JD21-100開(kāi)式曲柄壓力機(jī)的設(shè)計(jì)
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通過(guò)傾斜樣品鐓粗加工實(shí)現(xiàn)成形壓力機(jī)加載
K. Chodnikiewieza*, S.B. Petersenc, R.Baiendrab, P.A.F. Martinsc
a波蘭華森、85.02-524、那巴特科技大學(xué)
b斯特拉斯克萊德大學(xué)，格拉斯哥，蒙特羅斯大街75號(hào)，英國(guó)
c.葡萄牙Lisboa Codes1096號(hào)Rorisco Pais大街、專(zhuān)科高等教育學(xué)院
摘要：對(duì)傾斜樣品進(jìn)行鐓粗是加載成形壓力機(jī)的一個(gè)途徑，而通過(guò)垂直和水平施力進(jìn)行鐓粗加工是一種可行的方法。然而，由于樣品界面的條件分配不均，需要對(duì)該方法的使用范圍進(jìn)行量化。傾斜樣品的塑性形變通過(guò)使用一種名為PAST2的FE代碼進(jìn)行分析。通過(guò)分析，本文提出了試驗(yàn)樣品選擇及試驗(yàn)范圍的指導(dǎo)方針。很明顯，潤(rùn)滑條件、樣品的減少、及垂直與水平力度比，在變形的整個(gè)過(guò)程中并非恒定不變。因此，當(dāng)研究這些統(tǒng)一特性的范圍時(shí)，有對(duì)壓力特性進(jìn)行分必要析。
關(guān)鍵詞：成形壓力,鐓粗,樣品,有限元法
1.引言
鐓粗也許是最常用的金屬成形方法。實(shí)踐中，鐓粗用于單獨(dú)的成形工序，或用于更加復(fù)雜成形工序的初期階段。在機(jī)械測(cè)試中，鐓粗用于提取流變曲線、摩擦參數(shù)及可加工性。鐓粗試驗(yàn)還常用于確定分析方法和數(shù)值方法的可靠性，以描述與金屬流等有關(guān)的具體現(xiàn)象。
為了便于評(píng)估壓力彈性，對(duì)平行表面的金屬樣品進(jìn)行鐓粗，從而產(chǎn)生一種與壓型壓力（通常是垂直的）軸相平行的壓力。這種通過(guò)對(duì)壓型壓力的彈性偏向進(jìn)行測(cè)量的方法，引申出成形壓力的一個(gè)垂直的和兩角的剛性系數(shù)[1,2]。
盡管如此，在許多情形中，成形壓力的加載來(lái)自垂直和水平兩個(gè)方向。水平方向的壓力FH和垂直方向的壓力FV的比例構(gòu)成了成形壓力F，其值可高達(dá)0.2；
因此，在壓力彈性檢測(cè)的過(guò)程中，須對(duì)這些加載條件進(jìn)行模擬實(shí)驗(yàn)?？梢酝ㄟ^(guò)在兩個(gè)斜墊圈（圖1（a））之間的液壓千斤頂進(jìn)行加壓，但活塞與氣缸的摩擦力會(huì)使得該方法有失準(zhǔn)確。通過(guò)最近提出的另一方法能獲得更具代表性的加壓條件，這種方法建立在鐓粗傾斜樣品的基礎(chǔ)上（圖1（b））
遺憾的是，這種鐓粗方法并不常見(jiàn)：其流程的某些方面Ramaeker和Kals[4]已進(jìn)行過(guò)報(bào)道。兩人皆考慮到了
材料流動(dòng)的不穩(wěn)定性是因工具角度未對(duì)準(zhǔn)造成的。然而，Ramaekers和Kals并未對(duì)此流程進(jìn)行詳述。因此，在使用鐓粗傾斜樣品進(jìn)行壓力彈性實(shí)驗(yàn)之前，需要加以更全面的分析。
2. 求解方法
對(duì)傾斜樣品的鐓粗可使用2-D有限元程序PLAST2進(jìn)行模擬。該程序建立在變分原理的基礎(chǔ)上，由葡萄牙里斯本技術(shù)專(zhuān)科高等教育學(xué)院開(kāi)發(fā)。該原理要求所有容許速度uj能滿(mǎn)足兼容性和不可壓縮性條件，并能使如下函數(shù)成立：
在這個(gè)表達(dá)式中，是有效應(yīng)力，而是有效應(yīng)變率，Tj是表面牽引力，SF是牽引力作用的表面，V是體積。有效應(yīng)力和有效應(yīng)變率分別做如下定義：
其中和分別表示偏應(yīng)力和偏應(yīng)變率。若函數(shù)的值不變，其一階變分消失；即=0.不可壓縮性的定義如公式：
其中，是體積應(yīng)變率。為將其考慮在內(nèi)，使用了補(bǔ)償函數(shù)，這要求對(duì)函數(shù)進(jìn)行修改[5]。
修改后的函數(shù)的公式如下：
其中，K是一個(gè)大的正罰常數(shù)。若函數(shù)的第一個(gè)變分消失，得到：
那么，平衡方程式和體積固定性約束將會(huì)同時(shí)得到滿(mǎn)足（5）。公式（6）對(duì)以上變分方程進(jìn)行了描述。
忽略樣品及模具的彈性形變，則有效應(yīng)變率和偏應(yīng)力之間的關(guān)系可通過(guò)Levy-Mises公式進(jìn)行表達(dá)：
其中，代表塑性區(qū)，與屈服應(yīng)力相等；的公式如下：
其中，C和n表示材料常數(shù)，表示有效張力：
其中，表示張力。
另外，使用了Wanheim和Bay[7]提出的摩擦力模型。按照該模型，摩擦應(yīng)力的公式是：
當(dāng)比例小于1.5，工作界面的摩擦力和正應(yīng)力p成比例；當(dāng)大于3時(shí)，相對(duì)摩擦應(yīng)力=f·a接近一個(gè)恒定值，該值等于f（圖2）。為了消除在中心處摩擦應(yīng)力突變，得出如下近似值：
其中，j是單位矢量，其方向與模具的工作材料速度Us 的方向相反；并且與Us 相比，V0是一個(gè)小的正數(shù)（6）。
[8]中提供了PLAST2的有關(guān)具體信息。使用PLAST2進(jìn)行的金屬流動(dòng)分析結(jié)果與實(shí)驗(yàn)結(jié)果吻合。
3. 假設(shè)
本分析采用了如下假設(shè)：
（i）具備平面應(yīng)變鐓粗條件
（ii）當(dāng)工作材料相對(duì)上模進(jìn)行運(yùn)動(dòng)時(shí)，在下模樣品界面上主要以黏著摩擦為主。這種假設(shè)與實(shí)驗(yàn)條件相符，即下模粗糙，而上模及樣品較光滑，潤(rùn)滑良好。
（iii）低碳鋼的抗屈強(qiáng)度和有效應(yīng)變速率質(zhì)檢的關(guān)系假設(shè)為：
（iv）樣品的初始幾何關(guān)系可通過(guò)Ho/Bo的比例體現(xiàn)，其中Ho是沿著樣品中心線測(cè)得的原始平均高度，Bo是樣品原始寬度，而β是模具和樣品構(gòu)成的角度（詳見(jiàn)圖1）。
（v）如下比例
用于確定樣品高度的減少量，其中H是樣品在中心線處的當(dāng)前高度。
