EFFECTIVE NUMERICAL ANALYSIS METHOD APPLIED TO THE ROLL-TO-ROLL SYSTEM HAVING A WINDING WORKPIECE Sungham Hong 1, Juhwan Choi 1, Sungsoo Rhim 2 and Jin Hwan Choi 2 1 FunctionBay, Inc., Seongnam-si, Korea 2 Department of Mechanical Engneering, Kyunghee University, Korea E-mail: jhchoi@khu.ac.kr ICETI-2014, Y1032_SCI No. 15-CSME-38, E.I.C. Accession 3813 ABSTRACT The design and development of Roll-to-Roll (R2R) system has been mainly executed by the expert s experience. There are some important issues in the numerical analysis method about a roller path and the control of the R2R system. This study proposes the efficient R2R system analysis methods. The first one is an Approximated Winding Length Estimation (AWLE) algorithm which can calculate the analytic winded length of a workpiece. The winder can be approximated with line and arc segments at this algorithm. As a result, in the numerical model of the R2R system, we can replace the winder characteristics with the AWLE algorithm. The second one is the contact algorithm between workpiece and rollers. This contact algorithm must be stable and fast for precise analysis. The third one is the flexible workpiece model. The workpiece can be modeled by finite elements. By describing the implementation of these important methods, this paper proposes an efficient R2R system analysis method. Keywords: roll-to-roll (R2R); approximated winding length estimation (AWLE); 2D contact; flexible workpiece; efficient analysis. MÉTHODE D ANALYSE NUMÉRIQUE EFFICACE APPLIQUÉE AU SYSTÈME ROULEAU À ROULEAU (R2R) AYANT UNE PIÈCE DE TRAVAIL ENROULÉE RÉSUMÉ La conception et le développement d un système rouleau à rouleau (R2R) ont principalement été conçus par l expérience qu en avaient les experts. Il y a d importants facteurs dans la méthode d analyse numérique au sujet du trajet du rouleau et de la commande d un système R2R. Cette étude propose des méthodes d analyse efficace d un système R2R. La première consiste en un algorithme d estimation approximative de la longueur de l enroulement (AWLE) lequel peut calculer la longueur enroulée d une pièce de travail. L enrouleur peut être approché avec des segments de lignes et arcs avec cet algorithme. Comme résultat dans le modèle numérique d un système R2R, nous pouvons remplacer les caractéristiques de l enrouleur avec l algorithme AWLE. La deuxième méthode est l algorithme de contact entre la pièce de travail et les rouleaux. Cet algorithme de contact doit être stable et rapide pour une analyse précise. La troisième est le modèle de la pièce de travail flexible. Cette pièce peut être modélisée au moyen de la méthode des éléments finis. En décrivant l application de ces méthodes importantes, cet article propose une méthode d analyse efficace d un système R2R. Mots-clés : rouleau-à-rouleau (R2R); estimation approximative de la longueur d une pièce (AWLE); contact 2D; pièce de travail flexible; analyse efficace. Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015 615
1. INTRODUCTION Recently, the R2R system has been used widely because of effective mass production. But, in general, the design and development of R2R system is very difficult because the operating speed is high in the R2R system. The precise working process is needed for the R2R system, and uncertainties such as tension, alignment and skew phenomena should be carefully controlled. The modeling and control of web handling systems have been studied for a long time. Mainly, these studies have been proceeded in order to improve control unit [5] or in order to estimate the real plant parameter using experimental methods [6]. Currently, the numerical method has some critical issues that need attention. First, the calculation time takes too long because of some factors such as a large nonlinear property and a contact force between the long workpiece and many rollers. For this reason, until now, the roller path design and the control of the R2R system are mainly performed by the expert s experience based on the experimental design method. Generally, when designing and developing the R2R system, the first target is the tension control. If the tension is not carefully controlled, there can be large fluctuations. This unexpected situation can easily occur in a winding process such as battery manufacturing. In order to reduce these kinds of fluctuations and noises, an optimized path design and a control unit are necessary. In particular, the winding process itself is very complicated and there can be many noises in the process of numerical contact calculations. As a result, if the real winder model having large