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 replace the nom. 3-inch hemispherical wood plug with a 3-inch diameter glass sphere. The objective is to determine whether the nature of the plug surface influences in any way the contact between the plug and the stretching sheet. Again, we use the same equipment and techniques described in Parts 1 and 2.

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. 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.

This study uses a glass plug. The plug used is a 3-in diameter solid glass sphere, euphemistically called a ‘feng shui orb.’ It sits on a glass pedestal in a 3 ¼-in hole in the center of a vacuum box. For each experiment, we cleaned the glass surface with rubbing alcohol. This was done prior to applying grease dots.

The experimental set-up is seen in Figure 11.

Experimental set-up with glass plug in place.

Figure 11. Experimental set-up with glass plug in place.

The marking system was the same as described in Part 1, viz, small dots of grease, approximately 2.5-4 mm in diameter, placed at ½ -inch intervals down the surface of the plug, beginning at the apex. This is seen in Figure 12.

Formed FPVC sheet in contact with glass plug, left, and grease dots on everted formed sheet, right.

Figure 17. Formed FPVC sheet in contact with glass plug, left, and grease dots on everted formed sheet, right.

Experiments with Rubber Sheet

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 objective of the first set of experiments whether the rubber sheet slides against the very smooth glass plug in a manner similar to that seen against the wood plug as described in Part 1.

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 inches radially outward. The sheet was then stretched and while the sheet was still under vacuum, the distance between the dots was measured. Table 8 gives these data, along with the data from Table 1 for the similar experiment with the wood plug.

Table 8 Comparison of Dots Prepositioned at ½ inch Marks On Rubber Sheet Prior to Stretching –Measurement with Vacuum On
Position from Apex, in Distances between Dots on
Glass Wood
0.5 0.62 0.5
1.0 0.62 0.625
1.5 0.70 0.6875
2.0 0.80 0.8125
2.5 0.74 1.0

Figure 13 graphically compares these data.

Comparison of dot distances on 20-mil natural rubber sheet stretched against wood and glass plugs.

Figure 13. Comparison of dot distances on 20-mil natural rubber sheet stretched against wood and glass plugs.

The 20-mil natural rubber sheet was then vacuum formed against the glass plug. The characteristics of the grease dots were then examined on both the glass plug and the rubber sheet. The 1 ½-inch grease dot on the glass plug after contact with the sheet is shown in Figure 14. The shape of the grease is characteristic of but more exaggerated than the shapes of the grease dots at the 1-inch and 2-inch positions. The importance of this will also be discussed later.

Grease dot at 1 ½-in from the glass plug apex, after contact with rubber sheet

Figure 14. Grease dot at 1 ½-in from the glass plug apex, after contact with rubber sheet

The distances between grease dots on the relaxed rubber sheet are given graphically in Figure 15 and in tabular form in Table 9, along with the similar data from Part 1. The differences are discussed later.

Table 9 Distances between Grease Dots Spaced ½ inch Apart Then Transferred to Rubber Sheet, Relaxed Distances
Position from Apex, in Distances between Dots on
Glass Wood
0.5 0.5 0.5
1.0 0.5 0.533
1.5 0.46 0.633
2.0 0.30 0.727
2.5 0.30 0.799
Comparison of distances between grease dots, wood and glass plug, rubber sheet in relaxed state

Figure 15. Comparison of distances between grease dots, wood and glass plug, rubber sheet in relaxed state

Experiments with FPVC Sheet

In Part 2, we described experiments with 30-mil [0.020 inch] flexible PVC sheet. These experiments were repeated with the glass plug replacing the wood one. As before, the sheet was heated to 275oF prior to vacuum forming against the glass plug. The transfer times and hold times were similar to those used in the experiments with the wood plug.

Again, the extent of stretching of the sheet was determined first by placing black dots at ½-inch intervals radially outward on the sheet, beginning at the point of first contact with the plug. The sheet was then vacuum formed against the plug. The plug sat in the mold base at a height that allowed the sheet to partially wrap under it during forming. As a result of this undercut, the formed sheet had to be peeled from the plug. The distances between dots on the formed sheet were then measured. The values are given in Table 10 and are compared graphically in Figure 16 with data obtained from the similar experiment with the wood plug.

