1. Introduction
Free-form buildings refer to the structures that are not rectangular but tilted, narrowed, deformed, or have free curves as a whole or partially [
1]. Nowadays, the technology to build free-form buildings is constantly evolving [
2]. It is possible to see the development of technology by comparing the latest free-form buildings to the past buildings [
3]. With the development of computer technology, it is becoming easier to engineer free-form buildings with geometric shapes. Engineers can use Building Information Modeling (BIM), such as Rhino, CATIA, and Revit, to easily express and modify curves, distortions, and free forms [
4,
5]. However, it is still very difficult to build an exterior with complicated designs [
6,
7].
Free-form buildings, in contrast with formal architecture, cannot be built out of a single massive mold as the exterior consists of curves [
8]. Therefore, the free-form exterior is divided into panels that can be fabricated and constructed separately [
6]. For example, the Sydney Opera House consumed around 10,000 sheets of free-form concrete panels to complete the shell-shaped roof, and Louis Vuitton Maison Seoul was completed in 2019 using about 19,000 sheets of free-form concrete panels [
9]. In addition, the Dongdaemun Design Plaza (DDP) used about 40,000 pieces of free-form metal panels. About 76,000 free-form concrete panels was used to fabricate the 316 roof disks of the National Museum of Qatar [
10]. About 20 different panels were fabricated to complete a single disk and about 150 disks with different curvature were fabricated to cover the entire museum [
11]. In order to build the roofing on top of the museum, about 3000 molds were fabricated to complete the panels that were unique in shape [
12].
Each free-form panel has a unique curvature, shape, and size, and the molds cannot be reused. With a greater number of molds to fabricate, it consumes a considerable amount of time and labor. This leads to greater cost of materials and waste disposal to delay the construction period and increase overall cost. The total construction cost of the Sydney Opera House was about 120,000,000 USD, which was 15 times greater than the initial estimate, and the cost of constructing the Guggenheim Museum Bilbao increased to 127,000,000 USD by 14 times [
13,
14,
15]. Many other free-form buildings, such as the MIT Stata Center and Walt Disney Concert Hall, consume more than they cost due to technical limitations [
16].
In particular, free-form panels can hardly be accurate due to the manual processes. In the case of free-form concrete panel (FCP) fabrication, the thickness of materials can vary according to the skillfulness of workers in surface treatment, as concrete has a flexible characteristic. In addition, quality issues are likely to occur as even the same team of workers can deliver inconsistent accuracy each time [
17,
18]. When there are errors in the fabrication process, even a small error can cause gaps between the panels in the assembly stage, and the accumulation of errors leads to construction errors. Severe construction errors lead to re-fabrication of panels for re-construction. Some technologies have applied Computer Numerical Control (CNC) devices to fabricate highly accurate molds out of various materials, but all of them have still failed to resolve the problem of disposable molds. Many studies have applied CNC devices to develop mold fabricating equipment and resolve these issues. The CNC devices receive the engineered curves in numerical data and fabricate the molds through mechanical movements. This technology significantly reduces the time and cost required to build free-form buildings, but it has caused shape errors due to the variables in the mold fabrication process. Therefore, it is necessary to improve the accuracy of free-form concrete panel fabrication technology for high-quality shapes. For that purpose, the current study aimed to improve the multi-point CNC technology for mold fabrication. The new method can modify the shape of molds as it moves countless rods to create the curves. However, the accuracy of curvature varies according to the materials of molds and the types of connections, resulting in errors. Therefore, the current study suggested the connection technology of shape part suitable for the multi-point CNC to enhance the accuracy of curvature fabrication and tested the accuracy of the technology. The study consisted of four sections:
Analysis of limitations of the existing multi-point CNC technology.
Development of multi-point CNC’s connection technology of shape part.
Testing the accuracy by testing the shapes of curves.
Testing the technology by fabricating free-form concrete panels.
4. Free-Form Concrete Panel Fabrication Test
The aforementioned curve test confirmed that the technology suggested by the current study created a more accurate curved mold. However, errors may be caused by deformation of molds when it was actually used to fabricate the panels. Therefore, it was necessary to check the rigidity of molds to test the effect of technology. For that purpose, the current study used a manual multi-point press applying the detachable type to fabricate the free-form concrete panel according to the panel fabrication technology suggested by Yun (2021) [
31]. First, a double-sided curve panel that was 1000 mm × 1000 mm with 20 mm thickness as in
Figure 10a was engineered. Considering the maximum size of manual multi-point press, the panel was divided into four square panels that was 500 mm on one side as in
Figure 10b. The top
Figure 10e of the divided panel was a curve built with a mold, so the moving values of rods should be calculated based on the top part. Therefore, the panel was rotated by 180° and 3D CAD was used as in
Figure 10c to calculate the moving values of rods. Once the moving values of rods were calculated, the rods were elevated according to them as in
Figure 10d and a silicone plate was placed on top to create a curve.
The moving values of rods were calculated using the 3D CAD considering the joints and the moving values of rods of all four panels were equal as the divided panels were identical in shape as in
Table 3.
