczyk proposed a piece of metal-working equipment using a pin-type tool [
29]. Among its disadvantages, the pin-type tool requires a very dense layout of pins, resulting in a significant rise in the unit cost and operating time. In addition, the absence of error analysis further compromises its trustworthiness. Vedel-Smith and Lenau proposed a pin-type tooling approach intended to print patterns on the surface [
30]. Im et al. [
31] compared pressing techniques widely used in forming metal shapes by applying pressure to metal with multiple pins. Tan et al. analyzed the multi-point forming (MPF) approach using multiple pins to apply pressure to form metal into curved shapes [
32]. These studies dealt with metal with different research scopes and necessitated precision error testing. Savvides [
33] developed the free-form formwork system technology (3FST), which makes free-form shapes using equally spaced rods on both sides. A total of 25 rods are installed to produce concrete members of 1 × 1 m. Moreover, 3FST uses a round head that can be rotated in all directions to produce curved shapes. However, Savvides did not go beyond the level of presenting the idea, and there was no verification of the performance of 3FST in producing shapes and errors.
5. Measurement of FCP Quality
The CNC machine can implement shapes freely. In addition, it delivers smooth shapes when a rubber- or silicone-based shape-smoothing plate is employed. However, the CNC machine may incur minute errors, and it is limited in terms of implementable shapes. Minor curves applied to buildings can be implemented sufficiently, but there is a limit in fabricating the dynamic shapes found in artwork. This project identifies the error of the CNC machine via a shape implementation test and analyzes its limitations. The shape implementation test was conducted by implementing a shape that reflects the curvature of existing buildings.
The subject of the test was selected as the area with the greatest curvature, and the test compared the size and curvature of the produced shape with those of the original building. The first case was the Guggenheim Museum. As shown in
Figure 9a, the area of greatest curvature was selected, and the size and curvature were reviewed, as shown in
Figure 9b. Area A in
Figure 9 is a semi-circle about 15 m wide, and it was divided into six panels about 4 m wide to produce the members. The divided panel was 3.88 mm long with vertical variation of 0.76 m and a curvature radius of 7.5 m.
The second case was the Sydney Opera House. The area with the greatest curvature is marked “A” and indicated with dotted lines in
Figure 10a. This area was selected as the subject of review, and the size and curvature were examined, as shown in
Figure 10b. Area “A” in
Figure 10 is a free form about 15 m high, and it was divided into four equal panels about 4 m wide. Each divided panel was 4 mm long horizontally and varied 0.33 m vertically.
The third case reviewed was Club House “S” in Korea. The roof of this building varies significantly in terms of shape, as shown in
Figure 11b. The conventional technique of placing concrete after fabricating and installing a metal formwork was applied to the construction of the free-form roof. An interview with the construction contractor revealed that the actual cost exceeded the contract amount 10-fold, and most of the overrun was in labor costs. The roof of the building, which was responsible for most of the cost increase, has many inflection points, and the area with the greatest curvature shows vertical variation of about 70 mm per 1 m. This project conducted the shape implementation test on the roof shape of Club House “S,” which was thought to be more challenging.
The shape of Club House “S” was reproduced in parts, with sharp curves and relatively gentle curves repeated, as in Panels A and B shown in
Figure 12a. The reproduced design is 4 m long and varies about 0.45 m in elevation with two inflection points and three centers of curvature. The shape implementation test was conducted on Panels A and B, which had the greatest curvature. The CNC machine prototype was fabricated in reflection of the actual curvature of the as-built architecture. Since the other panels had little curvature, no difficulties were expected when implementing their shapes with the CNC.
Panel A’s center was convex with the center of curvature existing in one direction. Panel B had an inflection point with the center of curvature in both directions. Three different designs adopting the mold of Panel A were prepared, as shown in
Figure 13a. Two other designs adopting the mold of Panel B were fabricated as shown in
Figure 13b, and a sixth design, shown in
Figure 13c, was fabricated by doubling the variation in elevation in Panel B. Designs 1 through 5 were 360 mm long with a maximum height of 25 mm and contoured in reference to the curvature of Panels A and B of Club House “S”, which is the reference case. In the case of Panel B, an arbitrary inflection point that did not exist in the case was inserted to measure the shape implementation capability. Design 6 reflected the shape of Design 4, but its variation in elevation was set to 50 mm to increase the experimental strength.
It is difficult to see any difference between the shape implemented by the CNC machine and the design. However, precise measurements reveal errors in each panel as shown in
Figure 14. Given the precise operation of the NCR, most of the errors are deemed to have occurred in the shaping plate during the CNC machine operation.
