1附 錄附錄 A 英文文獻On Welding-Installation Fixtures Design of Sheet StampingAbstract: Due to forming error and compliance of stamp-ing, the fixture design of sheet stamping assembly is different from the fixture design of common machining component. In recent years, the new principles and algorithms of fixture design of sheet stamping have been developed. In the paper, the concept of shape closure and force closure, screw theory were firstly introduced. Secondly, the deterministic locating and total fixturing conditions were derived. Thirdly, an “N-2-1”locating principle and optimal design method for sheet stamping were described. Finally, the varia-tional method of robust fixture configuration design for 3-D workpieces was discussed. It can be predicated that the locating error can be reduced by this method.Key Words: Fixture; Sheet Stamping; Optimal Design; Ro-Bust DesignDue to its high productivity and material utilization, stamping is widely used in automobiles, aircraft, and various household appliances manufacturing industry. The welding assembly of stamping becomes the key process of those products manufacturing, because welding fixture not only affects the performance of productivity, but also is directly related to the quality of the product. Statistics from the U.S. auto industry show that 72% of the body manufacturing errors are from the position error of welding fixture, so how to effectively reduce and control the positioning error is essential to improve the welding quality. Sheet stamping assembly is significantly different from general machining, which not only meets the common requirements of precise positioning, but also gives full consideration to the easy deformation of sheet metal parts and stamping manufacturing characteristics of large deviations to adapt the products’ quality requirements. Over the last decade, many scholars working in the design of sheet stamping assembly have proposed design theories and methods of some new sheet stamping assembly, and achieved remarkable results. At first, this paper introduces the research progress of fixture design, and then systematically elaborates the N-2-1 locating principle of fixture and the methods of optimal design and robust design, finally makes the conclusion.2Manufacturing process (such as machining, welding, assembly and testing, etc.), the fixture is used in three-dimensional positioning and clamping device. The central problem of fixture design is to choose the optimal positioning points and determine their best position to achieve the determine constraints positioning of work piece. If the work piece can be full restriction depending on the geometry of contact area will, we called it “shape closed“; If it also have to be fully bound with friction, we called it “force closure.“ Generally, shape closure stresses dynamic analysis, but force closure focuses on the work piece of static stability. In 1885, Reuleaux first studied the mechanism of two-dimensional objects’ shape closure, and proved that the formation of two-dimensional objects’ shape closure need four anchor points [2]. After that Somoff proved the formation of three-dimensional objects’ shape closure need seven anchor points. In 1978, Lakshminarayana [3] further proved the formation of three-dimensional objects’ shape closure need at least seven anchor points in the perspective of static equilibrium using