being supplied to the drive, and figures are available on the efficiencies of various drives. The power delivered to the melt can be calculated. The material manufacturer should be able to furnish data on heat capacity. From the delivery, then, the rise in temperature, T i - TO, can be computed. But these two temperatures can easily be measured. If the calculated rise is divided by the observed, the result is the fraction of the total heat that is being mechanically generated. If the screw were being cooled, an adjustment of the observed rise would have to be made. Mallouk and XcKelvey ( 3 )showed that the power required by a melt screw is roughly proportional to the second power of the speed. The output, on the other hand, increases almost in direct proportion to the speed. The mechanical input of heat per pound put through can, therefore, be raised by running a t higher speed. To illustrate this point, consider a screw turning a t 30 r.p.m. in which half the heat is being supplied by the screw’s motion and half by transfer through the barrel. If the speed is raised to 60 r.p.m., the power consumption is quadrupled, while the output is only doubled, approximately. The mechanical input of heat per pound of product delivered is therefore doubled, and no heat need be transferred. It should be remembered that the torque required and therefore the shear stress in the shaft also increase proportionally with speed. Adjustment of the power to throughput ratio may also be made by alterations in the die screv dimensions.
SUMMARY
To sum up, formulas have been developed relating the perforrnance characteristics of geometrically similar melt extruders, and these probably apply to plasticizing extruders too. The formulas make it possible, before investing in a large extruder, to test the design cheaply on a small scale model. I n designing plasticining extruders, more consideration should be given the possibilities of using the drive motor, rather than barrel heaters, as the chief source of heat to the polymer. LITERATURE CITED
(1) Carley,
J. F., Mallouk, R. S., and LIcKelvey, J. b4 , IXD.ENG.
CHEY.,45, 974 (1953). (2) Carley, J. F., and Strub, R. A , Ibid., 45, 970 (1953). (3) Mallouk, R. S., and McKelvey, J. M., Ibid., 45, 987 (1953). (4) Simonds, H. R., Weith, -4. J., and Schack, TV., “Extrusion of‘ Plastics, Rubber and hIetals,” New York, Reinhold Publishing Corp., 1952. (5) Strub, R. A , , Proceedings of the Second Midwestern Conference on Fluid Mechanics, Ohio State L-niversity, March 17-19, 1952. RECEIVEDfor review October 2 1 , 1952.
ACCEPTED3Iaicii 6 , 1953.
Future Extrusion Studies T h e earlier papers of this symposium have used the literature of extrusion where possible and developed some new ideas where required, in order to form an understanding of the basic theory of extrusion. Although this development is based on an idealized case, it has been shown by examples that these principles can be put to practical use in the design of extruders to handle melts (or any viscous fluid) and to predict the performance of large extruders from tests of models. An additionaI and equalIy important effect of an understanding of extrusion theory is to permit more efficient operation of extruders by substituting rational thinking for the trial and error procedures frequently used. C . H. JEPSON Polychemicals Department, E. I . d u Pont de Nemours & Co., Inc., Wilmington, Del.
A
LTHOUGH a good beginning toward a complete understanding of the extrusion process has been made, there are many problems that have been considered only superficially and others that are totally unexplored. Several important problems requiring further theoretical and experimental work are:
1. Heat transfer 2 . Movement of solids in the feed section of the screw 3. Movement of solids just before and during- the initial stages of melting 4. The behavior of molten polymers under high shear stresses for short periods of time.
