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Top2. Finite Element Modeling Of Machining And Micromachining
The Finite Element Method is employed in almost every engineering discipline. Through the years and with the advances in computer power and memory this method has become very powerful. In addition, special FEM software that can deal with several kinds of loading conditions, e.g. stress-strain, thermal, electrical, fluid dynamics analysis, perform coupled analysis, with more than one of the aforementioned loading conditions in the same model and provide 2D or 3D analysis has made the technique the most prevalent one used in modeling and simulation in many scientific areas, including the field of machining.
Modeling and simulation of micromachining with FEM shares the same background with conventional machining and thus common aspects will be briefly discussed. Simulations of orthogonal machining using the finite element method have a background of about three decades; in Refs (Mackerle, 1999; Mackerle, 2003; Markopoulos, 2012) a wide collection of papers can be found.
The first models that appeared employed the Eulerian formulation for modeling orthogonal cutting. In this approach the finite element mesh is spatially fixed and the material flows through it in order to simulate the chip formation. The advantages of the method are the quantity of the elements for modeling the workpiece and the chip employed for the analysis which is rather small allowing the reduction of the total analysis time and the fact that they do not undergo severe distortion since the mesh and thus the form of the produced chip is a priori known. The disadvantages of the method are that it requires complex programming and that experimental data must be known prior to the construction of the model in order to determine the chip geometry. This method is still utilized by some researchers for the simulation of the steady state condition of the cutting process.
The updated Langragian formulation is the approach where the elements are attached to the material and the undeformed tool is advanced towards the workpiece. The chip is formed by using a chip separation criterion in front of the tool edge; so far, geometric or physical criteria, involving critical distance between the tool and the workpiece, critical values of e.g. stress or strain, or even crack propagation criteria have been proposed. Today, the Langragian is more preferable than the Eulerian formulation by the machining researchers. A drawback of the method is connected to the large mesh deformation observed during the simulation. Due to the attachment of the mesh on the workpiece material, the mesh is distorted because of the plastic deformation in the cutting zone. In order to overcome this, usually, continuous re-meshing and adaptive meshing are applied, adding considerably to the required calculation time. Nevertheless, the advances in computers have made it possible to reduce the time needed for such an analysis to acceptable levels. Note that, an arbitrary Langragian-Eulerian formulation (ALE), a method that aims to combine the advantages of the two methods, has also been proposed.
The techniques described in the previous paragraph can also be applied in micromachining. In metal cutting, size effect, the non-linear increase in the specific energy and thus in the specific cutting force with decreasing depth of cut, influences process parameters, e.g. the minimum cutting edge radius, and therefore the analysis of the size effect is very important.