Comparison of dot spacing for FPVC sheet stretched over wood and glass plugs

Figure 16. Comparison of dot spacing for FPVC sheet stretched over wood and glass plugs

Table 10 Comparison of Dots Prepositioned at ½ inch Marks On 20-mil FPVC Sheet Prior to Stretching
Position from Apex, in Distances between Dots on
Glass Wood
0.5 0.5 0.512
1.0 0.68 0.512
1.5 0.72 0.63
2.0 0.72 0.709
2.5 0.80 0.827
3.0 0.60 0.748

Grease dots were again applied to the glass plug at ½-inch spacing, as before. The FPVC sheet was again heated to 275oF and vacuum formed against the glass plug. This time, because of the undercut to the plug, the sheet was razor-cut from the plug. This hopefully minimized smearing of the grease dots on both the plug and the plastic surfaces. The formed plastic hemisphere was then everted and the distances between the grease dots were measured. All dots were essentially 0.5 inches apart, within allowable error. This agrees with the FPVC-wood data in Table 7 of Part 2. Figure 17 provides an interesting comparison of the dots on the everted plastic form with the dots on the glass plug with formed sheet still in place.

Formed FPVC sheet in contact with glass plug, left, and grease dots on everted formed sheet, right.

Figure 17. Formed FPVC sheet in contact with glass plug, left, and grease dots on everted formed sheet, right.

Observation

We observed in Part 2, “In other words, there appears to be no stretching taking place once the sheet has contacted the plug.” This observation holds for both wood and glass plugs.

In Part 1, we also proposed two mechanisms for non-sliding contact between the sheet surface and the plug surface – compression and shear. We now reexamine Figure 14, the grease dot at 1 ½ inches from the apex of the glass plug after contact with the rubber sheet. The original dot was approximately 1.4 mm in diameter. The width of the grease dot is now about the same but the length is at least 4 times the original diameter. More importantly, the shape indicates that the original dot has been spread downward and outward. This indicates that the spreading action is one of shear rather than compression. The shearing action was depicted in Figure 7B of Part 1 and is repeated here.

Schematic of sheet shearing grease dot against plug

Figure 7B (Part 1) Schematic of sheet shearing grease dot against plug

Consider now that the grease dot is not present. Instead, the gap between the sheet and the plug is air, as seen in the cropped version of Figure 10 from Part 2, viz:

Contact angle between sheet and plug

Figure 10, cropped (Part 2). Contact angle between sheet and plug

Instead of a shearing action as given in Figure 7B, the action is one of squeezing, or pushing the air from the gap between the sheet and the plug.

Plug Surface Characteristics

In Parts 1 and 2, we used a coarse-surfaced wood plug. In this study, we used a smooth glass surface that was usually cleaned with isopropyl alcohol prior to use. [See Figure 12 for exception.] As seen in Figure 16, the surface characteristic of the plug seemed to cause little difference in the local FPVC sheet stretching dimensions. One additional set of experiments was conducted to see if a dramatic change in the interface between the sheet and plug surface could change the stretching characteristics of the sheet. The thinking being that a film of oil should alter the sliding frictional coefficient between the plug and the sheet. To ensure that any effect could be observed, we opted to coat the plug and the sheet, in turn, with a thin film of very low viscosity oil.

First, the glass plug was coated with a very thin film of vegetable oil [Pam]. The FPVC sheet was pristine. The sheet was then heated to 265oF and vacuum formed against the oiled plug. The dimensions between dots are given in Table 11, along with the data graphically illustrated in Figure 18.

