A plasticating model for single-screw extruders

By measuring the solid-bed transfer velocity, width and thickness under various conditions, die following results are obtained. As the result of melting, the solid bed decreases in width and thickness almost with the same rate, and the solid-bed transfer velocity is constant, while a melt layer exists between the solid bed and the screw root; also, when the phenomenon of dam-up occurs, caused by the combined effect of decreasing depth of the screw channel with tin insufficient decrease of solid-bed thickness, the transfer velocity increases proportional to the rate of decrease of channel depth. Consequently, the solid bed is considered to behave us loosely packed particles. A new plasticating model is developed by making the above results an assumption and adopting finite differential calculus with the Newton-Raphson method to obtain accurately the melting velocity, melt profile, and solid-bed temperature. Calculated values are in remarkably good agreement with the experimental values Solid-bed softening point, pressure, and screw torque are also successfully estimated.     

Fundamentals of plasticating extrusion. I. A theoretical model for melting

A steady state model for melting in a screw extruder has been developed based on the assumption that a stable solid bed of polymer granules is melted by heat that is conducted from a hot barrel and heat that is generated by viscous dissipation in the film that separates the solid bed and the surface of the barrel. The solid bed gradually decreases in width, as it proceeds in the channel, until it disappears at which point the melting is terminated. The model predicts the solid bed width profile and the required length of melting in terms of physical properties, operating conditions, and geometry of the screw. The model has been tested based on experimental data.     

Pressure profiles in plasticating extruders

The pressure distribution through the melting and melt zones of a plasticating extruder is discussed, and an analysis is described for predicting the pressure profile. In the stable melting zone, the pressure profile is calculated based on flow in the melt pool, and the pressure is strongly influenced by the flow of the solid bed of plastic. The solid bed flow is primarily determined by the polymer rigidity in the screw compression section. If the size (through a melting analysis) and the velocity (through a solid bed acceleration parameter) of the solid bed along the screw channel are reasonably approximated, the pressure profile is reasonably approximated by this analysis. Inaccurate representations of the size or velocity of the solid bed can yield inaccurate pressure profile prediction. In the unstable melting region, the assumption of a complete melt yields reasonable pressure predictions. The introduction of these concepts into an extrusion model permits a more accurate prediction of the operating RPM of a given screw design in a given machine.     

The effect of design and operating conditions on melting in plasticating extruders

A previously proposed but further modified theoretical model for melting in plasticating extruders, in the form of a computer program, which predicts the amount of unmelted polymer at any point in the extruder, was used to simulate the effect of geometrical and operating variables on the melting performance of the extruder. The results indicate in increasing screw length required to complete melting with increasing throughput and a decreasing length of melting with increasing frequency of screw rotation. They further indicate the existence of an optimum barrel temperature for a maximum rate of melting, an optimum number of threads for a maximum melting rate, and a significant decrease in the rate of melting with increasing flight clearance. The effect of other geometrical variables and of operating conditions on the rate of melting and power consumption are also discussed.     

A critical review of dynamic modeling and control of plasticating extruders

This is a critical review of the recent literature on plasticating extruder dynamic modeling and control, The papers reviewed are divided into three categories: extruder disturbance studies, classical control and modeling studies, and stochastic control studies. It was found that most researchers have concentrated on modeling the long-term disturbances associated with the extruder melt temperature, melt pressure or extrudate thickness. The control problem for these variables has been treated to a much lesser extent. The difficult to control and industrially important high frequency disturbances have been, in the most part, neglected. Recommendations are made for the future direction of research into extruder control.     

A mathematical model of the melting of polymeric materials in extruders

Conclusions The contemporary state of the theory of melting of polymeric materials in plasticizing extruders has been discussed.A new, more refined theory of melting in the screw channel has been presented, based on solution of the fundamental equations of motion, energy transfer, heat conductance, and state.Translated from Khimicheskie Volokna, No. 3, pp. 51–53, May–June, 1984.     

A theoretical melting model for a reciprocating-screw injection molding machine

A theoretical model for the transient melting behavior in a reciprocating-screw injection molding machine is proposed. The model is based on a steady state extrusion model, Neumann's melting problem, and a heuristic postulate for the transient behavior. The model predictions are compared to experimental melting data for low density polyethylene, acrylonitrile-butadiene-styrene polymers and polyvinyl chloride for a variety of operating conditions and two screw designs. A useful degree of correlation is demonstrated for all experimental cases.     

