開鐵口機(jī)設(shè)計【含8張CAD圖紙、說明書】,含8張CAD圖紙、說明書,開鐵口機(jī),設(shè)計,cad,圖紙,說明書,仿單 第 8 頁 本科生畢業(yè)設(shè)計（論文） Influence of roll geometry and strip width on flatting in flat rolling The size of local roll flattening and its distribution along the direction of the roll axis in flat rolling were calculated by means of 3-dimensional finite element method. For analysis of elastic flattening deformation of the roll stack the well-known classical and analytical solutions are usually employed which were derived from elastic half space theory or two dimensional contact theory. By comparison of results from both the different methods the validity of the classical formulae was examined. Some of the formulae are more appropriate for calculating local flattening along the work roll/strip interface, however, they may result in a great deviation in calculating the flattening along the work roll /back-up roll interface, especially for the back-up roll. Using the Fe model the influence of roll geometry and strip width under a specific rolling force on the flattening was taken in account, which is difficult to be treated with classical models. Control of flatness and profile of the rolled strip is one of the important and necessary technologies in the present rolling process. When the restoration of elastic deformation of the exit strip is generally neglected, a roll gap shape determined by elastic deformation of the roll stack presents the distribution of the exit strip thickness. Therefore, the flatness and profile have a direct connection with the deformation of the roll .It is well know that local elastic flattening along the direction of the roll axis is one of the important components in the deformation. It plays the following roles: - the flattening between strip and work roll directly affects the strip profile and the edge drop; - the flattening between work roll and back-up roll or intermediate roll affects the pressure distribution between the rolls, so that the roll gap shape is also simultaneously influenced. At present methods of predicting roll gap shape have been widely discussed. Perhaps the most fundamental and effective approaches to the solution of the roll stack deformation problem are as follows: - equations relating to roll deflection were derived from simple beam theory with refinements, so that the deformation of rolls was calculated as the sum of three or four separate displacement contributions[1;2],namely, bending, shear, local flattening or Poisson’s ratio expansion; - by means of the theory of elasticity, the roll deformation was derived from 6 stress components of a roll. The external load acting on the roll surface produced not only the above 4 displacement components, but also 2 additional contributions caused by the roll stress in three dimensions [3]. For the two approaches with the roll divided into small segments and applying the influence coefficients .the net displacement of the rolls for a given pressure distribution was determined by summation. However, the local flattening in the approaches stems from a elastic half-space subjected to a point load or form an infinite long cylinder subjected to a distributed normal surface load. In any case, the employed models for flattening are far away from the actual geometric configuration of the roll and an approximate solution is obtained. Sometimes they lead to a serious calculation error. In recent years the 3-d finite element method has been applied to simulate the deformation of rolls [4; 5]. Because of the advantage of the method without assumption of roll geometry, a more satisfactory solution can be found, in which the calculation accuracy of the accuracy of the flattening can be also be greatly improved as compared with the above two approaches. However, the method is characteristic of very fine 3-d mesh in