Table 11 Comparison of Dots Prepositioned at ½ inch Marks On 20-mil FPVC Sheet Prior to Stretching Clean Glass, Oil on Glass, Oil on Sheet
Position from Apex, in Distances between Dots
Clean Glass Oil on Sheet Oil on Glass
0.5 0.5 0.5 0.51
0.5 0.5 0.5 0.51
1.0 0.68 0.60 0.62
1.5 0.72 0.72 0.69
2.0 0.72 0.72 0.72
2.5 0.80 0.70 0.70
3.0 0.60 0.55 0.60

Then the glass plug was thoroughly cleaned with isopropyl alcohol and the portion of the sheet that would contact the plug surface was coated with vegetable oil. The oiled sheet was heated to 265oF and vacuum formed against pristine plug. The dimensions between dots are also given in Table 11. Figure 18 now shows the data of Table 11.

Comparison of dot spacing for FPVC sheet stretched over wood and glass plugs, including data for oil interface between glass and FPVC sheet

Figure 18. Comparison of dot spacing for FPVC sheet stretched over wood and glass plugs, including data for oil interface between glass and FPVC sheet

We believe it can be argued that there is little difference in the curves of Figure 18 (within experimental accuracy). These data also support our contention that the local grease dots used as markers in earlier studies did not alter the measured values by affecting the local interfacial conditions.

Plug-Sheet Interfacial Dynamics

In our presentation at the SPE Thermoforming Conference in 2004, we reviewed the various types of frictional coefficients. They include:

  • Static frictional coefficient – Initiation of sliding between plug (and mold wall) and sheet
  • Sliding frictional coefficient – Continuation of sliding between plug (and mold wall) and sheet
  • Dry v. wet sliding
    We detailed more than one type of wet sliding, including boundary lubrication – low sliding velocity, low interfacial viscosity, high loading – and hydraulic or hydrodynamic lubrication – high sliding velocity, high viscosity, low loading, as shown in Figure 19.

Characteristic types of wet sliding.

Figure 19. Characteristic types of wet sliding.

From some rudimentary experiments, we concluded that the nature of the dry plug surface did not substantially affect the amount of force needed to stretch the membrane and that it appeared that from simple measurements, the sheet adhered to rather than slid on the dry plug.

From similar experiments, with liquid layers on the plug, we concluded that when an oil layer existed between the sheet and the plug, the amount of force needed to stretch the sheet was the same as if the plug were dry. In this set of experiments, we conclude that the extent of stretching is also essentially unchanged by the nature of the interface (wet v. dry).

It appears to us that the currently accepted sheet-stretched-by-plug mechanism that relies on a coefficient of friction is wrong. If the sheet slid on a wet surface and did not on a dry surface, we would see substantial difference in the sheet dimensions in Figure 18 and in the required forces, as displayed in the 2004 Conference presentation. We do not. We believe that there is no evidence that the sheet ever slides on the plug.

Conclusions

We combine the observations of Parts 1, 2, and 3 to draw the following conclusions.

  • We used a rough-surfaced wood plug and a smooth-surfaced glass plug. We found relatively little difference in the nature of sheet stretching over the plug. Therefore, we conclude that neither the nature of the plug (wood v. glass) nor the surface roughness (rough v. smooth) influences the way in which the sheet forms over the plug.
  • We observed grease dot deformation by vacuum forming both rubber and plastic sheets. The grease dots away from the apex of the plug appeared to be deformed down the plug surface. We conclude that the shapes of the deformed grease dots indicate squeezing between the sheet and the plug rather than the sheet sliding against the plug.
  • We altered the interface between the sheet and the glass plug by applying a thin layer of oil to one surface or the other. We found no appreciable change in the way the sheet formed over the plug.
  • In essence, we were unable to devise an experiment where we observed an effect different from the other experiments. We conclude from our experiments that the sheet does not slide against the plug.

In our presentation at the SPE Thermoforming Conference 2004, we quoted the following:

The relation that the power required to move a body bears to the weight or pressure on the body is known as the coefficient of friction.

W.M. Davis, Friction and Lubrication, A Handbook For Engineers, Mechanics, Superintendents and Managers, The Lubrication Publishing Co., Pittsburgh PA, 1903.

And we asked the question:

In plug-assist thermoforming, what is sliding against what?

If the sheet does not slide against the plug, then, by definition, there cannot be a coefficient of friction, regardless of which definition is used.

Part 4 will discuss alternative mechanisms that may affect the way in which a sheet is stretched against a plug.

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