Finite element analysis screws

For the coarse estimation of extruder size and screw speed, simple mass and energy balances based on a fixed output rate can be used. For the more detailed design of a twin-screw extruder configuration it is necessary to combine implicit experience knowledge with simulation techniques. Theses simulation techniques cover a broad range from specialized programs based on very simple models up to detailed Computational Fluid Dynamics (CFD) driven by Finite Element Analysis (FEA) or Boundary Element Method (BEM). 

Maurer, P., Holwig, S., and Schubert, J. (1999), Finite-element analysis of different screw diameters in the sagittal split osteotomy of the mandible,/. Craniomaxillofac. Surg. 27 365-372. 

Tanguy, P. A., R. Lacroix, F. Bertrand, L. Choplin and E. B. Delafuente, Finite Element Analysis of Viscous Mixing with a Helical Ribbon-Screw Impeller, A.I.CkE. Journal, 38, 939-944 (1992). 

It was also assumed that the viscous dissipation in the flight clearance does not affect the melt temperature in the screw channel. This would appear to be a questionable assumption. However, finite element analysis has shown that the actual melt temperature rise in the clearance region is relatively small [278]. The reason for this is that the heat transfer in the flight clearance is very effective because the clearance is generally quite thin. 

In order to confirm whether the mechanism proposed in the previous section is correct, predictions of the temperature distribution in extruder screw processing of FEP were made using finite element analysis. The program used is FEHT [150], developed at the University of Wisconsin-Madison. 

Alonso-Vazquez A et al. (2004) Initial stability of ankle arthrodesis with three-screw fixation. A finite element analysis. Clinical Biomechanics 19 751-759... 

Reynolds equation was solved by the finite element method. Fraser et al. [42] performed FEM analysis on a metering screw channel that had slots in the flights. The slots increased the mixing ability of the screw by permitting flow between adjacent channels. 

Expressions for the limiting shape factors when the width of the channel is small relative to the depth (W H ) are given hy Booy [29]. However, this type of channel geometry is generally not encountered in commercial twin screw systems. Numerical simulation of the flow and heat transfer in twin screw extruders is covered in Chapter 12. Section 12.3.2 discusses 2-D analysis of twin screws, and Section 12.4.3.3 deals with 3-D analysis of flow and heat transfer in twin screw extruders. Since 2000, major advances have been made in the numerical methods used to simulate twin screw extruders. The boundary element method now allows full 3-D analysis of flow in TSEs. A significant advance in the finite element method is the mesh superposition technique that allows analysis of complicated geometries with relative ease. This is discussed in more detail in Chapter 12. 

Rauwendaal [84] developed a finite element method (FEM) program to determine temperature profiles in the melt conveying zone of extruders. This FEM program allows the calculation of three-dimensional velocities and temperatures at any point in the screw channel. The program is based on a 2 A-D analysis, which means that the velocities are assumed to change little in the down-channel direction. 

Another classification is based on the presence or absence of translation in a symmetry element or operation. Symmetry elements containing a translational component, such as a simple translation, screw axis or glide plane, produce infinite numbers of symmetrically equivalent objects, and therefore, these are called infinite symmetry elements. For example, the lattice is infinite because of the presence of translations. All other symmetry elements that do not contain translations always produce a finite number of objects and they are called finite symmetry elements. Center of inversion, mirror plane, rotation and roto-inversion axes are all finite symmetry elements. Finite symmetry elements and operations are used to describe the symmetry of finite objects, e.g. molecules, clusters, polyhedra, crystal forms, unit cell shape, and any non-crystallographic finite objects, for example, the human body. Both finite and infinite symmetry elements are necessary to describe the symmetry of infinite or continuous structures, such as a crystal structure, two-dimensional wall patterns, and others. We will begin the detailed analysis of crystallographic symmetry from simpler finite symmetry elements, followed by the consideration of more complex infinite symmetry elements. 

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