Coefficients of dynamic friction as a function of temperature, pressure, and velocity for several polyethylene resins.
In a plasticating extruder, the coefficient of dynamic friction is in many cases the controlling factor for solids conveying, pressure generation, thermal decomposition of the resin, and flow surging at the die. The coefficient of friction is, however, very poorly understood and very difficult to measure. Moreover, interpretation of experimental data are complicated by the dissipation of frictional energy at the sliding interface. This energy flux at the interface makes it extremely difficult to determine the coefficient as a function of temperature, pressure, and velocity at conditions of extrusion.
A new friction-measuring device has been designed and fabricated based on a first generation machine built at Rensselaer Polytechnic Institute by C. I. Chung (1,2). The unit is capable of studying the forces, resulting from frictional and viscous drag, on a small slab of polymer at conditions typical of extrusion. With this equipment and a numerical technique for computing the interface temperature (3), the coefficient can be measured as a function of temperature, pressure, and velocity.
The accepted solids conveying mechanism for the feed section is based on the theory developed by Darnell and Mol (4). The basic theory assumes constant density for the solid bed and constant coefficients of dynamic friction for both the barrel and screw root surfaces in order to estimate solids conveying and power consumption. More sophisticated forms of the theory (5) use bulk density as a function of pressure and temperature (6) and coefficients of friction as a function of pressure, temperature, and velocity (3). Frictional coefficients at conditions typical of extrusion, however, are generally not available because of the difficulty in measuring them and the lack of precise measuring devices.
Several types of friction coefficients are commonly measured. They include coefficients of dynamic (3), static, and storage friction (6). Each coefficient is used for different applications, and they must not be interchanged. The coefficient of static friction is the ratio of the frictional force on a body divided by the load force perpendicular to the frictional surface at static equilibrium. If the frictional force is increased by a differential amount, then the body will start to move. If the body is moving, the ratio of the frictional force to the load force is the coefficient of dynamic friction. This coefficient is typically lower than that for the static case. The dynamic coefficient is the type of coefficient of interest to extrusion. It will be referred to in this paper as the coefficient of dynamic friction or simply coefficient of friction. Storage friction describes how pressure is transmitted or dissipated in a confined column of particles; it is a combination of friction between particles and friction between the particles and the chamber wall.
All friction measuring devices measure the temperature at a location away from the interface where the sliding is occurring. At the sliding interface, frictional dissipation of energy will result in temperatures at the interface that are considerably higher than those temperatures measured. This effect can be quite large at conditions typical of extrusion. Frictional heat dissipation at the interface is directly proportional to pressure, coefficient of friction, and the velocity (3).
Six different commercial grade polyethylene (PE) resins were used for this study. The resins studied had varying solid densities and were as follows: 1) ultra low-density PE (ULDPE) with a density of 0.912 g/[cm.sup.3], 2) linear low-density PE (LLDPE), density of 0.920 g/[cm.sup.3], 3) low-density PE (LDPE), density of 0.922 g/[cm.sup.3], 4) LLDPE with a density of 0.935 g/[cm.sup.3], 5) high-density PE (HDPE), density of 0.9495 g/[cm.sup.3], and 6) HDPE resin with a density of 0.951 g/[cm.sup.3]. All resins were manufactured by The Dow Chemical Company and were in the form of spheroid-shaped pellets with an average diameter of about 4 mm. The HDPE resin with a density of 0.9495 g/[cm.sup.3] was designed for grooved-barrel extruders. All other resins were designed for smooth-barrel extruders.
The device used to measure the coefficient of friction was described in a previous paper (3), and a schematic of the instrument is shown in Fig. 1. PE pellets were placed in a 12.9 [cm.sup.2] (5.08 x 2.54 cm) sample chamber positioned above a 30.48 cm diameter rotating roll. The force applied to the pellets by a plunger was set by the operator and was also measured by a load cell. In order to keep the roll speed constant, a torque was applied to the roll shaft. This torque was measured by a sensor and the value was used to calculate the coefficient of friction. The coefficient is defined as the frictional force at the roll surface (obtained from the torque measurement) divided by the applied load. Calculation of the coefficient was defined previously (3). All instrument sensors and devices were controlled and monitored using a CAMILE data acquisition and control system (3, 7, 8). (Camile is a trademark of The Dow Chemical Company.)
The surface treatment of the roll with the resin will affect the coefficient of friction. For these experiments, the roll was first cleaned to a shiny finish. Next, the test resin was added to the chamber and a trial experiment was performed. This experiment was used to condition the roll only and thus the frictional data were discarded. The sample was then removed and replaced with fresh resin. Numerous trial experiments were performed before the frictional measurements were collected. Coefficients measured during the trial experiments tended to decrease slightly with consecutive measurements. Trial experiments were continued until several experiments showed no trends with replicate measurements.
The roll surface temperature underneath the polymer sample is not practical to measure, but it can be calculated based on the experimental data and steady-state, two-dimensional heat transfer equations derived and solved for the equipment geometry using an implicit finite difference technique (3). This technique was verified experimentally using acrylonitrile-butadiene-styrene polymer (ABS). Without the calculation of the interface temperature, the effects of pressure, temperature, and velocity on the coefficient cannot be separated. The calculated interface temperature will be referred to as simply the temperature in the remainder of the paper.
COEFFICIENTS OF DYNAMIC FRICTION
The coefficients of dynamic friction for the PE resins were measured as a function of temperature at pressures of 0.69, 3.45, and 6.9 MPa and at roll velocities of 7.6, 15.2, and 30.5 cm/s. The coefficients and trend curves are shown by Figs. 2 through 19. The curves fitted to the data on these Figures are only meant to aid in the identification of the trends. As indicated by these Figures, the coefficients of dynamic friction are complicated functions of temperature, pressure, velocity, and resin type.
