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3.2.3 在靜態(tài)應(yīng)力下的強(qiáng)度設(shè)計(jì)
3.2.3.1對(duì)于韌性材料的設(shè)計(jì)
試驗(yàn)結(jié)果說(shuō)明了無(wú)論是第三強(qiáng)度理論和第四強(qiáng)度理論對(duì)分析材料在延展性上的失效是可以采用的。一個(gè)或其他這兩種理論是工程師必須選擇的東西。為了設(shè)計(jì)的目的，用第三強(qiáng)度理論是簡(jiǎn)單快速的。但如果問題是理解失敗部分的原因的話，或許更適合運(yùn)用第四強(qiáng)度理論。
從簡(jiǎn)單的拉伸試驗(yàn)中，在剪切屈服強(qiáng)度和張力的關(guān)系中，可以預(yù)測(cè)的第三和第四強(qiáng)度理論如下
τ= （3.19）
（1） 在單軸應(yīng)力σ的情況下
最大應(yīng)力準(zhǔn)則將是
σ≤［］ （3.20）
Τ≤［］ （3.21）
安全系數(shù)的條件是
=≥［］
== ≥［］
［］,［］和［］,［］分別是設(shè)計(jì)的許用壓力和屈服于正常應(yīng)力和剪應(yīng)力的設(shè)計(jì)許用安全系數(shù)
（2）在合并彎曲和扭轉(zhuǎn)的情況下，強(qiáng)調(diào)的最大應(yīng)力條件下將
σ=≤［σ］ 第三強(qiáng)度理論
σ= ≤［σ］ 第四強(qiáng)度理論
其中和分別是后面和扭轉(zhuǎn)的應(yīng)力
安全系數(shù)的條件是
S= ≥［s］ (3.26)
or
S= ≥［s］ (3.27)
其中［s］是一個(gè)安全的允許結(jié)合因素
3.2.3.2 脆性材料的設(shè)計(jì)
本節(jié)關(guān)注的是故障，或強(qiáng)度，脆性材料或通?？紤]由于某些原因在脆性斷裂方式的失效的材料，根據(jù)第一強(qiáng)度理論，發(fā)生脆性破壞的三個(gè)主應(yīng)力的其中一個(gè)等于或超過(guò)材料的強(qiáng)度極限或部分。
脆性材料的最大應(yīng)力準(zhǔn)則可以通過(guò)分別指定或以有限的拉伸和剪切應(yīng)力或在公式（3.15）和（3.16）來(lái)呈現(xiàn)
3.2.4在不同應(yīng)力下的強(qiáng)度設(shè)計(jì)
3.2.4.1疲勞失效
機(jī)械零件經(jīng)常在反復(fù)或波動(dòng)的應(yīng)力作用下磨損，盡管實(shí)際最大應(yīng)力遠(yuǎn)低于材料的極限強(qiáng)度。當(dāng)應(yīng)力被多次重復(fù)是的這種磨損被稱為疲勞破壞
疲勞破壞開始于一個(gè)小裂縫，只發(fā)生在宏觀水平并并且可能是一個(gè)不連續(xù)點(diǎn)，或者材料上的非常微小缺陷和小的表面損傷。由于應(yīng)力集中的影響，可能在沒有預(yù)示的情況下導(dǎo)致在循環(huán)應(yīng)力作用下使材料反復(fù)變形并且裂紋不斷擴(kuò)大直到該區(qū)域的抵抗變得非常小時(shí)瞬間發(fā)生斷裂
疲勞破壞是以兩個(gè)不同區(qū)域?yàn)樘卣?，一個(gè)是被稱為疲勞區(qū)的光滑表面，他的裂縫會(huì)隨著不斷反復(fù)按壓在一起和配合表面的分離而逐步擴(kuò)大.另一個(gè)是會(huì)發(fā)生突然的脆性斷裂的粗糙結(jié)晶區(qū)。圖片3.2表示了疲勞失效的表面，他有三個(gè)初始裂紋并且他在一個(gè)小的，旋轉(zhuǎn)的彎曲載荷上。通過(guò)電子顯微鏡可以觀察到一些弧形疲勞線（也可以叫做海灘波紋）
3.2.4.2應(yīng)力壽命的定義
當(dāng)周期數(shù)N的所需的失敗記錄時(shí)，在這個(gè)疲勞區(qū)域的材料強(qiáng)度是