The shape errors were measured to check the accuracy of mold curve. A 3D scanner was used to scan the curve and compare it to the engineered shape. As a result of error analysis, the errors ranged between −1.466 mm and 1.477 mm as shown in
Table 4 and the range of error was 2.944 mm. As in
Figure 11, most silicone plate showed ±1.000 mm errors. However, the error was about −1.500 mm in several tiny circles in the areas where the curvature changed radically as in (a). The silicone plate was pressed down by the force that bends inwards while forming the curve. As the silicone cap supported it, the center with greater bearing force showed smaller errors, but the edges with smaller bearing force showed greater errors. However, the measured errors were within 3.000 mm and the shape was not corrected because the errors did not exceed the allowable error of panel fabrication [
9,
17,
18,
31,
32].
As the mold curve’s accuracy was proven by measuring the errors, the free-form concrete panel was fabricated as in
Figure 12. The current study fabricated several panels that are 500 mm on one side using the same mold to fabricate a free-form concrete panel that is 1000 mm × 1000 mm. A side mold that was 20 mm in thickness was installed on the lower mold from the manual multi-point press as in
Figure 12a, the right amount of concrete was poured to finish the top as in
Figure 12b, and the concrete was cured as in
Figure 12c. Then, the mold was removed to complete the fabrication as in
Figure 12d. In order to analyze the shape error of fabricated panels, the panels were scanned as in
Figure 12e and the quality of shape part was tested as in
Figure 12f. Steps
Figure 12a through
Figure 12d were repeated to fabricate four free-form concrete panels and steps
Figure 12e,f were repeated for the quality test.
The current study divided the panels to match the size of manual multi-point press, so shape error was analyzed for each panel. First, the shape error of Panel 1 and the curve error of mold were compared to see if there is any deflection caused by the load of concrete. This was the first panel where concrete was poured immediately after completing the mold and it is affected only by natural deflection as there is no error caused by the removal of mold and the disposition of shape panel. The deflection by concrete can be identified by comparing the errors between the curve of mold and the curve of the panel fabricated with the mold. As shown in
Table 5, the curve error of the mold before pouring concrete was 2.944 mm and the curve error of the top of free-form concrete panel was 3.486 mm. The difference between the two curve errors was 0.542 mm. In other words, the deflection by the load of concrete was about 0.500 mm. As a result, there was an error smaller than 1.000 mm, manifesting that the silicone cap from the study has outstanding resistance against the load of concrete.
Next, the shape error of four panels was analyzed to check the error caused by repeated fabrication. As shown in
Figure 13, the error was large in the center where the curvature changed sharply on Panel 2. However, the error at that part reduced as fabrication was repeated. This manifests that the deflection error was offset by the change in the revolving angle of rods and the bearing position of silicone cap with more fabrication. However, there were errors found on other parts and the overall error did not change.
The shape error of free-form concrete panel was 3.486 mm for Panel 1, 3.069 mm for Panel 2, 3.319 mm for Panel 3, and 3.270 mm for Panel 4 as in
Table 6. The shape error did not show much change caused by repetition, but the shape error was measured to be within 3.000–3.500 mm.
The deflection by the load of concrete was about 0.5 mm and the shape error of panel was no larger than 3.5 mm. This was a very small error and it can be judged that the rigidity of mold was great for panel fabrication. However, it exceeded the allowable error of 3.000 mm and additional improvement would be needed to reduce the error to allowable error. The error of fabrication was about 0.5 mm, so it was necessary to correct the mold through the aforementioned reverse engineering, so the maximum error did not exceed 2.500 mm.
The panel assembled after the quality test of each panel showed minor errors as in
Figure 14. This was because there was no rear space frame fixing the panel in place and the panel was not accurately positioned. Therefore, the overall panel would be almost free of errors when a rear space frame was installed to support the panel at the right height and calibration was inserted at a regular interval.
5. Conclusions
The current study developed a connection technology of shape part suitable for multi-point CNC, and it analyzed the limitations of the existing fixed type and developed the detachable type connection technology for improvement. The detachable type places the silicone plate on the rods without any fixtures. A silicone cap was placed at the end of each rod and the rods were elevated as engineered to place the silicone plate on top. Then, the joints revolved freely to create the curve. This method was easily fixed without additional fixtures and did not cause elasticity due to connection. In addition, it can create a smooth curve with no unevenness and prevent any deflection by concrete. For verification, the existing fixed type and the new detachable type were applied to create curves and analyze the shape error. The detachable type’s shape error was smaller than that of the existing fixed type and the error reduced by up to 2 mm. This indicated that the shape was more accurate than the existing method. Panel fabrication test was conducted to test the errors that occur when the new technology was applied to fabricate the panels and the rigidity of the mold equipment. The error of the mold curve was within 3 mm, which was the allowable error suggested by the current study. Next, as a result of shape analysis after panel fabrication, the deflection by the load of concrete was about 0.5 mm. This was a minor error, manifesting that the detachable type suggested in the current study has excellent resistance against the load of concrete. The range of shape error caused by repeated fabrication was within 3–3.5 mm. There was about 0.5 mm of error, but it was a minor error, meaning that the rigidity of mold was also suitable for panel fabrication. The current study suggested a new technology to overcome the limitations of the existing technology and fabricated the panels to prove outstanding accuracy. Therefore, the technology would be able to fabricate high-quality panels. However, the shape error of the fabricated panels exceeded the allowable error suggested by the current study although it was very small. Therefore, additional studies would be required for the shape error to satisfy the allowable error in panel fabrication. In addition, the current study can only fabricate panels of certain sizes and additional studies would be necessary to fabricate free-form concrete panels for actual structures and test the accuracy in order to apply the new technology to real life.