Predicting the effect of screw wear on the performance of plasticating extruders

The effect of screw wear on the performance of a 2.5 in. diameter extruder is studied with the aid of computer simulations. The effect of progressively increasing flight clearance on the extrusion of low density polyethylene, polypropylene and nylon 6/6 is presented. The remedial effect of increased screw speed and its side effects on melting behavior, solids content, extrudate temperature and power consumption are also described.     

The melting performance of single screw extruders

A number of recent screw designs is analyzed for melting performance, using a simple analytical approach based on Tadmor's original work. The melting length for a screw with constant depth channel is used as reference. An ideal compression screw will have a melting length of one-half the melting length of the reference screw. The Maillefer melt separation principle is discussed. The Maillefer screw melts in 2/3 of the length of the reference screw. Screws by Barr, by Dray and Lawrence and by Kim are shown to approach the ideal compression screw. A new design screw, using ideal compression and multiple channels and having a very large screw pitch, is shown to be a considerably more efficient melting device than any of the other, screws discussed.     

Plastification or melting: A critical process for free radical grafting in screw extruders

This paper shows for the first time that when a monomer is to be grafted onto a polymer backbone by a free radical mechanism in a twin screw extruder, the grafting process occurs mainly, if not exclusively, in the plastification (melting) zone. For this purpose, the free radical grafting of glycidyl methacrylate (GMA) onto polypropylene (PP) and polyethylene (PE) was chosen as model systems. A co-rotating self-wiping twin screw extruder of type Werner Pfleiderer ZSK-30 (L = 42D) was used to process the grafting. Owing to its modular character in terms of barrel arrangement, screw element combination and barrel temperature, the position and length of the plastification zone can be adjusted virtually at will. This allowed us to follow up the grafting not only at the die exit, but also in the plastification zone under different grafting conditions. Our results clearly show that it is in the plastification (melting) zone that the entire grafting process occurs. This length is usually very short in a co-rotating twin screw extruder like ours. Under the grafting conditions, it varied from 1D to 5D. Thus, any relevant analysis or model of a free radical grafting process carried out in a screw extruder must be based on detailed information generated not only at the die exit, but also and most importantly in the plastification zone. Otherwise, it may lead to incomplete and/or wrong conclusions.     

The simulation of the plasticating screw extrusion process with a computer programmed theoretical model

A fundamental mathematical model of the plasticating extruder was assembled by combining a previously reported melting model with an improved melt pumping model. The validity of the model was tested with numerous experiments on 2 1/2 in. and 8 in. diameter extruders. The experiments were performed with low and high density polyethylene, plasticized polyvinyl chloride, rigid polyvinyl chloride powder, polypropylene, ABS and nylon 66. The mathematical model proved to be excellent in predicting pressure and plastic temperature profiles in the extruder channel, temperature fluctuation, solids content, and power consumption.     

Theoretical analysis of residence time distribution functions and strain distribution functions in plasticating screw extruders

The residence time distribution (RTD) function in a single screw plasticating extruder was theoretically calculated. The calculation is based on the solids conveying, melting, and melt conveying models in extruders. The screw channel is divided into small axial increments and the path of each exiting fluid particle is followed from hopper to die. In addition to the residence times the total shear deformation or strain imposed on the fluid particles was also calculated. This together with the RTD function has led to the definition and calculation of the strain distribution function (SDF). This function is proposed for quantitative characterization of the mixing performance of screw extruders as well as other laminar mixers. Some simple idealized batch and continuous laminar mixers are analyzed in terms of the SDF. Finally, the effect of extruder operating conditions and screw design on the RTD and SDF were investigated by computer simulations.     

Analysis of the performance of plasticating single-screw extruders with a new concept of solid-bed deformation

The performance of plasticating single-screw extruders is analyzed by combining three functional sections: (a) solids-conveying section, (b) melting section, and (c) melt-conveying section. In the analysis of the melting section, we have incorporated a new concept of solid-bed deformation (i.e., the rheology of the solid bed) into Lindt-Elbirli's analysis and included convective heat transfer in the energy equation. Specifically, we have computed stresses on the surfaces of the solid bed, which is surrounded by thin melt films and a melt pool, and, also, computed the apparent modulus of the solid bed in the bulk state as a function of temperature and position within the solid bed, along the extruder axis. From this information, we were able to compute the extent of solid-bed deformation, by assuming a linear stress-strain relationship as the constitutive equation of the solid bed. In this approach, we do not assume a priori whether the solid bed is rigid or freely deformable. The solution of the system equations gives us the following information: (a) whether or not the solid bed deforms and if it does, then, how much; (b) the solid-bed velocity along the extruder axis; (c) pressure profiles along the extruder axis; (d) solid-bed profiles in the melting zone along the extruder axis; (e) temperature profiles along the extruder axis; (f) velocity and temperature distributions in the melt pool along the extruder axis; and (g) thicknesses of thin melt films surrounding the solid bed. Theoretically predicted solid bed and pressure profiles along the extruder axis are compared with experimental results reported in the literature. We have pointed out an urgent need for measurements of the apparent modulus of the solid bed in the bulk state as a function of temperature and pressure, under a combined shear/drag flow field.     

