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小型二輥式冷軋機(jī)結(jié)構(gòu)設(shè)計(jì)-兩輥冷軋機(jī)【含7張CAD圖帶開(kāi)題報(bào)告-獨(dú)家】.zip,含7張CAD圖帶開(kāi)題報(bào)告-獨(dú)家,小型,二輥式,冷軋機(jī),結(jié)構(gòu)設(shè)計(jì),CAD,開(kāi)題,報(bào)告,獨(dú)家
目 錄
1 英文文獻(xiàn)翻譯 1
1.1 英文文獻(xiàn)原文題目 1
1.2中文翻譯 15
2 專業(yè)閱讀書(shū)目 26
2.1 機(jī)械設(shè)計(jì)手冊(cè) 26
2.2 機(jī)械設(shè)計(jì) 26
2.3 現(xiàn)代工程制圖 27
2.4 材料力學(xué) 27
2.5 互換性與測(cè)量技術(shù) 28
2.6 機(jī)械制造基礎(chǔ) 28
2.7 機(jī)械原理 29
2.8 機(jī)電傳動(dòng)控制 29
2.9 機(jī)械制造技術(shù) 30
2.10 機(jī)械制造技術(shù) 30
1 英文文獻(xiàn)翻譯
1.1 英文文獻(xiàn)原文題目
A new method for prediction of forward slip
in the tandem cold rolling mill
M. Poursina & M. Rahmatipour & H. Mirmohamadi
Abstract A new method for prediction of forward slip in the tandem cold rolling mill without the velocity meter sensors based on rolling geometry is proposed here. According to this proposed method, an algorithm is developed for online estimation of friction coefficient and strip’s behavior. Online exertion of friction coefficient and strip’s behavior in the rolling’s program results in better control. So, the unsaturated actuators are satisfied and the possibility of strip tearing is decreased. The strip’s material is st12. The material is considered elastic-plastic, homogenous, and it follows the Ludwick’s constitutive equation law. The yield stress of strip and Young modulus are determined by simple tension test on a specimen of strip before rolling. For validation of the developed scheme, two operating samples are considered and the results are compared with the available literature.
Key words : Cold rolling .Forward slip .Friction .Constitutive equation
Nomenclature
P :Rolling force
D :Diameter of work roll
R :Radius of work roll
W: Width of strip
h: Thickness of strip
t: Inter-stand tension
C, n: Constitutive equation’s constants
: Deformed roll radius
Φ: Neutral point angle
K: Strip deformation resistance
μ: Friction coefficient
fs: Forward slip
σ: Flow stress
E: Strain
R: Reduction
L: Length of contact
E: Young modulus
v: Poison ratio
1.Introduction
Tandem cold rolling mill control is a complicated process. The objective of this process is to obtain desirable thickness of strips through exact control of rolling force and forward slip. The magnitude of difference between the measured and calculated rolling force and forward slip lead to saturated actuators. Under this circumstances the slightest oscillation in the control system of tandem cold rolling mill, would enhance the possibility of the strip tearing [1]. Rolling force and forward slip depend on the different parameters specially the friction coefficient and mechanical behavior of the strip. These parameters vary during rolling process, while in most of the control programs, they are considered constant. For lack of online information of the friction coefficient and constants of constitutive equation, several researchers have presented models based on the inverse method in order to determine online magnitude of friction coefficients and constitutive equation.
Table 1 The list of equations, applied in the presented flowchart
Fig. 1 Rolling geometry and roller pressure distribution along contact arc [7]
Byon et al. determined the friction coefficient and constants of constitutive equation instantaneously in a reversible cold rolling mill equipped with full sensors in order to measure forward slip by adopting the inverse method [2]. Tieu et al. [3, 4] evaluated the friction coefficient and constitutive equation of the strip in a four Table stand cold rolling mill and offered an applicable model for the friction coefficient.