algebraic theory In 1988, Nguyen researched the mechanism of the machine hand’s force closure [4], and in 1989 Asada and Kitagawa [5] researched the machine hand’s shape closure which used for convex and concave parts Generally six positioning principles requires clamping force to make work piece fully constrained, so usually it is force closure.Over the last decade, the “spiral theory” widely used in fixture design, which describes the three-dimensional motion as translating along one direction and rotating around this axis. Originally spiral theory proposed by Ball [6], and developed by literature [7] and [8]. According to spiral theory, literature [9] studied seven different types of finger contact, and suggested using finger-like shape to completely fix objects. Literature [10] using the extended spiral theory analyzed that rigid body’s full or part restriction exist frictional clamp. Literature [11] proposed mathematical theory of fixture’s automatic layout for prismatic work pieces. Literature [12] discussed the ability of different fixtures position contact preventing work pieces from spiral movement, and proposed a restrict method of work piece movement for the fixture design. Using small spiral model literature [13] discussed the positioning errors of fixture impact work pieces’ geometry accuracy. Literature [14] researched surface contact and friction problems in the analysis of fixture restriction. Considering dynamic constraints, completely clamping, and tool path errors, literature [15] developed fixture design and analysis software. It can be said that spiral theory of fixture design has been used for determining position, full clamping, contact type, 3and friction problems and achieved remarkable results.Lots of literatures focus on the fixture design of rigid pieces, but the fixture design of flexible sheet pieces is rarely involved, especially considering the deformation of the work piece under processing loads is almost none. In fact, as in the aviation industry and the automotive industry, the deformation of sheet may result in serious bias. For easily deformed sheet, positioning fixture not only has basic functions that limiting rigid body motion, but also must be able to limit excessive deformation of the work piece. The research that earlier considering the rigidity of work pieces or fixture positing cell will be found in the literature [16] based on the experimental results they studied fixture stiffness and wear’s effects on the size accuracy. Literature [17] proposed a finite element model of the fixture system for flexible positioning fixture, and the power in process of processing can be seen as the force acting on the node. Based on this model, you can calculate the deformation of the work piece, the clamping force, stress distribution and friction between the work piece and fixture positioning unit’s contact points can be calculated by Coulomb's law. Although by considering the deformation of the work piece and the finite element analysis this area have been promoted, but it has neither proposed any specific positing principle, nor proposed positioning scheme for flexible sheet. In addition, this model does not combine the finite element analysis results of the work piece with the fixture design; it is more than the analysis of the work piece other than fixture design. Literature [18] proposed a analysis method of