Analysis of Thermoforming

If a thermoplastic sheet is softened by heat and then pressure is applied to one of the sides so as to generate a freely blown surface, it will be found that the shape so formed has a uniform thickness. If this was the case during thermoforming, then a simple volume balance between the original sheet and the final shape could provide the wall thickness of the end product. 

Heated sheets placed between open mould halves 

This would leave a volume of (3 x 10 -2.52 x 10 ) to form the walls. The area of the walls is 

This ignores a small area in the base of the box, outside the edges of the plug. Hence, the thickness of the walls in this case would be 

These calculations can give a useful first approximation of the dimensions of a thermoformed part. However, they will not be strictly accurate because in a real situation, when the plastic sheet is being stretched down into the cold mould it will freeze off at whatever thickness it has reached when it touches the mould. 

Consider the thermoforming of a plastic sheet of thickness, h, into a conical mould as shown in Fig. 4.55(a). At this moment in time, t, the plastic is in contact with the mould for a distance, 5, and the remainder of the sheet is in the form of a spherical dome of radius, R, and thickness, h. From the geometry of the mould the radius is given by 

---

Fong, L. L. and Advani, S. G., Preforming analysis of thermoformable fiber mats -Fh-eformine effect on mold filling , Journal of Reinforced Plastics and Composites, 13(7), 637-663, 1994. 

Erchiqui, F Souli, M., and Ben Yedder, R. (2007) Nonisothermal finite-element analysis of thermoforming of polyethylene terephthalate sheet incomplete effect of the forming stage. Polym. Eng. Sci., 47, 2129-2144. 

An overview is presented of TrexeTs MuCell microcellular foam extrasion technology and a description is given of its application to the manufacture of thermoformable PP sheet. The results of pilot scale thermoforming trials carried ont to optimise forming conditions and obtain data abont potential cycle time effects, measurements of the densities, flexnral modnlns and wall thicknesses of the sheets and containers made from the sheets and cell stmcture analysis are presented and discussed. 

G. Marckmann, E. Verron, and B. Peseux, Finite Element Analysis of Blow Molding and Thermoforming Using a Dynamic Explicit Procedure, Polym. Eng. Sci., 41,426 139 (2001). 

S. Shrivastava and J. Tang, Large Deformation Finite Element Analysis of Non-linear Viscoelastic Membranes With Reference to Thermoforming, J. Strain Anal. 28, 31 (1993). 

Fourier number n (Np). A dimensionless group important in analysis of unsteady heat transfer in solids, such as sheets being heated or cooled in thermoforming, or cooling of extrudates and moldings, ATp = a f/x , where a is the material s thermal diffiisivity, t the heating or cooling time, and x is the a thickness or half-thickness in the direction of heat flow. 

Song, W.N., Kouba, K., Mirza, EA., and Vlachopoulos, J. (1991). Finite Element Analysis of Practical Thermoforming. ANTEC, Montreal, 1025—1027. 

Modelling and analysis of composites thermoforming KINEMATIC APPROACH... 

Petrie, C. J. S., Film Blowing, Blow Moulding, and Thermoforming, in J. R. A. Pearson and S. M. Richardson, Eds., Computational Analysis of Polymer Processing, Applied Science Publishers, London, 1983, pp. 217ff. 

Shrivastava S, Tang J (1993) Large deformation finite element analysis of non-linear viscoelastic membranes with reference to thermoforming. J Strain Anal 28(1) 31-51... 

R. Truckenmiiller, Z. Rummler, T. Schaller, and W. K. Schomhurg, Low-cost thermoforming of micro fluidic analysis chips. Journal of Micromechanics and Microengineering, 12(4), 375—379, 2009. 

Karamanou et al. [65] have performed finite element analyses to large strains to simulate the thermoforming process, in which thin sheets of polymer are inflated using gas pressure. They adopted a model comprising hyperelastic components and a linear viscous element. Applying a thin shell analysis enabled them to produce realistic predictions of the inflating membrane. 

Films of 2a were cast from chloroform and were translucent to opaque. The films were very tough and displayed a high modulus, in the 6-8 GPa range as measured by dynamic mechanical thermal analysis (DMTA). Samples could also be prepared by compression molding, however, some degradation occurred when the polymer powder was heated in the press above the Tm d in an air atmosphere. The resulting thermoformed sample displayed a drop in the intrinsic viscosity from 0.70 to 0.48 dL/g, relative to the polymer powder. 

Now let us assume that our pin is made of thermoplastic and it is injection molded. So, we know it cannot be a pure cylinder with a perfect diameter, as there is going to be some amount of draft added somewhere—regardless of how we orient the part in the mold—and perhaps even some mold mismatch. Then we have a hole in another part, which is thermoformed, or perhaps rotationally molded. That hole is not going to be a perfectly round hole (or straight), no matter how much we may want it to be. Now, we have to establish size targets for the pin and for the hole, evaluate the tolerances for a typical production scenario, and then do a tolerance analysis to ensure that everything always fits. 

---