圖3.2 旋轉(zhuǎn)彎曲載荷下疲勞破壞的截面
通過(guò)樣品承受指定大小的反復(fù)載荷來(lái)確定。建立材料的疲勞強(qiáng)度，由于反復(fù)載荷的大小可能從極限強(qiáng)度下降直到?jīng)]有疲勞失效的數(shù)值，所有一定數(shù)量的測(cè)試是必要的。測(cè)試結(jié)果的繪制是例如一個(gè)σ-N的示意圖或應(yīng)力循環(huán)的示意圖，它也叫做在對(duì)數(shù)坐標(biāo)紙上的疲勞曲線，或是疲勞強(qiáng)度。失效周期數(shù)值N.A的典型的 σ-N示意圖在圖3.3上顯示。它說(shuō)明了對(duì)鋼制材料UNSG42300的完全扭轉(zhuǎn)軸向疲勞測(cè)試的結(jié)果。
應(yīng)力循環(huán)次數(shù)
圖3.3一個(gè)典型的鋼的疲勞曲線
如圖3.3，疲勞失效，從n = 1到n = 1000周期一般分為低周疲勞而相應(yīng)的應(yīng)力循環(huán)周期大于1000被認(rèn)為是高周疲勞。
圖3.3也表示，σ-N曲線是通過(guò)有限壽命區(qū)和無(wú)限壽命區(qū)來(lái)區(qū)別的。在這個(gè)區(qū)域的邊界線N叫做周期的臨界值，較遠(yuǎn)的疲勞曲線變成水平線，疲勞曲線將不會(huì)出現(xiàn)不管周期有多大。疲勞強(qiáng)度對(duì)應(yīng)的臨界周期數(shù)叫做耐久極限或疲勞極限，疲勞應(yīng)力設(shè)定為或， 或 和 或 ，應(yīng)力的比例r=/,r=1（對(duì)稱的脈沖應(yīng)力）和r=0（變動(dòng)應(yīng)力）。
對(duì)于一些材料比如有色金屬和合金，他們的疲勞曲線不會(huì)變成水平，故而一個(gè)真正的疲勞曲線是不會(huì)出現(xiàn)的。對(duì)于這樣的金屬他實(shí)際上接受指定的一個(gè)疲勞強(qiáng)度，被定義為對(duì)應(yīng)于所選生活的斷裂應(yīng)力值N（應(yīng)力循環(huán)次數(shù)）在σ-N 曲線中，例如 N= 曲線。
在工程中，一般來(lái)說(shuō)，疲勞壽命小于1000或10000（N＜或N＜在一些參考中）周期的部分可以采用靜態(tài)設(shè)計(jì)準(zhǔn)則。然而，對(duì)于一些重要的部分或結(jié)構(gòu)例如化工容器在壓應(yīng)力下，采用低循環(huán)的設(shè)計(jì)標(biāo)準(zhǔn)。因?yàn)閷?duì)于的大多數(shù)通用機(jī)械零部件的疲勞壽命需要高于10周期，低循環(huán)的設(shè)計(jì)標(biāo)準(zhǔn)在本書中不需要詳細(xì)論述。
在有限壽命區(qū) ≤N＜，σ-N的方程式可以被畫出，C 和
從試驗(yàn)結(jié)果建立了常數(shù)，m是一個(gè)指數(shù)有關(guān)的材料的類型和應(yīng)力條件，比如說(shuō)呢，當(dāng)鋼承受拉伸，壓縮，彎曲和剪切應(yīng)力，m=9;接觸應(yīng)力,m=8
假設(shè)臨界的周期數(shù)為，疲勞極限和 是已知的，疲勞強(qiáng)
度到選定的應(yīng)力循環(huán)次數(shù)N可以定義 =被稱為壽命系數(shù)。
臨界的周期數(shù)是由材料的類型來(lái)確定，一般來(lái)說(shuō)，用硬度鋼≤350HB,≈~和用硬度鋼＞350HB, ≈10×~25×而有色金屬，≈25×
