A review of the fundamentals of the finite element simulation of metal cutting

Transcription

1 A review of the fundamentals of the finite element simulation of metal cutting Q. XU', B. ill er^ & D.G. ~ord' he Ultra Precision Engineering Centre, University of HuddersJield, UK 2 Wilde FEA Ltd, Stockport, UK (www. WildeFEA.co.uk) Abstract Metal cutting is one of the most widely-used manufacturing processes. Finite element simulation of this process has matured enough to give valuable insight of this process and, sometimes, good agreement with experiment. However, due to the complex nature of the metal cutting process, finite element simulation of metal cutting is not straightforward. This paper reviews the fundamentals of the finite element simulation of metal cutting. It also includes some significant advancements and applications reported recently. Conclusions and comments on future research are also presented. This paper contributes by helping to establish comprehensive knowledge about the finite element simulation of metal cutting and the state-of-the-art knowledge in this field. 1 Introduction The competitive nature of the global economy demands that, for an industry to survive, it must maximize the efficiency and quality, as well as minimise response time and costs in production [l -21. Metal cutting is one of the most widely-used manufacturing processes to produce the final shape of products, and its latest advancements are paralleled with the developments in materials, computers, and sensors [2]. The final shapes of most mechanical parts are obtained by a series of manufacturing operations. Bulk deformation processes, such as forging and rolling, are mostly followed by a series of metal removing operations in order to acheve parts with desired shapes, dimensions, and quality of surface finish.

2 392 Laser Metrology und Muchiize Performance VI Though those two types of manufacturing processes are distinct, both rely on the behaviour of material past yield point. Further more, hgh speed machining has been developed over the last twolthree decades in order to increase productivity. Its advent requires a new understanding of cutting mechanics under such new conditions [l-21. Due to its importance, a great deal of research has been devoted to understanding the mechanics of this process. The purpose of analysing metal cutting is to understand and predict process variables such as stresses, temperatures and cutting forces for given tool geometrical parameters (rake angle, clearance angle and edge preparation), cutting conditions (feed, cutting speed and depth of cut) and workpiece and tool material properties. To achieve this goal, experimental, mechanistic and analytical techniques are used. In recent years, however, with the surge in computational power and capacity, the focus has turned to numerical simulation of the process through finite element methods. More and more such simulations have appeared in the literature [4-121 and in the proceedings of conferences (such as the CIW Workshop on FEM Modelling of Machning Operations) [ The Ultra Precision Engineering Centre has a long history and wide range of interests in precision engineering ranging from machine tool error characterisation to error reduction through either direct or indirect ways; from machine tool structural dynamics (model testing and FEA) to surface methods. Recently it has extended its research interest into finite element simulation of the cutting process. This paper has resulted as a preliminary literature review in ths topic. Owing to existing expertise of computational plasticity and its application in engineering (metalforming, creep damage and super-elasticity of Nitinol) experienced by member of ths research group, this paper will not address the basic concepts involved in finite element analysis nor detail a comprehensive published work. Instead it will focus on to the hndamental questions and the key issues to be encountered in the application concerning the finite element simulation of metal cutting process. In addition to that, the authors' own comments and views will be presented whenever it is pertinent and appropriate. Ths paper contributes to broad views on the frame-work of computational plasticity and some practical aspects about metal cutting simulation. 2 The main characteristics of metal forming The cutting process is a very complex one [l-41. From a computational mechanics point view, the following main characteristics can be summarised as: 1. Large deformation of the material with high strains (1 or higher) 2. High strain rates (103 to 1 O5 i' and higher) 3. Thermal-coupled with high temperatures in the range of 200 to l OOOOC and higher 4. Complicated friction conditions at the interface 5. Chip incipient and separation 6. Serrated chip or continuous chp depending on process parameters

3 Laser Metrology and Machine Performance VI Highly localized heat generation associated with large plastic deformation and high friction 8. Tool wear and vibration in real machining processes In the machining process the stress, strain, strain rate and temperature variables will all be dependent on the cutting parameters such as the feed rate, and the cutting speed as well as on the geometrical features of the tool such as the rake angle and the nose radius. From a computational mechanics point of view, machininglcutting process is essentially a thermal-coupled elasticviscoplastic problem. However, it is often simplified and a rigid-viscoplastic material model is used instead - it gives equivalent accuracy for chip morphology, contact stresses and tool wear etc. while being more CPU efficient. The chip separation complicates ths problem further. Thus, the finite element method is a natural choice. In fact, as far as the author's awareness is concerned the development of a computational method with a finite element techmque has been inspired by potential applications in civil, mechanical and manufacturing engineering (such as metalforming and machining) and its rigour has benefited from the input of mathematical knowledge. 3 PE formulation The FEM has been used for the simulation of metalworking operations. The majority of these analyses use either the Lagrangian approach or the Eulerian approach. The Lagrangian approach is a natural choice for solid mechanics. The FE mesh consists of material elements and the computational grid deforms with the material (workpiece andlor tool). This approach is particularly convenient to track unconstrained material flow as the FE mesh presents the material boundaries. The Eulerian approach is more suitable for fluid-flow problems. The mesh consists of spatially fixed grids and the material properties are calculated at fixed spatial locations as the material flows through the mesh. Interested readers can find comprehensive coverage of general computational plasticity in references [l Critical observations have been made about those approaches with respect to machining process simulation in several publications (say, such as [18]). 1. The Lagrangian approach is relatively easy in formulation and implementation. 2. The analysis can be started from indentation to the incipient stage to steady state. The chp is formed easily to its proper thickness, and no prior assumption is needed about the shape of the chip. 3. The mesh is severely distorted adjacent to the tool tip and re-mesh is needed. Not All the FEA packages have this capability. 4. A separation of nodes from in the front of the tool tip may be needed. Machining can essentially be considered a (shear) extrusion process on a rnicro-level- material will flow either across or under the cutting tool as in any forging operation.