Although rolling forces and forward slips in the previous works have been measured directly through load cells and velocity meter sensors, in some strip-manufacturing plants, the velocity meters do not register the strip speed well enough because the existing rolling mill is not in its standard shape or, in some cases, due to variety of reasons, there is no proper location to install the velocity meter sensors. In this type of rolling process lines, the forward slips are not accurately measured and the calculation of rolling process is made according to constant experimental magnitudes of forward slips.
This deficiency leads to more errors in the calculation of rolling line process, and the strip tearing will occur while the actuators are saturated and cannot remove these errors.
In this study, a new approach is presented based on rolling geometry in order to predict the online magnitudes of forward slips in a tandem cold rolling mill which is not equipped with enough velocity meter sensors or the existing sensors do not respond accurately. Subsequently, through the inverse algorithm, the magnitudes of friction coefficients and constants of constitutive equation of strip are determined instantaneously. For validation of the developed scheme, two samples of a five stand tandem cold rolling mill at Isfahan Mobarakeh Steel Complex (IMSC) are studied. The comparison of the results between developed scheme and the results available in the related literature are in good agreement.
Fig. 2 Effect of inter-stand tensions on pressure distribution and neutral point, tf forward tension, tb backward tension
2.Mathematical model
Here, the synchronized solutions of the three equations of rolling force, the forward slip, and constitutive equation model are accomplished.
The first equation is rolling force model: different rolling force models are suggested to determine the rolling force where the following form is in common:
(1)
In online calculations, using simple equations are essential to increase the process speed. For this purpose, the Bland-Ford force model, Eq. (2), is selected [5].
（2）
Where f1 and f2 are the correction functions for tensile stress and friction coefficient, respectively (Table 1). The second equation is forward slip model: it is obtained when the pressure distributions along the contact arc of each side of the neutral point are equal [6]. This equation expresses forward slip as a function of friction coefficient and deformation resistance.
（3）
Where Ki and Ko are the strip deformation resistance at the entry and exit roll gap, respectively.
The third equation is material behavior model: in the tandem cold rolling mill, Ludwick’s constitutive equation law, Eq. (4), which predicts the strip behavior, is applied in this study.
（4）
Where ε is the effective strain and is calculated by Eq. (5) at each stand and σ is the flow stress.
（5）
An algorithm for computing the flow stress-strain curve of strip, C and n and friction coefficient, μ, is presented based on synchronized solution of the abovementioned three equations. The set of the equations is listed below:
（6）
Fig. 3 Upper bound of forward slip and neutral point place
Fig. 4 The flow stress-strain curve of strip
Fig. 5 Flowchart of the developed algorithm
Fig. 6 Schematic diagram of the five-stand tandem cold rolling mill (IMSC)
Table 2 Experimental data of IMSC (case 1)
3.Determination of forward slip
The aim of this study is to determine the magnitudes of forward slips, the fs in the second equation of the above set, in a five-stand industrial rolling process which is not equipped with enough velocity meter sensors. Teslikov et al. determined the pressure distribution along the contact arc of the strip and roller [7]. A segment of a strip during rolling is shown in Fig. 1. Parameter x indicates the place of neutral point along the roller and strip contact arc.
The relation between the location of the neutral point in rolling zone and forward slip is obtained according to Eq. (7) [8].
（7）
In Fig. 1, it is observed that the roller pressure at entrance and exit points are equal to the strip deformation resistance and at the neutral point the roller pressure is at its maximum. In this literature, it is observed that the inter-stand tensions have not been considered [7].
In rolling process, inter-stand tensions are applied to decrease the rolling pressure.
The effect of inter-stand tensions in a rolling stand is illustrated in Fig. 2 with the corresponding curves. By applying backward tension, the required pressure in deforming the strip is decreased constantly from entrance point to neutral point causing a decline in line (a) to form line (b), dotted line, with no change in the gradient. As observed here, the neutral point Na has changed place toward the exit point due to the downward movement of curve a.
