Prabhakar R. Pagilla

A heat transfer model that can predict the temperature distribution in moving flexible composite materials (webs) for various heating/cooling conditions is developed in this paper. Heat transfer processes are widely employed in roll-to-roll (R2R) machines that are used to perform processing operations, such as printing, coating, embossing, and lamination, on a moving flexible material. The goal is to efficiently transport the webs over heating/cooling rollers and ovens within such processes. One of the key controlled variables in R2R transport is web tension. When webs are heated or cooled during transport, the temperature distribution in the web causes changes in the mechanical and physical material properties and induces thermal strain. Tension behavior is affected by these changes and thermal strain. To determine thermal strain and material property changes, one requires the distribution of temperature in moving webs. A multilayer heat transfer model for composite webs is developed in this paper. Based on this model, temperature distribution in the moving web is obtained for the web transported on a heat transfer roller and in a web span between two adjacent rollers. Boundary conditions that reflect many types of heating/cooling of webs are considered and discussed. Thermal contact resistance between the moving web and heat transfer roller surfaces is considered in the derivation of the heat transfer model. Model simulations are conducted for a section of a production R2R coating and fusion process line, and temperature data from these simulations are compared with measured data obtained at key locations within the process line. In addition to determining thermal strain in moving webs, the model is valuable in the design of heating/cooling sources required to obtain a certain desired temperature at a specific location within the process line. Further, the model can be used in determining temperature dependent parameters and the selection of operating conditions such as web speed.

Roll-to-roll (R2R) printing is a continuous process in which thin flexible materials such as paper are passed through a printing press to print the required pattern onto the material. Each printing press may have several printing units depending on the number of colors to be printed and the complexity of the pattern. The flexible material, often referred to as a “web,” is passed successively through each print unit to create a multicolor pattern. Print registration is the process of overlapping successive printed patterns to form a complex multicolor pattern and the registration error is the position misalignment in the overlapped patterns. This paper develops a machine direction print registration model in a printing press with multiple print units whose print cylinders are driven using mechanical line shafts. The registration model considers the effects of interaction between adjacent print units due to variations in material strain and machine dynamics, including various dynamic elements, such as the print cylinder, doctor blade assembly, print unit compensator roller, print unit motor, friction at various locations, etc. Measured data from typical production runs on an industrial printing press are used to corroborate the developed print registration model. Mechanical design and control design recommendations to reduce registration error in print units are also provided. The developed registration model is applicable to many R2R printing technologies, such as offset, flexo, and rotogravure printing.

Since rotating machinery is used to transport flexible materials (commonly known as webs) on rollers, it is common to observe periodic oscillations in measured signals such as web tension and web transport velocity. These periodic oscillations are more prevalent in the presence of nonideal elements such as eccentric rollers and out-of-round material rolls. One of the critical needs in efficient transport of webs is to maintain web tension at a prescribed value. Tension regulation affects almost all key processes involved during web transport including printing, registration, lamination, winding, etc. Governing equations for web tension and transport velocity that can accurately predict measured behavior in the presence of nonideal rollers are beneficial in understanding web transport behavior under various dynamic conditions and the design of suitable web tension and speed control systems. The focus of this paper is on modeling the effect of eccentric rollers and out-of-round material rolls on web tension and web transport velocity. The new governing equations for web velocity on an eccentric roller and web tension in spans adjacent to the eccentric roller are presented and discussed; a web span is the free web between two consecutive rollers. To solve these governing equations, the location of the entry and exit point of the web on the eccentric roller as it rotates and the length of the web spans adjacent to the eccentric roller are required; a procedure for obtaining this information is described. To corroborate the models and the developed approach, data from experiments on a large experimental web platform are compared with data from model simulations, and a representative sample of the results are presented and discussed.

A dynamic model to describe the effect of compliance in a transmission system is presented. Analysis of this model shows that it is desirable to use feedback from driver-side of the transmission system. This model is extended to include the effects of both compliance and backlash in a mechanical transmission system. The proposed model considers compliance (which may be either due to the elasticity of the shafts or belt in a belt-pulley transmission system) and backlash appearing in series in a drive system. In contrast to the classical backlash model which considers both input and output to the backlash as displacements, the proposed model considers (torque) force as input to the backlash and (angular velocity) velocity of the driven member as the output of the backlash. Thus, the proposed model does not assume that the load is stationary when contact is lost due to backlash width, i.e., momentum of the load is taken into account. Using the proposed model, a bound on the speed error due to the presence of backlash is derived. Experiments were conducted on a rectilinear mass-spring system platform, which has a provision to change the backlash width by a known value. Experiments were conducted with different backlash widths and a velocity error bound was computed. The error bound obtained from the experimental results agrees with the theoretically computed bound.

This paper presents an optimal web guiding strategy based on the dynamic analysis of the lateral web behavior and a new fiber optic lateral web position measurement sensor. First, a lateral dynamic model of a moving web is revisited with an emphasis on correct application of appropriate boundary conditions. Then the dynamic models of two common intermediate guides (remotely pivoted guide and offset-pivot guide) are investigated. The effect of various model parameters on lateral web behavior is analyzed and discussions on proper selection of the parameters are given. Based on the model analysis, we discuss the design of a linear quadratic optimal controller that is capable of accommodating structured parametric uncertainties in the lateral dynamic model. The optimal guide control system is evaluated by a series of experiments on a web platform with different web materials under various operating conditions. Implementation of the controller with a new fiber optic lateral sensor for different scenarios is discussed. Results show good guiding performance in the presence of disturbances and with uncertainties in the model parameters.

A novel sensor to measure web flutter is proposed in this letter. The sensing principle is based on scattering of light and directionally sensitive coupling properties of optical fibers. A linear array of optical fibers, oriented appropriately, is used to collect light scattered from a web. The flutter amplitude is determined by observing the amount of light transmitted by the fibers in the fiber array. Experiments were conducted to demonstrate the ability of the proposed sensing strategy in measuring web flutter with different kinds of web material.