板料佈置為連續沖壓之模具設計程序中非常重要的一環，較佳的板料佈置將大幅節省成本與減少浪費。目前在連續沖壓模具設計過程中，板料佈置大部分仰賴設計人員的實務經驗，鮮少對材料利用率作全面數據分析，往往無法達到優化的利用率配置。有鑑於此，本論文嘗試以Minkowski Sum為學理基礎，在3D CAD系統Creo中建立一套能夠全盤考量各種板料佈置之材料利用率的方法，以針對單排及雙排板料佈置進行材料利用率之優化設計。
本論文所開發之板料佈置流程是將單位料帶面積作為目標函數，利用Creo的Multi Objective Design作為核心，搭配參數式特性，擷取各種板料佈置之單位料帶面積大小，能夠迅速掌握所有佈置狀態與數據，包含節距、佈置角度、料帶寬度….等，以減少探索設計參數之時間，大幅提昇板金設計之效率。
論文中以一個金屬彈片零件進行雙排板料佈置，最後求出最小單位料帶面積，該案例中最小化單位料帶面積與最大化單位料帶面積差異近1.75倍，此說明了優化的板料佈置對材料利用率有明顯程度之提昇。

In the design process for a progressive die, a good strip layout will significantly save costs and reduce waste. Currently, the strip layout mostly depends on the hands-on experience of the designer. Comprehensive data analysis for the materials utilization is rarely conducted. In view of this, this thesis attempts to use the Minkowski Sum as a theoretical basis and establishes a method that provides overall considerations of various strip layouts in Creo’s 3D CAD system in order to develop an optimal design for material utilization of single-part and paired parts in strip layouts.
The strip layout process developed in this thesis adopts the area of a strip per unit as the objective goal. Using Creo’s Multi Objective Design as the core in tandem with the parametric features, capturing the area of a strip per unit of each strip layout can quickly grasp all the layout states and parameters, including the pitch, angle of placement, width of strip, etc. This will reduce time spent in exploring the design parameters, and dramatically increase the efficiency of sheet metal design.
In this thesis, a metallic spring is arranged as a strip layout for paired parts, and finally the minimum area of the strip per unit is determined. The difference between the minimum area of the strip per unit and the maximum area of the strip per unit is nearly 1.75-fold. This demonstrates that an optimal strip layout permits a significant level of enhancement in the utilization of materials.

[1]林龍震，Pro/Sheetmetal Wildfire2.0板金設計，金禾資訊股份有限公司，台北，2004。
[2]T. J. Nye (2000), “Stamping strip layout for optimal raw material utilization,” Journal of Manufacturing Systems, Vol. 19, pp. 239-248.
[3]T. J. Nye (2000), “Stamping Die Strip Optimization for Paired Parts” ASME 2002 International Mechanical Engineering Congress and Exposition, Paper No. IMECE2002-33572, pp. 91-96.
[4]莊博文，「連續沖模之3D電腦輔助沖程佈置」（2003），碩士論文，國立台灣科技大學機械工程系研究所，台北市。
[5]戴偉翰，「彎形板金展開之3D CAD系統開發」（2003），碩士論文，國立台灣科技大學機械工程系研究所，台北市。
[6]邱贊源，「連續沖模板料設計之Pro/TOOLKIT程式開發」 （2006），碩士論文，國立台灣科技大學機械工程系研究所，台北市。
[7]林健安，「使用Creo進行連續沖模之板料設計」（2013），碩士論文，國立台灣科技大學機械工程系研究所，台北市。
[8]范盛涵，「使用Creo進行連續沖模設計之板標準作業流程」（2014），碩士論文，國立台灣大學機械工程系研究所，台北市。
[9]陳義章，「使用Creo進行連續沖模板料利用率之優化設計」 (2015)，碩士論文，國立台灣大學機械工程系研究所，台北市。
[10]T. F. Lam, W. S. Sze and S. T. Tan (2007), “Nesting of complex sheet metal parts,” Computer-Aided Design & Applications, Vol. 4, pp. 169-179.
[11]Rafael Mulero and Bradley Layton (2007), “Two-dimensional Minkowski sum optimization of ganged stamping blank layouts for use on pre-cut sheet metal for convex and concave parts,” Journal of Manufacturing Systems, Vol. 26, pp. 44-52.
[12]S Kumar and R Singh (2011), “An automated design system for progressive die,” Expert Systems with Applications, Vol. 38, pp. 4482-4489.
[13]Siemens Corporation, NX Progressive Die Wizard, Texas, USA, 2005.
[14]Parametric Technology Corporation, Progressive Die Extension Reference Guide, Release 2.2, Waltham, MA , USA, 2005.
[15]3D QuickTools Inc., 3D QuickPress, Hong Kong, 2003.
[16]https://en.wikipedia.org/wiki/Minkowski_addition
[17]M. de Berg, O, Cheong, M. van Kreveld, M., Overmars, Computational Geometry Algorithm Application, 3rd edition, Springer, Berlin, 2008.
[18]林龍震，Pro/EGINEER Wildfire 3.0 進階設計，上奇科技出版事業處，台北，2006。