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1、<p><b> 附錄1 中文譯文</b></p><p><b> 沖壓模表面設(shè)計(jì)</b></p><p><b> 1、引言</b></p><p> 據(jù)悉,金屬板料沖壓模產(chǎn)品的關(guān)鍵部分是從本質(zhì)上發(fā)展模具的表面設(shè)計(jì),在必需的質(zhì)量范圍內(nèi)找準(zhǔn)刀具表面幾何形狀以得到一個(gè)完全改進(jìn)型坯料的
2、外形沖壓成形。沖壓刀具的設(shè)計(jì)原理以零件幾何學(xué)作為基本輸入數(shù)據(jù)和為了一個(gè)特定的搗實(shí)模板用工程法設(shè)法去決定操作的最小數(shù),目的是當(dāng)滿足客觀的沖壓標(biāo)準(zhǔn)時(shí),以減少成形刀具的成本。這個(gè)工程方法為形成工藝流程設(shè)計(jì)連續(xù)運(yùn)轉(zhuǎn)到最后的車間傳導(dǎo)各式各樣的試驗(yàn),直到出現(xiàn)大量的沖壓零件產(chǎn)品階段為止。在沖壓模具表面設(shè)計(jì)和可使用性塑料的金屬片之間決定著空缺變形的特性,另外應(yīng)該考慮到要形成高強(qiáng)度鋼以適應(yīng)降低的可模鍛性和提高彈性變形。通過符合計(jì)算機(jī)輔助設(shè)計(jì)和分析刀具的模
3、具試驗(yàn)階段,會(huì)在計(jì)算機(jī)里產(chǎn)生可靠的實(shí)質(zhì)性的設(shè)計(jì)環(huán)境,以及方法和利用基于仿真有限元素的方法預(yù)先實(shí)現(xiàn)可成形性問題的刀具工程學(xué),例如,裂縫、皺紋或過分的稀釋,以及搗實(shí)模板涉及到的模具表面設(shè)計(jì)。它也能夠在清理焊縫和彈性變形后估計(jì)出最后的幾何形狀。這種工程學(xué)接近于在制圖過程中假設(shè)模具表面變形被忽略了,以及在傳統(tǒng)的鋼中,工業(yè)實(shí)踐已經(jīng)被有效的證實(shí)了這個(gè)假設(shè)有大的內(nèi)部嵌板模。這就是理想嚴(yán)格的模具概念,然而,當(dāng)提到形成新的高強(qiáng)度的中等濃度鋼變的可<
4、/p><p> 在這篇論文里,按照一個(gè)簡(jiǎn)短的沖壓模設(shè)計(jì)原則的回顧,在板料金屬的形成過程中,一種估計(jì)和控制模具表面變形的計(jì)算方法被提出,在第一部分和第二部分的研究中,基于計(jì)算機(jī)輔助設(shè)計(jì)和分析定義,醋酸丁酸纖維素體成份的形成過程中,這種被提議的方法被應(yīng)用,在模具加工過程的計(jì)算機(jī)輔助設(shè)計(jì)中,零件的可成形分析和彈性變形及加工變形,模具表面設(shè)計(jì)變形,以及想的剛性和可變形界面相對(duì)差都考慮了,通過增加沖壓鑄件的壁厚來執(zhí)行理想剛性
5、模具表面設(shè)計(jì)的假設(shè)。</p><p> 2、模具表面設(shè)計(jì)的概念</p><p> 金屬片形成模具的表面設(shè)計(jì)可以被定義為在確保剛性結(jié)構(gòu)條件下,使金屬片鑄塑成一種理想的沖壓形狀,使之成為完整的表面幾何形狀的一部分。這種設(shè)計(jì)過程始于零件的幾何形狀作為基本輸入數(shù)據(jù),提出這種方法的工程師首先通過推翻最有利的軸線和排除了冒險(xiǎn)的切口對(duì)制圖的說明書作出了決定,因而,利用材料的可成形性和最小允許的厚度,
6、取決于拉伸成形的數(shù)量和估計(jì)拉伸操作的次數(shù),設(shè)計(jì)者運(yùn)用金屬片零件半厚度偏移幾何學(xué),在計(jì)算機(jī)輔助設(shè)計(jì)的環(huán)境中,通過延長(zhǎng)零件的邊緣,嵌縫鋒利的刃口,伸展法蘭的形狀為沖壓表面設(shè)置了額外的表面。利用材料特性和最大拉伸變形的次數(shù),估計(jì)出可完成的最大化圖形進(jìn)深,并且一系列的連接桿和計(jì)數(shù)管的表面可被額外的穿孔和沖模,目的是在形成過程的初始階段最小化變形斜度,在對(duì)沖壓操作之后,用一系列平面和可曲展面來產(chǎn)生組合的幾何面,通常在焊頭和焊尾的連接之間用一種控制
7、方式來抑制材料在沖壓時(shí)溢出,在沖壓和粘接分界面的形成之后,他們通常由排除分界面數(shù)量的偏置法來發(fā)展相似幾何學(xué),這是用CAD軟件典型的板材大于金屬片幾個(gè)百分點(diǎn)的厚度,現(xiàn)階段允許使用的部分變薄,拉伸,并做空白大小可利用估算恒定假設(shè)。</p><p> 一旦工程師創(chuàng)造了整個(gè)幾何方法描述的空白,并在計(jì)算機(jī)輔助環(huán)境下進(jìn)行模具表面設(shè)計(jì),用有限元分析可完成以調(diào)查過程的可行性成形、 幾何部分回彈后形成剛性模量假設(shè)的理想的有限元模
8、擬及施工。隨著加入的金屬厚度分布,沖壓過程通常是做兩步,一種是進(jìn)行形成分析,確定某一變形金屬?zèng)_壓、裝粘合劑,其次是移動(dòng)后的彈性變形的計(jì)算與成型模具應(yīng)力、變形幾何學(xué)。依靠相對(duì)質(zhì)量的過程與材料參數(shù), 幾個(gè)虛擬試驗(yàn)要必須達(dá)到最佳成型模具及幾何要素。此時(shí), 成形載荷類型和圖形作用,是根據(jù)現(xiàn)有的沖壓路線規(guī)定的。最后,完成沖壓模具表面的校準(zhǔn),并提交模具建筑業(yè)和制造業(yè)部門。</p><p> 在汽車行業(yè),沖壓模具設(shè)計(jì)與施工實(shí)
9、踐,采用按類型的板材和借鑒行動(dòng),按照所選類型制造沖壓模,通常 一項(xiàng)內(nèi)部模具設(shè)計(jì)與施工的選材標(biāo)準(zhǔn)是其次的要件,包括詳細(xì)的模具,鑄造、熱處理規(guī)范程序。用發(fā)展模面設(shè)計(jì)為沖壓的起始尺度、上下結(jié)合分子,是指導(dǎo)該內(nèi)部標(biāo)準(zhǔn)是受制于標(biāo)注與融合的主要構(gòu)件元素。如上下模適配器板、沖床、鑄造粘結(jié)劑、導(dǎo)柱和引導(dǎo)套管磨損板. 另外,通過選擇運(yùn)用沖壓刀具,撐架-幾何學(xué)、沖床沖壓成型模具完全確定建造和使用于CAD系統(tǒng),這一階段的設(shè)計(jì)工程師,允許建立虛擬原型上、下半片
10、的成形,模具用一些幾何參數(shù),如內(nèi)部閉合高度、內(nèi)存儲(chǔ)金屬板、沖床、粘合劑壁厚或立體邊平衡塊. 一些位置分析沖模,拉深模和固定元素形成一個(gè)完整的循環(huán)進(jìn)行干涉和控制,以消除滑枕行程和制圖數(shù)量的不一致性。</p><p><b> 3、模具面形控制</b></p><p> 模具面形控制的成形過程是一個(gè)復(fù)合體系的組成、沖模 空白, 涉及機(jī)械、一套互動(dòng)沖壓,提供必要的基礎(chǔ)結(jié)