contact zones between rolls as well as work roll and strip, in order that the pressure distributions and the lengths of contact zones can rationally be determined in an iterative step .Because of a great number of mesh data and many iterative calculations, the model for the solution of roll deformation on power computer leads to high computation time and costs. On the other hand, the procedure of the model is too complicated. Therefore the above approaches with the influence function are now still widely employed to determine the deformation of rolls [6…13]. In view of restriction and drawback of the existing analytical models for local flattening along the roll axis, the purpose of the present paper is, by means of FEM for solution of a single roll, to explain the following points: - solution difference of flattening between the classical models and Fe model, and then validity of the classical models and Fe model, and then validity of the classical models to be examined; - influence of strip width and roll geometry on the axial flattening, which is difficult for the classical models to treat. Classical formulae and FE model for calculating the flattening The classical models work on the basic assumptions: - the contact length along the roll circumference between rolls or work roll and strip is much smaller than the roll radii; - two cases have to be considered for the contact length along the roll axial direction :for elastic half-space theory the length is considered to be much shorter than that of the roll barrel; on the contrary ,the two-dimension elastic contact theory assumes that the length is not only equal to the roll length, but also that the roll is infinitely long; - the flattening calculation is independent of the two surface loads acting on both sides of a work roll, for example, the influence of roll force in the rolling zone on the flattening along the work roll/back-up roll interface is neglected. According to the assumptions, when a point load P (r , s) acts at a point (r ,s ) on the barrel, as shown in figure 1,the flattening deformation U(x, z ) was given by : (1) Because equation (1) gives too large a deviation from the solution, all efforts have been made to modify the equation, in order to obtain a desirable flattening in view of the finite long roll and finite contact zone. The generally accepted modified formulae are as follows [2…4]: , (2) , (3) , , (4) where in equation (4) was a modification term of displacement according to the elastic half-space stress. Equations (1) to (4) were derived from the half-space model. On the other hand, the typical flattening formula derived from the two-dimensional contact theory was proposed by A. Foeppl, which is usually used to determine the flattening along the work roll/back-up roll interface. Because of the basic assumptions, the resulting calculation error in the above models are unavoidable. However, the actual boundary conditions and geometric configurations can be presented in the Fe model, so that more accurate results can be obtained. Two single calculation models of FEM are established for the different load case of work roll and back-up roll as shown in figure 2. Because the result differences between the classical models and Fe models as well as the influence of strip width and geometric configuration on the flattening are of interest, it is acceptable that distributions of roll force and pressure along the direction of both roll axis and roll circumference are assumed to be uniform. For the sake of simplicity and easy comparison, the contact length along work roll/back-up roll interference is assumed to be equal to that in the rolling zone in circumferential direction. The basic idea of calculating flattening by means of FEM is that in the flattening deformation bases on a model, where the