研究發(fā)現(xiàn)，標(biāo)準(zhǔn)曲線，從眾多的耗時(shí)的疲勞試驗(yàn)得到的是難以用數(shù)學(xué)方法和疲勞設(shè)計(jì)中的應(yīng)用。因此，實(shí)驗(yàn)表明提出的簡(jiǎn)化疲勞強(qiáng)度失效的幾種獲取方法和實(shí)用方程。一個(gè)繪圖的韌性材料的簡(jiǎn)化疲勞強(qiáng)度圖稱為折線簡(jiǎn)化圖的方法。一個(gè)典型的韌性材料的疲勞強(qiáng)度圖是顯示在圖。3.4表示的應(yīng)力幅與平均應(yīng)力 在圖中點(diǎn)A（0，），B（ ，），S（，0）和 F(，0 )分別代表對(duì)稱脈動(dòng)強(qiáng)度，交替強(qiáng)度，屈服和材料的靜態(tài)極限強(qiáng)度。如果考慮收益最大應(yīng)力超過(guò)屈服強(qiáng)度的韌性斷裂準(zhǔn)則，直線是從點(diǎn)的135°一角的平均應(yīng)力軸和停止在E點(diǎn)，對(duì)延長(zhǎng)線AB，因此，虛線表示簡(jiǎn)化疲勞設(shè)計(jì)準(zhǔn)則構(gòu)造。破線內(nèi)的區(qū)域的屈服和疲勞安全帶而破線以外的地區(qū)是破壞區(qū)。很明顯，任何一點(diǎn)代表的工作應(yīng)力(，)，這是地址斷線內(nèi)，更安全的一部分。同時(shí)點(diǎn)或虛線外ABES顯示故障。
圖3.4 韌性材料的簡(jiǎn)化疲勞強(qiáng)度圖
對(duì)金屬畫折線簡(jiǎn)化圖，相關(guān)的強(qiáng)度可從設(shè)計(jì)手冊(cè)或其他工程設(shè)計(jì)手冊(cè)列出實(shí)際方程。
3.2.4.4 許用疲勞設(shè)計(jì)圖
分析和預(yù)測(cè)在機(jī)械設(shè)計(jì)中的一個(gè)部分的疲勞壽命，所考慮的因素很多，如應(yīng)力集中，零件的尺寸和表面條件，加載順序和頻率，各種各樣的環(huán)境條件，因此，結(jié)合影響因素的情況下，依賴的是采用疲勞壽命的三個(gè)最有影響力的因素的考慮。讓的應(yīng)力集中系數(shù)，規(guī)模因素和表面狀態(tài)的因素是(),()和() 分別，結(jié)合影響因素或可得到的
疲勞試驗(yàn)結(jié)果表明，這三個(gè)因素只影響應(yīng)力幅而不是平均應(yīng)力。因此，允許的疲勞設(shè)計(jì)圖是基于簡(jiǎn)化疲勞圖和組合的影響因素如3.5建立。
圖3.5許用疲勞設(shè)計(jì)圖
如圖3.5所示，該線是簡(jiǎn)化疲勞強(qiáng)度線的線A’B’E’是允許的疲勞強(qiáng)度設(shè)計(jì)線當(dāng)組合的影響因素或和被認(rèn)為是生命系數(shù)。這是可以理解的任何點(diǎn)代表的工作應(yīng)力(,) 必須在地區(qū) OA'B'E'SO（安全區(qū)），為了避免產(chǎn)生或疲勞的部分。這個(gè)圖形的方法是易于使用任何常見的工程分析和設(shè)計(jì)
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e pos 模具工業(yè)現(xiàn)狀Process simulation in stamping – recent
applications for product and process design
Abstract
Process simulation for product and process design is currently being practiced in industry. However, a number of input variables have a significant effect on the accuracy and reliability of computer predictions. A study was conducted to evaluate the capability of FE-simulations for predicting part characteristics and process conditions in forming complex-shaped, industrial parts.