Not much work has been done to determine the way in which heat is transferred from the barrel wall to the polymer in the flight. The following approach to this problem is suggested to illustrate the need for certain rheological data for polymer melts that we do not have at this time. Using flow concepts developed in the earlier papers, it can be seen that the transverse component of the flow causes a continuous movement of the polymer from a position near the barrel wall to a position near the root of the thread. This motion, coupled with the movement in the direction of the helix, should result in substantial mixing of the layer nest to the mall with the bulk of the polymer. Thus, for a single-flighted screw, the wall is wiped clean (except for polymer in the clearance) a t each revolution of the screw. The layer of polymer contacting the
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wall after the screw flight passes should be at the bulk tcmperature of the polymer in the flight. The problem is then one of heat transfer in the unsteady state, in which the time interval iE that required for one revolution of the screw. If the assumption is made that the heat generated in the clearance is small relative to the heat transferred and if the stagnant film in the clearance is thin enough to be considered a thermal resistance without appreciable heat capacity, the temperature gradient from the wall can be calculated by the method of Gurney and Lurk [IND. ENG.CHEW, 15, 1170 (1923)l. In the usual case, the time interval is so short that the polymer in the channel can be treatcd as if it were a slab of infinite thickness. The thermal situation can be visualized most clearly by taking a practical example for discussion. Figure 1 illustrates the case of a polymer at a bulk temperature of 300” F. being handled in an extruder with a wall temperature of 400” F. Immediately after the flight has swept a given point on the barrel, the thermal situation can be likened to that when a heated metal wall a t 400” F. is suddenly placed against a mass of polymer a t a uniform temperature of 300’ F. At the first instant in time, the temperature profile is that shown by profile to. At later times this profile changes as shown in tl and tz. Each time a flight wipes the wall, the heated layer is mixed with the bulk of the polymer and the process is repeated. Thus, any small area under the curve just before the nest sweep represents a volume of polymer heated to a definite
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Extrnsion temperature. Knowing the density and specific heat of the polymer, the amount of heat transferred per revolution of the screw can be calculated by graphically integrating the temperature distance profile. By carrying out these integrations over a range of conditions, the effect of design variables on over-all coefficients of heat transfer can be calculated. Whefi these calculations are carried out for molten polythene in a screw
truders of large capacity. The general thinking in the trade has always been that one must supply a large amount of heat by conduction from the barrel wall and accept the heat that comes from mechanical working as an added, but not planned or designed advantage. Thus if one looks a t the approximate capacities (and motor power supplied) for some commercial extruders one will find that they increase almost exactly as the second power of the diameter. This scale-up, based on the square of the diameter, does result in a constant ratio of throughput to heat transfer area as shown in Figure 3. The lines are drawn with a slope of exactly two, and fit the data very well.
DRIVE
NOMINAL
POWER
DELIVERY RATE
SUPPLIED
100
(HP)
(LBS / HR)
TO 50 40
Figure 1. Temperature Profiles vs. Time after Sweep of Flight Across Barrel
extruder, the calculated wall t o polymer heat transfer coefficient, h[B.t.u./(hr.)(sq. ft.)( O F,)], varies from about 20 to 150 depending on operating conditions. Figure 2 summarizes the results of these calculations in graphical form. According to this analysis, increased heat transfer can be obtained by decreasing clearance, increasing screw speed, and increasing the number of flights on the screw. Where operating conditions were .such that heat generation in the clearance could be neglected, over-all coefficients calculated in this manner are in good agreement with experimental measurements.
(RPM)(NUMBER OF FLIOHTS)
Figure 2. 1
Film Coefficient vs. Sweeps per Minute at Barrel
One of the major reasons for discussing heat transfer in some detail is to point out that there are many instances where heat generation in the clearance is so great that it cannot be neglected. Here the problem could be solved with relative ease if the effect of temperature, time, and shear rate on shear stress were known for the polymer in question. With these rheological data, more accurate and more general calculations of power consumption and heat transfer in extruders should be possible. Another interesting problem is that of designing small ex-
30 20 DIAMETER OF SCREW I
Figure 3.
2
3
4
5
7
10 IO
Output and Drive Horsepower of Commercial Extruders
Although it appears that present extruders are designed on the basis of heat transfer considerations, it would be a mistake to draw the conclusion that the polymer actually gets more heat by transfer than by conversion of mechanical work into heat. Again looking a t Figure 3, if these commercial extruders are operating a t their rated capacities and are using about three fourths of the available power, about 10 pounds output can be expected for each hp.-hour expended. This amount of, work represents a heat input of 250 B.t.u./pound of polymer-well over half the total heat input required in most extrusion operations. Thus we conclude that in normal operation more heat is supplied to the polymer by conversion of mechanical work into heat than by transfer of heat from the barrel wall. Recognition of the importance of conversion of mechanical work into heat makes one wonder if extruders could be designed t o do 4ll the heating by mechanical working, thus removing the necessity t o go to large sizes and large heat transfer areas in order to get large capacities, The operation of the model extruder described earlier in this symposium showed that operation without heat transfer is perfectly feasible. SUMMARY
In this symposium we have tried t o survey the literature of extrusion, discuss some theoretical and experimental work that we have done, and indicate some interesting work that remains to be done in this field. We expect to continue our work aimed a t a complete understanding of the extrusion process, and we hope that we have been able to interest others in the problems of extrusion. If a number of people become interested in the mechanism of extrusion, the time will not be long before people will speak of extrusion as science rather than art. RECEIVED for review October 21, 1952.
ACCEPTED March 6, 1953.
End of Symposium Reprints of this symposium may be purchased for 50 cents each from the Reprint Department, American Chemical Society, 1155 Sixteenth St., N.W., Washington 6, D. C.
May 1953
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