Statistical analysis for the manufacturing of multi-strip patterns by roll-to-roll single slot-die systems

Roll-to-roll (R2R) slot-die coating systems are mostly devoted to the mass manufacture of printed electronics. This study examined the correlation among the operating conditions, thickness, and width of the patterned strip fabricated by the R2R slot-die system. A full factorial experiment was conducted to screen for effective parameters. The velocity of a moving substrate was found to be the most dominant parameter affecting the thickness and width of the patterned strips. The flow ratio of the supply to the slot-die, and gap between substrate and slot-die did not affect the width of the strip, but affected the thickness; therefore, the flow ratio and gap can be employed for the independent patterning of thickness against width. In addition, it was proposed to determine the R2R process conditions, such as gap, velocity, and flow ratio for the desired thickness and width of the patterned strips.     

A study on tension behavior considering thermal effects in roll-to-roll E-printing

The mathematical model for tension in a moving web by Shin [1] was extended by considering thermal strain due to temperature fluctuations in the drying of a roll-to-roll system. The extended model describes variations in tension and includes terms that represent the change of the Young’s Modulus, the thermal coefficient, and the thermal strain. In this paper, a new control scheme based on the extended model is proposed for mitigation of tension disturbances due to thermal strain in the drying process. Tension feedback control logic generally is not be applied due to the fact that register errors can be induced by speed alterations that help to compensate for tension disturbances. But in our approach, the thermal strain in the web is compensated for by means of velocity adjustments without adding extra register errors in the steady state. A computer simulation followed by an experimental validation was carried out to confirm the performance of the proposed method. The results show that the proposed model is useful for describing tension behavior and suggest that tension control logic improves control precision for the drying module of a roll-to-roll e-printing system.     

Reliability measure approach for confidence-based design optimization under insufficient input data

Structural and Multidisciplinary Optimization - In most of the reliability-based design optimization (RBDO) researches, accurate input statistical model has been assumed to concentrate on the...     

Effect of taper tension profile on the telescoping in a winding process of high speed roll to roll printing systems

Winding is an integral operation in almost every roll to roll system. A center-wound roll is one of the suitable and general schemes in a winding mechanism. In general, the quality of wound roll is known to be related to the lateral displacement error and starring defect of a wound roll. Especially, a telescoping within a center-wound roll can cause damages such as misalignment between layers, folding, wrinkle, etc. Taper tension is known to be one of the major factors which affect the shape of a wound roll. It is therefore necessary to analyze the relationship between taper tension profile and telescoping within the center-wound roll to prevent winding failure and to sustain high quality of the printed materials. It is hard to compensate for undesirable winding roll shapes such as telescoping, because a winding is commonly a final process in roll to roll systems and has no feedback control mechanism to correct winding roll shape directly during winding operation. Therefore, an optimal taper tension profile and the accurate control of it in a winding section could be one way to shape the fail-safe of a wound roll. Through the correlation between taper tension profile and telescoping in a winding process, a mathematical model for the telescoping due to tension distribution in cross machine direction was developed, and verified by experimental study. A new logic to determine the proper taper tension profile was designed by combining and analyzing the winding mechanism which includes nip induced tension model, relationship between taper tension profile and telescoping, relationship between taper value and telescoping. Numerical simulations and experimental results show that the proposed method is very useful for determining the desirable taper tension profile during the winding process and preventing defects of winding roll shape such as telescoping.     

Variable selection using Gaussian process regression-based metrics for high-dimensional model approximation with limited data

In recent years, the importance of computationally efficient surrogate models has been emphasized as the use of high-fidelity simulation models increases. However, high-dimensional models require a lot of samples for surrogate modeling. To reduce the computational burden in the surrogate modeling, we propose an integrated algorithm that incorporates accurate variable selection and surrogate modeling. One of the main strengths of the proposed method is that it requires less number of samples compared with conventional surrogate modeling methods by excluding dispensable variables while maintaining model accuracy. In the proposed method, the importance of selected variables is evaluated using the quality of the model approximated with the selected variables only. Nonparametric probabilistic regression is adopted as the modeling method to deal with inaccuracy caused by using selected variables during modeling. In particular, Gaussian process regression (GPR) is utilized for the modeling because it is suitable for exploiting its model performance indices in the variable selection criterion. Outstanding variables that result in distinctly superior model performance are finally selected as essential variables. The proposed algorithm utilizes a conservative selection criterion and appropriate sequential sampling to prevent incorrect variable selection and sample overuse. Performance of the proposed algorithm is verified with two test problems with challenging properties such as high dimension, nonlinearity, and the existence of interaction terms. A numerical study shows that the proposed algorithm is more effective as the fraction of dispensable variables is high.