（vi）分析采用了如下基本參數(shù)：Ho/Bo = 0.5, f= 0,5,β= 10 °。對(duì)于該分析，在其它參數(shù)保持不變的時(shí)候，每個(gè)參數(shù)都會(huì)與規(guī)定值有所差異。
4. 實(shí)驗(yàn)結(jié)果
平形及傾斜樣品的變形中，后者的特點(diǎn)可從圖3的基本參數(shù)及相對(duì)壓力p/σo在樣品上表面的分部可以看出。樣品與上模之間的間隔受到接觸面的摩擦力的影響。傾斜樣品的變形描述如下：
（i）流變模型并不關(guān)于中心線對(duì)稱(chēng)。
（ii）流向楔形樣品較厚一邊的金屬體積比流向其較薄的一邊的金屬體積大。
（iii）中點(diǎn)N向樣品較薄一邊位移。在該點(diǎn)上，物質(zhì)流沒(méi)有相對(duì)于上模的正切分量。
（iv）在樣品較厚一邊處，產(chǎn)生了上模與傾斜樣品之間的間隔。傾斜樣品的變形是減值e、摩擦力f，角度β及Ho/Bo比例的一個(gè)復(fù)變函數(shù)。對(duì)于不同減值e及當(dāng)常數(shù)f=0.5, β= 10 ° 和 Ho/Bo=0.5時(shí)，樣品的對(duì)應(yīng)形狀如圖4（a）所示。N-N線代表了中點(diǎn)在鐓粗過(guò)程中所處的位置，而R-R則代表了由于成形力的加載而產(chǎn)生的位移。對(duì)于一個(gè)較小的減值，中點(diǎn)的相對(duì)坐標(biāo)XN/Bo會(huì)保持不變（如圖4（b）），但是對(duì)于較大的減值，XN/Bo比值會(huì)明顯改變。變形在不同截面的值與上模和樣品之間的間隔相關(guān)：這種關(guān)系在圖4（a）中得到明顯體現(xiàn)。由于間隔改變樣品與上模的接觸面積，中點(diǎn)會(huì)向樣品較薄一邊偏移。當(dāng)e = 20%, β= 10 ° 及 Ho/Bo = 0.5時(shí)，對(duì)于各種摩擦因子的樣品形狀如圖5所示。進(jìn)行了如下觀察：
（i）間隔取決于摩擦因子：當(dāng)f= 0時(shí)，在變形初期間隔較大；而當(dāng)f= 1.0時(shí)，則不會(huì)產(chǎn)生間隔。
圖7 比FA/ FV作為過(guò)程參數(shù)的函數(shù)：(a）（FA / FV）（FL）為E和f= 0.5不同的值，f= 0.5；（b）(FH / fvxe）為和常數(shù)f = 0.5的值不同，f= 0.5；（C）（FH / fvxe）為F和FL =常數(shù)10 f的不同值=0.5；（d）（FH / FV）（E）不同F(xiàn)m / Fv= 10，F(xiàn) = 0.5
（ii）摩擦因子對(duì)中點(diǎn)位置的影響比對(duì)樣品形狀的影響大。相對(duì)于常數(shù)e、f及Ho/Bo比例的實(shí)際線性函數(shù)XN(β)/Bo如圖6（b）所示。所得的結(jié)論與前一種情況類(lèi)似：即角度β影響到中點(diǎn)的位置，而非樣品變形后的軸向截面的形狀。
鐓粗合力F（FH, Fv）傾向中線。因?yàn)楣ぷ鞑牧蠌纳媳砻婊驑悠返谋∵吅秃襁?，其結(jié)果是，合力的傾斜角度會(huì)比上模的傾斜角度β小，即：
相對(duì)于不同的e，常數(shù)f及Ho/Bo比值的函數(shù)(FH/Fv) (β)如圖7（a）所示。其中可見(jiàn)FH/Fv比率并不受e的水平的影響。這種情況中，可使用如下的等式：
這種特點(diǎn)符合壓型彈性實(shí)驗(yàn)，因?yàn)樗?jiǎn)化了對(duì)力比相關(guān)數(shù)據(jù)的使用。所選的β及常數(shù)f和Ho/Bo的函數(shù)(FH/Fv)(e)（如圖7（b）所示）證實(shí)了如上特點(diǎn)。圖7（c）和圖7（d）表明，在壓型機(jī)剛性實(shí)驗(yàn)的過(guò)程中，應(yīng)確保降低摩擦力和Ho/Bo比值。如果這點(diǎn)可以保證，F(xiàn)H/Fv比值會(huì)實(shí)際上不受樣品減少的影響。當(dāng)Ho/Bo = 1.0時(shí)（如圖7（d）所示），函數(shù)(FH/Fv) 偏離于其它曲線趨勢(shì)是因?yàn)槭褂玫臉悠诽?，后者在形變初期階段產(chǎn)生了彎曲。單位成形壓力（與樣品長(zhǎng)度相關(guān)）垂直分量與減值e的關(guān)系如圖8所示。在圖8（b）的基礎(chǔ)上，能得出結(jié)論：對(duì)于相對(duì)較小的變形，成形壓力的垂直分量實(shí)際與模具之間構(gòu)成的角度無(wú)關(guān)，包括當(dāng)β= 0時(shí)。該特點(diǎn)簡(jiǎn)化了用于壓型機(jī)彈性測(cè)試的樣品選擇流程。成形壓力的垂直分量可以按照表面平形的樣品鐓粗常用的等式計(jì)算而得。
合力的第三個(gè)特點(diǎn)是作用點(diǎn)i。該點(diǎn)的位置在圖4（a）已經(jīng)以R-R線的形式進(jìn)行了確定。正式的作用點(diǎn)與中點(diǎn)一致。因此，對(duì)于中點(diǎn)所得出的結(jié)論，同樣適用于合力的作用點(diǎn)。
圖8.的關(guān)系，C：，：成形力的Fv／L作為過(guò)程參數(shù)的函數(shù)：（一）皮質(zhì)部分的]和P = 10T選定的值Ho / B O = 0.5；（b）的選定值/我和F = 0.5，H = 0.5.
5. 結(jié)論
1. 對(duì)于樣品的固定摩擦和固定相對(duì)高度 Ho/Bo，成形壓力水平分量與垂直分量的比例FH/Fv主要取決于樣品對(duì)上模的傾斜度。
2. 可以選擇一個(gè)傾斜樣品，以便FH/Fv比例不會(huì)受到樣品的減少的影響。為了達(dá)到該目的，應(yīng)滿(mǎn)足如下條件：（i）樣品的減少應(yīng)保持相對(duì)較低，如當(dāng)f= 0.5時(shí)，其值不應(yīng)超過(guò)20°，而當(dāng)摩擦較高時(shí)，允許較大的減少值；（ii）樣品相對(duì)高度Ho/Bo應(yīng)小于0.5；（iii）樣品與上模界面之間的摩擦應(yīng)保持相對(duì)較低。
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9
