Research Papers

Modeling and Analysis of Web Span Tension Dynamics Considering Thermal and Viscoelastic Effects in Roll-to-Roll Manufacturing

[+] Author and Article Information
Kadhim A. Jabbar

Department of Mechanical Engineering,
Thi-Qar University,
Nasiriyah, Iraq
e-mail: kadhim@okstate.edu

Prabhakar R. Pagilla

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: ppagilla@tamu.edu

1Corresponding author.

Manuscript received January 5, 2017; final manuscript received December 20, 2017; published online March 6, 2018. Assoc. Editor: Satish Bukkapatnam.

J. Manuf. Sci. Eng 140(5), 051005 (Mar 06, 2018) (9 pages) Paper No: MANU-17-1007; doi: 10.1115/1.4038888 History: Received January 05, 2017; Revised December 20, 2017

A governing equation for web tension in a span considering thermal and viscoelastic effects is developed in this paper. The governing equation includes thermal strain induced by web temperature change and assumes viscoelastic material behavior. A closed-form expression for temperature distribution in the moving web is derived, which is utilized to obtain thermal strain. A model for web tension in a multispan roll-to-roll system can be developed using this governing equation. To evaluate the governing equation, measured data from an industrial web process line are compared with data from model simulations. Since the viscoelastic behavior of web materials is affected by the web temperature change, elevated temperature creep, and stress-relaxation experiments are conducted to determine the temperature-dependent viscoelastic parameters of the utilized viscoelastic model. Comparisons of the measured data with model simulation data are presented and discussed. An analysis of the web tension disturbance propagation behavior is also provided to compare transport behavior of elastic and viscoelastic materials.

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Fig. 1

Two web spans and control volume

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Fig. 2

Temperature notation of various components

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Fig. 3

Standard linear viscoelastic solid model

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Fig. 4

Web 1 stress-relaxation response at different temperatures under a constant strain of 1%

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Fig. 5

Temperature dependence of modulus

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Fig. 6

E1 as a function of temperature

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Fig. 7

Schematic of the coating, heating and cooling rollers in the coating and fusion web line

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Fig. 8

Simplified process model of Fig. 7

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Fig. 9

Control strategy to regulate web tension and velocity

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Fig. 10

The output of the developed model and the measured data for web 1

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Fig. 11

Comparison between model simulation and measured data for web 1

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Fig. 12

Tension variation in web span L1 for web 1

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Fig. 13

Sketch of a multispan system

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Fig. 14

Bode plot of the transfer function Gtn(s) in web spans L1, L2, and L3 for web 1 (viscoelastic case)

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Fig. 15

Bode plot of the transfer function Gtn(s) in web spans L1, L2, and L3 for web 1 (elastic case)



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