nonlinear properties is included in the numerical analysis, the precise estimation for the tension control cannot be achieved. In order to overcome this situation, this paper proposes an effective 2D R2R system analysis method using the AWLE algorithm. The AWLE algorithm can calculate the analytic winded length of the workpiece. We can replace the real winder characteristics with the AWLE algorithm in the numerical model of the R2R system. This method can support some profit for an effective analysis of the R2R system. Because the winder can be removed from the R2R analysis model, the calculation time can be considerably reduced. Also, it is possible to effectively estimate the tension variation and to efficiently develop the control unit for R2R system. The contact algorithm must be stable and fast for precise analysis of the contact force between workpiece and rollers in the R2R system. In general, the contact calculation time is increased according to the complexity of the R2R system. The 2D contact algorithm does not take into account the contact effects in the depth direction of the web. In this study, the pre-search and the detailed search algorithms are applied to effectively search the contact point. Also, efficient collision detection algorithms are considered for the stability of the 2D contact algorithm. 2. CONFIGURATION OF R2R SYSTEM Figure 1 shows a simple schematic R2R system which includes a winder, rollers and workpiece. The material of the workpiece is determined according to the characteristics of the final product. A roller is a rotating mechanical device of cylinder shape. The roller is used to design a path of workpiece and is used to control the tension of workpiece. A winder is a device to wind the workpiece, as the winder is rotated, workpiece is sucked and attached on the outside surface of winder. The winder is rotated at high speed in order to make more products. The final target is a constant tension of workpiece in order to always make the same quality products in the R2R system. Also, the path design and tension control need to be optimized in order to make products more effectively. The most important indicator is a tension of workpiece just before entering into the winder. In this study, this indicator has been observed to verify the variation of the system. 616 Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
Fig. 1. Simple schematic R2R system including a winder. 3. APPROXIMATED WINDING LENGTH ESTIMATION (AWLE) ALGORITHM When a workpiece is winded into the winder, the following assumptions are valid: 1. The thickness of workpiece is not changed. 2. The workpiece is ideally attached on the winder or the winding surface object. The winder can be geometrically approximated with line and arc segments. We can replace the winder characteristics with the AWLE algorithm in the numerical model of the R2R system. The estimation procedure of approximated winding length algorithm is as follows: 1. Input the geometry information of the system. a) The geometry information of winder. i. The control position of line and arc curve (p 0, p 1, p 2, p 3,... ). ii. The angle and radius of the arc curve (r 1, θ 1,r 2, θ 2 ). b) The thickness of workpiece (h t ). c) The reference point (p r ) of the winder. d) The current rotational angle of winder. 2. Calculate the tangent point (p t ) or the connection point of winder. 3. Calculate the distance from the tangent point to the reference point of core wining. 4. Calculate the distance variation from the total winding length. 5. Apply this variation to the motion at the end node of workpiece. In the line segment of winder, the winding length is easily calculated from the connection and tangent point of line. In this case, the winding length is discontinuously increased whenever the new contact point Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015 617
Fig. 2. The geometry information of winder at initial time. Fig. 3. Winding distance calculation: (a) The winding workpiece; (b) The tangential distance. of workpiece passing by the control point of winder. But, in the arc segment of winder, the winding length is calculated from the tangent point of arc curve and is continuously increased whenever the winder is rotating. Finally, the winding length is calculated from the final tangent point, the number of winding and thickness of the workpiece. In Fig. 3, the tangent point of the arc segment can be calculated as follows. The center position (p c ) of circle is changed whenever the winder is rotated. Equation (1) of circle is defined with respect to the reference point (p r ) of winder as follows: (x x 0 ) 2 + (y y 0 ) 2 = r 2 (1) 618 Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