In industrial applications, there are two objectives for conducting FE-simulations of the stamping process; (1) to optimize the product design by analyzing formability at the product design stage and (2) to reduce the tryout time and cost in process design by predicting the deformation process in advance during the die design stage. For each of these objectives, two kinds of FE-simulations are applied. Pam-Stamp, an incremental dynamic-explicit FEM code released by Engineering Systems Int'l, matches the second objective well because it can deal with most of the practical stamping parameters. FAST_FORM3D, a one-step FEM code released by Forming Technologies, matches the first objective because it only requires the part geometry and not the complex process information.
In a previous study, these two FE codes were applied to complex-shaped parts used in manufacturing automobiles and construction machinery. Their capabilities in predicting formability issues in stamping were evaluated. This paper reviews the results of this study and summarizes the recommended procedures for obtaining accurate and reliable results from FE simulations.
In another study, the effect of controlling the blank holder force (BHF) during the deep drawing of hemispherical, dome-bottomed cups was investigated. The standard automotive aluminum-killed, drawing-quality (AKDQ) steel was used as well as high performance materials such as high strength steel, bake hard steel, and aluminum 6111. It was determined that varying the BHF as a function of stroke improved the strain distributions in the domed cups.
Keywords: Stamping; Process ;stimulation; Process design
1. Introduction
The design process of complex shaped sheet metal stampings such as automotive panels, consists of many stages of decision making and is a very expensive and time consuming process. Currently in industry, many engineering decisions are made based on the knowledge of experienced personnel and these decisions are typically validated during the soft tooling and prototyping stage and during hard die tryouts. Very often the soft and hard tools must be reworked or even redesigned and remanufactured to provide parts with acceptable levels of quality.
The best case scenario would consist of the process outlined in Fig. 1. In this design process, the experienced product designer would have immediate feedback using a specially design software called one-step FEM to estimate the formability of their design. This would allow the product designer to make necessary changes up front as opposed to down the line after expensive tooling has been manufactured. One-step FEM is particularly suited for product analysis since it does not require binder, addendum, or even most process conditions. Typically this information is not available during the product design phase. One-step FEM is also easy to use and computationally fast, which allows the designer to play “what if” without much time investment.
Fig. 1. Proposed design process for sheet metal stampings.
Once the product has been designed and validated, the development project would enter the “time zero” phase and be passed onto the die designer. The die designer would validate his/her design with an incremental FEM code and make necessary design changes and perhaps even optimize the process parameters to ensure not just minimum acceptability of part quality, but maximum achievable quality. This increases product quality but also increase process robustness. Incremental FEM is particularly suited for die design analysis since it does require binder, addendum, and process conditions which are either known during die design or desired to be known.
The validated die design would then be manufactured directly into the hard production tooling and be validated with physical tryouts during which the prototype parts would be made. Tryout time should be decreased due to the earlier numerical validations. Redesign and remanufacturing of the tooling due to unforeseen forming problems should be a thing of the past. The decrease in tryout time and elimination of redesign/remanufacturing should more than make up for the time used to numerically validate the part, die, and process.
Optimization of the stamping process is also of great importance to producers of sheet stampings. By modestly increasing one's investment in presses, equipment, and tooling used in sheet forming, one may increase one's control over the stamping process tremendously. It has been well documented that blank holder force is one of the most sensitive process parameters in sheet forming and therefore can be used to precisely control the deformation process.
By controlling the blank holder force as a function of press stroke AND position around the binder periphery, one can improve the strain distribution of the panel providing increased panel strength and stiffness, reduced springback and residual stresses, increased product quality and process robustness. An inexpensive, but industrial quality system is currently being developed at the ERC/NSM using a combination of hydraulics and nitrogen and is shown in Fig. 2. Using BHF control can also allow engineers to design more aggressive panels to take advantage the increased formability window provided by BHF control.
Fig. 2. Blank holder force control system and tooling being developed at the ERC/NSM labs.