Jeurmd or Materials Processing Technology ELSEVIER Journal of Materials Processing rcchnolog 68 (1997 13 I . . . . . . . Loading of forming presses by the upsetting of oblique specimens K. Chodnikiew;z ,*, S.B. Petersen , R. Balendra b P.A.F. Martins ll2trs, Unirerity o/TcImoh,gv ul.Vmhutta $5. 02-524 lVtr.a,. P, hmd h Utlircrsil) d Stralhclvdc. 75 .llotlrose Street. Glasgow GI IX J, I.:K bl.titulO Superior Tc;cnico.41. Rori.co Pai. 1096 Lishoa C,&,. Porlu,tttl Received 21 September 1995 Abstract The upsetting of oblique specimens as a means of loading forming presses with vertical and horizontal forces is a feasible concept, however, due to the changing distribution of conditions at the specimen intertace, the scope of this approach needs to be quantified. The plastic deformation of cbaque specimens was analysed using an FE code named PLAST2. The analysis suggests guidelines for the sciectiou of test specimeas and the scope of such tests: it is apparent that the lubrication conditions and specimen reduction, and the ratio between the vertical and horizontal forces, do not remain constant over the entire course of the deformation. Hence, the analysis of measurements of the behaviour of the press would be meaningful if the range of uniform behaviour of such tests was obse,wed. , 1997 Elsevier Science S.A. Kevword*: Forming presses: Upsetting: Specimen: Finite element method 1. Introduction Upsetting is. perhaps, the most commonly exploited metal forming process. In practice, upsetting is used either as a separate forming process or as the primary stage of more complex forming operations. In mechani- cal testing, upsetting is used for extracting flow curves and friction-dependent parameters and for defining workability. Frequently, upsetting experiments are per- formed to determine the reliability of analytical and numerical methods, to illustrate specific phenomena which relate to metal flow etc. In order to evaluate press elasticity, metal specimens with parallel faces are upset, this producing a force which is parallel to the main (normally vertical) axis of the press. This method of loading together with mea- surements of the elastic deflections of the press enables the development of definition of a vertical and two angular stiffness coefficients of the press 1,2. However, in many practical cases, the press is loaded not only vertically but also horizontally. The ratio between the horizontal F H and vertical Fv components of the forming force F may be as high in value as 0.2; * Corresponding author. Fax: + 351 I 8474045. 0924-0136/97/$17.110 1997 Elsevier Science S.A. All rights reserved. Pll S0924-0136(96)02517-4 hence, these loading conditions would have to be simu- lated during press elasticity measurements. It is possible to load the press with a hydraulic jack located between two oblique washers (Fig. I(a), but friction between the piston and the cylinder renders the mcthod inaccu- rate. A recently proposed 3 alternative method which is based on the upsetting of oblique specimens (Fig. l(b) provides a more representative loading condition. Unfortunately, this form of upsetting is not common: some aspects of this process have been reported by Ramaekers and Kais 4, who considered the unstable L I I I Ram i Ram I L Upper Die spo i ,;-.