Jim Throne, Sherwood Technologies, Inc., Dunedin Florida 34698 Copyright 2006

Introduction

In Part 1, we focused on simple experiments to determine the interaction between a 3-inch hemispherical wood plug and a 0.020-inch thick natural rubber sheet. We examined the transfer of grease dots from the wood plug to the rubber sheet. In addition, we noted local differential down-plug orientation of the grease dot on both the wood plug and the rubber sheet, particularly at the 1 ½-inch position on the plug where the sheet had been stretched locally about 50%.

In Part 2, we used a 0.020-inch flexible PVC sheet, heated to 275oF. We microphotographed these grease dots before and after vacuum forming the sheet onto the plug. From these experiments, we determined that the distances between the grease dots transferred to the sheet were essentially the same as the spacing between the initial grease dots on the plug. From this we concluded that no sliding occurred between the PVC sheet and the wood plug during vacuum forming.

In Part 3, we replaced the nom. 3-inch hemispherical wood plug with a 3-inch diameter glass sphere. The objective was to determine whether the nature of the plug surface influences in any way the contact between the plug and the stretching sheet. From our experiments, we concluded that no sliding occurred between the PVC sheet and the glass plug during vacuum forming. In addition, we coated first the plug, then the sheet with a thin film of oil to see if interfacial conditions could be affected this way. Neither the force required to stretch the sheet nor the local degree of stretch was affected.

For the three-part set of experiments, we conclude that no sliding occurs between the sheet and the plug, regardless of the nature of the sheet or the surface condition of the plug.

In Part 4, we discuss a possible cause for problems seen in plug-assisted thermoforming.

A New Understanding

From the data presented in this set of experiments and those given in the 2004 presentation, we believe that a new understanding of interfacial dynamics between the plug and the sheet is needed.

So, what is happening as the sheet contacts the plug? First, we believe that the air (or any other low viscosity substance) between the sheet and the plug is squeezed out as the sheet lies against the plug surface. This is demonstrated in Figures 7B and 10, given earlier. If the two surfaces are perfectly smooth, all the air would move ahead of the closing gap. But this is usually not the case with conventional plug materials. If the plug has irregularities, as the wood plug has in our experiments, we would expect that the asperities would support the sheet as it is being drawn over the plug, as shown in schematic in Figure 20.

Schematic of plug asperities that support the stretching sheet

Figure 20. Schematic of plug asperities that support the stretching sheet

Depending on the microscopic architecture of the plug surface, the regions around these asperities may trap the air between the plug and the sheet surface or the air may be squeezed from these regions through tortuous paths along the plug surface. Although one might expect that hotter sheet would minimize the volume of the air trapped between the asperities and the sheet, as envisioned in Figure 21, the softer sheet might actually trap a greater amount of air by sealing off “escape routes” as the sheet is drawn against the plug.

Interfacial resistance between sheet and plug surface, demonstrating the effect of hot, pliable sheet on air trap.

Figure 21. Interfacial resistance between sheet and plug surface, demonstrating the effect of hot, pliable sheet on air trap.

Figure 22, a close-up of Figure 11 (Part 3) shows air bubbles trapped between the sheet and the very smooth glass plug. In many plastic processes – injection molding, blow molding, thermoforming – air pockets at mold surfaces are often called “lakes.”

Air pockets formed when smooth FPVC sheet contacts smooth glass plug.

Figure 22. Air pockets formed when smooth FPVC sheet contacts smooth glass plug.

The most obvious effects of air trap are shiny spots or areas on the molded part surface. These are the result of the plastic not replicating the mold surface, or in our case, the plug surface.

Heat Transfer through Interstitial Air

In addition to causing a surface blemish, air trap may also alter the rate at which the sheet cools against the solid surface.

