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

Introduction

Nearly all thermoforming processes employ mechanical assists to differentially stretch the heated sheet prior to contact with the mold surface. The mechanical assist is usually referred to as a plug. It has always been assumed that, as the plug enters the hot sheet, the sheet slides against the plug. Mathematical models such as T-Sim (trademark of Accuform, Zlin, Czech Republic) require values for the coefficient of friction between the hot sheet and any solid surface (i.e., the plug and any and all mold elements). It is well known that it is very difficult to measure frictional coefficients in general and frictional coefficients between hot plastic and solid surfaces, in particular.

At the 2004 SPE Thermoforming Conference, we presented a talk on the type and nature of frictional coefficients and asked, “What is sliding on what?” The talk has generated substantial discussion among plug material suppliers, formers, and software manufacturers. The PPT presentation is available on our website.

This paper continues our investigation into “What is sliding on what?”

The Experimental Set-Up

For the set of experiments detailed below, we are using EZFORMTM thermoformer (Centroform, 820 Thompson Ave., Unit 5, Glendale CA 91201), having a 13-in x 18 ¾-in clamp frame is used. The thermoformer heats the sheet only from the top. This study uses a 3-in diameter wood plug that sits in a 3 ¼-in hole in the center of a vacuum box. The vacuum box edge is ¾-in quarter-round. The vacuum box bottom is tempered pegboard. The vacuum system is a shop vacuum pulling approximately 25 in water. The experimental set-up is seen in Figure 1.

Vacuum former set-up, showing top heater shroud, sheet clamp, vacuum box, and plug in place.

Figure 1. Vacuum former set-up, showing top heater shroud, sheet clamp, vacuum box, and plug in place.

Two sets of experiments have been performed using this set-up. The first is described here. In this set of experiments, a 20-mil [0.020-in] natural rubber sheet is used at room temperature. The objectives of the first set of experiments are to determine

  1. whether a simple marking system can yield useful information about local stretching and orientation, and
  2. whether, in fact, the rubber sheet slides against the plug.

The first set of experiments involved determining the local degree of rubber sheet stretching. The sheet was dot-marked at ½ -in intervals from the point where the sheet contacted the center of the plug to 3-in radially outward. The sheet was then stretched and the distance between the dots was then measured. Table 1 gives these data. Figure 2 shows them in graphical form. As expected, the sheet at the very apex of the plug shows no stretching, whereas there is substantial stretching around the 2 ½-inch mark.

Table 1 – Measured Distance between Current Location and Previous Location On 20-mil Natural Rubber Sheet Stretched over Plug
Dot Location from Apex, in Distance, in
0.5 0.5
1.0 0.625
1.5 0.6875
2.0 0.8125
2.5 1.0
Location of dots on stretched 20-mil natural rubber sheet and vacuum formed 20-mil FPVC sheet.

Figure 2. Location of dots on stretched 20-mil natural rubber sheet and vacuum formed 20-mil FPVC sheet.

The Marking System

A marking system was then employed to determine how the sheet contacts the plug. After several false starts, a very simple method was employed. Small dots of grease, approximately 2.5-4 mm in diameter, were placed at ½-inch intervals down the surface of the plug. This is seen in Figure 3.

Photograph of wood plug showing location of grease dots.

Figure 3. Photograph of wood plug showing location of grease dots.

The dots were micro-photographed for dimensional reference, as seen in Figure 4 for the dots at the ½-inch and 1 ½-inch positions. It should be noted here that the dots were not planar but instead were mostly domed or conical in shape. In addition, it should be noted that the dots were somewhat irregular in shape, not circular in diameter.

Grease dots at 0.5-in and 1.5-in positions on plug before contact with sheet

Figure 4. Grease dots at 0.5-in and 1.5-in positions on plug before contact with sheet

The rubber sheet was then vacuum-drawn down against the plug. After the vacuum was released, the sheet was carefully lifted from the plug. The transfer of grease dots to the rubber sheet is seen in Figure 5.

Photograph of grease dots transferred from plug to rubber sheet

Figure 5. Photograph of grease dots transferred from plug to rubber sheet

The dots on the plug were again micro-photographed along with the dots on the rubber sheet. The raw data are presented in Table 2. A composite of the dots on the rubber sheet, along with a dimensional bar, is given in Figure 6. The numbers on the figure are reproduced in Table 2.

Table 2 – Dimensions of Grease Dot Originally on Plug, On Plug after Rubber Sheet Contact, and On Rubber Sheet after Contact
Dot Dim, a x b, mm Product, a x b, mm2
Position from apex: 0 in
Original dot Not measured
After, on plug 4.3 x 3.6 15.48
After, on rubber 3.9 x 3.6 14.04
Position from apex: 0.5 in
Original dot 2.3 x 2.7 6.21
After, on plug 2.9 x 3.6 10.44
After, on rubber 3.1 x 3.6 11.16
Position from apex: 1.5 in
Original Dot 2.4 x 2.6 6.4
After, on plug 2.9 x 3.5 10.15
After, on rubber 3.3 x 3.7 12.21
Position from apex: 2.0 in
Original dot Not measured
After, on plug 3.4 x 4.6 15.64
After, on sheet 0.5 x 0.6 0.3

Composite of grease dots as transferred from the wood plug to the rubber sheet. Arrows on individual dots represent the direction down from the plug apex.

Figure 6. Composite of grease dots as transferred from the wood plug to the rubber sheet. Arrows on individual dots represent the direction down from the plug apex.

Analysis of the Data

As noted above, the marking dots were not planar, but domed or conical in shape. As a result, when the sheet contacted a dot, it flattened it. The nature of the flattening is important.