-fl i p I I I I I (a) (b) Fig. 1. Methods of loading a press with vertical and horizontal forces: (a) using a hydraulic jack; Ib using the upsetting of an oblique specimen. 14 K. Chodnikiewicz et aL / Journal oJ Materials Processhlg Technology 68 (1997) 13-18 the functional/7 5; the modified functional, /Tin, hav- t ing thivfrm: J fs 1.0 ( 1 . I, x/k ,0 o9 f Ht= 0dV+K 2-(e) .-dV- Tju/dS (5) 08 - 0.8 i. - 0. where K is a large positive penalty constant. Now, if the 06 -o6 first variation H in the functional / vanishes, then: o, ; f o, o., 6/7= g6dV+K vt,dV- T;ujdS=O (6) - 0.3 02 and both the equilibrium equations and the volume o.z constancy constraint will be, approximately, satisfied 0.1 p/Go simultaneously 5. The above variational equation is 0 ! 2 3 , 5 Fig. 2. Relative frictional stress as a function of normal stress and friction factor 71. flow of material which results from the angular mis- alignment of the tools. However, Ramaekers and Kals did not provide a detailed insight to the process, thus prior to the use of the upsetting cf oblique specimens for press elasticity experiments, a more comprehensive process analysis is required. 2. Method of solution The upsetting of oblique specimens was simulated using the 2-D finite-element program PLAST2 which was developed at lnstituto Superior Tcnico, Lisbon. This program is based on the variational principle which requires that all admissible velocities uj, which satisfy the conditions of compactibility and incompress- ibility, make the functional: /7= fvatdV- s TjujdS (I) F stationary. In this expression 0 is the effective stress, is the effective strain-rate, Tj is the surface traction, SF is the surface on which tractions are prescribed and V is the volume. The effective stress and effective strain-rate are defined as follows: -2 , t 12 0 = t aoaj (2) = (23 eoe) ;2 (3) where a and v. are the deviatoric stress and the deviatoric strain-rate, respectively. When the functional H is given a stationary value, its first order variation H vanishes; i.e. / = 0. The definition of incom- pressibility has the form: , = kk = 0 (4) where b is the volumetric strain-rate. In order to take this condition into account, the penalty function method was applied, which requires the modification of presented in detail in 6. The elastic deformation of the specimen and dies is neglected and the relationship between the effective strain-rate and the deviatoric stresses is provided by the Levy-Mises flow rule: 3, in which 0 for the plastic region is equal to the yield stress ao which, in turn, is defined by the equation: