本研究中之尺寸公差設計透過輥軋成型製程精準且精確的形成線型輪廓部件，此製程是非常有前景且具挑戰性的研究。透過槽型滾輪進行的滾壓製程於工業製造產業中應用於生產電線、彈簧和醫療設備。滾壓成型製程研究中進行有限元素模擬研究了製程後圓形斷面之線型材料，模擬中之剛塑性模型分別用來模擬滾筒模型與線型材料。本研究除了優化線型物件公差尺寸外也執行了線成型製程中最大應力與應變的優化。公差設計是品質特性分析中最有價值的一部分。本研究採用了結合模擬與統計的方法，尋找生產T型鋼線製程中最佳公差設計。一開始將複雜的模擬設計由最小尺寸模擬建構，接著建立基於T型輪廓型狀並且提取其中尺寸特徵。最後建立一複雜的數據驅動模型(神經網絡模型)用以預測於不同參數中兩個滾筒路徑製程偏移和間隙偏差效應。本研究中也透過建立替代模型來減少電腦的計算時間。本文中也提出了一些新的準則，如應力、應變和變形準則來限制參數並接近最佳參數區域。最後，模擬的時間消耗與實驗次數將會有效的被減少。透過有限元素分析與數據挖掘技術，實現了優化T型輪廓尺寸並最小化兩個滾筒路徑製程偏移和間隙偏差效應。最後，在兩個滾筒路徑製程中，0.035到-0.035mm的製程偏移量和0.023到-0.018mm的間隔偏差是公差設計中T型線型輪廓中最佳匹配參數。同樣的，在最佳區間的損壞參數小於0.55。因此，他們符合T行冷壓的最終的品質需求。

The tolerance design is a promising and challenging work for shape rolling process to form a precisely and accurately shaped-wire profile in different process parameters. The shape rolling process with grove rollers is an industrial manufacturing process to manufacture the wire, spring and medical components. A study of the rolling process with groove rolls fed with a circular cross-section wire is presented through 3D finite element simulation. A rigid-plastic model is used to simulate the roller as rigid model and wire material as a plastic model in the cold rollering process, respectively. The required tolerance in the dimension of the shaped-wire and the damage value of the wire are studied in optimization.
In this study, the method of integrating the simulation and statistical techniques is proposed to find the optimal tolerance design process for manufacturing the trapezoid-shaped (T-shaped) steel wire. At the beginning, the complex simulation design is constructed to minimize the simulation size and then simulation model would be set up based on T-shaped wire and dimensional characteristics would be extracted. And then a complex data-driven model (neural network) is built to predict the wire dimension and its damage value regarding to the offset and gap deviation effects in two rolling die alignments. By creating the surrogate model in reducing the running time in a computer is also accomplished in this study. Some criteria like the dimension and the damage value of the wire are characterized to approach the optimal zone. After all, the time consumption of simulation and number of the experiments could be reduced effectively.
As a result, based on the FEM analysis and data mining technique, an optimal 2.1 mm diameter of the round wire as an input for rolling to the T shaped-wire are accomplished with the minimum offset in 0.035mm to -0.035mm and minimum gap deviation in 0.023mm to -0.018mm. The perfect fit for the required tolerance design in Heights A and B and Width C for a T shaped-wire profile is achieved. In addition, the deviation angle at 0.350 to -0.350 in the optimal zone is found. Also, it is noted that the damage value in the optimized zone is less than 0.55. Therefore, they are acceptable in the final request of the tolerance design in cold rolling T-shaped wire.

Ambrogio, G., Costantino, I., De Napoli, L., and Filice, L. "Influence of some relevant process parameters o the dimentional accuracy in incremental forming: a numerical and experimental investigation." Journal of material processing technology, pp 501-507, 2004.

Brierley, P., and Batty, P. "Data mining with neural networks - an applied example in understanding electricity consumption patterns." in Knowledge Discovery and Data Mining (ed Max Bramer), pp.240-303, 1999.

Byon, S. M., Na, D. H., and Lee, Y. “Effect of roll gap adjustment on exit cross sectional shape in groove rolling—Experimental and FE analysis.” Journal of Materials Processing Technology, pp 4465–4470, 2009.

Carlsson, B. "The contact pressure distribution in flat rolling of wire." Journal of Materials Processing Technology, pp.1-6, 1998.

Carlsson, B., and Lagergren, J. The deformation of drawn wire in flat rolling, ESDA 96, Third Biennial Joint Coenference on Engineering Systems Design and Analysis. New York, pp. 175-180, 1996.