4 394 Laser Metrology und Muchiize Performance VI 5. A fracture criteria is only required where the chps break off following formation if the chip is discontinuous (which as in reality will depend on the tool geometry and cutting parameters). This is currently possible with DEFORM using a 'Damage Criteria'. Reference [3] described this aspect, too. 6. The Eulerian approach is more computationally efficient and is best for modelling the region around the tool tip. 7. It requires a prior assumption of the shape of the chp. 8. An iterative procedure is needed for the convergence of boundaries. 9. History-dependent material properties have to be interpolated in an approximate way and material points have to be traced back to the fixed mesh points. Consequently, the Arbitrary Lagrangian-Eulerian (ALE) approach has been applied to the machining process recently [18]. Ths development is inspired mainly by the realisation of the strength of the combination of the Lagrangian and Eulerian methods in modelling some of the characteristics of the machining process. Interested readers can refer to those publications directly (such as [18-191). The choice of finite element formulation is a very serious issue if it is intended to develop in-house software. Although it is true that traditionally researchers were mainly using in-house software in their research work (over 70% up to mid 90's) [8], the use of commercial packages has increased significantly over the last 5 to 7 years. The question for most application researchers who are not intending to develop their in-house software is which software to select and which finite element formulation should be considered. 4 Basic problem 4.1 Material model and flow stress A realistic material behaviour model is very important and it should be able to depict the main behaviour under large strain, high strain rate, and thermal effects. However, various simplifications have been introduced for specific research application. The well-known Johnson-Cook formulation is often used. The flow stress is given by: where E is the plastic strain, 5 is the strain rate, T is the temperature, Tomb is the room temperature, TmeI, is the melting temperature. A, B, C, and n and m are rheological parameters. Some variation has been proposed in [12]. Recent development in the determination of flow stress highlighted the use of inverse method.

5 4.2 Friction in chip-tool interface Laser Metrology and Machine Performance VI 395 A typical stress distribution on the rake face is illustrated in Figure 1. It is mathematically presented as: Z, =k when z, 2 k (3) where zf is the frictional stress, 0, is the normal stress, p is the coefficient of friction, and k is the shear stress of the chip material. Work published in [l l] proposed a different model and its effects on residual stress. 4.3 Chip formation Chip separation from the workpiece and chip formation (either continuous for discontinuous) is one of very important aspects in metal cutting. It was observed that over the past 8 years or so, numerical simulation of machining processes has been the subject of intensive research, in which aspects of discontinuous chp formation and algorithms for element separation have been addressed, but the modelling and analysis of such problems still require further attention [3]. Many criteria have been proposed in the literature, ranging from simple geometrical or strain criteria to more complex fracture-mechanics criteria. Even if the appropriate type of criterion is chosen, there is no clear physical justification as to what critical value should be adopted [18]. Ths is an area further fundamental research is needed. m i V) E U U) sliding region Figure 1. A typical stress distribution on the rake

6 396 Laser Metrology und Muchiize Performance VI Nevertheless, pertinent to practical application of finite element simulation of the cutting process with commercial software, it has been reported that the Johnson-Cook failure mode has been used with ABQUSIExplicit [g]. The strain at failure was assumed to be function of stress state and temperature as: where W is the damage parameter and the material is deemed failed when it reaches to unity. dl, d2, d3, d4,and d5 are the failure constants to be determined by experiment. It has also reported [20] that a continuum damage based chp breaking model has been developed by the researchers at Scientific Forming technologies Corporation. 5 Available software The following software has been reported to be able to analyse the metal cutting process. They include: ABAQUSIStandard and ABAQUSIExplicit ALGOR DEFORM 2D AND DEFORM 3D FLUENT LS DYNA A detailed comparison of their functionality is desirable but that information is not available yet. In addition to that information about their computational efficiency is scattered in various publications and it is not readily available. 6 Recent applications of Deform 2D13D Deform 2D and Deform 3D is special software dedicated to metalworking processes (metalforming and machining). Recently, significant advancements and its applications have been reported (either the Scientific Forming Technologies Corporation [ or other research groups [8, 13-14]). Some of the significant applications are [20-221: 1. 3D simulations (drilling and milling). Example is shown by Figure Chp control. Example is shown by Figure 3.

