Screw horsepower dependence on screw speed and size—theory and experiment

Within a normal operating range of extruders, it has been well established that the output increases nearly proportionally to the screw speed but the screw horsepower increases more than proportionally to the screw speed, making the screw HP difficult to predict. It has been also known in scale-up of extruders that the output may be predicted with reasonable accuracy but the screw HP is difficult to predict. No sound theoretical or empirical method predicting screw HP in a scale-up calculation has been offered heretofore. Since a screw performs solid conveying, melting and pumping (or metering) functions simultaneously, any theoretical analysis of screw HP has to consider all three extrusion theories; solid conveying theory, melting theory and pumping theory. In this paper, semi-theoretical equations for predicting screw HP as a function of screw speed and size are developed. Experiments are conducted to test the utility of these equations and the implications of the experimental results on extrusion theories are discussed.     

On the scale-up of plasticating extruder screws

In the most commonly used scale-up method of plasticating extruder screws, the screw channel depth is increased by the square root of the diameter ratio while the screw RPM is decreased by the square root of the diameter ratio such that the output rate increases proportionally to the square of the diameter ratio. This scale-up method, largely based on the pumping function of the screw, often leads to a higher melt temperature, a higher screw horsepower consumption per unit output rate and an inferior melt quality from the larger diameter screw. Analysis of the common scale-up method reveals that, although the shear rate in the melt is kept constant, the average residence time and the peripheral screw speed are increased for the larger diameter screw. Our recent study on the melting mechanism also reveals that the melting capacity increases less than the pumping capacity. A detailed examination of the common scale-up method in this paper shows that the pumping capacity and the solid conveying capacity increase more than necessary while the melting capacity increases insufficiently.     

单螺杆挤出机熔融机理研究的发展

介绍了国内外单螺杆挤出机熔融机理研究的发展，分析了熔融理论发展历程及所面临的问题，以及现有熔融理论的适用范围，指出在熔融理论研究应用过程中应根据具体问题，合理选择熔融理论模型，并提出动态熔融机理研究的两个研究重点及理论研究思路。     

Scale-up rules for mixing in a non-intermeshing twin-screw extruder

Various scale-up rules and theories have been presented for extrusion, including both single- and twin-screw extruders. Until now, however, most of these theories have concerned fully-filled channels, not only for twin screw extruders of the co-rotating fully intermeshing type (COTSE) or non-intermeshing counter-rotating type (NITSE), but single screw extruders as well. As the demand for distributive mixing and devolatilization devices increases, more and more nonintermeshing twin screw extruders with regions of partially-filled channels are being used. Therefore, developing scale-up rules for such screw extruders is imperative. In this paper, scale-up rules are developed, theoretically and experimentally, by examining the relationship between distributive mixing and important flow parameters. Two partially-filled NITSE's, with screw diameters of 0.8 and 2 inches, have been studied by using a flow visualization technique entailing a dye tracer to study the effects of distributive mixing by varying such parameters as: percentage of drag flow, screw stagger, and screw velocity. Qualitative evaluation of the spread of the dye with the number of screw revolutions was obtained from videotape of the experiments. Factorial experimental design method has been applied for evaluating these results. Finally, new scale-up rules were developed and compared with rules in the literature.     

三螺杆挤出机熔体输送能力的评价

通过三螺杆挤出机模拟机对熔体替代料进行挤出实验,对三角形排列三螺杆挤出机、“一字型”排列三螺杆挤出机及双螺杆挤出机的熔体输送能力进行了系统评价。利用无量纲参数评价体系与传统评价方法,通过控制挤出过程螺杆转速和产量,对三类挤出机的熔体输送段建压能力及挤出能耗水平进行研究,并研究工艺参数对熔体输送能力的影响。实验表明,三角形排列三螺杆挤出机熔体输送能力及能耗水平优于其他类型挤出机,且无量纲参数评价体系具有很高的可靠性和更广泛的适用性,可用于挤出加工设备的选择。     

耦合双槽单螺杆挤出机停留时间研究

提供了一种全新的分析挤出机停留时间的方法。在相同螺杆转速下,耦合双槽单螺杆挤出机物料的停留时间低于传统光滑机筒单螺杆挤出机和螺旋沟槽IKV单螺杆挤出机;耦合双槽单螺杆挤出机可以有效提高挤出机的熔融效率,实现高固体输送产量下的熔融效率与固体输送效率的匹配。     

Maximum pressure developed by solid conveying force in screw extruders

There are two distinct solid conveying theories that can be applied to plasticating screw extruders. One is Darnell and Mol's theory based on a solid-to-solid friction model and the other is Chung's theory based on a viscous shearing model. The two theories predict very different solid conveying performances for a same set of conditions. In this paper, the maximum pressures that can be developed inside plasticating screw extruders by the solid conveying force are calculated using each of the two theories. Comparison of the results may shed some light on the applicability of each theory for a particular extrusion operation.     

普通螺杆和屏障螺杆挤出机的计算机模拟

提出了普通螺杆和屏障螺杆的计算机模拟方法，所用模拟包括：喂料区、固体输送区、熔融区和熔体输送区。在屏障型螺杆中，其固体熔融速率是按Ｔａｄｍｏｒ模型计算出来的，而Ｔａｄｍｏｒ模型的固体床速率是以固体床厚度和宽度的变化为基础的。模拟的数据同试验数据相比，可精确合理以预测出普通型和屏障型螺杆的挤出特性。     

Minimum transport boundaries for pneumatic conveying of powders

For the reliable design of pneumatic conveying systems, an accurate estimation of the minimum transport boundary is of significant importance. This paper presents results from an effort to establish a unified criterion for scaling-up the unstable boundary for the dense-phase pneumatic conveying of powders. An existing method of representing minimum transport criteria (based on superficial air velocity and solids loading) has been found inadequate for accurately predicting the unstable boundary, especially under diameter scale-up conditions. Using the experimental data from twelve different powders conveyed over a wide range of pipe lengths and diameters, a newly validated improved design procedure has been developed in this study using a Froude number based criterion at the entry to the pipe. The physical significance of Froude number in representing the minimum transport boundary is also discussed.     