A mathematical model for predicting dynamic behavior of a plasticating extruder

A mathematical model was developed to predict the dynamic behavior of flowrate and melt temperature in a plasticating extruder caused by changes in operating variables such as screw speed, back pressure and barrel temperature. The model has application for on-line computer control of an extrusion process or for simulation purposes off-line. Experimental data for developing the model was obtained from a 2½ in. diameter plasticating extruder producing high impact polystyrene sheet.     

The melting performance of single screw extruders. II

In the previous paper (1) the melting performance of a number of recent screw designs was analyzed, using a rather simple theory. A new screw design was proposed. Here the results of more elaborate calculations, are given in which the influence of the flight clearance and of a shear-thinning temperature dependent viscosity are investigated. The former conclusions are not altered in essence by these effects. Experimental results with a prototype screw are presented, showing that melting capacity is increased. Up to 100 percent increase in throughput is possible in the high RPM range (in comparison with a much longer traditional compression screw), provided that the feed capacity is sufficient. This usually requires the use of a grooved, well-cooled, feed section; the capacity of such a feed section depends, for a given screw geometry, on channel depth and granule dimensions. The melt leaves the melting section at a relatively low temperature. The melting section only melts the material and does not raise, its temperature unnecessarily. A further step towards separating distinct tasks of the extruder by functional screw design has been made.     

Mathematical modeling of melting of polymers in barrier-screw extruders

Some of today's modern screws contain melt-separating secondary (barrier) flights in the transition zone. With increasing utilization of barrier screws, the availability of proper and accurate design methods for the melting zone remains of paramount importance. A modified version of a mathematical model developed by the authors previously is applied to two most common types of barrier screws, viz. —The Mailefer screw (varying pitch and constant depth); —The Barr screw (constant pitch and varying depth). The present analysis provides valuable insight into the operating principles of these screws. A comparative study is presented demonstrating the possible advantages and disadvantages of the Maillefer and Barr screws in relation to conventional compression screws.     

Dynamic model of a plasticating extruder

A theoretical model for the simulation of dynamic operation of a plasticating extruder is proposed. The model can be recommended as a tool to study various dynamic situations of interest in the operation of an extruder. Several responses to changes in operating conditions are discussed. They indicate the occurrence of transient maximas and occasional oscillations. The controlling of flow rate by adjusting a valve at the die seems to cause temporary local high peaks in pressure, whereas its control through screw speed seems to be satisfactory.     

Melting performance of single screw extruders with a grooved melting zone

A novel melting model for single screw extruders with a grooved melting zone was established. The whole solid plug, which came from the grooved feed zone, was ruptured and melted mainly by continuously changing the volume of the barrel grooves and the screw channel in the grooved melting zone. A new single screw extruder platform with hydraulic clamshell barrels was constructed to investigate the melting of solid polymer with different combinations of barrels and screws. The melting model was verified by experiments. The results showed that the melting started earlier and finished in a shorter length for single screw extruders with a grooved melting zone than that for conventional single screw extruders and the melting efficiency was improved by introducing a grooved melting zone to a single screw extruder. The theoretical values are consistent with experimental results. The novel single screw extruder with grooved melting zone can dramatically increase the plasticizing efficiency and the throughput.     

A dynamic melting model for a single-screw extruder

A new theoretical concept is given which provides an efficient and consistent method for predicting flow and heat transfer characteristics of the melting zone for a large single-screw extruder. In contradistinction to previous, theories, significant melt accumulation in the molten films as observed experimentally is considered, instead of postulating the melt accumulation in the “melt pool”. The mathematical model has been obtained by the simultaneous solution of the momentum and energy equation of the melt flow and. solid bed, allowing for the existence of the pressure gradient: The theory is supplemented by a numerical example which shows good agreement with experimental data obtained on a 90 mm extruder with polypropylene, where the down-channel pressure profile and me profile of the solid bed Were taken as yardsticks for the melting process. For exact determination of the area for applicability of this theory, more experimental information is required.