external normal surface load acts on a roll which is subjected to a volume force in the contrary direction [3]. In order to verify the validity of the FE model with respect to accuracy of results, a simply supported cylinder subjected to a symmetric normal surface loading is taken as an example. The analytical solution was derived from Fourier series and Bessel function [16]. Its calculation procedure is too complicated for practical use. Figure 3 shows the variation with Z/L and B/L of the surface displacement of the cylinder. Comparing both results, it is found that the Fe model can provide much more accurate displacement in good agreement with the analytical solution. 應(yīng)用軋輥幾何學(xué)以及長條寬度在平滾軋制中的影響使之矯平 軋輥的局部平整，因其分布沿著平滾動軋輥坐標(biāo)軸方向可以經(jīng)由第三空間的有限機(jī)械要素方法來計算。因為將軋輥柔性變形的修整分析累積成眾所周知的經(jīng)典分析結(jié)論，這種結(jié)論已經(jīng)通常被應(yīng)用了，它起源于柔性的半空間理論或二個空間的接觸理論。憑借兩個的不同方法的結(jié)果經(jīng)典公式的比較檢查其有效性，一些公式對計算局部趨前平整的工作輥/ 長條接口是更適當(dāng)?shù)?然而他們可能在計算那個趨前平整工作輥 /支承輥接口方面造成一個很大的偏差,尤其是支承輥。在一個特定的軋制力作用下的軋輥幾何學(xué)和長條寬度的影響中使用 Fe 模型使之變平,這樣一種方法來考慮應(yīng)用經(jīng)典模型將是很困難的。 對于平坦度的控制和被卷的長條輪廓在目前的軋制程序中是重要的和必需的技術(shù)之一。當(dāng)出口長條的柔性變形恢復(fù)被通常疏忽的時候,被軋輥疊層的柔性變形決定的軋輥間隙形呈現(xiàn)出口長條厚度分布。因此, 軋件的平直度和輪廓對軋輥的變形有直接的聯(lián)系。即可得出沿軋輥坐標(biāo)軸方向的柔性趨前的局部平整是使其變形的重要組成部分之一。它可以應(yīng)用于下列的敘述來表示： -在長條和工作輥之間的平整程度直接影響著長條輪廓和邊緣落差； -那個在工作輥和支承輥或中間輥之間的平整程度影響著在軋輥之間壓力的分布,所以軋輥間隙形也被同時影響著。 目前能夠預(yù)知軋輥間隙形的方法已經(jīng)被廣泛地討論著。 也許最基礎(chǔ)的以及有顯著效果的對軋輥疊層變形問題的解決方法為下列的各項: -等價關(guān)聯(lián)于軋輥的偏斜起源于經(jīng)典的簡單繞曲梁理論,所以軋輥的變形同樣地是有計劃的三個或四個獨立的變位方程[1;2],即,彎曲，剪，局部平整或Poisson比率扭轉(zhuǎn)； -通過柔性理論可知，軋輥的變形來源于軋輥的 6個應(yīng)力組成部分對軋輥表面引起反應(yīng)的外部負(fù)載產(chǎn)生了不僅僅超過 4個變位尺寸組成, 而且額外的 2個組成部分是由于三個尺寸的軋輥應(yīng)力[3]所引起的。 相互接近的兩個軋輥歸類為小片段部分結(jié)構(gòu)，并且其軋輥的影響力系數(shù)相互接近。軋輥的凈變位被一個給定的壓力分布的總和所決定了。然而, 局部的趨向平整度是由柔性半空間中對點的負(fù)載程度引起的，或是由于一個無限長軋輥中分布著一些表面負(fù)載點而引起的。無論如何，這些使之平整的應(yīng)用模型與軋輥的理論幾何學(xué)的結(jié)構(gòu)是存在著一些距離的，當(dāng)然通過近似來得到解決的方法是可以的。不可避免，這有時會導(dǎo)致一個嚴(yán)重的計算誤差。近幾年來，機(jī)械要素方法已經(jīng)應(yīng)用于模擬軋輥了[4；5]。 因為沒有軋輥幾何學(xué)的假定方法的優(yōu)勢，一個較滿意的解決方法就不可能會被發(fā)現(xiàn),而在平直度精確理論計算也有了非常大的提高，以使實際與理論計算二者有了比較似的接近?？墒牵谲堓伜凸ぷ鬏佉约伴L條之間的接觸區(qū)形成網(wǎng)狀的第三空間的方法，是以壓力分布和接觸區(qū)的長度能更好地在反復(fù)的階段所決定著。因為在大量的網(wǎng)狀數(shù)據(jù)和許多反復(fù)的計算中，模型在以電力驅(qū)動的軋輥變形的解決辦法會導(dǎo)致非常高的成本和計算時間。另一方面，模型的程序卻又太復(fù)雜了。因此，在其功能的影響下前者現(xiàn)在仍然被廣泛地應(yīng)用于決定軋輥 [6 … 13] 的變形的方法。 由于視力的限制因素，以及分析模型中存在的一些缺陷，對與沿著軋輥軸向的局部修整方式來說，目前需要解決的目的即為：通過FEM 的單一軋輥的解決方法來說明以下各項: -在經(jīng)典模型和 Fe 模型之間中對于平整解決方式的差別, 另外還有經(jīng)典模型和 Fe 模型的有效性的鑒別, 以及經(jīng)典模型有效性的檢查過程； -在平整坐標(biāo)軸上長條寬度和軋輥幾何學(xué)的影響力, 也是很難應(yīng)用經(jīng)典模型來處理的。 經(jīng)典公式和 FE 模型對于平整度的計算 在基本假定的基礎(chǔ)上進(jìn)行應(yīng)用古典模型的計算: -沿著軋輥或工作輥和長條之間的軋輥圓周的接觸長度比軋輥半徑小的多； -在沿著軋輥坐標(biāo)軸方向的接觸長度中需要考慮的二種情況 : 其中考慮其柔性半空間理論長度對比于軋輥的更短些； 相反, 它的第二尺寸中的柔性接觸理論假定了其長度不僅與軋輥的長度相等，而且軋輥的長度可看作為無限長； -平直度的計算是獨立于工作輥輥身的兩表面的任意負(fù)載，舉例來說，軋制力在軋輥區(qū)域平整時沿著工作輥和支承輥的影響程度往往被忽略。 依照假定,當(dāng)一受力點P (r , s)作用于輥身上任意點(r ,s )時，如圖 1 所示，對于U(x, z )的平直變形將會發(fā)生作用，如： ⑴ 從結(jié)果來看，因為方程⑴帶來了非常大的偏差，所有的效果都是在修正方程，這樣，為了要得到一個有價值的平直度參數(shù)，而且它是在有限長輥的角度以及有限接觸區(qū)域中的。 一般的，通常需要承認(rèn)修正公式如下[2~4]： , (2) , (3) , (4) 方程(4)所處的位置恰恰是依照柔性半空間應(yīng)力變化的修正期。而方程(1)到(4)來源于半空間模型。另一方面，來源于第二空間的接觸理論的典型平直度公式已經(jīng)被 A. Foeppl 設(shè)計完成了，它通常是用來決定沿著工作輥/支承輥接口的平直度。因其基本的假定，上述的模型產(chǎn)生的計算誤差是不可避免的。然而，它的邊緣條件與幾何機(jī)構(gòu)條件都可能在 Fe 模型中被呈現(xiàn),以便更多更較正確的結(jié)果被得到。二個單獨計算的模型FEM也已經(jīng)在工作輥和支承輥的不同負(fù)載因子中建立，如圖2所示。因為在對于在經(jīng)典模型和 Fe 模型以及長條寬度的影響條件下，當(dāng)然還有幾何結(jié)構(gòu)的影響之間的結(jié)果差別在于投入的不同,那么對于沿著軋輥坐標(biāo)軸方向以及軋輥圓周范圍的區(qū)域的軋制力由到分布的都被假定為一種形式，這樣假定的條件是可以被接受的。因為簡便和容易進(jìn)行比較的緣故，則沿著工作輥/支承輥相干涉的接觸區(qū)域長度都被假定為與軋輥圓周方向區(qū)域相等。在通過FEM計算平直度時的基本思想是：軋輥平直的變形程度是以一種模型為基礎(chǔ)的，而這種模型是由常規(guī)的外表面載荷作用在軋輥于相反方向[3]的最大容載力。 在為了檢驗FE 模型對于計算結(jié)果精確性上是否有效，我們可以簡單的拿一種類似性的常規(guī)下對稱外表面載荷的圓柱面為例。分析的結(jié)果是由Fourier系列以及Bessel作用[16]得出的。不過，它的計算程序?qū)嶋H的使用而言是非常復(fù)雜的。圖 3 圖解了圓柱面的表面變位中 Z/ L 和 B/ L 變動。比較兩種結(jié)果,可以發(fā)現(xiàn)在分析處理方面， Fe模型能夠提供更好的精確變位。