Three separate studies were undertaken to study the various stages of the design process. The next section describes a study of the product design phase in which the one-step FEM code FAST_FORM3D (Forming Technologies) was validated with a laboratory and industrial part and used to predict optimal blank shapes. Section 4 summarizes a study of the die design stage in which an actual industrial panel was used to validate the incremental FEM code Pam-Stamp (Engineering Systems Int'l). Section 5 covers a laboratory study of the effect of blank holder force control on the strain distributions in deep drawn, hemispherical, dome-bottomed cups.
2. Product simulation – applications
The objective of this investigation was to validate FAST_FORM3D, to determine FAST_FORM3D's blank shape prediction capability, and to determine how one-step FEM can be implemented into the product design process. Forming Technologies has provided their one-step FEM code FAST_FORM3D and training to the ERC/NSM for the purpose of benchmarking and research. FAST_FORM3D does not simulate the deformation history. Instead it projects the final part geometry onto a flat plane or developable surface and repositions the nodes and elements until a minimum energy state is reached. This process is computationally faster than incremental simulations like Pam-Stamp, but also makes more assumptions. FAST_FORM3D can evaluate formability and estimate optimal blank geometries and is a strong tool for product designers due to its speed and ease of use particularly during the stage when the die geometry is not available.
In order to validate FAST_FORM3D, we compared its blank shape prediction with analytical blank shape prediction methods. The part geometry used was a 5?in. deep 12?in. by 15?in. rectangular pan with a 1?in. flange as shown in Fig. 3. Table 1 lists the process conditions used. Romanovski's empirical blank shape method and the slip line field method was used to predict blank shapes for this part which are shown in Fig. 4.
Fig. 3. Rectangular pan geometry used for FAST_FORM3D validation.
Table 1. Process parameters used for FAST_FORM3D rectangular pan validation
Fig. 4. Blank shape design for rectangular pans using hand calculations.
(a) Romanovski's empirical method; (b) slip line field analytical method.
Fig. 5(a) shows the predicted blank geometries from the Romanovski method, slip line field method, and FAST_FORM3D. The blank shapes agree in the corner area, but differ greatly in the side regions. Fig. 5(b)–(c) show the draw-in pattern after the drawing process of the rectangular pan as simulated by Pam-Stamp for each of the predicted blank shapes. The draw-in patterns for all three rectangular pans matched in the corners regions quite well. The slip line field method, though, did not achieve the objective 1?in. flange in the side region, while the Romanovski and FAST_FORM3D methods achieved the 1?in. flange in the side regions relatively well. Further, only the FAST_FORM3D blank agrees in the corner/side transition regions. Moreover, the FAST_FORM3D blank has a better strain distribution and lower peak strain than Romanovski as can be seen in Fig. 6.
Fig. 5. Various blank shape predictions and Pam-Stamp simulation results for the rectangular pan.
(a) Three predicted blank shapes; (b) deformed slip line field blank; (c) deformed Romanovski blank; (d) deformed FAST_FORM3D blank.
Fig. 6. Comparison of strain distribution of various blank shapes using Pam-Stamp for the rectangular pan.
(a) Deformed Romanovski blank; (b) deformed FAST_FORM3D blank.
To continue this validation study, an industrial part from the Komatsu Ltd. was chosen and is shown in Fig. 7(a). We predicted an optimal blank geometry with FAST_FORM3D and compared it with the experimentally developed blank shape as shown in Fig. 7(b). As seen, the blanks are similar but have some differences.
Fig. 7. FAST_FORM3D simulation results for instrument cover validation.
(a) FAST_FORM3D's formability evaluation; (b) comparison of predicted and experimental blank geometries.
Next we simulated the stamping of the FAST_FORM3D blank and the experimental blank using Pam-Stamp. We compared both predicted geometries to the nominal CAD geometry (Fig. 8) and found that the FAST_FORM3D geometry was much more accurate. A nice feature of FAST_FORM3D is that it can show a “failure” contour plot of the part with respect to a failure limit curve which is shown in Fig. 7(a). In conclusion, FAST_FORM3D was successful at predicting optimal blank shapes for a laboratory and industrial parts. This indicates that FAST_FORM3D can be successfully used to assess formability issues of product designs. In the case of the instrument cover, many hours of trial and error experimentation could have been eliminated by using FAST_FORM3D and a better blank shape could have been developed.