ao = C(g) (8) where C and n denote the material constants, and g is the effective strain: g = ( ee,/) 12 (9 in which e e is the strain. Further, the Wanheim and Bay 7 friction model was applied. According to this model, the frictional stress r is described by: r =j- k (10) in which f is the friction factor, is the ratio between the real and apparent contact areas, and k is the shear yield stress of the work-material, defined by: k = (l l) The frictional, , and normal, p, stresses at the die- workpiece interface are proportional for p/ao 3 the relative frictional stress z/k = f approaches a constant value which is equal to f (Fig. 2). In order to eliminate the sudden changes of the frictional stress at the neutral point, the following ap- proximation was defined: : . tan - t (12) /r in which j is the unit vector in the direction opposite to the velocity us of the work-material relative to the die and vo is a small positive number in comparison with us 61. Detailed information about PLAST2 is provided in 8. Metal-flow analysis achieved using PLAST2 com- pares well with the results of experiment 9. K. Chmhtikwwic- tt al. .lourmd ftl Materials Proccsing Techmdogy 6g (19971 I3-18 15 ,1 ! 1+/ i _-._. _,_= . .=-:- :. _ -_-:- -. Oo (a) p/Co Z / 3 ,;- t ! ,. ,/ -.-. o I . , - . - _ - ._=,. B (b) Fig. 3. Distorted mesh for the upseuing of: la) a parallel pecimen: and (b) a edge-shaped specimen: together :ith the distribution of normal p and frictional r stresses. .-.- . / . : 1:) . ,j o (a) x N i) o :; - QI - ttl 0 30 4, 50 0 , -q -01- -02 - - -0.3 - I -0.4 :- (b) , +o.-.- Fig. 4. Presenting: (a) specimen shapes and positions of the neutral point N; and (b) the function Xn(e)Bo for.f= 0.5, fl = 10 and H,:B, = 0.5. 3. Assumptions The following assumptions apply to the analysis: (i) Plane-strain upsetting conditions prevail. (it) Sticking friction prevails on the lower die-speci- men interface, whilst the work-material slides relative to the upper tJie. This assumption corresponds to experi- mental condi0ons where the lower die is rough whilst the upper die and the specimen are smooth and well lubricated. (iii) The relationship between the yield strength and the effective strain rate for mild steel has been assumed to be: ao= 740() TM (MPa) (13) (iv) The initial geometry of the specimen is character- ised by the ratio Ho/Bo in which Ho is the original average height measured along the centre line of the specimen, B0 is the original width of the specimen and fl is the angle between the die and the specimen (refer to Fig. 1). (v) The ratio: Ho-H e - - - 100% (14) Ho is used to define the reduction in height of the speci- men, where H is its current height at the center line. (vi) The following basic parameters were used for the analysis: Ho/Bo = 0.5, f= 0,5, fl = I0 . For the analysis. each parameter was varied about these prescribed val. ues, whilst other parameters were retained constant. 