Research Papers

Modeling of Temperature Distribution in Moving Webs in Roll-to-Roll Manufacturing

[+] Author and Article Information
Youwei Lu

School of Mechanical and
Aerospace Engineering,
Oklahoma State University,
Stillwater, OK 74078
e-mail: youwei.lu@okstate.edu

Prabhakar R. Pagilla

Fellow ASME
School of Mechanical and
Aerospace Engineering,
Oklahoma State University,
Stillwater, OK 74078
e-mail: pagilla@okstate.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received March 5, 2014; final manuscript received July 11, 2014; published online August 5, 2014. Assoc. Editor: Srinath V. Ekkad.

J. Thermal Sci. Eng. Appl 6(4), 041012 (Aug 05, 2014) (9 pages) Paper No: TSEA-14-1044; doi: 10.1115/1.4028048 History: Received March 05, 2014; Revised July 11, 2014

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.

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Fig. 1

Web span and web wrapped on a heat transfer roller

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Fig. 2

Multilayer web sketch

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Fig. 3

Convective heat transfer in web span

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Fig. 4

Web wrapped and transported on a heated/chilled roller

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Fig. 5

Web nipped between two heat transfer rollers

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Fig. 6

Web and roller surface contact: (a) imperfect contact model and (b) equivalent model

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Fig. 7

Graphs of τ(x, t), ts is the abscissa of intersection of τ = t and τ = g(x, t)

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Fig. 8

Illustration of numerical method to determine τ

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Fig. 9

Schematic of a coating and fusion process line

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Fig. 10

Gel and clearcoat section of the R2R machine

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Fig. 11

Heat transfer roller with web and temperature sensors

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Fig. 12

Web temperature profile from model simulations and experiments with the heat transfer roller

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Fig. 13

Evolution of temperature at S1, S2, and S3

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Fig. 14

Temperature at different web thicknesses wrapped on the roller

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Fig. 15

A heating/cooling section of an embossing process line with infrared temperature sensors A and B

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Fig. 16

Top layer temperature of web in the heating/cooling section of the embossing line



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