In this section, we demonstrate the projection results by proposed projection algorithm based on flattening surface and compare with other projection method. The procedure of details on the projection algorithm are mentioned above.
5.2.1 Experimental Setup
In the experiment, the cooperation of the additive and subtractive manufacturing is implemented through inverse kinematics. In other words, the 3D printer and carving tool can be controlled precisely and be cooperated to complete the product. The specification
of gantry-type hybrid machine is explained that the length of the X and Y axes are 1.5m and 1.8m respectively. The height of additive and subtractive are 0.36m, and the tool tip offsets in X, Y and Z direction are 0, 100mm and 120mm respectively.
After that, the integration system with additive and subtractive manufacturing is demonstrated. 3D printer can print the model and the subtractive tool follows the position and direction that are obtained by proposed projection method. In the additive process, the 3D STL model is sliced to generate the moving path from the slicing software. One kind of materials called polylactic acid (PLA) is used as the printing material. The melting point of PLA is from 155 to 170 degrees centigrade.
As mentioned above, the path of the additive information is passed to the subtractive process as the reference data. The reference data and the coordinate of the subtractive tool are considered to adjust the carving path brought by the projection method. Three different kinds of tool tips (shown in Figure 5.2-1) are tested in our experiment.
The rotational speed of the subtractive tool is up to 12000 revolutions per minute (RPM). When the subtractive tool contacts the printed model, the temperature of the material rises quickly due to high speed friction. As we known, the PLA material becomes stickier with the rise of the temperature so that the extra material will attach to the drill probably (Figure 5.2-2).
The final results of the test using three kinds of drills are shown in Figure 5.2-3 in order. In this test, three same square sheets are printed by the additive part using PLA.
And then the aforementioned drills are installed respectively to complete the subtractive Figure 5.2-1 The three different carving tools. Left to right : (a)
The cone drill. (b) The twist drill. (c) The round drill.
Figure 5.2-2 The tool tip after subtractive process.
Obviously, the cone drill of Figure 5.2-1 (a) performs best. Compared with results of (b) and (c), the carving path in Figure 5.2-3 (a) is not only clearer and smoother but also less in the width. It is because no extra material, which is molted by heat of high-speed friction, attaches to the tip while doing subtractive process. The attached material increases the width of carving path so that it affects smoothness of the subtractive performance as well.
This phenomenon is also seen in the result of the subtractive process with the twist drill shown in Figure 5.2-2 (b). The green point is the start point of the subtractive path that moves along the clockwise direction while the red point is the point where the width of the subtractive path starts to be enlarged. This point is also where the molted material starts to attach to the drill. And comparing the drill after subtractive processing and the results of (b) and (c), the width of path of the twist drill is narrower than that of the round drill while more extra material is stuck to the round drill than that of the twist drill. So it is verified that the more extra material attaches to the drill, the larger radium of the drill will be and the wider the subtractive path will be generated.
5.2.2 Experimental Results
Figure 5.2-4 and Figure 5.2-5 show the surface models and flattening results, respectively. In the Table 13 and Table 14, compare with other flattening method that is angle based flattening (ABF). In the results of proposed method, the angle error is a little larger, but the edge length error and the area error is much less.
Figure 5.2-3 The carving results by using the different tools: Left to right: (a) The cone drill. (b) The twist drill. (c) The round drill.
Table 13 Compare with typical methods on hemisphere surface Length
error
Angle error
Area error EBF(proposed) 0.0885 0.11365 0.049692
ABF 0.13159 0.10302 0.097674
Figure 5.2-4 (a) the triangular mesh of the 3D model. (b) flattening result.
(hemisphere mesh data: number of vertex : 145; number of face : 264 ).
Figure 5.2-5 (a) the triangular mesh of the 3D model. (b) flattening result. (wave mesh data: number of vertex : 400; number of face : 722 )
Table 14 Compare with typical methods on wave surface
In the data processing, if the input data is the 2D image or figure, it is processed by image processing that contains the color transformation from RGB to gray level and edge detection. Afterwards, the points that are extracted from the edge image can be planned into a continue path using greedy algorithm or genetic algorithm. Then, as for the subtractive part, the tool can touch the corresponding triangles of top part on the model because of its 5-DOF. Thus, the available triangular flats on the STL model are reserved and filtered out the useless flats by determining whether the normal vector norm of the flat is more than zero or not. In other words, choose the flats (label yellow color in Fig.
