小型二輥式冷軋機結構設計-兩輥冷軋機【含7張CAD圖帶開題報告-獨家】.zip
小型二輥式冷軋機結構設計-兩輥冷軋機【含7張CAD圖帶開題報告-獨家】.zip,含7張CAD圖帶開題報告-獨家,小型,二輥式,冷軋機,結構設計,CAD,開題,報告,獨家
目 錄
1 英文文獻翻譯 1
1.1 英文文獻原文題目 1
1.2中文翻譯 15
2 專業(yè)閱讀書目 26
2.1 機械設計手冊 26
2.2 機械設計 26
2.3 現代工程制圖 27
2.4 材料力學 27
2.5 互換性與測量技術 28
2.6 機械制造基礎 28
2.7 機械原理 29
2.8 機電傳動控制 29
2.9 機械制造技術 30
2.10 機械制造技術 30
1 英文文獻翻譯
1.1 英文文獻原文題目
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
一種冷連軋機前滑預測的新方法
M. Poursina & M. Rahmatipour & H. Mirmohamadi
摘要： 本文提出了一種無速度表傳感器的串聯(lián)冷軋機前向滑移的新方法。根據該方法，提出了一種在線估計摩擦系數和條紋行為的算法。在軋制過程中，摩擦系數的在線發(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。該材料被認為具有彈塑性、同質性、同質性等特點。通過對試件試樣的簡單拉伸試驗，確定了帶鋼的屈服應力和楊氏模量。對開發(fā)方案進行了驗證，并對兩種操作樣本進行了考慮，并與現有文獻進行了比較。
關鍵詞：冷軋壓 前滑 摩擦 本構方程
術 語：P 軋制力 t機架間的張力 D工作輥直徑
C, n本構方程的常數 R工作輥半徑 R′變形輥半徑
W帶鋼寬度 Φ中性點角 h帶鋼厚度
K帶變形阻力 μ摩擦系數 fs前滑
σ屈服應力 Ε應變 R減少
L接觸的長度 E楊氏模量 υ泊松比
1．介紹
連續(xù)冷軋機組控制是一個復雜的過程。這一過程的目的是通過對軋制力和前滑的精確控制獲得理想的條帶厚度。測量和計算的軋制力和前向滑移之間的差值是飽和的致動器。在此情況下，串列冷軋機控制系統(tǒng)中最輕微的振動，可能會導致帶鋼撕裂[1]。軋制力和前向滑移依賴于不同的參數，特別是帶鋼的摩擦系數和力學性能。這些參數在滾動過程中變化，而在大多數控制程序中，它們被認為是常量。由于缺乏摩擦系數和本構方程常數的在線信息，一些研究人員提出了基于逆方法的模型，以確定摩擦系數和本構方程的在線大小。
表1 方程、應用的流程圖
Byon等人通過采用逆方法[2]，在具有全傳感器的可逆冷軋機中，瞬間確定了本構方程的摩擦系數和常數。Tieu等人[3,4]對四臺架冷軋機帶鋼的摩擦系數和本構方程進行了評價，并給出了摩擦系數的適用模型。
雖然在之前的工作中，軋制力和向前滑動都是通過載荷傳感器和速度計傳感器直接測量的。在一些帶鋼制造工廠中，由于現有軋機的標準形狀不合格，或者由于各種原因，沒有合適的位置安裝速度計傳感器，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程中，由于前向滑移量的不斷增大，使得前滑塊的測量精度不高，軋制過程的計算也不準確。
圖1 滾動幾何和沿接觸弧的輥壓分布[7]
圖2 壓力分布與中性點間張力、tf正向張力、tb反向張力的影響。
這種缺陷導致軋制過程的計算中出現了更多的誤差，當執(zhí)行器飽和時，會發(fā)生條帶撕裂，無法消除這些誤差。
在本研究中，提出了一種基于滾動幾何的新方法，以預測一個不具備足夠的速度計傳感器或現有傳感器的串聯(lián)冷軋機組的前向滑移的在線模量。隨后，通過逆算法，瞬時確定了帶鋼結構方程的摩擦系數和常數的大小。為了驗證開發(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臺立式冷軋機的兩個樣品。研究結果與相關文獻的結果比較吻合。
圖3前向滑動和中性點位置的最大值
圖4 帶鋼的流動應力應變曲線
2．數學模型
在此基礎上，完成了滾動力、前滑、本構方程三個方程的同步解。
第一個方程是軋制力模型:建議不同的軋制力模型來確定以下形式的軋制力:
（1）
在在線計算中，使用簡單的方程是提高過程速度的關鍵。為了達到這個目的，我們選擇了福特動力模型，即Eq.(2)。
（2）