  1. If the sheet simply compressed the dot, one would expect the final dot shape to be simply larger in all dimensions, without any preferential orientation. This would imply that the sheet compressed the dot without sliding on it.
  2. If the dot became distorted in one direction – particularly in the sheet draw direction – one could conclude that the dot had been differentially sheared by the sheet. In addition, one might conclude from that evidence that the sheet slid locally, not only on the dot, but also on the plug as a whole.

To determine the nature of the flattening, the ratios of the dot dimensions on the plug, before and after sheet contact, were determined. These data are given in Table 3. Note that the initial dot dimensions for dots at 0-inch, 1-inch, and 2-inch positions were not determined. In addition, the ratios of the dot dimensions on the plug before sheet contact and on the sheet were determined. These data are also given in Table 3.

Table 3 – Effect of Rubber Sheet on Grease Dot Dimensions for Dot Positions 0.5-in and 1.5-in
Across Down Ratio, D/A
Position from apex: 0.5-in
After, on plug/original 1.26 1.33 1.06
After, on rubber/original 1.35 1.33 0.99
Position from apex: 1.5 in
After, on plug/original 1.21 1.35 1.12
After, on rubber/original 1.38 1.42 1.03

Sheet Orientation Factor

At first glance, there appears to be relatively little difference between the dot dimensions on the plug and those on the sheet. However, keep in mind that the sheet is stretched locally over the dot. An average of the stretching values of Table 1 is used to determine the local degree of stretch. These values are given in Table 4. The data of Table 3 for the rubber dimensions are now corrected by multiplying by the local stretch values, as shown in Table 4.

Table 4 – Correction for Local Rubber Sheet Stretch and Recovery At Dot Positions of 0.5-in and 1.5-in
Position from apex: 0.5-in
Stretch between 0 and 0.5 in 0.500 in
Stretch between 0.5 and 1 in 0.625 in
Avg 0.559 in
Stretch ratio, 0.559/0.5 1.12
Position from apex: 1.5-in
Stretch between 1 and 1.5 in 0.6875 in
Stretch between 1.5 and 2 in 0.8125 in
Avg 0.747 in
Stretch ratio, 0.747/0.5 1.49
Across Down Ratio, D/A
Position from apex: 0.5-in
After, on plug/original 1.26 1.33 1.06
After, on rubber/original 1.35 1.33 0.99
D/A, corrected for stretch recovery 0.99 x 1.12 = 1.11
Position from apex: 1.5-in
After, on plug/original 1.21 1.35 1.12
After, on rubber/original 1.38 1.42 1.03
D/A, corrected for stretch recovery 1.03 x 1.49 = 1.53

Observations

Plug stretching is considered as plane-strain stretching. For a hemispherical plug such as that used in this study, there is relatively little circumferential or radial stretching compared with down-plug stretching. As a result, the observations focus on down-plug stretching only.

Consider the importance of local down-plug sheet stretching. It seems that at the ½-inch position, there is little down-plug differential orientation evidenced on the rubber sheet. At that position, the sheet has been locally stretched a little more than 10%.

However, there appears to be significant down-plug differential orientation at the 1 ½-inch position as evidenced on the rubber sheet. At that position, the sheet has been locally stretched about 50%. There is no equivalent down-plug differential orientation on the plug itself. This implies that the sheet first contacted the dot at the 1 ½-inch position in compression. This allowed the grease to be adsorbed by the rubber.

Because the down-plug dimension of the dot on the plug is not substantially greater than the cross-plug dimension, it appears that the sheet did not smear the grease down the plug surface. However, it appears that the sheet was stretching while it was contacting the grease. If the sheet had been stretched prior to contacting the grease, the down-plug dimension of dot on the sheet would now be substantially smaller owing simply to the sheet recovery.

Tentative Conclusion

If we reword the question “What is sliding on what?” to read “Is the sheet sliding on the plug, and if so, where?”, then the tentative answer seems to be, “It may be sliding, but not everywhere.” The experiments indicate that down to perhaps the 1 ½-inch point on the plug surface, the sheet simply lays onto the plug, as evidenced by the compression of the grease dot without apparent shear. Figure 7A is a schematic of what this effect might appear to be.

Schematic of the possible compression of grease dot by advancing sheet.

Figure 7A. Schematic of the possible compression of grease dot by advancing sheet.

Schematic of the possible shear of grease dot by advancing sheet.

Figure 7B. Schematic of the possible shear of grease dot by advancing sheet.

Beyond that point on the plug surface, there appears to be elongation of the grease dot in the down-plug direction. Because the grease dot is not substantially elongated on the plug but is on the sheet, it would indicate that the sheet is smearing the adhered grease dot in the down-plug direction. This effect might be considered a type of sliding. However, it might also be considered a shearing or squeezing effect. As the sheet contacts the dot, the initial portion of the grease dot is forced against the sheet. As the sheet continues to stretch, that portion adheres to the sheet. As grease is picked up by the stretching sheet and adheres to the sheet, it resides behind the initial portion. Perhaps the roughness of the plug or the rapid absorption of the grease prevents any portion of grease initially adhering to the sheet to be transferred back to the plug as the sheet presses against the plug. Figure 7B is a schematic sequence of what this effect might look like.

Consider a conclusion that the sheet is in fact sliding against the plug at the 1 ½-inch point. If one surface is truly sliding against another, some form of a frictional coefficient is needed. But can it be concluded that sliding is also taking place at the ½-inch point? If not, then a frictional coefficient is not warranted. More importantly, is there some property or combination of properties that varies with the angle of attack between the plug surface and the sheet?

Continuing Work

The second set of experiments, described in Part 2, employs the same set-up described above except that the rubber sheet is replaced by 20-mil [0.020 inch] transparent flexible PVC, heated to various temperatures.

An analysis of the interrelationship between sliding force and stretching force will also be considered in Part 2.

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