Sheet bowing in thermoforming

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

Sheet temperature in thermoforming

“…Figure 7 shows the effect shading can have on the integration limits. As such, this analysis only applies to geometries that obey the following inequality: Substituting (20) and (21) in (4), using Equation 13, and then evaluating the net flux to the concave surface yields:…”

“…On a sagging sheet, the bottom of the sheet will be convex, 9 while on a solid sheet that is bowing upwards, the topside is convex. 10 As with the concave face, our radiant heat flux analysis applies equally to both. Figure 10 defines our cylindrical coordinates r, , and z, whose moving origin approaches the sheet.…”

“…[1][2][3][4][5][6] Whereas textbook or handbook treatments give view factors for total heat flux, 7,8 we need the heat flux distribution over the surface of the sheet. Sheet curvature, either from thermal expansion of the solid sheet before softening (called bowing) or from self-weight of the solid sheet (called droop) 9 has been obtained previously and analytically, 10 as has curvature from the gravitational flow of a molten plastic sheet after softening (called sag). 9 In this article, we derive the heat flux distributions over both faces of a bowing or sagging sheet, along with the corresponding temperature profiles through and across the bowing or sagging sheet.…”

Studies on the stretching behaviour of medium gauge high impact polystyrene sheets during positive thermoforming

“…They have also derived the heat flux distributions over both faces of a bowing or sagging sheet, along with the corresponding temperature profiles through and across the sheet. [12][13][14][15] An ideal thermoforming material should not sag much during heating. However, it should flow well during forming.…”