11、構(gòu)和能源。假定一個(gè)理想的剛性壓模構(gòu)造相連了托板和理想的剛性沖壓支承板,忽略所有模具表面的扭曲來幫助工程師設(shè)計(jì)形成過程的方法,成形過程只有按照純圖形表式法,否則,在形成過程中為了模擬板材變形反應(yīng),努力把所有這些系統(tǒng)力學(xué)模型去運(yùn)算,這將是一個(gè)巨大的工程。這是最實(shí)際的做法,因此形成孤立接口,即模面設(shè)計(jì)和空白。從其余空白變形和模擬下形成壓力產(chǎn)生摩擦接觸,用純幾何描述模具表面設(shè)計(jì). 此外, 這一主張?jiān)诠I(yè)中已得到普遍使用,即使是在常規(guī)的金屬板內(nèi)部
12、面板下. 最理想的觀念吸取模施工,不過, 當(dāng)談到有可能成為可疑的形成是由于高強(qiáng)度鋼的成形載荷較高. 此外,在產(chǎn)生信任方面形成規(guī)模結(jié)構(gòu)部分與非對(duì)稱分布,可能適用于很高負(fù)載平衡塊板之間的磨損,在沖壓和粘合劑之間增加磨損和扭曲的標(biāo)簽. 在這些變形模具的生產(chǎn)中,應(yīng)列入計(jì)算模型的形成過程. </p><p> 目前, 考慮計(jì)算機(jī)硬件躍進(jìn)與有限元軟件,建立一個(gè)計(jì)算機(jī)模型模擬系統(tǒng)是完全可以實(shí)現(xiàn)的, 然而由于高角度分析計(jì)算機(jī)時(shí)
13、代, 基于個(gè)別特征的變形經(jīng)驗(yàn),一個(gè)完整沖壓周期,從一個(gè)企業(yè)家的觀念來看是幾乎不可行的, 反而比較簡(jiǎn)單的實(shí)際工程方法是可解耦系統(tǒng)的沖壓過程,加上部分組成空白模面設(shè)計(jì)、模具只完成部分拉深模具設(shè)計(jì)。與模具表面扭曲相比,審議過程只有部分時(shí)間依賴性的相互作用和成型板材空白界面帶來大變化空白. 因此, 由于運(yùn)動(dòng)學(xué)特征的變形空白,基于增量應(yīng)變和有限元素變形理論,模擬部分的過程應(yīng)制定基于有限元大變形理論。在另一方面,在單一元素成形周期間,有小變形疊加過
14、渡到大位移變形沖模的特點(diǎn). 因此,小應(yīng)變的彈塑性有限元分析得出的模具可能適合建作。</p><p> 兩方的相互作用是指在計(jì)算適當(dāng)?shù)臄?shù)據(jù)傳輸路線。在該部分過程中,成型模具資料模擬用幾何面設(shè)計(jì)為剛性表面實(shí)體和空白作為彈塑變形體、時(shí)效位移驅(qū)動(dòng)粘合劑、沖壓成型工藝實(shí)現(xiàn)議案. 主要產(chǎn)生幾何變形的應(yīng)力分布和生產(chǎn)空白的歷史后,回彈和成形載荷以及摩擦接觸應(yīng)力分布較大分子面前. 另一方面,為模具專用部分,負(fù)載歷史形成的基本投入
15、評(píng)估模具表面變形分析部分. 完全沖模設(shè)計(jì)模面材料點(diǎn)的有限元分析得出沖壓周期的位移、只有對(duì)下一迭代更新模具表面設(shè)計(jì)可反饋過程的一部分。同時(shí)計(jì)算彈塑性應(yīng)力應(yīng)變?cè)谝粋€(gè)完整的歷史循環(huán)和沖壓同期之間的接觸力沖壓、粘合劑。通過相互借鑒模建筑元素,分子與平衡塊板磨損帶來了很大的啟示。</p><p><b> 4、工業(yè)應(yīng)用</b></p><p> 上一節(jié),在刀具生產(chǎn)前,對(duì)于前
16、道邊體前沖壓模具設(shè)計(jì),工程概述方法論是利用結(jié)構(gòu)評(píng)估沖壓模具設(shè)計(jì),如(Fig. 2)。這部分是強(qiáng)度沖壓能源管理結(jié)構(gòu)的特性。 這種傳統(tǒng)的設(shè)計(jì)方式是為大型構(gòu)件利用吸取1.7–2.2 mm厚度的優(yōu)質(zhì)鋼材。隨著減重約10-15%, 商業(yè)可供1.5毫米高強(qiáng)度低合金鋼與屈服應(yīng)力、成形、中度變形,推出一個(gè)可行的能增大強(qiáng)度特性的替代品。</p><p> 成形工藝設(shè)計(jì)部分沖壓形成純幾何造型做以下辦法,所有模具表面變形假定,忽略了
17、剛性沖壓模具。利用三維CAD模型的一部分, 首先進(jìn)行的是一種損人利己檢查,以確定是否可能形成一個(gè)單一的部分操作。隨后對(duì)零件頂錐角尖端的調(diào)查表明, 三維旋轉(zhuǎn)的部分是幾何撞擊運(yùn)動(dòng)方向,因此,零件被適當(dāng)?shù)姆胖迷诘葔合到y(tǒng)中,這種系統(tǒng)使坐標(biāo)系統(tǒng)中的緊迫軸成平行于部分繪制軸線,如:(Fig. 3).。利用三維CAD模型的一部分,表面上一套模具的幾何學(xué)產(chǎn)生了相當(dāng)于抵消了一半的板材厚度,區(qū)編一套加上這套表面幾何。自零件的邊界線沿著曲線形成,是延長(zhǎng)表面以
18、下類似的幾何形式和粘合劑,因此沖去粘合劑表面和法蘭產(chǎn)生完整的模具及粘合劑表面上的沖壓模具。 如:(Fig. 4)。這一三維組合形式表面形成界面幾何學(xué),其他模具分子從中得到。在CAD環(huán)境中,通過一個(gè)簡(jiǎn)單的幾何復(fù)制,沖壓和粘合劑界面被產(chǎn)生了。通過使用其對(duì)應(yīng)的幾何厚度沖抵正常的壓力和方向。現(xiàn)階段,完整的描述模具計(jì)算機(jī)輔助面設(shè)計(jì),能夠獲得雇用的有限元網(wǎng)格,成形回彈的評(píng)估和分析。沖壓,網(wǎng)狀粘合劑、模具表面與21908三、四個(gè)節(jié)點(diǎn)殼單元共有,所有曲
19、率是由六層分子描繪,如:(Fig. 5)。</p><p><b> 5、總結(jié)</b></p><p> 本文,一個(gè)工程的定量評(píng)價(jià)方法,在設(shè)計(jì)過程中形成的板材沖壓件,提出了精確的理想假說通常采用剛性模具。 以下簡(jiǎn)要回顧沖壓模具設(shè)計(jì)實(shí)踐,基于計(jì)算機(jī)輔助設(shè)計(jì)與分析概念的計(jì)算方法,并在第一部分和第二部分中,這項(xiàng)研究提出了測(cè)定與控制模面變形期間的形成過程。工業(yè)應(yīng)用的基本步
