Numerical Methods for the Modelling of Chip Formation
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Archives of Computational Methods in Engineering https://doi.org/10.1007/s11831-018-09313-9 ORIGINAL PAPER Numerical Methods for the Modelling of Chip Formation J. M. Rodríguez1 · J. M. Carbonell2 · P. Jonsén1 Received: 23 August 2018 / Accepted: 13 December 2018 © The Author(s) 2018 Abstract The modeling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. During the last few decades, there has been signifcant progress in the development of numerical methods for modeling machining operations. Furthermore, the most relevant techniques have been implemented in the relevant commercial codes creating tools for the engineers working in the design of processes and cutting devices. This paper presents a review on the numerical modeling methods and techniques used for the simulation of machining processes. The main purpose is to identify the strengths and weaknesses of each method and strategy developed up-to-now. Moreover the review covers the classical Finite Element Method covering mesh-less methods, particle-based methods and diferent possibilities of Eulerian and Lagrangian approaches. 1 Introduction for decades. However, commercial codes employed for the numerical evaluation of cutting conditions to analyze the 1.1 Motivation cutting forces, torques, and chip loads are using mainly leveraging methods that have not evolved during last dec- Machining is used for manufacturing components in various ade. Without successful models, experimental testing will industries including automotive, aerospace, defense, elec- continue being the reference for the process development in tronics, construction, electrics, shipbuilding and others. It practice. Although experimental testing is expensive, right is the most prevalent manufacturing operation in terms of now it is the reference source for the models used in the volume and expenditure. Machined components are used in industry. The above considerations constitute the compelling almost every type of manufactured product. However, it has reasons that pushed researchers to pursue diferent lines of been estimated that machining expenditure contributes to research in the feld of numerical simulations of metal cut- approximately 5% of the GDP in developed countries, while ting processes. in the U.S. alone it translates into approximately $250B per year [47]. Common machining processes includes sawing, 1.2 Objectives broaching, grinding, drilling, milling, turning and shaping (see Fig. 1). It is classifed as a subtractive manufacturing During last years new revolutionary techniques appeared method and it provides various advantages to the fnished extending the capabilities of the classical numerical meth- products such as closer dimensional accuracy, surface tex- ods. The research in most of these techniques became stuck ture or fnish, complex shaping, and required sizes. presenting a lot of shortcomings and a limited range of appli- Machining presents a challenging and exciting intellec- cation. With the aim of fnding a way to go further in the tual problem that has fascinated researchers and practitioners development of a numerical method applied to the modelling of chip formation we present here a review of the numerical methods that have been used or created for that purpose. * J. M. Rodríguez The common denominator for the most of them is the Finite [email protected] Element Method (FEM) from which other techniques has 1 Division of Mechanics of Solid Materials, Luleå University evolved. In this review, the methods under analysis that in of Technology (LTU), Luleå, Sweden this review are classifed as methods supported by a mesh, 2 International Center for Numerical Methods in Engineering including the FEM in a Lagrangian, Eulerian and Arbitrary (CIMNE), Campus Nord UPC, Gran Capitán, s/n., Lagrangian Eulerian formulations (ALE), the Multi-material 08034 Barcelona, Spain Vol.:(0123456789)1 3 J. M. Rodríguez et al. Fig. 1 The three most common types of machining processes. a Turning, b milling and c drill- ing [36] Eulerian Method (MMEM), the Volume of Solid (VOS), in orthogonal cutting conditions are explained. In Sect. 5, the Material Point Method (MPM) or Point in Cell (PiC). most important meshless methods that have been applied in Another set of methods can be classifed as mesh free meth- the numerical simulation are presented. Finally, in Sect. 6, ods and particle methods, including the Smoothed Particle some conclusions are presented and a discussion provided Hydrodynamics (SPH), the Finite Point Method (FPM), the on the need for improvements of the available numerical Constrained Natural Element Method (CNEM), the Discrete techniques. Element Method (DEM), the Maximum Entropy MeshFree, and the Particle Finite Element Method (PFEM). They all represent the most important techniques applied to the mod- 2 Chip Formation Fundamentals elling of chip formation using diferent approaches to solve the physical phenomena occurring in a cutting process. The purpose of this section is to explain the usual types of Initially all characteristics of the physical problem will machining processes and parameters for their description be presented, giving a description of the problem, the theo- and to bring together observations on the shape of chips. The retical approaches and the magnitudes of interest. Then, the role of mechanics in this context is more to aid the descrip- current experimental methods to analyze the problem will be tion than for the chip formation prediction. However, the mentioned as well as the most common numerical method chip formation in all machining processes (turning, milling, to solve it. Numerical challenges arising from the theoreti- drilling and so on) can be described in a common way, a tip cal approach and solutions developed to resolve them, are of a cutting tool removing a layer of material and creating a going to be extensively explained in the frame of the FEM. chip (see Fig. 2). Therefore the physics and numerical pre- They include the thermo-mechanical coupling, the material dictions explained in this paper relate to any process. behavior, the treatment of the incompressibility, the thermo- For modeling of material removal of material caused by a mechanical contact and friction, adaptive discretizations, machining process (chip formation), some important issues breakage and separation criteria for the chip. Finally, an are: how the thicknesses of chips vary with tool geometry, evaluation of the extended characteristics of the diferent how the thicknesses of chips vary with the friction between numerical techniques (fnite element methods, particle meth- the chip and the tool, which infuence has the work harden- ods and mesh free methods) will be presented telling how ing behavior of the machined material, how the forces on good they are resolving the identifed numerical challenges. a tool during cutting may be related to the observed chip shape, how the friction between the chip and the tool and the 1.3 Contents plastic fow stress of the work material will vary. In order to answer these questions we must start describing the physical The paper is organized as follows. After this introduction, process of chip formation and its characteristic parameters. Sect. 2 presents the chip formation fundamentals based on classical models for the diferent machining techniques 2.1 Physical Description in a descriptive manner. Furthermore, in Sect. 3, all the numerical ingredients that are necessary to the numerical In a cutting process, the tool cutting edge penetrates into the simulation of machining processes using the Finite Ele- workpiece material, which is thus plastically deformed and ment Method are explained in detail. In Sect. 4, improved slides of along the rake face of the cutting edge. This is the Eulerian Formulations capable to reproduce chip formation fundamentals of a chip formation process. 1 3 Numerical Methods for the Modelling of Chip Formation Fig. 2 Orthogonal and non-orthogonal chip formation [54] The main terms are the cutting speed vcut , the chip fow Depending on the deformation behavior of the workpiece vchip , and the relative directions between them determine if material, there are diferent mechanisms of chip formation the formation of the chip is orthogonal or non-orthogonal, with either continuous or discontinuous chip fow. This see Fig. 2. Considering the geometrical description, the mechanisms are presented in the next section. general used terms are: rake angle (positive by conven- Before presenting the diferent type of chips there are tion), the clearance angle , inclination angle , major some important mechanical parameters that describe the cutting edge angle , feed f and depth of the cut d. process in terms of forces. The tool-workpiece interaction Moreover, the defnition of some terms changes a little is usually characterized by the cutting and thrust forces. bit between machining processes, for example the defni- However, the resultant of the contact force between the tool tion of the feed f. In turning and drilling, the feed f means and the workpiece can be decomposed in the cutting force the distance moved by a cutting edge in one revolution of and the thrust force. Moreover, the cutting force Fc is the the work; in milling it means the distance that the cutter component of the resultant in the direction of the cutting advances across the workpiece in the time taken for each speed (which is the relative