For all resins, the coefficient of friction increased with increasing velocity. This increase with velocity was the largest for the ULDPE, LLDPE, and LDPE resins. The coefficients for the HDPE resins did not increase with increasing velocity to the same extent. This increase in the coefficients with increasing velocity is very beneficial to stable solids conveying in an extruder. This topic will be discussed in detail later.
The coefficients of friction decreased with increasing pressure for all resins. Like the effect of velocity on the coefficient, the ULDPE, LLDPE, and LDPE resins showed stronger dependencies with pressure as compared with the HDPE resins.
The coefficients depended on temperature for all resins. The effect of temperature was consistent for all resins at high pressure. At a pressure of 6.9 MPa, the coefficients for the resins decreased nearly linearly with increasing temperature. The coefficient for the ULDPE did, however, increase slightly with increasing temperature at temperatures above about 115 [degrees] C, and the coefficient for the HDPE resin with a density of 0.9510 g/[cm.sup.3] increased slightly with increasing temperature in the range of 30 to 60 [degrees] C. At a pressure of 3.45 MPa, the effect of temperature for the resins was mixed. For example, the coefficients for the ULDPE, LLDPE, and LDPE resins decreased with increasing temperature, and the coefficients for the HDPE resins increased with increasing temperature up to about 80 [degrees] C and then decreased with increasing temperature. At a pressure of 0.69 MPa, the coefficients for the ULDPE have minimum values for the temperature range, LLDPE with a density of 0.935 g/[cm.sup.3] and LDPE (velocity dependent) have maximum values for the temperature range, and the HDPE resins increased with increasing temperature.
Relationships between polymer structures and the coefficients of friction are possible, but they are beyond the scope of this paper. The frictional data as it relates to solids conveying in plasticating extruders is discussed next.
Relations to Solids Conveying
Solids conveying depends on the frictional forces exerted on a differential slab of solids in the feed channel (4). In general, the force acting on the slab at the barrel-solids interface (force acting in the direction of flow) must be greater than that at the screw root-solids interface (force acting opposite to the flow direction). For this condition, pressure will increase in the feed channel. If the force at the barrel interface is only slightly greater than that at the screw root, then the solids will convey but at reduced rates. If the force at the screw root interface is greater than that at the barrel, then the solids must convey via pressure; i.e., a pressure drop will accompany any forwarding of the solid bed. After a very short distance at this condition, however, the pressure will drop to zero and the solids will no longer convey. At this point the frictional force will change because the pressure has dropped to near zero, and the solids will again convey via frictional forces. The net result is a pulsing polymer flow from the solids conveying section to the transition section, causing unacceptable flow surging in the extruder and at the die. These forces at the interface are directly related to the coefficient of dynamic friction.
If the coefficients were such that the forwarding forces at the barrel interface were always greater than the drag forces at the screw root interface, then the conveying of the solids will always occur. If the coefficient of friction does not show a minimum and/or a maximum in the temperature processing range (excluding end temperatures) and if the coefficient increases with increasing velocity, then the above conditions will be easily satisfied via processing conditions and thus solids conveying will occur. But, if a minimum, maximum, or the coefficient decreases with increasing velocity, then solids conveying can be difficult because there is a possibility for the drag force on the slab at the screw root interface to exceed that at the barrel wall. Rheological forces at the barrel wall also contribute to solids conveying (9). These forces become important when the temperature of the polymer-metal interface temperature approaches or exceeds the melting temperature or the glass transition temperature.
As previously discussed (3), the velocity of the solid bed relative to the metal surfaces is considerably higher at the barrel wall than at the screw root. The coefficients of friction for these resins increase with increasing velocity, and thus for a given pressure and temperature the coefficient will be higher at the barrel interface than at the screw root interface. The increase in the coefficient with velocity is advantageous to solids conveying. The temperatures at the interfaces, however, can be quite different.
The PE friction data are consistent with their relative ease of solids conveying during extrusion. The ULDPE, LLDPE, and LDPE resins under most situations forward well during extrusion, and thus there is no loss of feeding and there are no wide variations in the first extruder zone pressures. Other problems downstream from the solids conveying section may, however, cause flow surging at the die for these resins. The coefficients for these resins are fairly high and vary to a large degree with velocity and pressure. Because of this wide variation, process conditions are easily found where the solids convey well, The HDPE resins, however, have coefficients that are considerably lower than the other PE resins. These lower coefficients and the low levels of variation with velocity, temperature, and pressure in many cases require the extruder system to be optimized to a higher degree as compared with those machines using low-density resins. To increase the rates and maintain stable extrusion, some converters prefer to extrude HDPE resins using grooved-barrel machines, creating a drag force at the barrel surface that is considerably higher than that at the screw root.
The coefficients of dynamic friction for several PE resins were measured as a function of temperature, pressure, and velocity. The data indicated that the coefficients increased with increasing velocity, decreased with increasing pressure, and were complicated functions of temperature.
The authors acknowledge the help of Myron Mauer and Brian Hilton in obtaining some of the raw data, and Prof. C. I. Chung of Rensselaer Polytechnic Institute for his input into the design of the friction measuring instrument.
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3. M. A. Spalding, D. E. Kirkpatrick, and K. S. Hyun, Polym. Eng. Sci., 33, 423 (1993).
4. W. H. Darnell and E. A. J. Mol, SPE J., 12, 20 (1956).
5. S. R. Strand, M. A. Spalding, and K. S. Hyun, Plast. Eng., July 1992, p. 17.
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Received July 8, 1993
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|Author:||Spalding, Mark A.; Hyun, Kun S.|
|Publication:||Polymer Engineering and Science|
|Date:||Apr 15, 1995|
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