In Fig. 3(b), we can see two lines. The first line is connected from the reference point (p r ) to the tangent point (p t ). The second line is connected from the center point of circle (p c ) to the tangent point (p t ). This two line segment must always be orthogonal (p t p r p t p c ). We can obtain the equation from this property as follows: The tangent point (p t ) must exist on the circle This equation can be summarized as d 2 + r 2 = p 2 a 2 + b 2 + r 2 = x 2 0 + y 2 0 a 2 + b 2 = x 2 0 + y 2 0 r 2 (2) (a x 0 ) 2 + (b y 0 ) 2 = r 2 (3) a 2 + b 2 = r 2 + 2ax 0 x 2 0 + 2by 0 y 2 0 (4) The left equation (a 2 +b 2 ) can be replaced with Eq. (2). Therefore, the tangent point is calculated as follows: a = y 0 b + x2 0 + y2 0 r2 = eb + f x 0 x 0 where b = e f ± e 2 f 2 (1 + e 2 )( f 2 p 2 + r 2 ) (1 + e 2 ) e = y 0 x 0, f = x2 0 + y2 0 r2 x 0 (5) 4. EFFECTIVE 2D R2R CONTACT ALGORITHM This contact algorithm must be stable and fast for precise analysis between workpiece and rollers in the R2R system. In general, the workpiece of the R2R system consists of many elements that are contacted with many rollers. So, the contact calculation time is increased according to the complexity of the R2R system. To effectively understand the R2R system, the effective 2D contact algorithm is needed to calculate the contact force between workpiece and rollers. The pre-search and the detailed search algorithms are applied to effectively search the contact point. In general, the length of workpiece is relatively much longer than the radius of the roller. So, the workpiece is separated by some units which is then called as a bounding box. The bounding box is used to roughly find the possibility of contact between rollers and workpiece. To calculate the continuous and stable contact force, a contact force is recommended to be generated at one segment of the workpiece. The 2D contact algorithm consists of three contact methods such as nodeto-line, node-to-arc and line-to-arc. The contact force is generated with respect to the x y plane coordinate because the depth direction is ignored. The basic contact is node-to-arc and node-to-line, if nodes are not contacted, the contact point is searched again by the line-to-arc contact algorithm (Fig. 4). 5. NUMERICAL EXAMPLE The models are used to verify the performance of the effective 2D R2R system analysis method using the AWLE algorithm (Fig. 5). The first model is a 3D R2R system having the real winder model. The second model is a 3D R2R system which is applied with a AWLE algorithm without the real winder model. The third model is a 2D R2R system which is also applied with the AWLE algorithm. Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015 619
Fig. 4. Contact algorithm: (a) pre-search; (b) detailed search. Fig. 5. Numerical test models: (a) 3D real winder model; (b) 3D AWLE model; (c) 2D AWLE model. 5.1. Apply Approximated Winding Length Estimation (AWLE) Algorithm The geometry information of the real winder model is as given in Fig. 6. Figure 7 shows the moving distance of displacement motion with respect to time. This data can be obtained from the estimation procedure of approximated winding length. The number of revolution of winder is 7 that can be known from the pattern of data. Even though the winder is constantly rotated, the moving distance is not increased with the same slope. The applied properties of workpiece in the test models are given in Table 1. The 3D winder model can be analyzed using the AWLE numerical method. Figure 8 shows the tension of workpiece which is calculated at the position of the T1 tension sensor (Fig. 5). The rotational velocity is constant. But the moving distance of workpiece is not constantly changed 620 Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
Properties Value The number of control points 5 The number of arc center points 2 The initial rotation angle of the core (deg.) 30 The rotating velocity of winder (RPM) 30 Fig. 6. The geometry information of real winder model. Fig. 7. The moving distance of displacement motion with regard to time. according to the shape of the winder. For this reason, it is difficult to keep the tension of workpiece constant. We can verify from the simulation result (Fig. 8). Also, the simulation time can be reduced as much as the calculation time which is needed to analyze the winder model having large nonlinear property between the workpiece and the winder. Until now, it is difficult to get a reasonable result with the real winder model using a numerical method. But, because the real winder model can be replaced with the AWLE algorithm, this method is effective in the numerical analysis of the R2R system. Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015 621
