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Moreover, because metal cutting is the purposeful fracture of the layer being removed [7, 10], it is necessary to model the propagation of cracks with arbitrary and complex path and track the growth and phase boundaries and extensive microcracking.

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These models are not well suited for conventional computational methods such as FE, finite volume or finite difference methods.

The underlying structure of these methods, which originates from their reliance on a mesh, is not well suited to the treatment of discontinuities which do not coincide with the original mesh lines. To deal with moving discontinuities in methods based on meshes is to re-mesh in each step of the evolution so that the mesh lines remain coincident with the discontinuities throughout evolution of the problem.

An emerging new technique is the element-free Galerkin EFG method, also called the meshless or meshfree method. The objective of EFG methods is to eliminate at least part of this structure by construction the approximation function entirely in terms of nodes.

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Thus, it becomes possible to solve large classes of problems which are very awkward with mesh-based methods. However, despite its great potential, there are a number of limitations and approximations in the commercially available FE programs.

Although many papers have been published on FEA of the metal cutting process, the issue of accuracy and adequacy of the modelled results remains widely open due to the inherent drawbacks of the traditional FEA, highly idealized models involved and inadequate representation of boundary conditions.

The highly structured nature of FE approximations imposes severe penalties in the solution of metal cutting problems, and it is the decrease in structure that makes meshless methods appealing.

Meshless methods, however, require considerable more central processing unit CPU time [52]. The results obtained using FEA strongly depend on the experience and judgment of the engineers involved in the analysis of the problem and definition of a simulation model. It should be clear that FEM makes sense if and only if a physically sound and adequate model of the metal cutting process is included at the very foundation of this modelling.

Therefore, the construction of such a model, careful selection and justification of the proper boundary conditions and then model validation should be the cornerstone of FEM. The market is overpopulated with FE codes and tools for metal cutting simulations, but the issue of model validity is silently set aside.

Metal Cutting Mechanics, Finite Element Modelling 23 The best way to validate the model used in FE simulation is through relevant testing conducted under the same conditions assumed in the model construction. However, this is rarely done because there are a number of problems with adequate metal cutting tests. The existence of scatter in metal cutting experiments, it appears, has now been widely accepted and is no longer under discussion. The uncertainty behind work and tool materials properties, working loads, boundary conditions at the tool—chip and tool—workpiece interfaces and other particularities of the machining system is the main reason why two supposedly identical machining operations will yield different results in terms of tool life, quality of the machined part and achievable production rate.

This fact is well known and yet, surprisingly, engineers are involved in building very detailed models with the intention of capturing the results of one particular test. It is difficult to understand what exactly is detailed in these models, given the fact that the real world is neither detailed, nor accurate, nor precise.

  • Machining: fundamentals and recent advances

Now, since tests are, for very good physical reasons, nonrepeatable, this race for accuracy is lost from the very beginning. Astakhov showed that the chip compression ratio is the one of the most important process output in terms of process evaluation and optimization. Besides the cutting force and energy considered in this chapter, it directly correlates with the tool—chip contact length, contact stresses and temperatures [7, 9, 10].

Using this parameter, one can easily validate a FE model. Such a validation can be as simple as that: Therefore, the FE model cannot be considered as valid. The FEM of thermal process in metal cutting may need more sophisticated validation. Commercially available and specially designed infrared imaging equipment, which includes both hardware and software, are available for temperature distribution measurements in the deformation zone in three-dimensional cutting process.

The high flexibility and low cost of this equipment make it suitable to evaluate high temperature gradients, such as those produced by metal cutting 24 V. These results should be compared with those obtained using FEM. Then the model used in the modelling should be fine tuned to mach the experimentally obtained result.

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Temperature C 75 50 25 0 a b Figure 1. No cutting fluid was used in the tests a b Figure 1. Distribution of the temperatures on the: Moreover, the concept of FE model must be broadened in order to embrace important facets of physics including uncertainty, which unfortunately has been axiomatized out of modern metal cutting research. Model validation should be considered as the mandatory step in FEM.

Breakthroughs in these directions will have considerable impact by making metal cutting numerical simulation useful for practical optimization of various metalworking operations including the cutting and machine tools, the metal working fluids and fixtures, adaptive CNC controllers and programs. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] Armarego EJA Predictive modelling of machining operations — a means of bridging the gap between the theory and practice — A keynote paper at the 13th Symposium on Engineering Applications of Mechanics.

Oxford Komanduri R Machining and grinding: A historical review of the classical papers. Appl Mech Rev J Mater Process Technol Int J Machine Tools Manuf Int J Mech Sci Wiley, New York 26 V. Outeiro [19] Barrenblatt GI Mechanical theory of equilibrium cracks. Advances in Applied Mechanics. Academic, New York, pp. J Mech Phys Solids 8: Int J Mach Tools Manuf J Mater Process Technol 98 1: Int J Numer Methods Eng J Manuf Sci Eng 2: J Mater Process Technol 86 1—3: J Eng Ind 4: Int J Mach Tools Manuf 36 3: Oneonta [o-nee-on-ta] is a Christian church in South Pasadena, California.

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