In case of applying forward tension as illustrated in Fig. 2, the same phenomenon takes place with the exception that the Na changes place toward the entrance Point. Since the thickness of strip is reduced continuously during tandem cold rolling mill, the forward tensions are greater than backward tensions at stands 1 to 4. In these stands, the neutral point moves toward the entrance point leading to a value increase in the forward slip; therefore, the forward slip in the absent of inter stand tensions shows the minimum value of true forward slip and can be calculated by Eq. (8)[ 8].
（8）
The details regarding upper bound of forward slip are illustrated in Fig. 3. In order to determine the forward slip, the following steps are defined:
1. The place of neutral point along the contact arc with no inter stand tension (xmin) is determined by combination of Eqs. (7) and (8).
2. The actual pressure distribution with no inter stand tension (diagonal lines (a) and (b) ) could be approximated by diagonal line (a′) and horizontal line (b′) which are determined by the three data (Ki, Ko, and xmin). Consequently, the slope of line (a′) has the minimum possible value due to the zero gradient of (b′).
3. After applying the inter-stand tensions , the lines (a) (b) and (a′) (b′) drop downward in parallel forming the lines (a″) (b ″) and (a ?) (b?), respectively.
4. Because the slope of line (a′) is less than that of the line (a), the intersection of lines (a?) and (b ?) is closer to the entrance point and is calculated as follows:
5. The upper bound of forward slip fsmin is calculated through Eq. (7), where x=xmax
At the fifth stand which is the last rolling stand , the forward tension is always less than backward tension; therefore, the method discussed above is not applicable in determining forward slip in this stand. After determining the constants of constitutive equation of the strip according to forward slips and rolling forces of the first four stands, Eq. (6), and considering the available strip strain in stand 5, Eq. (5), the forward slip of this stand and the deformation resistance of strip at the exit point are calculated, Fig. 4.
Table 3 Experimental data of IMSC (case 2)
Table 4 Comparison for final solution of constants of constitutive equation with different initial assumption
Fig. 7 Variation of flow stress strain curve with the iteration for case 2
4 .Flow stress-strain curve of strip and friction coefficient computation
In Fig. 5, the flowchart of the developed algorithm in this study is presented with the related details in order to determine the friction coefficient and flow stress strain curve with respect to the actual mill data. It should be mentioned that the list of equations presented in Table 1 are applied in this flowchart. In reference to this newly developed flowchart, after the initial values of forward slip and constitutive equation constants are assumed, the new values are determined for the mentioned parameters. Under these circumstances, the difference ratio of the newly obtained values in sequential loops is less than the special value; convergence criteria is fulfilled.
Fig. 8 Comparison of flow stress-strain between predicted and actual curve: a case 1 and b case 2
5 .Discussion and results
A schematic diagram of a five-stand tandem cold rolling mill at IMSC is shown in Fig. 6. In each stand, the rolling force is measured by a load cell and the inter-stand tensions are measured by tension meters. Two sets of experimental data of IMSC are applied in verifying this developed algorithm. The material of the strip is St12. The rolling data of each case is listed in Tables 2 and 3. In the first case, the thickness of strip is reduced from 3 to 0.8 mm and in the second case is reduced from 2 to 0.57 mm. The yield stress of strip and Young modulus are determined by simple tension test by Zwick/Roell Z400 in quasi-static condition on a specimen of strip before rolling at IMSC. The algorithm runs with several initial assumptions for constants of constitutive equation to check whether convergence of the proposed algorithm takes place. The results of constitutive equations constants are compared with three initial assumptions for each case in Table 4. After checking the results with different assumptions, the behavior of the flow stress-strain curve in terms of iteration number for case 2 is shown in Fig. 7. The curves demonstrate how the constants of constitutive equation converge to the final solution as the iteration goes on. By considering the convergence criteria as being small, the predicted curve will correspond to the actual curve. It should be mentioned that the loops are converged in less than ten iterations. This algorithm is suitable for online calculations. The comparisons between predicted flow stress-strain curve from this algorithm and true stress-strain curve from simple tension test of both the cases are presented in Fig. 8. The calculated yield stress at fifth stand along with the strip yield stress obtained from simple tension test on the final product is tabulated in Table 5. The values obtained from forward slips and friction coefficients of all five stands in both cases are listed in Table 6. The values of friction coefficient in both cases of this study are obtained in the absence of velocity meter. The results are in a good agreement with the ones obtained in [3], where velocity meters were installed.