20、驟是用來展示、 雙方更進(jìn)一步的分析計(jì)算和模具表面變形的過程,是一個(gè)完整的沖壓模具設(shè)計(jì)成形??沙尚涡院突貜椬冃芜^程進(jìn)行分析,一個(gè)汽車沖壓結(jié)構(gòu)由部分高強(qiáng)度鋼組成的。通過增強(qiáng)沖壓件的硬度,在最后的沖壓成形模具表面變形結(jié)果中,沖壓形成決定的理想剛性和被論述的可變形的分界面之間有著不同的幾何學(xué)。最高沖壓表面變形發(fā)現(xiàn)有不到一半的厚度了,確認(rèn)的空白界面形成了剛性假說。</p><p><b> 附錄1 英文原文&l
21、t;/b></p><p> Stamping die-face design</p><p> 1. Introduction</p><p> It is known that a crucial part of the production of asheet metal stamping die is essentially the develo
22、pment of a die-face design aiming a tooling surface geometry that gives a fully developed blank shape a defect-free stamping form within the necessary quality constraints. The design of stamping tooling elements starts w
23、ith the part geometry as the basic input data and the methods engineers try todetermine the minimum number of operations for a given stamping form in order to reduce the formin</p><p> The methods engineer
24、conduct svarious tryouts for the forming process design continuing up to the end of workshop try-outs until to the mass production phase of the stamping part. Since both the stamping die-face design and the plasticworkab
25、ility of the sheet metal determine the characteristics of blank defor-mations, additional care should be paid in the forming of high strength steels to adapt to the lower formability and higher springback deformations [2
26、]. In line with the advance-ments in th</p><p> Hence, the die-face deformations and its implications should be considered in connection with the draw die design before submitting to the production. In this
27、 paper, following a short review of the stamping die design practice; a computational methodology is presented for the assessment and control of die-face defor-mations during the sheet metal forming processes. The propos
28、ed approach is employed in the forming process design for a cab body member based on the computer aided design and analysi</p><p> 2. Die-face design concepts</p><p> The die-face design for a
29、 sheet metal forming die may be defined as the composition of a complete surface geometry that deforms a sheet metal blank plastically into a desired stamping shape by ensuring a rigid tooling construction. The design pr
30、ocess starts with the part geometry as the basic input data, the methods engineer firstly decides on the drawing direction by tipping the part to the most favorable axis, and eliminating the risk of an undercut. Then, us
31、ing the material formability and mi</p><p> Once the methods engineer has created a entire geometric description of the blank and die faces in a CAD environment, the finite element analyses may be performed
32、 in order to investigate the process feasibility in terms of the formability, part geometry after springback and forming loads by assuming an ideally rigid die construction [6,7]. The finite element simulation of the sta
33、mping process is done usually in two steps. A forming analysis is conducted to determine the metal deformation for a g</p><p> 3. The die-face shape control</p><p> The sheet metal forming pro