     

MPP-based approximated DRM (ADRM) using simplified bivariate approximation with linear regression

Structural and Multidisciplinary Optimization - Conventional most probable point (MPP)-based dimension reduction methods (DRM) show better accuracy in reliability analysis than first-order...     

Reliability-based design optimization of wind turbine drivetrain with integrated multibody gear dynamics simulation considering wind load uncertainty

This study aims to develop an integrated computational framework for the reliability-based design optimization (RBDO) of wind turbine drivetrains to assure the target reliability under wind load and gear manufacturing uncertainties. Gears in wind turbine drivetrains are subjected to severe cyclic loading due to highly variable wind loads that are stochastic in nature. Thus, the failure rate of drivetrain systems is reported to be higher than the other wind turbine components, and improving drivetrain reliability is critically important in reducing downtime caused by gear failures. In the numerical procedure developed in this study, a wide spatiotemporal variability for wind loads is considered using 249 sets of wind data to evaluate probabilistic contact fatigue life in the sampling-based RBDO. To account for wind load uncertainty in evaluation of the tooth contact fatigue, multiple drivetrain dynamics simulations need to be run under various wind load scenarios in the RBDO process. For this reason, a numerical procedure based on the multivariable tabular contact search algorithm is applied to the modeling of wind turbine drivetrains to reduce the overall computational time while retaining the precise contact geometry required for considering the gear tooth profile optimization. An integrated computational framework for the wind turbine drivetrain RBDO is then developed by incorporating the wind load uncertainty, the rotor blade aerodynamics model, the drivetrain dynamics model, and the probabilistic contact fatigue failure model. It is demonstrated that the RBDO optimum for a 750 kW wind turbine drivetrain obtained using the procedure developed in this study can achieve the target 97.725% reliability (2 sigma quality level) with only a 1.4% increase in the total weight from the baseline design, which had a reliability of 8.3%. Furthermore, it is shown that the tooth profile optimization, tip relief introduced as a design variable, prevents a large increase of the face width that would result in a large increase in the weight (cost) of the drivetrain in order to satisfy the target reliability against the tooth contact fatigue failure.     

A study on the tension estimator by using register error in a printing section of roll to roll e-printing systems