16 K. Chodnikiewicz et al./Journal oJ Materials Processing Technology 68 (1997) 13-18 .,S 7- f=oo ,- _ _11 11 /I , f=o.ol,./ - . L-oo ,.I, I . 1 O: (b) (a) X _ 3 _ . B0. ! 0.2 z 0. - 0.25 0.5 0.75 , i 17 . . -o.t L -0.2 -0.3 -0.4 r I .o -f Fig. 5. Presenting: (a) specimen shapes and the position of the neutral point N; and (b) the function X(J)/Bo for e = 20%, # = 10 and Ho/Bo = 0.5. , / t.;/= X N . 0 0 0 i i i .5 10 lfi (a) (b) Fig. 6. Presenting: (a) specimen shapes and the position of the neutral point N; and (b) the function XN(fl)/B o for e = 20/,. fl = 0 and Ho/Bo = 0.5. 4. Results The deformation of parallel and oblique specimens, the latter being charat:terised by basic parameters, are shown in Fig. 3, together with distributions of relative normal pressures P/go on the upper face of the speci- men. Gaps which can be observed between specimens and the upper dies are due to the difference in friction at the contact surfaces. The deformation of the oblique specimen may be described as follows: (i) The flow pattern is not symmetrical about the center line. (ii) A larger volume of metal flows toward the thicker side of the wedge-shaped specimen than towards its thin side. (iii) The neutral point, N, at which material flow has no tangential component relative to the upper die, is displaced towards the thin side of the specimen. (iv) A gap between the upper die and the oblique specimen is created at the thick side of the specimen. The deformation of the oblique specimen is a com- plex function of the reduction e, the friction factor f, the angle # and the ratio Ho/Bo. Specimen shapes are shown in Fig. 4(a) for different reductions and constant f=0.5, fl= 10 and Ho/Bo=0.5. The line N-N repre- sents the position of the neutral point over the course of the upsetting whilst the line R-R refers to the displacements location of the resultant forming force. For a small value of reduction, the relative coordinate XN/Bo of the neutral point remains practically constant (Fig. 4(b), but for greater reductions, the ratio Xr/Bo changes significantly. The trans-sectional value of de- K. Chodnikiewic: et al./Journal of Materials Processing Iechnolog), 68 (1997) 13-18 17 formation refers to the development of the gap bet,veen the upper die and the specimen: this is shown magnified in Fig. 4(a). Since the gap changes the contact area between the specimen and the upper die, the neutral point moves towards the thin side of the specimen. Specimen forms tar e = 20%, fl = 10 and Ho/Bo = 0.5 are shown in Fig. 5 for various friction factors. The following observations are made: (i) The creation of the gap depends on the friction factor: for f= 0 the gap prevails at an early stage of the deformation whilst for f= 1.0 the formation of the gap is not initiated. F.I. FdF. FH,rL, c 2s 0 2 0 05- X - s (a) 0 deg 1 C 25 02 0:5 01 0 05 0 o- . -. . . . . . -o- -o,- S e=lO% 20% 30% 40% 50% J - 15 - 50 -X- 0 - 10 x - t0 2c (b) o ,o C %1 so 025 - FJFv 0 2- ._._.