2) that can be carved by the subtractive tool.
After the steps of data preprocessing, the processed data can be utilized in projection procedure. Fig 11 shows the result that how the 2D data is projected onto the geometric models. On the model, the data of each point on the projected path contains three components. The first is the coordinate of the point. The second is the carving signal that determines whether the point should be carved or not. The third component is the normal vector of the triangle where the point is inside. After that, it can be ensured that the machine moves to the correct coordinate and the subtractive tool is perpendicular to the surface of the 3D model.
The projection distortion evaluation, which is proposed in the paper [2], is a common used and quantitative analysis method. Compare the length between two adjacent points on 2D data with the distance between two corresponding points on 3D, the average error in length 𝑒𝑙_𝑎𝑣𝑒 can be calculated by Equation (5-4).
𝑒𝑙_𝑎𝑣𝑒 = ( ∑ |𝑙2𝑑_𝑖− 𝑙3𝑑_𝑖|
𝑁𝑝−1
𝑖 = 1
) /(𝑁𝑝− 1) (5-4)
The 𝑁𝑝 represents the number of the point on 2D path while 𝑙2𝑑_𝑖 and 𝑙3𝑑_𝑖 are the distance from the ith point to (i+1)th point on 2D and 3D individually. For example, Fig. 12 shows the two projection algorithms, and the red line is our proposed projection algorithm and the blue line is orthogonal projection method. In Table 15, the (a) and (c) can be flattened into the 2D plane without distortion. In other words, the edges, angles and areas of the triangles in the 3D mesh are transferred to 2D plane without any change.
However, the (b) exists error when the surface of 3D mesh is flattened into 2D plane. As a result, the proposed algorithm can minimize error with the original surface to ensure
Figure 5.2-6 The left is 2D image and the right is the planned path by greedy algorithm. The red line is the transition path and the carving path is labeled as blue line.
obtaining the better projection results.
Figure 5.2-7 Show the projected results on the geometric models.
Figure 5.2-8 The black line which 2D data is projected onto the 3D different models. Compared with projection algorithms, the red line is our proposed algorithm and the blue line is orthogonal projection method.
Table 15 Compare average length error (mm per unit) with orthogonal projection on projection results in Figure 5.2-8.
Orthogonal projection Projection based on flattening surface
(a) 0.0069 ~0
(b) 0.0087 0.0013
(c) 0.025 ~0
In this experiment, the additive and subtractive processing is shown in the Figure 5.2-9. Firstly, the 3D printer machine print the object by using the additive manufacturing, and then the subtractive tool is going to carve process after the additive manufacturing is completed.
Figure 5.2-9 the process of additive and subtractive manufacturing with front view and side view
projection procedure obtains the path for carving. Figure 5.2-10 (b) displays the blue and red curves on the 3D surface, and the carving path is labeled as blue line. Figure 5.2-10 (c) is the carving result on printed model.
Figure 5.2-10 (a) The original STL model. (b) The projected simulation on the model. (c) The carving result on printed model.
Chapter 6 Conclusions and future work
In this thesis, there are two parts about multiple heterogeneous objects fabrication and carving process. On the one hand, the proposed method is about optimizing the additive manufacturing path for multi-objects with generic algorithm. There are two important key to reduce the production time. One is motion path optimization and the other is that increase the speed of the extruder nozzle. In summary, proposed approach can significantly reduce the length of transition path comparing to the path which is produced by common slicing software to save extra production time.
On the other hand, an integrated gantry-type system combining additive and subtractive manufacturing is proposed to fabricate 3D models and then carve the designed shape on the surface of printed objects. In this paper, we proposed a new projection algorithm based on flattening surface to obtain the sculpturing path on the 3D surface.
Therefore, the flattening surface process can combine the conformal mapping and spring mass model based on edge mesh which can minimize error with the original surface to ensure obtaining the better projection results. In addition, the hybrid process combining additive and subtractive processes completes the designed production. The additive process can print main structures of 3D model while the detailed part can be carved by subtractive process. The advantage of cooperation in this method is not only omits repositioning process but also preserves the accuracy of the production.
There are more applications for industrial manufacturing can be performed. In additive manufacturing, we plan to design the 5-DOF 3D printer machine to do more complex models. As for subtractive process, various other kinds of cutting tools like laser or water jet will also be used for corresponding materials.