7 Laser Metrology and Machine Performance VI Tool life prediction and comparison. Good agreement between predicted tool life and experimental observation is obtained in reference W]. 7 Conclusion Finite element simulation is the new trend in research to understand metal cutting mechanics. Significant progress has been acheved in both the theoretical fi-ame-work and application. Valuable insights have been obtained and good agreements with experiment have been reported. Whllst computer simulation of metal cutting processes has gained reasonable success, certain fundamental issues still need to be addressed by the research community. These issues include the development and then its implementation of more advanced plasticity theory (such as non-local plasticity theory) and physically-based damage mechanics model for chip separation. Acknowledgement The support from EPSRC (EPSRC Grant: GR l R ) and industrial partners is acknowledged by the Ultra Precision Engineering Centre. Figure 2. Chip Formation in Drilling [21]

8 398 Laser Metrology und Muchiize Performance VI Figure 3. Three dimensional simulation of a spiral chip [21] References [l] Chdds, T. H. C., Maekawa, K., Obkawa, T. & Yamane, Y., Metal machining: theory and applications, 2000, London, Arnold. [2] Altintas, Y., Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design, Cambridge University Press, [3] Owen, D.R.J & Vaz Jr. M., Computational techniques applied to highspeed machining under adiabatic strain localization conditions. Comput. Methods Appl. Engrg. 171: p , [4] Ng, E.-G, Aspinwall, D.K., Brazil, D. & Monagham, J., Modelling of temperature and forces when orthogonally machining hardened steel. International Journal of Machme Tools & Manufacture 39: p , [5] Dirkolu, M. H., Childs, T. H. C. & Maekawa,. Finite element simulation of chip flow in metal machining. International Journal of Mechanical Sciences, 43: p ,2001. [6] Altan, T. & Ozel, T., Process simulation using finite element methodprediction of cutting forces, tool stresses and temperatures in high speed flat end milling. International Journal of Machme Tools & Manufacture 40: p ,2000. [7] Kim, K. W., Lee, W. Y. & Sin, H., A finite element analysis for the characteristics of temperature and stress in micro-machining considering

9 Laser Metrology and Machine Performance VI 399 the size effect. International Journal of Machine Tools & Manufacture 39: p , Ng, E.-G & Aspinwall, D. K., Modelling of hardpart machining. Journal of material Processing Technology, 127: p , Mackerle, J., Finite element analysis and simulation of machining: an addendum A bibliography ( ).. International Journal of Machine Tools & Manufacture 43: p ,2003. Yang, X. & Liu, C. R., A new stress-based model of friction behaviour in machining and its significant impact on residual stresses computed by finite element method, International Journal of mechanical Sciences, 44: p ,2002. Maekawa, K. Ohhata, H., Kitagawa, T. & Childs. T. H. C., Simulation analysis of machinability of leaded Cr-MO and Mn-B structural steels, Journal of Materials Processing Technology, 62: p , Altan, T., Modeling of metal cutting using FEM-a brief progress report, CIRP Workshop on FEM modeling of machming operations, Paris, France, January 29,2003. Altan, T., Modeling of metal cutting using FEM-a brief progress report, CIRP Workshop on FEM modeling of machining operations, Paris, France, January 23,2002. Owen, D. R. J. & Hinton, E., Finite elements in plasticity: theory and practice. Pineridge Press Limited, Swansea, U.K., 1980, ISBN Crisfield, D., Non-linear Finite Element Analysis of Solids and Structures, Imperial College of Science, Technology and Medicine, London, UK, John Wiley & Sons, 1997, ISBN X Bathe, K. J., Finite element procedures in engineering analysis (Prentice- Hall., Englewood Cliffs, NJ, 1996), ISBN Movahhedy, M. Gadala, M. S. & Altinas, Y., Simulation of the orthogonal metal cutting process using an arbitay Lagrangian-Eulerian finiteelement method, Journal of Materials Processing Technology, 103: p ,2000. Wang, J. & Galada, M. S., Formulation and survey of ALE method in nonlinear solid mechanics, Finite element Anal. Des. 24: p. 253, Fischer, C. E., Chigurupati, P., Jinn, J. T. & Li, G., Computer simulation of the chip forming process in metal cutting, SFTC Paper 373, Scentific Forming Technologies Cirporation, Columbus, OH, U.S.A. Fischer, C. E., Wu, W. T., Oh, J. Y. & Chigurupati, P., Recent Advances in finite element simulation of the chip forming process, SFTC Paper, Scentific Forming Technologies Cirporation, Columbus, OH, U.S.A. Fischer, C. E. & Chigurupati, P., Using computer simulation to understand and optimize high speed machining, SME High Speed Machining Conference, Chicago, Illinos, April 8-9,2003.

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