34、cess is a compound system made up of the stamping die and the blank, and involves a set of mechanical interactions with the press and the foundation structure that provide the necessary forming energy[4,5,10,11]. Assumin
35、g an ideally rigid die construction connected to the ram and bolster plates of an ideally rigid press and neglecting all die-face distortions help the methods engineer designing the forming process following a pure geome
36、tric modeling procedure only [2–5</p><p> ing a computer model in order to simulate the complete process system is achievable considering the advancements in computer hardware and finite element software, n
37、oneth-</p><p> eless it is hardly feasible from an industrial perspective due to the high computer analysis times. Instead a rather simple but a practical engineering approach may be the decoupling the stam
38、ping system in to the process-only part composed of the blank plus the die-face design and tooling-only part containing complete draw-die design, based on the individual characteristics of the deformations experienced du
39、ring a complete pressingcycle, respecti-</p><p> vely. Considering process-only part, there are time-dependent interactions of the sheet met-</p><p> al blank and the forming interface bringin
40、g about large changes in the blank shape when compared with the scale of die-face distortions. Consequently, the process-only part should be simulated using a finite element formulation based on large-strain and finite i
41、ncremental deformation theory due to the kinematic characteristics of the blank deformations [8]. On the other hand,small deformation transientssuperimposed on to the large displacements histories characterize the deform
42、ations of the draw</p><p> lacement-driven binder and punch motion realize the forming process. The major outputs are deformed geometry and production stress distributions of the blank after springback and
43、the forming load histories as well as the frictional contact stress distributions over the die-face elements. On the other side, for the tooling-only part, the forming load histories are the basic input for the assessmen
44、t of the die-face deformation analysis. The finite ele-</p><p> ment analysis of the complete draw-die design for a given press cycle provides the displace</p><p> -ments of dieface material p
45、oints, and the updated die-face design may be fed back to process-only part for the next iteration. Also the computed elastic–plastic stressstrain histo-</p><p> ries during a complete press cycle and the c
46、ontact forces between the punch and binder elements through the wear plates and balancer blocks bring about a significant insight to the interaction of draw-die construction elements.</p><p> 4. Industrial
47、application</p><p> The engineering methodology outlined in the previous section is employed in the structural assessment for the stamping die design of a front-side cab body member before the tooling produ
48、ction (Fig. 2). The strength of this part is an essential feature in the crash-energy management of a cab frame. The conventional design practice for this type of large-scale structural elements is to use draw-quality st