Chapter 7 Other Applications
Reverse engineering of machines
Reverse engineering, also known as back engineering, is the processes of extracting knowledge or features from anything man-made and reconstructing it or reconstructing anything based on the extracted information. In the experiment, using the Skanect 3D scanning software [29] and Kinect one reconstructs the model and the printing result is shown in Figure 7.1-1.
Figure 7.1-2 Skanect 3D scanning software and printing result
References
[1] W. Du, Y. Tang, S. Leung, L. Tong, A. V. Vasilakos, and F. Qian, "Robust Order Scheduling in the Fashion Industry: A Multi-Objective Optimization
Approach," IEEE Transactions on Industrial Informatics, 2017.
[2] B. Cao, J. Zhao, Z. Lv, and X. Liu, "A Distributed Parallel Cooperative Coevolutionary Multi-Objective Evolutionary Algorithm for Large-Scale Optimization," IEEE Transactions on Industrial Informatics, 2017.
[3] M. S. Brown and C. J. Pisula, "Conformal deskewing of non-planar documents," in Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on, 2005, vol. 1, pp. 998-1004: IEEE.
[4] Q. Li and J. Xue, "Conformal flattening of non-planar surface," in Advanced Computer Theory and Engineering (ICACTE), 2010 3rd International Conference on, 2010, vol. 1, pp. V1-676-V1-679: IEEE.
[5] A. Sheffer and E. de Sturler, "Parameterization of faceted surfaces for meshing using angle-based flattening," Engineering with computers, vol. 17, no. 3, pp. 326-337, 2001.
[6] A. Sheffer, B. Lévy, M. Mogilnitsky, and A. Bogomyakov, "ABF++: fast and robust angle based flattening," ACM Transactions on Graphics (TOG), vol. 24, no. 2, pp.
311-330, 2005.
[7] G. Chen, L.-s. Zhou, L.-l. An, and K. Zhang, "A novel surface flattening method based on mesh edges," in Intelligent System Design and Engineering Application (ISDEA), 2012 Second International Conference on, 2012, pp. 129-133: IEEE.
[8] J. Li, D. Zhang, G. Lu, Y. Peng, X. Wen, and Y. Sakaguti, "Flattening triangulated surfaces using a mass-spring model," The International Journal of Advanced Manufacturing Technology, vol. 25, no. 1, pp. 108-117, 2005.
[9] S. von Enzberg and A. Al-Hamadi, "A Multiresolution Approach to Model-Based 3-D Surface Quality Inspection," IEEE Transactions on Industrial Informatics, vol.
12, no. 4, pp. 1498-1507, 2016.
[10] F. Schmick, N. O. Lüders, and J. Wollnack, "Automated assembly of large CFRP structures: Adaptive filling of joining gaps with additive manufacturing," in Assembly and Manufacturing (ISAM), 2016 IEEE International Symposium on, 2016, pp. 126-132: IEEE.
[11] F. G. Sisca, C. M. Angioletti, M. Taisch, and J. A. Colwill, "Additive manufacturing as a strategic tool for industrial competition," in Research and Technologies for Society and Industry Leveraging a better tomorrow (RTSI), 2016 IEEE 2nd International Forum on, 2016, pp. 1-7: IEEE.
[12] S. Lin, C. Lin, D. Lin, and C. Chuang, "Laser additive manufacturing technology in titanium 64 implant of microstructure fabrication and analysis," in Nano/Micro Engineered and Molecular Systems (NEMS), 2013 8th IEEE International Conference on, 2013, pp. 594-597: IEEE.
[13] T. Wasley et al., "Enabling Rapid Production and Mass Customisation of Electronics Using Digitally Driven Hybrid Additive Manufacturing Techniques," in Electronic Components and Technology Conference (ECTC), 2016 IEEE 66th, 2016, pp. 849-856: IEEE.
[14] O. Arslan, B. Demirci, H. Altun, and N. S. Tunaboylu, "A novel rotation-invariant template matching based on HOG and AMDF for industrial laser cutting
applications," in Mechatronics and its Applications (ISMA), 2013 9th International Symposium on, 2013, pp. 1-5: IEEE.
[15] Z. Xia, K. Zhou, X. Li, and X. Cui, "A method of robot laser cutting for small holes,"
in Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI), International Congress on, 2016, pp. 1887-1891: IEEE.