Table 5 comparison of the calculated and actual values of yield stress
Table 6 The forward slip and friction coefficient of each stand
6. Conclusion
In this article, a new method for prediction of forward slip in the tandem cold rolling mill without the velocity meter sensors based on rolling geometry is described. According to this method, an algorithm is being developed for determining the online friction coefficient and the constants of constitutive equation of the strip for a five-stand tandem cold rolling mill. Through this algorithm, the upper and lower bound of forward slip and friction coefficient are determined for each stand and the mill’s control program works in a more accurate manner. The difference between calculated and measured rolling force is reduced and the possibility of strip tearing is decreased. The obtained results through the numerical samples are in good agreement with the results obtained for the same purpose where the mills are equipped with velocity meter.
References
1. Mashayekhi M , Torabian N, Poursina M (2010) Continuum damage mechanics analysis of strip tearing in a tandem cold rolling process. Simul Model Pract Theory 19:612–625
2. Byon SM, Kim SI, Lee Y (2008) A numerical approach to determine flow stress–strain curve of strip and friction coefficient in actual cold rolling mill. J Mater Process Technol 201:106–111
3. Wang JS, Jiang ZY, Tieu K, Liu XH, Wang GD (2007) A method to improve model calculation accuracy of process control in tandem cold mills. 2nd IEEE Conference on Industrial and Electronics and Applications ICIEA, pp 2787–2790
4.Tieu AK , You C (2005) Material resistance and friction in cold rolling. 6th world congresses of structural and multidisciplinary optimization, Rio de Janeiro, 30 May?3 June 2005, Brazil