Carlos, C. Antonio., Catarina, F. Castro., and Luisa, C. Sousa. "Optimization of metal forming process," Journal of compuer and structures, vol. 82, pp. 1425-1433, 2004.

Downey, K., Alan, P., and Ken, C., “An introduction to smart assemblies for robust design” The Journal of Research in Engineering Design, vol. 14, pp. 236–246, 2003.

ENCYCLOPESIA,BRITANNICA https://www.britannica.com/technology/rolling-technology.

Fang, KT., Li, R., and Sudjianto, A. Design and modelling for computer experiments. Chapman and Hall/CRC Press, Boca Raton (2005).

Fortini, E. T. Dimensioning for Interchangeable Manufacture. New York: Industrial Press, 1967.

Gene, R. Cogorno., Geometric Dimensioning and Tolerancing for mechanical Design. McGraw-Hill, 2006.

HONG, Y. S., CHANG, T.-C. “A comprehensive review of tolerancing research,” The International Journal of Production Research, vol. 40, pp. 2425-2459, 2002.

Hussein, A., Hao, L., Yan, C., and Everson, R., "Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting," Journal of Materials & Design, pp. 638-647, 2013.

Kamath, Chandrika. "Data mining and statistical inference in selective laser melting." The International Journal of Advanced Manufacturing Technology, pp: 1659-1677, 2016.

Kazeminezhad, M., and Karimi, A. "A theoritical and experimental investigation on wire flat rolling process using deformation pattern." The International Journal of Materials and Design, pp. 99-103, 2004.

Kenneth, W. Chase., and Alan, R. Parkinson. “A Survey of Research in the Application of Tolerance Analysis to the Design of Mechanical Assemblies.” The International Journal of Research in Enginnering Design, Volume 3, pp. 23–37, 1991.

Larrnaga, J., Berner, S., Galdos, L., and Groche, P., "Geometrical accuracy improvement in flexible roll forming." International Conference on Advances in Materials and Processing Technologies, 2010.

Lambiase, F., and Antoniomaria, Di. Ilio. "A parametric study on residual stresses and loads in drawing process with idle rolls." The International Journal of Materials and Design, pp. 4832-4838, 2011.

Mahshid, R., Zahra, M., and Hans, N. H. "Tolerance analysis in manufacturing using process capability ratio measurment uncertainty."Journal of Precision Engineering, 2017.

Mihu, Adria-M., Ioana, M. Sas-Boca., Ionut, M., Mihu, I. S., Dorina, S. I., and Liviu, N. Dana-A. "Finite Element Analysis of Drawing Wire in Cassette Roller Die (Part2)." The International Journal of Procedia Technology, pp. 34-39, 2015.

Oehlert, G. W. and Freeman, W. H. A first course in design and analysis of experiments, Available from http://users.stat.umn.edu/gary/Book.html, 2000.

Saeidi, F., Meylan, B., Hoffman, P., and Wasmer, K. "Effect of surface texturing on cast iron reciprocating against steel under streved lubrication conditions: A parametric study." International Journal of Wear, pp. 17-26, 2016.

Sheu, J. J. "Simulation and optimization of the cold roll-forming process." The Journal of Materials Processing and Design: Modeling, Simulation and Applications, 2004.

Shuhui, L., Xing, H., Yixi, Z., Zhongqin, L., and Nanqiao, X. “Cyclic hardening behavior of roller hemming in the case of aluminum alloy sheets.” International Journal of Materials and Design, pp 2308-2316, 2011.

Tseng, C-C., and HO, Shi-Pin., "Shape Rolling Process Combined With In-line Induction Heat Treatment for Rectangular Wire Die Springs." Journal of Advanced Mechanical Design, vol. 07, No 04, 2013.

Vallellano, C., Cabanillas, P.A., and Garcia-Lomas, F. J. "Analysis of deformations and stresses in flat rolling of wire." Journal of Materials Processing Technology, vol. 195, pp. 63-71, 2007.

Wang, Bojian., Zhang, Wupeng., Wang, Yongjie. "Strain Distribution Characteristics in the Rolling Process of Shaped Wire." Internation Journal of Advanced Materials Research, vol. 340, pp. 64-69, 2009.

Wang, Rui., and Georg, T., Ma, Y. “Review: Geometric and Dimensional Tolerances Modelling.” The International Journal of Advanced Manufacturing Technology, Volume 51, pp 871–889, 2010.