Theory of J
Extrusion A symposium presented b y members of the Polychemicals Department of E. I . d u Pont de Nemours & Co. bef o r e the Division of Paint, Varnish,
and Plastics Chemistry a t the 122nd Meeting of the American Chemical Society, Atlantic City, N . J .
BASIC CONCEPTS OF EXTRUSION J. F. Carley and R. A. Strub
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SIMPLIFIED FLOW THEORY FOR SCREW EXTRUDERS J. F. Carley, R. S. Mallouk, and J. M. McKelvey.
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970
974
APPLICATION OF THEORY TO DESIGN OF SCREW EXTRUDERS J. F. Carley and R. A. Strub 978
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During the past several years extrusion has become an increasingly important operation in the plastics industry. Today an enormous growth is taking place in this field, both in the amount and type of plastics which are extruded and in the number of extrusion machines which are in operation. The basic principles of the extrusion process are, however, little known, and a wide diversity of opinion is held regarding the design and operation of extruders. A few articles have appeared in the past which have presented some of the fundamentals of an extrusion theory. However, most of these articles appeared in scientific and technical journals of limited circulation and most of them seem to have gone relatively unnoticed. Consequently, extrusion today is more of an art than a science and most
EXPERIMENTAL STUDIES OF MELT EXTRUSION J. M. McKelvey.
982
POWER R E Q U I m M E N T S OF MELT EXTRUDERS R. S. Malloukand J. M. McKelvey
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987
EXTRUDER SCALE-UP THEORY AND EXPERIMENTS J. F. Carley and J. M. McKelvey
989
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.......... FUTURE EXTRUSION STUDIES C. H. Jepson . . . . . . . . . . . . . . . . . . .
992
of the extruders that have been built have been designed on the basis of practical experience and by trial and error. Difficulties have arisen when extruders had to be designed for new plastics and when larger capacity extruders had to be designed on the basis of the performance of small extruders. Also, i t is our opinion that many extruders that are today operating “successfully” are producing a t rates far below their ultimate capacity. The purpose of this symposium is to outline the fundamental theory of plastics extrusion, as far as i t is now known, and to show how it is used in design. Many of the concepts and equations which are presented apply strictly to certain idealized conditions. However, experimental yesults 80 far show that these equations describe fairly
well the behavior of real extruders. Just as the ideal gas laws serve in the study of real gases, so do these equations serve i n extrusion. The quantitative description given in these papers of the flow behavior of plastics melts in the channels of extruder screws does not necessarily apply directly to the rear portion of a n extruder where the plastic enters the screw channel as small solid particles. Attempts to describe the motion of these solid particles have been only partially successful to date. In general, i t appears that if the solid particles are small relative to the depth of the screw threads-i.e., particle diameter 1/4 thread depth-r if for some other reason the frictional coefficient of the material against the extruder casing is small in comparison to the shear resistance of the layer of plastic particles in the screw channel, shearing does not occur in the layer and very different mechanisms may be operating. In some cases the material rides the
screw and does not progress down the screw thread channel, In other designs a material may ride the extruder cylinder walls and progress down the channel a t the extremely high rate of one thread turn per revolution of the screw. The well known trick of threading both the cylinder and screw a t the rear of an extruder ensures t h a t the solid material will be sheared and hence progress down the threaded channeIs. The papers that follow relate to conditions after the plastic has softened, and the operation is then described as “melt extrusion.’’ The combined operation of melting and extruding is called “plasticating extrusion.” In successful screw designs for plasticating extrusion, the capacity a t the rear of the screw is equal to or greater than the capacity of the melt extrusion or forward part of the screw. In these extruders the melt extrusion part of the operation controls the output and the pressure generated. Therefore the melt extrusion flow theory enables one to calculate with considerable reliability the pressure and output characteristics of any extruder.
W. L. Gore
Basic Concepts of Extrusion T h e growing interest in extrusion of plastics stimulated an investigation of the literature of this subject. The basic notions of the behavior of viscous liquids in screw extruders are presented. The historical development of the work leading up to this symposium is briefly surveyed, and the principal findings are presented. The foundation for the development presented in the succeeding papers (2, 5 ) was laid by Newton, Poiseuille, and others. As early as 1922 Rowell and Finlayson (13) had derived equations of flow for screw pumps. J. F. CARLEY
AND
R. A . STRUB’
Polychernicals Department, E. I . d u Pont de Nemours & Co., Inc., Wilmington,Del.
I
N T H E last century a great deal of fundamental work has been done on the laminar flow of viscous liquids. This m-ork has laid the foundation for the present theory of extrusion, and it is reviewed in this paper. It was recognized very early that a moving plate separated from a fixed plate by a viscous liquid will drag along with it a certain amount of fluid. Nen ton first postulated that the shear stress, 7, b e h e e n tv,o adjacent layers in relative motion is proportional to the velocity gradient or rate of shear, d s / d y . r =
pds/dy
(1)
A liquid whose flow behavior satisfies this equation is said t o be Sewtonian, and the constant of proportionality, p, is called the viscosity coefficient or simply the viscosity of the liquid. It has long been knonn that the viscosities of liquids are inversely related to temperature. I t is only relatively recently that we have found that for many liquids the quantity, p, is not constant but depends on the shear rate or shear stress. I n some liquids, the value of p is related also t o the length of time for which the liquid has been exposed to the stress. Molten plastics are the liquids usually dealt with in extrusion and many of these are non-Nevtonian. I n a surprisingly large fraction of practical cases, however, it has been found that the flow relations established for I
Present address, % Sulzer Bros., Winterthur, Svvitzeiland.
970
Semtonian fluids can still be used providing a suitable “apparent” viscosity is introduced. .4n extruder consists of a threaded shaft or screw rotating in a fixed cylinder or barrel, plus a feed port and a die. The screxchannel is constantly changing its position relative to the barrel, and the advance of the liquid through the barrel of the extruder follows a helical path which is a mirror image of the helix on the screw. This situation is rather difficult t o visualize. The end results mould be the same if the screw were held stationary and the barrel rotated in the direction opposite to the actual rotation of the screm, since the relative velocities of screw and barrel are unaltered. But in this case, the liquid moves along the helical path defined by the screw channel. Because the channel walls are attached t o the screw, it is far easier t o visualize and discuss the situation in which the barrel rotates. For this reason, the ?crew is taken as the frame of reference throughout this symposium. The upper picture in the first figure represents a portion of a n extruder. The speed of rotation of the barrel, U,is resolved into two components, T and V,perpendicular to the direction of the screw thread and parallel to it, respectively. The flow pattern within the channel cross section is a combination of four types of flow. The first is the drag flow, QD, in the direction of the axis of the channel created by the velocity com-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 5