The heat transfer effect of an air trap was detailed in J.L. Throne, Technology of Thermoforming, Hanser Gardner, Cincinnati OH, 1996, pp. 318-321. The general heat conduction equation through the plastic sheet is:

general heat conduction equation through the plastic sheet

The general heat conduction equation through the plug is:

general heat conduction equation through the plug

The boundary condition at the sheet/air interface is:

boundary condition at the sheet/air interface

The boundary condition at the center of the plug is:

boundary condition at the center of the plug

The heat flux equation that accounts for conduction through the air layer between the sheet and the plug is:

heat flux equation that accounts for conduction through the air layer between the sheet and the plug

Where kp, ki, and km are the thermal conductivities of the polymer, interstitial air, and plug, respectively, and Δxp, Δxi, and Δxm are the differential thicknesses of the polymer, interstitial air gap, and plug, respectively.

The initial sheet temperature is:

initial sheet temperature

The initial plug temperature is:

initial plug temperature

If Ti1 is the polymer surface temperature at the polymer/air interface and Ti2 is the plug surface temperature at the air/plug interface, the interfacial temperatures are related to the interior plastic and plug temperatures, Tp and Tm, are:

polymer surface temperature

plug surface temperature

Where the following combination of thermal conductivities is noted:

kp thermal conductivity

kp thermal conductivity

km thermal conductivity

ki thermal conductivity of the interstitial air

kp thermal conductivity of the interstitial air

km thermal conductivity of the interstitial air

kim thermal conductivity of the interstitial air

Here ki is the thermal conductivity of the interstitial air and Δxi is the apparent air gap thickness.

Because the plug is usually substantially thicker than either the polymer sheet or any air gap, km‘ is usually much smaller than kp‘ or ki‘. Even though thermal conductivity of air is around 20% of that of most polymers, the polymer sheet thickness is many times that of the air layer. As a result, we would expect ki‘ to be larger than kp‘. In other words:

ki‘ > kp‘ > km

As a result:

ki ” ≤ 1 and ki,m ” ≅ 1.

The denominator in the temperature equations given above, viz,
(1 – k i ” – K i,m “), becomes very small. The interfacial temperature difference can be written as:

interfacial temperature difference

Parametrically, we can show that ΔTi becomes quite large (several degrees F) with even a modest air gap (on the order of 0.001 inch or so). In addition to the values for thermal conductivities and sheet and plug thicknesses, the actual value for ΔTi depends on the sheet and plug temperatures.

Some Thoughts on Process Variability

So far, no consideration has been given to differential pressure across the sheet or to the speed of plug penetration into the sheet, which may be a contributing factor to the differential pressure issue. Consider the following cases.

Differential Pressure across the Sheet is Zero

Mechanical stretching is the only force moving the sheet against the plug surface. In the case of the hemispherical plug of Parts 1-3, the initial contact is one of compression of the air between the sheet and the plug. As the sheet continues to stretch, the air is squeezed from between the sheet and the plug.

If the plug is not hemispherical but flat, the initial contact is still one of compression. But as the plug penetrates the sheet, the plastic at the edge of the plug may be pulled over the edge.

We discussed a similar problem in J.L. Throne, Technology of Thermoforming, Hanser Gardner, Cincinnati OH, 1996, pp. 499-503 where we compared the force required to slide draw polymer along the edge of a mold with the force required to stretch the polymer. If D is the diameter of the plug, h is the sheet thickness, β is the angle between the sheet and the flat plug surface, cf is the coefficient of friction, τ is the tensile strength of the polymer at temperature, and P is the pressure holding the sheet against the plug surface, the angle beyond which the sheet stretches rather than slides is given as:

angle beyond which the sheet stretches rather than slides

As the sheet temperature increases, its tensile strength decreases. For high temperature thick sheet, the angle at which the sheet stretches rather than slides is very small. High frictional coefficients favor sliding rather than stretching as do large diameter flat plugs. Nevertheless, for most practical cases the plug does not penetrate the sheet very far, viz, the angle is not very large, before stretching forces prevail.