5. Poursina M, Torabian N, Fattahi A, Mirmohammadi H (2012) Application of genetic algorithms to optimization of rolling schedules based on damage mechanics. Simul Model Pract Theory 22:61–73
6. Sims RB (1952) The forward slip in cold strip rolling . Sheet Metal Ind 29:869–877
7. Tselikov AI, Nikitin GS, Rokotyan SE (1981) The theory of lengthwise rolling. Mir, Moscow
1.2中文翻譯
一種冷連軋機(jī)前滑預(yù)測(cè)的新方法
M. Poursina & M. Rahmatipour & H. Mirmohamadi
摘要： 本文提出了一種無(wú)速度表傳感器的串聯(lián)冷軋機(jī)前向滑移的新方法。根據(jù)該方法，提出了一種在線估計(jì)摩擦系數(shù)和條紋行為的算法。在軋制過(guò)程中，摩擦系數(shù)的在線發(fā)揮和帶鋼的行為都得到了較好的控制。因此，不飽和致動(dòng)器得到滿足，撕裂的可能性降低。這條帶子的材料是st12。該材料被認(rèn)為具有彈塑性、同質(zhì)性、同質(zhì)性等特點(diǎn)。通過(guò)對(duì)試件試樣的簡(jiǎn)單拉伸試驗(yàn)，確定了帶鋼的屈服應(yīng)力和楊氏模量。對(duì)開(kāi)發(fā)方案進(jìn)行了驗(yàn)證，并對(duì)兩種操作樣本進(jìn)行了考慮，并與現(xiàn)有文獻(xiàn)進(jìn)行了比較。
關(guān)鍵詞：冷軋壓 前滑 摩擦 本構(gòu)方程
術(shù) 語(yǔ)：P 軋制力 t機(jī)架間的張力 D工作輥直徑
C, n本構(gòu)方程的常數(shù) R工作輥半徑 R′變形輥半徑
W帶鋼寬度 Φ中性點(diǎn)角 h帶鋼厚度
K帶變形阻力 μ摩擦系數(shù) fs前滑
σ屈服應(yīng)力 Ε應(yīng)變 R減少
L接觸的長(zhǎng)度 E楊氏模量 υ泊松比
1．介紹
連續(xù)冷軋機(jī)組控制是一個(gè)復(fù)雜的過(guò)程。這一過(guò)程的目的是通過(guò)對(duì)軋制力和前滑的精確控制獲得理想的條帶厚度。測(cè)量和計(jì)算的軋制力和前向滑移之間的差值是飽和的致動(dòng)器。在此情況下，串列冷軋機(jī)控制系統(tǒng)中最輕微的振動(dòng)，可能會(huì)導(dǎo)致帶鋼撕裂[1]。軋制力和前向滑移依賴于不同的參數(shù)，特別是帶鋼的摩擦系數(shù)和力學(xué)性能。這些參數(shù)在滾動(dòng)過(guò)程中變化，而在大多數(shù)控制程序中，它們被認(rèn)為是常量。由于缺乏摩擦系數(shù)和本構(gòu)方程常數(shù)的在線信息，一些研究人員提出了基于逆方法的模型，以確定摩擦系數(shù)和本構(gòu)方程的在線大小。
表1 方程、應(yīng)用的流程圖
Byon等人通過(guò)采用逆方法[2]，在具有全傳感器的可逆冷軋機(jī)中，瞬間確定了本構(gòu)方程的摩擦系數(shù)和常數(shù)。Tieu等人[3,4]對(duì)四臺(tái)架冷軋機(jī)帶鋼的摩擦系數(shù)和本構(gòu)方程進(jìn)行了評(píng)價(jià)，并給出了摩擦系數(shù)的適用模型。
雖然在之前的工作中，軋制力和向前滑動(dòng)都是通過(guò)載荷傳感器和速度計(jì)傳感器直接測(cè)量的。在一些帶鋼制造工廠中，由于現(xiàn)有軋機(jī)的標(biāo)準(zhǔn)形狀不合格，或者由于各種原因，沒(méi)有合適的位置安裝速度計(jì)傳感器，所以速度表不能夠很好地記錄條紋速度。在這種類型的軋制過(guò)程中，由于前向滑移量的不斷增大，使得前滑塊的測(cè)量精度不高，軋制過(guò)程的計(jì)算也不準(zhǔn)確。