-.- -o- t=-o o - 050 ooS 1.0 -o- 0.25 -x- 0.75 0 + I I SO ,o 20 (c) = ,o e%l 025 . 0.2 . # . . / HO/BO=0 25 005 - -O- 1.0 o ,o e%1 so 0 2o (d) 0 Fig. 7. The ratio F,/Fv as a function of process parameters: ta) (Fa/Fv)(fl) for different values of e and = 0.5, Ho/Bo = 0.5; (b) (FHFvXe) for different values of # and constant f= 0.5, Ho/Bo = 0.5; (c) (FH/FvXe) for different values of f and constant fl = 10 Ho/Bo = 0.5; (d) (FH/Fv)(e) for different Ho/8o and constant # = 10 , f= 0.5. (ii) The friction factor has a greater influence on the location of the neutral point than the specimen fonn. The practically linear function (,(/S)/B, foi con- stant e, f and Ho/Bu is shown in Fig. 6(b). A con- clusion drawn is similar to that in the previous case: the angle / influences the position of the neutral point rather then the form of the axial section of the defonned specimen. The resultant upsetting force F(FH, Fv) is inclined relative to the central line. Since the work-material slides along the upper surface towards both the thick and the thin sides of the specimen, it follows that the angle of inclination of the resultant force 7 would be smaller in value then the angle fl of the inclination of the upper die, i.e.: F. ;=tan-J-f-vl (151 The function (FH/Fv)(fll for different values of e, constant f and Ho,Bo is shown in Fig. 7(a), from hich it can be observed that the ratio FH:Fv does not depend on the level of e. In this specific case the following equation applies: F _ _ H = 0.0132 fl deg (16 Fv This feature suits press elasticity experiments, as i simplifies the use of data pertaining to the force ratio The function (FH/Fv)(e) for selected fl and constan f and Ho/Bo (Fig. 7(b) confirms the above feature Fig. 7(c) and 7(d) show that, during the press stiff hess experiments, both low friction and a low valu of Ho/Bo should be ensured. If it is the case, the ratk FH/Fv remains practically independent of the speci men reduction. The departure of the trend (FwFv)(e for Ho/Bo = 1.0 (Fig. 7(d) from the other graphs re suits from using too large a specimen, the latter un dergoing bending at the early stage of deformation Relationships between the vertical component o the unit forming force (related to the specime: length) and the reduction e are shown schematicall in Fig. 8. On the basis of Fig. 8(b), it can be con eluded that, for a relatively small deformation, th vertical component of the forming force is practicail independent of the angle between the dies, includin the case /= 0. This feature simplifies the procedm for the selection of specimens for press elasticity me surements. The vertical component of the formin force may be calculated from the commonly-know equation for the upsetting of a parallel-faced spec men. The third feature of the resultant force is the point ofi application. The position of this point has been defined Fig. 4(a) in a form of line R-R. The point of the for. application follows the neutral point. Hence, conclusio which have been drawn for the neutral point app K. Chodnikiewk: et aL / Journal of Material, Processing Technology 68 (1997) 13- 18 18 Fv/L kN/mm Fv/L + f=1.0 60 . 