其中f1和f2分別為拉伸應力和摩擦系數的校正函數(表1)。第二個方程為正向滑移模型:當中性點每一側的接觸弧的壓力分布相等[6]時得到。該方程表示為摩擦系數和變形阻力的函數。
（3）
其中Ki和Ko分別為進入和出口輥縫的帶鋼變形抗力。
第三個方程是材料行為模型:在串聯(lián)冷軋機中，魯德維克的本構方程法，即預測條帶行為的公式(4)在本研究中應用。
（4）
其中ε是計算有效的應變和Eq。(5)在每個站和σ是流壓力。
（5）
流動應力應變曲線的計算算法,C和n和摩擦系數μ,提出了基于同步解決上述三個方程的設置
圖5 開發(fā)算法流程圖
圖6 五機架串聯(lián)冷軋機示意圖(IMSC)
表2 IMSC實驗數據(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，在上述的第二個方程中，在一個不具備足夠速度測量器的5個機架工業(yè)軋制過程中。特利科夫等。確定了帶和輥接觸弧的壓力分布[7]。在軋制過程中，帶鋼的一部分如圖1所示。參數x表示沿輥和帶鋼接觸弧的中性點位置。
根據Eq.(7)[8]得到了滾動區(qū)中性點位置與前向滑移之間的關系。
（7）
在圖1中，觀察到出入口點的滾子壓力與帶鋼的變形阻力相等，在中性點處的輥壓最大。
在軋制過程中，為了減小軋制壓力，采用了機架間的張力。
表3 IMSC實驗數據(案例2)
表4 不同初始假設的本構方程常數的最終解比較
由圖2所示，圖2所示的展臺間張力的影響如圖2所示。采用后向拉力，從入口點到中性點，從入口點到中性點時，需要的壓力不斷減小，導致直線(a)的直線下降(b)，虛線，在梯度上沒有變化。如圖所示，由于曲線a的向下運動，中性點Na已經發(fā)生了改變。
如圖2所示，在應用正向張力的情況下，同樣的現象發(fā)生，但Na的變化指向入口點。由于連軋冷軋機中帶鋼的厚度不斷減少，因此，在1 ~ 4點之間的正向張力大于向后張力。在這些情況下，中性點向入口點移動，導致前滑值增加;因此，在無間隙狀態(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]計算。
（8）
前向滑移的上界細節(jié)如圖3所示。為了確定前滑，定義了以下步驟:
1.通過Eqs的組合，確定了在接觸電弧上的中性點的位置，不存在任何相互之間的張力(xmin)。(7)、(8)。
2.實際的壓力分布不存在交叉張力(對角線(a)和(b))可以用對角線(a)和水平線(b)近似，由三種數據(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迭代過程中流動應力應變曲線的變化。
圖8 預測與實際曲線之間的流動應力-應變比較:案例1和案例2
表5 屈服應力計算值與實際值的比較
3.所示。應用國際米蘭站的緊張局勢后,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?)的交點離入口點更近，計算如下:
5.前向滑移(fsmax)的上界是通過Eq.(7)計算的，其中x=xmax。在此基礎上，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上的前滑。
4．帶鋼的流動應力應變曲線和摩擦系數計算。
在圖5中，本研究中所開發(fā)的算法流程圖與相關的詳細信息，以確定實際軋機數據的摩擦系數和流量應力應變曲線。應該提到表1中給出的方程的列表應用于這個流程圖中。在此新開發(fā)的流程圖中，假定前向滑移值和本構方程常數的初始值，為上述參數確定新值。在這種情況下，新獲得的順序循環(huán)值的差比小于特殊值;收斂性判別準則滿足了。
表6 各支架的前滑和摩擦系數
5．討論和結果
如圖6所示，在IMSC中一個五機架串聯(lián)冷軋機的原理圖如圖6所示。在每個展臺上，滾動的力是由一個測壓元件來測量的，而國際間的張力是用張力計來測量的。
應用IMSC的兩組實驗數據驗證了該算法的有效性。這條帶子的材料是St12。每個案例的滾動數據列在表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的簡單拉伸試驗確定了條帶和楊氏模量的屈服應力，并對其進行了準靜態(tài)試驗。
該算法對本構方程的常數進行了幾個初始假設，以驗證所提算
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