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Sheet bowing in thermoforming

Authors

  • P.B. Vodak,

    1. Rheology Research Center and Mechanical Engineering Department, University of Wisconsin-Madison, Madison, Wisconsin 53706-1572
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  • A.W. Mix,

    1. Rheology Research Center and Mechanical Engineering Department, University of Wisconsin-Madison, Madison, Wisconsin 53706-1572
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  • A.J. Giacomin

    Corresponding author
    1. Rheology Research Center and Mechanical Engineering Department, University of Wisconsin-Madison, Madison, Wisconsin 53706-1572
    • Rheology Research Center and Mechanical Engineering Department, University of Wisconsin-Madison, Madison, Wisconsin 53706-1572
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Abstract

Sheets to be thermoformed are often heated unevenly, with a higher temperature above the sheet. This results in upward bowing of the sheet, and this is caused by thermal expansion. We combine the analytical solution for the temperature gradient in a slab heated by radiation with a relationship developed from the cylindrical geometry of the sheet as it bows. We thus derive a dimensionless equation for sheet bowing as an implicit function of time for both top and dual heating. We thus uncover a new dimensionless group which we call sheet bowability. We find good agreement between our theory and our new top-heated sheet bowing measurements. We provide a worked example so that the engineer can see how to apply our results. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers

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