Table 1 shows the descriptive statistics from the test results on Designs 1 through 5. Four tests were performed on each design, and the tests were numbered Tests 1~20 to facilitate the overall analysis and differentiation. The value “N” is the number of points measured in one experiment. The distance was measured using a laser distance meter. The total number of tests on all designs was 740, and on average, the elevation of the NCRs was 359.91 mm, the standard deviation was 8.43, and the maximum and minimum values were 373.95 and 348.63 mm, respectively.
A standard tolerance of 3% for wall thickness was applied in accordance with the tolerance standard set forth in Article 20 of the Enforcement Decree to the Building Act of Korea. When the FCP thickness was set to 150 mm, the error range was 4.5 mm. The t test value (tx) of the test results for Designs 1~5 calculated using the T distribution was −61.46, which is smaller than the −1.65 threshold of t(0.05,739) at a significance level of 0.05 (one-tailed), enabling the rejection of the null hypothesis of Equation (2) (
H0).
Since it is elastic, the shaping plate can be deflected by gravity. In addition, unlike an NCR implemented with precision, it is likely to deviate from the designed shape. Thus, in the shape implementation test results, errors may increase as the distance from an NCR increases. This is investigated via data analysis.
To confirm whether the relationship between the distance from an NCR and error also relates to changes in the design, the shape implementation test results for Designs 1~5 were integrated and verified.
Table 2 shows the descriptive statistics and error occurrence in Designs 1~5. The “Error” means the vertical error arising in the implemented shape with the design in this test.
As listed in
Table 2, 740 datasets were analyzed, and an average error of 0.44 mm occurred when the distance from the NCR was 10 mm. When the distance was 20 mm, the average error was 0.8 mm, and it was 1.15 mm when the distance was 30 mm. Further, when the distance was 40 mm, an average error of 1.19 mm appeared. However, the maximum value incurred an error of 5.62 mm at a distance of 30 mm from the NCR, rather than 40 mm.
ANOVA analysis was conducted on the errors in Designs 1–5. The means of errors measured at distances of 10, 20, 30, and 40 mm from the NCR were denoted M1, M2, M3, and M4, respectively. As given in Equation (3), the null hypothesis (
H0) is that “the means of the four groups are the same,” and the project hypothesis (
H1) is that “the means of the four groups are different.” Verification was performed at a confidence level of 95%. The results of the ANOVA analysis on the 739 datasets are provided in
Table 3; the F-value was 12.48, and the
p-value was 0.0. Thus, the null hypothesis (
H0) can be rejected, and it is deemed that errors increase significantly as the distance from the NCR increases, with respect to the means of the four groups in Designs 1~5.
A regression model of the two variables was developed based on the NCR and the datasets of the shape implementation error tests. The regression model provides a basis for estimating errors that may arise in reference to the distance from the NCR. Due to the purpose and structural characteristics of the CNC machine, the spacing is not wide between the NCRs. Therefore, a linear regression model was applied without considering the case in which the error rate increased, which can arise if the spacing between the NCRs is wide.
Table 4 summarizes the details of the regression model for Designs 1~5. R squared was 0.06, and the standard deviation of the measured values was 1.6.
Equation (4) shows the estimated line of regression indicating the relationship between the NCR and the shape implementation error. In addition, as shown in
Table 5, the variance analysis results show that the F-value is 46.85 and the
p-value is 0.0, indicating statistical significance of the regression model at a confidence level of 0.05.
Design 6 was fabricated with the vertical variation rate of the curved surface doubled. The first shape implementation test on Design 6 revealed a maximum measurement error of 4.23 mm; the second biggest error was 2.37 mm, and the third biggest error was 2.32 mm. The overall shape did not deviate significantly from the design, but it was confirmed that errors occurred across a wide range.
The descriptive statistics of the test results for Design 6 are provided in
Table 6. The test was conducted four times in total, and they were numbered Tests 21~24 to facilitate the overall analysis and differentiation. The total measurement frequency during the tests of Design 6 was 148 times, and on average, the elevation of the NCR was 321.9 mm, the standard deviation was 18.96, and the maximum and minimum values were 290.28 and 342.03 mm, respectively.
The t test value of the test results for Design 6 was calculated to be −27.91, which is smaller than the −1.65 threshold of t(0.05,739) at a significance level of 0.05 (one-tailed), enabling the rejection of the null hypothesis of Equation (5) (
H0).