sheet fixture positing, they studied the fixture positioning system using the case and flat three-point and four-point to posit, so the fixture layout must make the stress in the work pieces below the yield stress. However, this method does not solve the essential problem of sheet fixture, because reducing deformation is the key to the positioning of sheet. Based on literature [17], literature [19] continued further study, that using the finite element modeling to choose fixture layout makes the deformation minimum in the first base-level. To determine the optimal fixture layout, using quasi-Newton optimization algorithm makes the deformation squares on the finite element mesh of the key nodes minimum. Design variables are the three anchor points on the first base required by “3-2-1“ principle.Sheet stamping assembly fixtures are widely used in automobiles, aircraft and household appliances industries, whose design quality directly affects the entire product manufacturing deviations. Due to sheet metal stamping’s characteristic of flexibility and manufacturing variations, the principle of traditional fixture design can not meet the design 4requirements, although the research of fixture design is already quite mature and the positioning principle of rigid part and the “spiral theory“ has been in-depth study. “N-2-1“ Location principle, for the characteristic of easy deformation on the horizontal of Sheet Metal Stamping, presents that when the number of anchor points is more than 3 in the first base surface, position effect depends not only on the number of anchor points, but also on the arrangement of the anchor points. Apart from that, it proposes the finite element analysis and the design of nonlinear programming method of the anchor, which provides theoretical basis and design methods for the design of sheet welding fixture. Because of the larger manufacture size deviation of sheet metal parts and the remarkable effect of the choice of anchor position for position deviation, robust fixture design can significantly improve the positioning error. Therefore, during the design of sheet welding fixture, implementing the “N-2-1“ location principle and robust design method is extremely important. It has been proved to have a multiplier effect.References[1] Li B, Tang H, Yang X,et al.Quality Design of Fixture Planning for Sheet Metal Assembly [ J ].International Journal of Advanced Manufacturing Technology,2007,32 (7-8):690-697.[2] Ceglarek D, Shi J. Dimensional Variation Reduction for Automotive Body Assembly [J].Manufacturing Review, 1995,8(2):139-154.[3] Ceglarek D, Shi J. Fixture Failure Diagnosis for Autobody Assembly Using Pattern Recognition[J].ASME Journal of Engineering Industry,1996,118(1):55-66.[4] Apley D, Shi J. Diagnosis of Multiple Fixture Faults in Panel Assembly[J].ASME Journal of Manufacturing Science and Engineering,1998,120(4):793-801.[5] Chang M, Gossard D C. Computational Method forDiagnosis of Variation-related Assembly Problems [ J ]. International Journal of Production Research,1998,36 (11):2985-2995.[6] Liu Y, Hu S. Assembly Fixture Fault Diagnosis Using Designated Component Analysis [ J].ASME Journal of Manufacturing Science and Engine ering,2005,127(2): 358-368.[7] Khan A, Ceglarek D, Shi J,et al.Sensor Optimization for Fault Diagnosis in Single Fixture Systems: a Methodology [ J ].ASME Journal of Manufacturing Science and 5Engineering,1999,121(1):109-117.