Fig. 8. Comparison of FAST_FORM3D and experimental blank shapes for the instrument cover.
(a) Experimentally developed blank shape and the nominal CAD geometry; (b) FAST_FORM3D optimal blank shape and the nominal CAD geometry.
3. Die and process simulation – applications
In order to study the die design process closely, a cooperative study was conducted by Komatsu Ltd. of Japan and the ERC/NSM. A production panel with forming problems was chosen by Komatsu. This panel was the excavator's cabin, left-hand inner panel shown in Fig. 9. The geometry was simplified into an experimental laboratory die, while maintaining the main features of the panel. Experiments were conducted at Komatsu using the process conditions shown in Table 2. A forming limit diagram (FLD) was developed for the drawing-quality steel using dome tests and a vision strain measurement system and is shown in Fig. 10. Three blank holder forces (10, 30, and 50?ton) were used in the experiments to determine its effect. Incremental simulations of each experimental condition was conducted at the ERC/NSM using Pam-Stamp.
Fig. 9. Actual product – cabin inner panel.
Table 2. Process conditions for the cabin inner investigation
Fig. 10. Forming limit diagram for the drawing-quality steel used in the cabin inner investigation.
At 10?ton, wrinkling occurred in the experimental parts as shown in Fig. 11. At 30?ton, the wrinkling was eliminated as shown in Fig. 12. These experimental observations were predicted with Pam-stamp simulations as shown in Fig. 13. The 30?ton panel was measured to determine the material draw-in pattern. These measurements are compared with the predicted material draw-in in Fig. 14. Agreement was very good, with a maximum error of only 10?mm. A slight neck was observed in the 30?ton panel as shown in Fig. 13. At 50?ton, an obvious fracture occurred in the panel.
Fig. 11. Wrinkling in laboratory cabin inner panel, BHF=10?ton.
Fig. 12. Deformation stages of the laboratory cabin inner and necking, BHF=30?ton.
(a) Experimental blank; (b) experimental panel, 60% formed; (c) experimental panel, fully formed; (d) experimental panel, necking detail.
Fig. 13. Predication and elimination of wrinkling in the laboratory cabin inner.
(a) Predicted geometry, BHF=10?ton; (b) predicted geometry, BHF=30?ton.
Fig. 14. Comparison of predicted and measured material draw-in for lab cabin inner, BHF=30?ton.
Strains were measured with the vision strain measurement system for each panel, and the results are shown in Fig. 15. The predicted strains from FEM simulations for each panel are shown in Fig. 16. The predictions and measurements agree well regarding the strain distributions, but differ slightly on the effect of BHF. Although the trends are represented, the BHF tends to effect the strains in a more localized manner in the simulations when compared to the measurements. Nevertheless, these strain prediction show that Pam-Stamp correctly predicted the necking and fracture which occurs at 30 and 50?ton. The effect of friction on strain distribution was also investigated with simulations and is shown in Fig. 17.
Fig. 15. Experimental strain measurements for the laboratory cabin inner.
(a) measured strain, BHF=10?ton (panel wrinkled); (b) measured strain, BHF=30?ton (panel necked); (c) measured strain, BHF =50?ton (panel fractured).
Fig. 16. FEM strain predictions for the laboratory cabin inner.
(a) Predicted strain, BHF=10?ton; (b) predicted strain, BHF=30?ton; (c) predicted strain, BHF=50?ton.
Fig. 17. Predicted effect of friction for the laboratory cabin inner, BHF=30?ton.
(a) Predicted strain, μ=0.06; (b) predicted strain, μ=0.10.
A summary of the results of the comparisons is included in Table 3. This table shows that the simulations predicted the experimental observations at least as well as the strain measurement system at each of the experimental conditions. This indicates that Pam-Stamp can be used to assess formability issues associated with the die design.
