Revision as of 17:14, 3 July 2017

Abstract

Metal cutting or machining is a process in which a thin layer or metal, the chip, is removed by a wedge-shaped tool from a large body. Metal cutting processes are present in big industries (automotive, aerospace, home appliance, etc.) that manufacture big products, but also high tech industries where small piece but high precision is needed. The importance of machining is such that, it is the most common manufacturing processes for producing parts and obtaining specified geometrical dimensions and surface finish, its cost represent 15% of the value of all manufactured products in all industrialized countries.

Cutting is a complex physical phenomena in which friction, adiabatic shear bands, excessive heating, large strains and high rate strains are present. Tool geometry, rake angle and cutting speed play an important role in chip morphology, cutting forces, energy consumption and tool wear.

The study of metal cutting is difficult from an experimental point of view, because of the high speed at which it takes place under industrial machining conditions (experiments are difficult to carry out), the small scale of the phenomena which are to be observed, the continuous development of tool and workpiece materials and the continuous development of tool geometries, among others reasons.

Simulation of machining processes in which the workpiece material is highly deformed on metal cutting is a major challenge of the finite element method (FEM). The principal problem in using a conventional FE model with langrangian mesh is mesh distortion in the high deformation. Traditional Langrangian approaches such as FEM cannot resolve the large deformations very well. Element distortion has been always matter of concern which limited the analysis to incipient chip formation in some studies. Instead, FEM with an Eulerian formulation require the knowledge of the chip geometry in advance, which, undoubtedly, restricts the range of cutting conditions capable of being analyzed. Furthermore serrated and discontinuous chip formation cannot be simulated.

The main objective of this work is precisely to contribute to solve some of the problems described above through the extension of the Particle Finite Element Method (PFEM) to thermo-mechanical problems in solid mechanics which involve large strains and rotations, multiple contacts and generation of new surfaces, with the main focus in the numerical simulation of metal cutting process. In this work, we exploit the particle and lagrangian nature of PFEM and the advantages of finite element discretization to simulate the different chip shapes (continuous and serrated) that appear when cutting materials like steel and titanium at different cutting speeds. The new ingredients of PFEM are focused on the insertion and remotion of particles, the use of constrained Delaunay triangulation and a novel transfer operator of the internal variables.

The remotion and insertion of particles circumvents the difficulties associated to element distortion, allowing the separation of chip and workpiece without using a physical or geometrical criterion. The constrained Delaunay improves mass conservation and the chip shape through the simulation, and the transfer allows us to minimize the error due to numerical diffusion.

The thermo-mechanical problem, formulated in the framework of continuum mechanics, is integrated using an isothermal split in conjunction with implicit, semi-explicit and IMPLEX schemes. The tool has been discretized using a standard three-node triangle finite element. The workpiece has been discretized using a mixed displacement-pressure finite element to deal with the incompressibility constraint imposed by plasticity. The mixed finite element has been stabilized using the Polynomial Pressure Projection (PPP), initially applied in the literature to the Stokes equation in the field of fluid mechanics.

The behavior of the tool is described using a Neo-Hookean Hyperelastic constitutive model. The behavior of the workpiece is described using a rate dependent, isotropic, finite strain j2 elastoplasticity with three different yields functions used to describe the strain hardening, the strain rate hardening and the thermal softening (Simo, Johnson Cook, Baker) of different materials under a wide variety of cutting conditions. The friction at the tool chip interface is modeled using the Norton-Hoff friction law. The heat transfer at the tool chip interface includes heat transfer due to conduction and friction.

To validate the proposed mixed displacement-pressure formulation, we present three benchmark problems which validate the approach, namely, plain strain Cook´s membrane, the Taylor impact test and a thermo-mechanical traction test. The isothermal-IMPLEX split presented in this work has been validated using a thermo-mechanical traction test.

Besides, in order to explore the possibilities of the numerical model as a tool for assisting in the design and analysis of metal cutting processes a set of representative numerical simulations are presented in this work, among them: cutting using a rate independent yield function, cutting using different rake angles, cutting with a deformable tool and a frictionless approach, cutting with a deformable tool including friction and heat transfer, the transition from continuous to serrated chip formation increasing the cutting speed. We have assembled several numerical tec niques which enable the simulation of orthogonal cutting processes. Our simulations demonstrate the ability of the PFEM to predict chip morphologies consistent with experimental observations.

Also, our results show that the suitable selection of the global time integration scheme may involve savings in computation time up to 9 times.

Furthermore, this work present a sensibility analysis to cutting conditions by means of a Design of Experiments (DoE). The Design of Experiments carried out with PFEM has been compared with DoE carried out with AdvantaEdge, Deform, Abaqus and Experiments. The results obtained with PFEM and other numerical simulations are very similar, while, a comparison of numerical simulations and experiments show some differences in the output variables that depend on the friction phenomena. The results suggest that is necessary to improve the modelization of the friction at the tool-chip interface.

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