[8] Djurdjanovic D, Ni J. Stream of Variation Based Analysis and Synthesis of Measurement Schemes in Multi-station Machining Systems [ C ]. Proceedings of the ASME International Mechamical Engineering Congress and Exposition, New York,2001,12:297-304.[9] Ding Y, Kim P, Ceglarek D,et al.Optimal Sensor Distribution for Variation Diagnosis for Multi-station Assembly Processes[J].IEEE Transactions of Robotics andAutomation,2003,19(4):543-556.[10] Camelio J A, Hu S. Sensor Placement for Effective Diagnosis of Multiple Faults in Fixturing of Compliant Parts [J].ASME Journal of Manufacturing Science andEngineering,2005,127(1):68-74.[11] Li B, Yang J, Ding H. A Rapid Location and State Memory Fixture System for Arbitrarily Part[J].Journal of Donghua University,2000,17(3):27-31.[12] Wang Q, Yang J, Li B. Application and Realization of Rapid Searching Technology in the RL然后,重點闡述了面向薄板沖壓件焊裝夾具設計的“N-2-1 ”定位原理和夾具的優(yōu)化設計方法;最后分析了夾具的穩(wěn)健性設計方法?？梢灶A料,采用該方法可有效地減少和控制定位誤差的影響。關鍵詞:夾具;薄板沖壓件;優(yōu)化設計 ;穩(wěn)健設計沖壓加工以其較高的生產率和材料利用率,廣泛應用于汽車、飛機和各種家用電器制造工業(yè),沖壓件的焊接裝配成為上述產品制造的關鍵工序,焊裝夾具的性能不僅影響到生產率,而且直接關系到產品的質量。美國汽車工業(yè)的統計表明[1],72%的車身制造誤差源于焊裝夾具定位誤差,因此如何有效地減少和控制定位誤差的影響,對提高焊裝質量至關重要。薄板焊裝夾具與通用的機加工夾具存在顯著的差別,它不僅要滿足精確定位的共性要求,還要充分考慮薄板沖壓件的易變形性和沖壓制造偏差較大的特征,以適應于產品的高質量要求。近十幾年來,許多學者在薄板焊裝夾具的設計上開展了大量工作,提出了一些新型的薄板沖壓件焊裝夾具的設計理論和方法,取得了顯著效果。本文首先介紹夾具設計方法的研究進展,然后系統地闡述夾具的 N-2-1 定位原理、優(yōu)化設計及魯棒性設計方法,最后給出本文的結論。制造過程(如加工、焊接、裝配和檢測等)中,夾具是用于在三維空間定位和夾緊工件的設備。夾具設計的中心問題就是選擇最優(yōu)定位點數并確定它們的最佳位置,以實現工件的確定約束定位。如果工件依靠接觸區(qū)域幾何形狀便可完全約束,稱為“形閉合”;如果還必須借助摩擦才能完全約束,則稱為“力閉合” 。通常形狀閉合強調動態(tài)分析,而力閉合則研究工件的靜態(tài)穩(wěn)定。1885 年,Reuleaux 首先研究了二維工件的形閉合機制,證明了形成二維物體的形閉合必需四個定位點[2]。之后,Somoff 證明三維物體的形閉合需要七個定位點,1978 年,Lakshminarayana[3]從靜態(tài)平衡角度利用代數理論進一步證明了三維工件的形閉合至少需要七個點。1988 年,Nguyen 研究了機器手力閉合機制[4],而 Asada 和 Kitagawa[5]于 1989 年研究了用于凸形和凹形工件的機器手的形閉合。通常的六點定位原理一般地需要夾緊力將工件完全約束,因此常常是力閉合。近十幾年來,“螺旋理論”廣泛流行于夾具設計中,螺旋理論將三維工件的三維空7間運動描述為沿某一方向的平移和繞這一軸線的轉動。最初由 Ball[6]提出,并得到文獻[7]和文獻[8]的發(fā)展。根據螺旋理論 ,文獻[9]研究了七種不同類型的指狀接觸,并建議用指狀外形去完全固定夾緊物體。文獻[10]利用擴展的螺旋理論就剛體的全部或局部約束分析了有摩擦夾緊。文獻[11]提出了用于棱柱形工件的加工夾具自動布置的數學理論。文獻[12] 討論了各夾具定位接觸阻止工件相互螺旋運動的能力,提出了一種用于夾具設計的工件運動約束方法。文獻[13]利用小螺旋模型考慮了夾具定位誤差對工件幾何精度的影響。文獻[14]在夾具約束分析中研究了表面接觸和摩擦問題。文獻[15]開發(fā)出了考慮動態(tài)約束、完全夾緊和刀具路徑偏差的夾具設計和分析軟件?？梢哉f,夾具設計的螺旋理論已經用于處理確定定位和完全夾緊問題、定位質量、接觸類型和摩擦等問題,并取得了明顯成績。大量的文獻集中論述了剛性件的夾具設計,但關于薄板柔性件的夾具設計研究很少涉及,特別是考慮加工載荷作用下工件變形的夾具設計的研究幾乎沒有。實際上,象在航空工業(yè)和汽車工業(yè),薄板變形可能導致嚴重的尺寸偏差。對于易變形薄板,定位夾具除了具備限制零件剛體運動的基本功能外,還必須能夠限制過多的工件變形。較早考慮工件或夾具定位單元剛性的研究見于文獻 [16],他們根據實驗結果研究了夾具剛度和磨損對尺寸精度的影響。文獻[17]提出了一種用于柔性定位夾具的夾具系統分析的有限元模型,加工過程中的加工力可看作是作用于節(jié)點的力?；谠撃Ｐ?可以計算出工件變形、夾緊力和應力分布,可運用庫侖摩擦定律去計算工件與夾具定位單元間接觸處的摩擦力。雖然通過考慮工件變形和有限元分析推動了這一領域,但它既沒有提出任何一種具體的定位原理,也沒有為具有柔性的薄板提出一種定位方案。此外,這種模型并沒有將工件的有限元分析結果同夾具設計規(guī)范聯系起來,它更多的是工件的分析而不是夾具設計。文獻[18]提出了一種薄板夾具定位分析的方法,他們研究了用于平板和殼體的三點和四點夾具定位系統,夾具布置必須使得工件中的應力低于材料的屈服應力。然而,這種方法并沒有解決薄板夾具的本質問題,因為減小變形是薄板件定位的關鍵所在。文獻[19]在文獻 [17]的基礎上進行了更深入的研究,利用有限元建模選擇使得工件在第一基準面法向的變形最小的夾具定位布置。為確定最佳夾具定位布置,利用擬牛頓優(yōu)化算法使有限元網格上的關鍵節(jié)點的變形的平方和最小。設計變量是“3-2-1” 定位原理所要求的第一基準面上的三個定位點。薄板沖壓件焊裝夾具廣泛應用于汽車、飛機及家用電器等工業(yè),焊裝夾具的設計質量直接影響到整個產品的制造偏差。由于薄板沖壓件的柔性和制造偏差特征,傳統的夾具設計原理不能滿足薄板沖壓件的設計要求,盡管夾具設計研究已經相當成熟,剛性零件的定位原理和“螺旋理論”得到了深入研究。 “N-2-1”定位原理針對薄板沖壓8件在橫向上的易變形特征,提出了在第一基面上的定位點數目大于 3,定位效果不僅取決于定位點的數目,而且取決于定位點的布置形式,并提出了采用有限元分析與非線性規(guī)劃的定位點設計方法。為薄板沖壓件焊裝夾具的設計提供了理論基礎和設計方法。由于薄板沖壓件的制造尺寸偏差較大,定位點位置的選擇對定位偏差的影響更明顯,夾具的穩(wěn)健設計可顯著地改善定位誤差。因此,在薄板焊裝夾具設計過程中,貫徹“N-2-1”定位原理和穩(wěn)健性設計方法是極為重要的,實踐證明,可以收到事半功倍的效果。