Table 3. Summary results of cabin inner study
4. Blank holder force control – applications
The objective of this investigation was to determine the drawability of various, high performance materials using a hemispherical, dome-bottomed, deep drawn cup (see Fig. 18) and to investigate various time variable blank holder force profiles. The materials that were investigated included AKDQ steel, high strength steel, bake hard steel, and aluminum 6111 (see Table 4). Tensile tests were performed on these materials to determine flow stress and anisotropy characteristics for analysis and for input into the simulations (see Fig. 19 and Table 5).
Fig. 18. Dome cup tooling geometry.
Table 4. Material used for the dome cup study
Fig. 19. Results of tensile tests of aluminum 6111, AKDQ, high strength, and bake hard steels.
(a) Fractured tensile specimens; (b) Stress/strain curves.
Table 5. Tensile test data for aluminum 6111, AKDQ, high strength, and bake hard steels
It is interesting to note that the flow stress curves for bake hard steel and AKDQ steel were very similar except for a 5% reduction in elongation for bake hard. Although, the elongations for high strength steel and aluminum 6111 were similar, the n-value for aluminum 6111 was twice as large. Also, the r-value for AKDQ was much bigger than 1, while bake hard was nearly 1, and aluminum 6111 was much less than 1.
The time variable BHF profiles used in this investigation included constant, linearly decreasing, and pulsating (see Fig. 20). The experimental conditions for AKDQ steel were simulated using the incremental code Pam-Stamp. Examples of wrinkled, fractured, and good laboratory cups are shown in Fig. 21 as well as an image of a simulated wrinkled cup.
Fig. 20. BHF time-profiles used for the dome cup study.
(a) Constant BHF; (b) ramp BHF; (c) pulsating BHF.
Fig. 21. Experimental and simulated dome cups.
(a) Experimental good cup; (b) experimental fractured cup; (c) experimental wrinkled cup; (d) simulated wrinkled cup.
Limits of drawability were experimentally investigated using constant BHF. The results of this study are shown in Table 6. This table indicates that AKDQ had the largest drawability window while aluminum had the smallest and bake hard and high strength steels were in the middle. The strain distributions for constant, ramp, and pulsating BHF are compared experimentally in Fig. 22 and are compared with simulations in Fig. 23 for AKDQ. In both simulations and experiments, it was found that the ramp BHF trajectory improved the strain distribution the best. Not only were peak strains reduced by up to 5% thereby reducing the possibility of fracture, but low strain regions were increased. This improvement in strain distribution can increase product stiffness and strength, decrease springback and residual stresses, increase product quality and process robustness.
Table 6. Limits of drawability for dome cup with constant BHF
Fig. 22. Experimental effect of time variable BHF on engineering strain in an AKDQ steel dome cup.
Fig. 23. Simulated effect of time variable BHF on true strain in an AKDQ steel dome cup.
Pulsating BHF, at the frequency range investigated, was not found to have an effect on strain distribution. This was likely due to the fact the frequency of pulsation that was tested was only 1?Hz. It is known from previous experiments of other researchers that proper frequencies range from 5 to 25?Hz [3]. A comparison of load-stroke curves from simulation and experiments are shown in Fig. 24 for AKDQ. Good agreement was found for the case where μ=0.08. This indicates that FEM simulations can be used to assess the formability improvements that can be obtained by using BHF control techniques.
Fig. 24. Comparison of experimental and simulated load-stroke curves for an AKDQ steel dome cup.
5 Conclusions and future work
In this paper, we evaluated an improved design process for complex stampings which involved eliminating the soft tooling phase and incorporated the validation of product and process using one-step and incremental FEM simulations. Also, process improvements were proposed consisting of the implementation of blank holder force control to increase product quality and process robustness.
Three separate investigations were summarized which analyzed various stages in the design process. First, the product design phase was investigated with a laboratory and industrial validation of the one-step FEM code FAST_FORM3D and its ability to assess formability issues involved in product design. FAST_FORM3D was successful at predicting optimal blank shapes for a rectangular pan and an industrial instrument cover. In the case of the instrument cover, many hours of trial and error experimentation could have been eliminated by using FAST_FORM3D and a better blank shape could have been developed.
Second, the die design