Modeling and control of transport behavior of moving webs through heat transfer processes

Abstract

Heat transfer processes are widely employed in Roll-to-Roll (R2R) process machines to heat/cool moving webs. The general goal is to efficiently transport webs over heating/cooling rollers and ovens while achieving the specified web temperature at different locations of the R2R machine. One of the key controlled variables 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. Because web strain and elastic modulus are functions of temperature distribution in the web, web tension resulting from mechanical strain is affected by heating/cooling of the web.

A multi-layer heat transfer model for composite webs is developed. Based on this model, temperature distribution in moving webs is obtained for webs transported on a heat transfer roller and in web spans between two adjacent rollers. 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 can be employed to design heating/cooling equipment that is required to obtain a certain desired temperature at a specific location within the process line. The governing equations for web strain and tension are then obtained by considering the temperature effects. Based on the web tension governing equation that includes both mechanical and thermal effects, a nonlinear adaptive tension control scheme is developed for control of tension in each tension zone of an R2R system. The control scheme is implemented on a modular R2R experimental platform containing two heat transfer rollers. Experimental results indicate that better tension regulation is obtained in the heated tension zone. Further, the temperature distribution model and the governing equations for web dynamics are utilized to design a tension observer for heating/cooling spans of a continuous strip annealing line where tension measurement is not available.