圖1 滾動(dòng)幾何和沿接觸弧的輥壓分布[7]
圖2 壓力分布與中性點(diǎn)間張力、tf正向張力、tb反向張力的影響。
這種缺陷導(dǎo)致軋制過(guò)程的計(jì)算中出現(xiàn)了更多的誤差，當(dāng)執(zhí)行器飽和時(shí)，會(huì)發(fā)生條帶撕裂，無(wú)法消除這些誤差。
在本研究中，提出了一種基于滾動(dòng)幾何的新方法，以預(yù)測(cè)一個(gè)不具備足夠的速度計(jì)傳感器或現(xiàn)有傳感器的串聯(lián)冷軋機(jī)組的前向滑移的在線模量。隨后，通過(guò)逆算法，瞬時(shí)確定了帶鋼結(jié)構(gòu)方程的摩擦系數(shù)和常數(shù)的大小。為了驗(yàn)證開(kāi)發(fā)方案的有效性，研究了伊斯法罕Mobarakeh鋼鐵聯(lián)合企業(yè)(IMSC)中5臺(tái)立式冷軋機(jī)的兩個(gè)樣品。研究結(jié)果與相關(guān)文獻(xiàn)的結(jié)果比較吻合。
圖3前向滑動(dòng)和中性點(diǎn)位置的最大值
圖4 帶鋼的流動(dòng)應(yīng)力應(yīng)變曲線
2．?dāng)?shù)學(xué)模型
在此基礎(chǔ)上，完成了滾動(dòng)力、前滑、本構(gòu)方程三個(gè)方程的同步解。
第一個(gè)方程是軋制力模型:建議不同的軋制力模型來(lái)確定以下形式的軋制力:
（1）
在在線計(jì)算中，使用簡(jiǎn)單的方程是提高過(guò)程速度的關(guān)鍵。為了達(dá)到這個(gè)目的，我們選擇了福特動(dòng)力模型，即Eq.(2)。
（2）
其中f1和f2分別為拉伸應(yīng)力和摩擦系數(shù)的校正函數(shù)(表1)。第二個(gè)方程為正向滑移模型:當(dāng)中性點(diǎn)每一側(cè)的接觸弧的壓力分布相等[6]時(shí)得到。該方程表示為摩擦系數(shù)和變形阻力的函數(shù)。
（3）
其中Ki和Ko分別為進(jìn)入和出口輥縫的帶鋼變形抗力。
第三個(gè)方程是材料行為模型:在串聯(lián)冷軋機(jī)中，魯?shù)戮S克的本構(gòu)方程法，即預(yù)測(cè)條帶行為的公式(4)在本研究中應(yīng)用。
（4）
其中ε是計(jì)算有效的應(yīng)變和Eq。(5)在每個(gè)站和σ是流壓力。
（5）
流動(dòng)應(yīng)力應(yīng)變曲線的計(jì)算算法,C和n和摩擦系數(shù)μ,提出了基于同步解決上述三個(gè)方程的設(shè)置
圖5 開(kāi)發(fā)算法流程圖
圖6 五機(jī)架串聯(lián)冷軋機(jī)示意圖(IMSC)
表2 IMSC實(shí)驗(yàn)數(shù)據(jù)(案例1)
下面列出的方程:
(6)
求解上述集合C、n和后確定。
3．前滑的確定
本研究的目的是確定前向滑移的模量，在上述的第二個(gè)方程中，在一個(gè)不具備足夠速度測(cè)量器的5個(gè)機(jī)架工業(yè)軋制過(guò)程中。特利科夫等。確定了帶和輥接觸弧的壓力分布[7]。在軋制過(guò)程中，帶鋼的一部分如圖1所示。參數(shù)x表示沿輥和帶鋼接觸弧的中性點(diǎn)位置。
根據(jù)Eq.(7)[8]得到了滾動(dòng)區(qū)中性點(diǎn)位置與前向滑移之間的關(guān)系。
（7）
在圖1中，觀察到出入口點(diǎn)的滾子壓力與帶鋼的變形阻力相等，在中性點(diǎn)處的輥壓最大。
在軋制過(guò)程中，為了減小軋制壓力，采用了機(jī)架間的張力。
表3 IMSC實(shí)驗(yàn)數(shù)據(jù)(案例2)
表4 不同初始假設(shè)的本構(gòu)方程常數(shù)的最終解比較
由圖2所示，圖2所示的展臺(tái)間張力的影響如圖2所示。采用后向拉力，從入口點(diǎn)到中性點(diǎn)，從入口點(diǎn)到中性點(diǎn)時(shí)，需要的壓力不斷減小，導(dǎo)致直線(a)的直線下降(b)，虛線，在梯度上沒(méi)有變化。如圖所示，由于曲線a的向下運(yùn)動(dòng)，中性點(diǎn)Na已經(jīng)發(fā)生了改變。