[16] J. Giannatsis, A. Vassilakos, V. Canellidis, and V. Dedoussis, "Fabrication of graded structures by extrusion 3D Printing," in Industrial Engineering and Engineering Management (IEEM), 2015 IEEE International Conference on, 2015, pp. 175-179:
IEEE.
[17] A. C. Brown and D. de Beer, "Development of a stereolithography (STL) slicing and G-code generation algorithm for an entry level 3-D printer," in AFRICON, 2013, 2013, pp. 1-5: IEEE.
[18] J.-J. Kim and J.-J. Lee, "Trajectory optimization with particle swarm optimization for manipulator motion planning," IEEE Transactions on Industrial Informatics, vol.
11, no. 3, pp. 620-631, 2015.
[19] M. Wojcik, L. Koszalka, I. Koszalka, and A. Kasprzak, "MZZ-GA Algorithm for Solving Path Optimization in 3D Printing," Proceedings to 8th ICONS, IARIA, vol.
30, pp. 30-35, 2015.
[20] S. Lensgraf and R. R. Mettu, "Beyond Layers: A 3D-Aware Toolpath Algorithm for Fused Filament Fabrication," in 2016 IEEE International Conference on Robotics and Automation (ICRA), 2016, pp. 3625 – 3631.
[21] K.-Y. Fok, N. Ganganath, C.-T. Cheng, and K. T. Chi, "A 3D printing path optimizer based on Christofides algorithm," in Consumer Electronics-Taiwan (ICCE-TW),
[22] G. E. Jan, K. Fung, P.-Y. Wu, and S.-W. Leu, "Shortest path-planning on polygonal surfaces with O (nlog n) time," in 2016 IEEE International Conference on Control and Robotics Engineering (ICCRE), 2016, pp. 1-5: IEEE.
[23] N. Ganganath, C.-T. Cheng, K.-Y. Fok, and K. T. Chi, "Trajectory planning for 3D printing: a revisit to traveling salesman problem," in Control, Automation and Robotics (ICCAR), 2016 2nd International Conference on, 2016, pp. 287-290: IEEE.
[24] V. Roberge, M. Tarbouchi, and G. Labonté, "Comparison of parallel genetic algorithm and particle swarm optimization for real-time UAV path planning," IEEE Transactions on Industrial Informatics, vol. 9, no. 1, pp. 132-141, 2013.
[25] B. Thompson and H.-S. Yoon, "Efficient path planning algorithm for additive manufacturing systems," IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 4, no. 9, pp. 1555-1563, 2014.
[26] N. Volpato, R. Nakashima, L. Galvão, A. Barboza, P. Benevides, and L. Nunes,
"Reducing repositioning distances in fused deposition-based processes using optimization algorithms," in High Value Manufacturing: Advanced Research in Virtual and Rapid Prototyping: Proceedings of the 6th International Conference on Advanced Research in Virtual and Rapid Prototyping, Leiria, Portugal, 1-5 October, 2013, 2013, p. 417: CRC Press.
[27] KISSlicer gcode generator is available at http://www.kisslicer.com/.
[28] Z. Zhu, V. Dhokia, and S. Newman, "A novel process planning approach for hybrid manufacturing consisting of additive, subtractive and inspection processes," in Industrial Engineering and Engineering Management (IEEM), 2012 IEEE International Conference on, 2012, pp. 1617-1621: IEEE.
VITA
姓名：曾柏凱 性別：男
生日：11.01.1992 籍貫：台南市 學歷：
1. 民國 106 年 國立臺灣大學電機工程學研究所 2. 民國 104 年 國立臺灣科技大學電機工程學系畢業 3. 民國 100 年 國立臺南高級工業職業學校電機科畢業
發表著作：
1. Ren C. Luo*, Po-Kai Tseng, "Trajectory Generation and Planning for Simultaneous 3D Printing of Multiple Objects," published by the 26st IEEE International Symposium on Industrial Electronics (ISIE 2017), 2017.
2. Ren C. Luo*, Po-Kai Tseng, "Carving 2D Image Onto 3D Curved Surface Using Hybrid Additive and Subtractive 3D Printing Process," accepted by IEEE Advanced Robotics and Intelligent Systems (ARIS), 2017.
榮譽事績：
2016/09/01 第九屆上銀智慧機器手實作競賽 開發組 亞軍 疊疊樂 冠軍