49、eels of thickness 1.7–2.2 mm. The commercial availability of 1.5 mm HSLA steel with a higher y</p><p> ies along with an approximately 10–15% weight reduction.</p><p> The forming process desi
50、gn of the part stamping form is done following a pure geometric modeling approach, and all die-face deformations are neglected assuming a rigid stamping tooling. Using the 3-D CAD model of the part, firstly an undercut c
51、heck is conducted in order to determine the possibility of forming the part in a single operat-</p><p> ion.Subsequent to the investigation of the tip angles for the part, the 3-D part geometry is rotated t
52、o the configuration of the ram motion direction, so that the part is positioned appropriately in the press coordinate system in which the pressing-axis became parallel to the part-drawing axis(Fig. 3). Using the 3-D CAD
53、model of the part, a set of surfaces</p><p> for the upper die geometry is generated with an offset equal to the half of the sheet metal thickness, and a set of addendum areas are added to this set of surfa
54、ce geometries.Since the part sidelines follow a curved form, the extended surface geometry follows approximately a similar form, and therefore a sweep binder surfaces and addendum flange are generated to complete the die
55、 and upper bindersurfaces of the stamping tooling (Fig. 4). This 3-D composite surface forms the forming interface geom</p><p> The formability assessment and springback deformation analyses are conducted u
56、sing the concepts and methodologies described in Part I and in Part II of this study. In the first finite element simulation run, the forming loads are defined using the predefined displacement–time history functions for
57、 the forming interface elements. During the forming process, the punch is kept fixed in its initial position,and both the binder and the die are loaded in displacement control, in which a constant clear</p><p&
58、gt; A set of simulation runs with a force-controlled binder closure using a constant blankholder loads are performed in which the blankholder force is increased from 100 to 300 ton with 50 ton increments (Fig. 7). The f
59、easibility of the sheet metal forming process conditions corresponding to each blankholder force value are evaluated using both the amount of thinning and the shape distortion after the springback deformations. In order
60、to assess the shape distortion between the forming geometry and t</p><p> geometry after the springback, the following parameter is introduced as a global measure of the springback deformation.</p>&
61、lt;p> In the above expression, x and X denote the position vector components of a node on the blank before and after springback, respectively, and N is the number of nodes on the blank mesh. An examination of the plo
62、ts of the shape distortion parameter and the maximum thinning with the increasing blankholder force, indicate that a blankholder force about 215 ton would be the limit considering the allowable thinning limit of 18% with