Table 1. The material properties of workpiece. Properties Value Thickness (mm) 1.8.e-001 The number of elements 2500 Element length (mm) 0.9183 Density (kg/mm3) 8.9e-6 Table 2. The performance comparison. 3D R2R (Real Winder Model) 3D R2R (AWLE) 2D R2R (AWLE) FE element type Beam Beam Beam The number of element 2500 2500 2500 Simulation time (sec) 7.0 7.0 7.0 Calculation Time (sec) 1364.50 823.46 Fig. 8. Tension of the 3D R2R model with the AWLE algorithm. 5.2. Apply 2D R2R Contact Algorithm The tension of workpiece, which is applied with the AWLE and 2D R2R contact algorithm at the same time, is shown in Fig. 9. The tension pattern of analysis result, which is applied by 2D contact algorithm, is similar when compared with that of the 3D contact algorithm (Figs. 8 and 9). In the case of 3D R2R analysis, we can see the noise of tension until 3 seconds. On the other hand, in the case of 2D contact, this noise is not seen from the result of 2D contact. These effects, which are obtained with the efficient contact algorithm and the reduced noise of tension, will reduce the calculation time of the R2R model. The improvement of the calculation time can be verified from Table 2. The numerical method, which is using the 2D contact algorithm, is more effective for the analysis of the R2R systems. 5.3. Apply Simple Passive Control We can monitor the characteristics of the system using this effective numerical method. The effect of control parameter can be easily known using this method. The spring-damper force element is applied to 2D R2R model in Fig. 5(c). 622 Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
Fig. 9. Tension of the 2D R2R model with the AWLE algorithm. Fig. 10. The 2D R2R model applied with the spring-damper (K = 10 N/mm, C = 1.e-3 N-sec/mm) and the AWLE algorithm. When the tension, in the case of the model having a spring damper, is compared to that of a model having no spring damper, as the result of Fig. 11, the convergence speed of model having a spring damper is improved than the other. If the more advanced active controller is used, the high-performance R2R system will be able to be designed. 6. CONCLUSIONS Until now, the numerical method has some critical points. Most of all, the calculation time takes too long because some issues such as the large nonlinear property and the contact force between the many work- Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015 623
Fig. 11. The tension of workpiece detected in the 2D R2R model (shadowed line: no spring damper; black line: spring damper). piece elements and rollers. So, this study suggests the effective roll-to-roll system analysis method using approximated winding length estimation algorithm which can calculate the analytic winded length of the workpiece. As a result, in the numerical model of the R2R system, we can effectively replace the nonlinear winder characteristics with the AWLE algorithm. The stability and performance of 2D R2R contact algorithm are verified with simulation between the many elements of workpiece and rollers. Also, the effect of simple passive controller is verified using the effective 2D R2R analysis method by implementing and testing these important issues. This paper proposed an efficient R2R system analysis method. ACKNOWLEDGEMENT This research is supported by 2015 KyungHee University Research Program. REFERENCES 1. RecurDyn User Manual, http://eng.functionbay.co.kr. 2. Johnson, K.L., Contact Mechanics, Cambridge University Press, 1985. 3. Choi, J., Ryu, H.S., Kim, C.W. and Choi, J.H., An efficient and robust contact algorithm for a compliant contact force model between bodies of complex geometry, Multibody System Dynamics, Vol. 23, No. 1, pp. 99 120, 2010. 4. Choi, J., A Study on the Analysis of Rigid and Flexible Body Dynamics with Contact, PhD Dissertation, Seoul National University, Seoul, 2009. 5. Koc, H., Knittel, D., de Mathelin, M. and Abba, G., Modelling and robust control of winding systems for elastic webs, IEEE Transactions on Control Systems Technology, Vol. 10, No. 2, pp. 197 208, 2002. 6. Giannoccaro, N.I., Messina, A. an Sakamoto, T., Updating of a lumped model for an experimental web tension control system using a multivariable optimization method, Applied Mathematical Modelling, Vol. 34, No. 3, pp. 671 683, 2010. 624 Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015