Differential Pressure is Positive

As the plug penetrates the sheet, the general effect is to hold the sheet against the plug surface. The sheet should preferentially stretch rather than slide. However, aggressive differential pressure may force the sheet against the plug in a compressive manner rather than in the squeezing fashion we observed in Parts 1-3. Air trap in the form seen in Figure 22 may occur if the sheet and plug surfaces are quite smooth, Air trap in interstices may occur between the sheet and the plug surfaces if the surfaces are quite rough.

Differential Pressure is Negative

In this case, the sheet is held away from the plug as it penetrates the sheet. As a result, the sheet is not chilled by the plug and the interstitial air temperature remains essentially constant. This mode is preferred regardless of the plug shape. Unfortunately, this mode is rarely achieved. One reason for this is that only a little negative pressure is needed. Excessive negative pressure forces the sheet against the mold surface, thus obviating the role of the plug, viz, to alter the final part wall thickness.

The Usual Case

Typically, as the plug enters the sheet, it acts as a piston to force residual cavity air through vents. If the residual cavity air is not vented sufficiently rapidly, pressure will build within the cavity, forcing the sheet against the penetrating plug. There are many technical and practical reasons for forcing the plug into the sheet. And there are many technical and practical reasons for minimizing the number of vent holes in the mold cavity. As a result, in most plug-assisted thermoforming operations, differential pressure is positive. At some time during the plug movement, the sheet will usually be forced against the plug surface.

Forward Thinking

From experiments given in Parts 1-3, we find that friction is not an issue in plug design. Altering the plug surface characteristics seems to have little effect on draw-down. The factors influencing efficient plug design must be sought elsewhere. One suggestion focuses on air trap. Interstitial air can substantially alter the local heat transfer from the polymer to the plug.

To verify the role of interstitial air on the performance of plugs, we propose two sets of experiments.

The first set of experiments is very simple. Relatively deep holes of varying diameters are drilled into the surface of a plug. The plug material is not important but should not have very high thermal conductivity. Syntactic foam and wood appear to be materials of choice. Sheet is formed over the plugs and the temperatures of the sheet over the holes and next to the holes are to be measured. The depths of the holes should be at least 5 times their diameters. This will maximize the amount of air that is trapped in the hole by the forming sheet. Because careful temperature measurement is needed to verify the air trap concept, thermal imaging should be used to measure the sheet temperature so that the overall temperature is measured as the sheet cools against the plugs.

A second, more complex set of experiments employs hemispherical plugs of identical character with the exception of their microsurfaces. Both sets of plugs are to be polished smooth to the same RMS level, as recorded with a surface micrometer and microphotographs.

The first set of plugs is to have microgrooves engraved as concentric horizontal rings, beginning at the plug apex and continuing to below the equator of each plug. The depth of each microgroove is to be at least twice its width. The width between pairs of microgrooves is to be equal to the width of each microgroove. If the plug material were aluminum, it could be EDM’d, the microgroove dimensions could be as little as 1 mm wide by 5 mm deep. Aluminum plugs could be cartridge-heated for accurate temperature control.

The second set of plugs is to have microgrooves engraved as concentric vertical rings, again beginning at the plug apex. The microgroove dimensions are to be the same as those in the first set.

What is the objective of this set of experiments? With the first set of plugs, the forming sheet should trap air in the concentric horizontal rings. With the second set, the concentric vertical rings should allow the air to be squeezed out ahead of the advancing sheet. Again, temperature measurement should be made using thermal imaging so that the overall sheet temperature is measured as it cools against the plugs.

Final Thoughts

  • We believe that we have put to rest the question “What is sliding on what?” by answering “Nothing is sliding on anything.”
  • We have proposed that interfacial air may have some influence on the way in which the plug affects sheet mechanics during stretching.
  • We have proposed some experiments to isolate the role of air trap.
  • However, we have not resolved the conundrum “What plug characteristics are necessary when designing a plug to yield the best sheet stretching protocol?”
  • At this point, we leave this discussion and debate to more competent and better equipped people.

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