63、 the material (Fig. 8). For higher blankholder force values, even thou</p><p> brane plastic straining. For instance, in the case of 100-ton holding force, the amount of maximum thinning over the stamping f
64、orm is reduced to 14.7% with a similar plastic strain distribution compared to 200-ton blankholder force case (Fig. 9). However, there is a remarkable increase in the springback deformations when compared with that predi
65、cted under a 200-ton blankholder force, and consequently the shape distortion parameter is almost tripled between these two blankholder loading cases. Fi</p><p> mations indicated that a blankholder force o
66、f 200 ton sets the maximum allowable forming load considering the process and material related constraints that can be used in the computer aided design of the sheet metal forming die. </p><p> 5. Conclusio
67、ns</p><p> In this paper, an engineering methodology is proposed for the quantitative assessment for the accuracy of the ideally rigid die hypothesis typically employed in the forming process design of shee
68、t metal stamping parts. Following a short review of the stamping die design practice, the computational approach based on the computer aided design and analysis concepts given in Part I and Part II of this study is prese
69、nted for the determination and control of die-face deformations during the forming pr</p><p> References</p><p> [1] High strength steel stamping design manual. Southfield-Michigan: American I
70、ron and Steel Institute A/SP Program; 2000.</p><p> [2] Sheet metal formability report. Southfield-Michigan: American Iron and Steel Institute; 1989.</p><p> [3] Automotive sheet design manual
71、. Southfield-Michigan: American Iron and Steel Institute; 2002.</p><p> [4] Schuler GmbH. Metal forming handbook. Berlin: Springer; 1998.</p><p> [5] Fundamental of tool design. New York: Soci
72、ety of Manufacturing Engineers; 1998.</p><p> [6] Firat M. Sheet metal springback prediction including initial plastic anisotropy. In: Proceeding of third international conference on design and production o
73、f dies and molds. Bursa: Dies and Molds –Metu; 2004, p. 248–54.</p><p> [7] Firat M, Kocabicak U. Sheet metal springback including the bauschinger effect. In: Proceeding of third international conference on
74、 design and production of dies and molds. Bursa: Dies and Molds –</p><p> Metu; 2004, p. 255–64.</p><p> [8] Firat M. U-channel forming analysis with an emphasis on springback deformation. Mat
75、er Design, 2005, in press, doi:10.1016/j.matdes. 2005.05.008.</p><p> [9] Suchy I. Handbook of die design. New York: McGraw Hill; 1997.</p><p> [10] Die design handbook. New York: Society of M
76、anufacturing Engineers; 1990.</p><p> [11] Lange K. Handbook of metal forming. Michigan: Society of Manufacturing Engineers; 1985.</p><p> [12] Hallquist J. LS-DYNA theory manual. Livermore (C
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