Analysis and experimental evaluation of twin screw extruders

Twin screw extruders can he classified according to their geometrical configuration. The main distinction is made between intermeshing and nonintermeshing extruders. Another distinguishing characteristic is the sense of rotation. The most important characteristics of the various twin screw extruders are examined, with particular emphasis on the effect of screw geometry on the conveying characteristics. A brief review is given of the state of the art in theoretical analysis of twin screw extruders. Experiments with two lab scale, intermeshing twin screw extruders are described, one co- and one counterrotating. Results are presented on power consumption, residence time distribution, and mixing characteristics of the two extruders. The counterrotating extruder exhibits a narrower residence time distribution and better dispersive mixing capability. The corotating extruder showed a better distributive mixing capability. These results can be explained in terms of the conveying and mixing mechanisms in both extruders. The overall extruder performance seems to be dominated by the effect of the intenneshing region. Any realistic, theoretical analysis of twin screw extruders should be centered around the flow behavior and mixing characteristics of the intermeshing region. The corotating extruder appears to be best suited for melt blending operations, while the counterrotating extruder seems to be preferred in operations where solid fillers have to be dispersed in a polymer matrix.     

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.     

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.     

Scale-Up Study of Dye RB-19 Ozonation in a New Gas-Inducing Reactor

The purpose of this research was to study the scale-up behavior of dye RB-19 ozonation in a new gas-inducing reactor, which has been used in the NTUST laboratory on various ozonation studies over the past few years. In this scale-up study, three geometrically similar gas-inducing reactors with different diameters (D _t =0.17, 0.29, and 0.51m) were employed. Three common scale-up criteria (i.e., equal liquid surface motion, equal specific power consumption, and equal impeller tip velocity) were investigated in this research. Under the equal liquid surface motion criterion, the scale-up exponent value and constant K of the modified onset Froude number were determined to be 0.5 and 0.61, respectively. The equal specific power consumption criterion was studied under gas input condition and the scale-up exponent was found to be 0.65. The regression equation for the power number of the three different scale reactors was also obtained. The scale-up exponent of equal impeller tip velocity was determined by theory to be 1.0. The scale-up investigation of dye RB-19 ozonation was then carried out in reactors with three different diameters under the same operating conditions (e.g., initial dye concentration, initial dye/ozone molar ratio, superficial gas velocity, temperature and pH value). From the experimental results, the best-fit scale-up exponent was found to be 1.18, resulting in same dye removal rate in reactors with different diameters. The enhancement factors and chemical ozone mass transfer coefficients were also obtained for these sets of ozonation experiments.     

单螺杆挤出机挤出理论研究进展

论文回顾了单螺杆挤出机挤出理论发展史,并从固体输送、熔融、熔体输送和混合四个方面详细介绍了近十年来挤出理论的最新研究进展。在指出现有不足的同时,提出了单螺杆挤出机未来的研究方向。     

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.     

Scale-up of power consumption in agitated ball mills

Previous investigations have shown that the specific energy input is the overall parameter of influence on product size during communition in agitated ball mills, from laboratory up to industrial scale. The specific energy input is the introduced energy related to the amount of comminuted material. This parameter can be used for mill scale-up. Consequently, a method had to be found of introducing power into the mill so as to obtain a given specific energy input. For this purpose, stirring tests with purely Newtonian liquids were carried out in absence of solids and hence, without comminution. Mathematical models are presented which describe the power consumption in agitated ball mills in absence of grinding beads. In addition, tests with grinding beads filling were also performed, leading to scale-up guidelines with respect to power consumption. Finally, the influence of size and material of grinding beads was investigated.     

双锥型螺杆挤出机固体输送离散元分析

利用EDEM软件对一种普通锥形和两种双锥型螺杆挤出机固体输送段进行模拟.分析了高密度聚乙烯(PE-HD)颗粒在锥形双螺杆挤出机内的运动状态和分布规律.对比分析了3种锥形螺杆挤出的质量流速率、填充率、平均速度、平均压力、平均剪切应力和力矩等参数,给出了普通型和双锥型螺杆挤出机固体输送机理以及主要影响因素.结果表明,相比于...     

Extruder scale-up by computer

Computer simulation technology is used to define the problems in scale-up of extruders from 2.5 to 3.5, 4.5, 6.0, and 8.0 inches in diameter. It is shown that the conventional practice of scaling-up channel depths by the square root of the diameter ratio does not take full advantage of the potential output capacity of larger extruders and a faster rate of channel depth increase is proposed. It is also shown that inherent limitations resulting from decreasing barrel surface area and increasing flight clearance with increasing screw diameter will always result in a higher discharge temperature from the larger machine at any practical output rate. Frictional heat generation and heat removal requirements increase with increasing diameter, regardless of the scale-up system used, and these limit the output capability of the larger sizes at low discharge temperatures.     

PET切片输送系统的节能改造

介绍了密相及稀相气力输送的基本工作原理及其特点。由于PET切片产量减少,为了节约能耗,PET切片输送系统由密相输送改为稀相输送。详述了稀相输送系统计算过程及设计方案,给出了稀相输送系统在较短距离内输送PET切片的应用范例,并对改造前后的能耗进行了对比。