The focus of this study is on the development of a mathematical model for estimating tension of a printing section by using the register error in R2R (Roll to Roll) e-Printing systems. In a printing section of conventional R2R printing systems, the tension is generally measured not for controlling but for monitoring, because the tension control may cause the occurrence of a register error. But, for high precision control, the tension in the R2R e-Printing system must be controlled as well as measured for more precise control of the register error. The tension can be measured by the loadcell in the conventional R2R systems. However, installing a loadcell on the R2R systems causes extra economic burden. In addition, the space for adding a loadcell on R2R systems is limited due to many components including dryers, lateral guider, doctor blade, ink supply unit and cooling unit. Therefore, a tension estimator can be another possibility for predicting the tension in a printing section. In this study, a new tension estimation model is proposed. The proposed model is based on the register error model, the equivalent torque equation, and the tension model considering tension transfer. Numerical simulations and experimental results showed that the proposed model was effective in estimating the tension in a printing section. This paper was recommended for publication in revised form by Associate Editor Hong Hee Yoo Chang-Woo Lee received a B.S. degree in Mechanical Engineering from Konkuk University in 2001. He received his M.S. and Ph.D. degrees from Konkuk university in 2003 and 2008, respectively. Dr. Lee is currently a researcher at the Flexible Display Roll to Roll Research Center at Konkuk University in Seoul, Korea. Dr. Lee’s research interests are in the area of fault tolerant control, R2R e-Printing line design, and tension-register control. He is the holder of several patents related to R2R e-Printing system. Jang-Won Lee received the B.S. and M.S.degrees in mechanical engineering from Konkuk University, Seoul, Korea. He studied continuous flexible process at the FDRC (Flexible Display R2R Research Center, Project Director: Kee-Hyun Shin), as a reseacher from the concentment to 2008. Since 2008, he has been a Research Engineer with the SKC Films R&D, Suwon, Gyeonggi-do, Korea. Now he is great on the plastic flim mechanics such as a scratch on the film surface, film extruding, winding/slitting mecha-nism and coating processes. Hyunkyoo Kang received the B.S. and M.S degree in 2000 and 2003 res-pectively from Konkuk Uni-versity, Seoul, Korea, where he is currently working toward the Ph. D. degree in mechanical design. He took part in the development of an autoalign guiding system for high-speed winding in a cable winding system, a 3-D roll-shape diagnosis method in a steel rolling system, a design of register controller for high-speed converting machine and real-time control design of electronic printing machine. His research topics include register modeling and control for printed electronics and distributed real-time control. Kee-Hyun Shin received the B.S. degree from Seoul National University, Seoul, Korea, and the M.S. and Ph.D. degrees in mechanical engineering from Oklahoma State University (OSU), Stillwater. Since 1992, he has been a Professor with the Department of Mechanical and Aerospace Engineering, Konkuk University, Seoul, Korea. For more than 18 years, he has covered several research topics in the area of web handling, including tension control, lateral dynamics, diagnosis of defect rolls/rollers, and fault-tolerant realtime control in the Flexible Display Roll-to-Roll Research Center, Konkuk University, of which he has also been a Director. He is the author of Tension Control (TAPPI Press, 2000) and is the holder of several patents related to R2R e-Printing system.     

Probabilistic sensitivity analysis for novel second-order reliability method (SORM) using generalized chi-squared distribution

Reliability-based design optimization (RBDO) requires evaluation of sensitivities of probabilistic constraints. To develop RBDO utilizing the recently proposed novel second-order reliability method (SORM) that improves conventional SORM approaches in terms of accuracy, the sensitivities of the probabilistic constraints at the most probable point (MPP) are required. Thus, this study presents sensitivity analysis of the novel SORM at MPP for more accurate RBDO. During analytic derivation in this study, it is assumed that the Hessian matrix does not change due to the small change of design variables. The calculation of the sensitivity based on the analytic derivation requires evaluation of probability density function (PDF) of a linear combination of non-central chi-square variables, which is obtained by utilizing general chi-squared distribution. In terms of accuracy, the proposed probabilistic sensitivity analysis is compared with the finite difference method (FDM) using the Monte Carlo simulation (MCS) through numerical examples. The numerical examples demonstrate that the analytic sensitivity of the novel SORM agrees very well with the sensitivity obtained by FDM using MCS when a performance function is quadratic in U-space and input variables are normally distributed. It is further shown that the proposed sensitivity is accurate enough compared with FDM results even for a higher order performance function.     

Confidence-based reliability assessment considering limited numbers of both input and output test data

Simulation-based methods can be used for accurate uncertainty quantification and prediction of the reliability of a physical system under the following assumptions: (1) accurate input distribution models and (2) accurate simulation models (including accurate surrogate models if utilized). However, in practical engineering applications, often only limited numbers of input test data are available for modeling input distribution models. Thus, estimated input distribution models are uncertain. In addition, the simulation model could be biased due to assumptions and idealizations used in the modeling process. Furthermore, only a limited number of physical output test data is available in the practical engineering applications. As a result, target output distributions, against which the simulation model can be validated, are uncertain and the corresponding reliabilities become uncertain as well. To assess the conservative reliability of the product properly under the uncertainties due to limited numbers of both input and output test data and a biased simulation model, a confidence-based reliability assessment method is developed in this paper. In the developed method, a hierarchical Bayesian model is formulated to obtain the uncertainty distribution of reliability. Then, we can specify a target confidence level. The reliability value at the target confidence level using the uncertainty distribution of reliability is the confidence-based reliability, which is the confidence-based estimation of the true reliability. It has been numerically demonstrated that the proposed method can predict the reliability of a physical system that satisfies the user-specified target confidence level, using limited numbers of input and output test data.