This new analysis for thermoforming cones focuses on the manufacturing process speed. Specifically, we’ve distinguished between what happens before and after (free versus constrained forming) the melt touches the conical mold. We derive analytical solutions for the time required for both cases, and sum them to get the total forming time. We restrict our analysis to the fabrication of cones, the simplest relevant problem in commercial thermoforming. We further confine our analysis to the Newtonian case, adimensionalizing our results at every step. For free forming, one dimensionless group arises, the geometric shape factor ( α<sub>0</sub>), and for constrained, two such factors arise ( α and sec β). We also calculate the stresses in the deforming melt, since these govern the residual stresses in the thermoformed part. We then derive an expression for wall uniformity; we find that it just depends on the mold geometry. Finally, we attack the problem of plug assist, deriving an expression for the improvement in wall uniformity achieved through plug assist. Our analytical solutions provide benchmarks for numerical analysts to test their code accuracy. Four worked examples illustrate how to reduce the results to engineering practice.
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