如圖2所示，在應(yīng)用正向張力的情況下，同樣的現(xiàn)象發(fā)生，但Na的變化指向入口點(diǎn)。由于連軋冷軋機(jī)中帶鋼的厚度不斷減少，因此，在1 ~ 4點(diǎn)之間的正向張力大于向后張力。在這些情況下，中性點(diǎn)向入口點(diǎn)移動(dòng)，導(dǎo)致前滑值增加;因此，在無(wú)間隙狀態(tài)下的前向滑移顯示了真向前滑移的最小值，可以由式(8)[8]計(jì)算。
（8）
前向滑移的上界細(xì)節(jié)如圖3所示。為了確定前滑，定義了以下步驟:
1.通過(guò)Eqs的組合，確定了在接觸電弧上的中性點(diǎn)的位置，不存在任何相互之間的張力(xmin)。(7)、(8)。
2.實(shí)際的壓力分布不存在交叉張力(對(duì)角線(a)和(b))可以用對(duì)角線(a)和水平線(b)近似，由三種數(shù)據(jù)(Ki, Ko, and xmin)確定。因此，直線(a)的斜率由于(b)的零梯度而具有最小的可能值。
圖7 案例2迭代過(guò)程中流動(dòng)應(yīng)力應(yīng)變曲線的變化。
圖8 預(yù)測(cè)與實(shí)際曲線之間的流動(dòng)應(yīng)力-應(yīng)變比較:案例1和案例2
表5 屈服應(yīng)力計(jì)算值與實(shí)際值的比較
3.所示。應(yīng)用國(guó)際米蘭站的緊張局勢(shì)后,線(a)(b)和(a′)(b′)并行下降下降形成了線(a″)(b″)和(a?)(b?)。
4.所示。由于直線(a′)的斜率小于直線(a)的斜率，直線(a?)和(b?)的交點(diǎn)離入口點(diǎn)更近，計(jì)算如下:
5.前向滑移(fsmax)的上界是通過(guò)Eq.(7)計(jì)算的，其中x=xmax。在此基礎(chǔ)上，正向張力總是小于向后張力;因此，以上討論的方法不適用于在此立場(chǎng)上的前滑。
4．帶鋼的流動(dòng)應(yīng)力應(yīng)變曲線和摩擦系數(shù)計(jì)算。
在圖5中，本研究中所開(kāi)發(fā)的算法流程圖與相關(guān)的詳細(xì)信息，以確定實(shí)際軋機(jī)數(shù)據(jù)的摩擦系數(shù)和流量應(yīng)力應(yīng)變曲線。應(yīng)該提到表1中給出的方程的列表應(yīng)用于這個(gè)流程圖中。在此新開(kāi)發(fā)的流程圖中，假定前向滑移值和本構(gòu)方程常數(shù)的初始值，為上述參數(shù)確定新值。在這種情況下，新獲得的順序循環(huán)值的差比小于特殊值;收斂性判別準(zhǔn)則滿足了。
表6 各支架的前滑和摩擦系數(shù)
5．討論和結(jié)果
如圖6所示，在IMSC中一個(gè)五機(jī)架串聯(lián)冷軋機(jī)的原理圖如圖6所示。在每個(gè)展臺(tái)上，滾動(dòng)的力是由一個(gè)測(cè)壓元件來(lái)測(cè)量的，而國(guó)際間的張力是用張力計(jì)來(lái)測(cè)量的。
應(yīng)用IMSC的兩組實(shí)驗(yàn)數(shù)據(jù)驗(yàn)證了該算法的有效性。這條帶子的材料是St12。每個(gè)案例的滾動(dòng)數(shù)據(jù)列在表2和表3中。在第一種情況下，從3到0.8 mm減少了帶鋼的厚度，在第二種情況下從2減少到0.57 mm。采用Zwick/Roell Z400的簡(jiǎn)單拉伸試驗(yàn)確定了條帶和楊氏模量的屈服應(yīng)力，并對(duì)其進(jìn)行了準(zhǔn)靜態(tài)試驗(yàn)。
該算法對(duì)本構(gòu)方程的常數(shù)進(jìn)行了幾個(gè)初始假設(shè)，以驗(yàn)證所提算
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