60 T -M 0 75 50 40 30 20- 10- 0 0 0.5 /11 50 -o- 0 25 / .-o- o.o /, 4o 2O 10 I I l i t 0 10 20 30 40 50 (a) kN/mm Q- = 15 -e- 100 ? _ 5 0 / I I , I I i 1 o 20 30 40 50 (b) Fig. 8. The relati,c :,:rtical component of the forming force Fv/L as a function of process parameters: (a) for selected values ofand p = 10t Ho/B o = 0.5; (b) for selected values of/I and f= 0.5, H,B, = 0.5. equally well to the point of application of the resultant force. 5. Conclusions 1. For constant friction and constant relative height of the specimen, Ho/Bo, the ratio between the horizontal and vertical components of the forming force, FH/Fv, depends mainly on the specimen/upper-die inclination 2. it is possible to chose an oblique specimen so that the ratio F./Fv remains practically independent on the specimen reduction. In order to achieve this, the follow- ing conditions should be fulfilled: (i) the specimen reduction should be kept relatively low, e.g. for,/= 0.5 it should not exceed 20, whereas for higher friction a greater reduction is permissible; (ii) the relative speci- men height Ho/Bo should be less than 0.5; and (iii) friction on the specimen/upper-die interface should be kept relatively low. References I E. Doege, Static and dynamic stiffness of presses and some effects on the accuracy of workpieces, A,. CIRP, 29 (1980). 2 DIN 55 189, Ermittlu,g ton Kenmrerten fiir Pressen der Blechrer- arbeitung hei stati.sher Belastung, Teil 1,2, 1985. 3 K. Chodnikiewicz, Balendra R. and T. Wanheim, A new concept for the measurement of press stiffness, J. Mater. Process. Tech- nol., 44 (1994) 293-299. 4 J.A.H. Ramaekers and J.A.G. Kals. lnstable material flow in extrusion and upsetting, Amt. CIRP, 31 (1992). 51 O.C. Zienkiewicz and K. Morgan. Finite Element and Applica- tip, Wiley, New York. 1983. 6 S. Kobayashi, S.I. Oh and T. Altan, Metal piThing mtd the Finite-Element Method, Oxford University Press, New York, Oxford. 1989. 7 N. Bay and T. Wanheim, Real area of contact and friction stress at high pressure sliding contact. Wear. 38 11976) 201 - 209. 8 P.A.F. Martins, J.M.C. Rodrigues and M.J.M. 8arata Marques, Numerical and experimental simulation of cold forging pro- cesses, XIII SemintJrio National de Forjamento, UFRGS, Porto Alegre, Brazil, 1993. 9 M. Arentoft, S.B. Petersen, J.M.C. Rodrigues, P.A.F. Martins, R. Balendra and T. Wa-heim, Review of the res-arch on the injection forging of tubular material, J. Meter. Process. Tech- nol., 52 (1995) 460-471.
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