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A Lagrangian Model to Produce Saw-toothed Macro-chip and to Study the Depth of Cut Influence on its Formation in Orthogonal Cutting of Ti6Al4V. F. Ducobu , E. Rivière- Lorphèvre , E. Filippi. Francois.Ducobu@umons.ac.be. Machine Design and Production Engineering Department
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A Lagrangian Model to Produce Saw-toothed Macro-chip and to Study the Depth of Cut Influence on its Formation in Orthogonal Cutting of Ti6Al4V F. Ducobu, E. Rivière-Lorphèvre, E. Filippi Francois.Ducobu@umons.ac.be Machine Design and Production Engineering Department SIMULIA Academic Seminar 2013
Chip formation specificities in micro-cutting | Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions Context • PhD Thesis: “Contribution to the study of Ti6Al4V chip formation in orthogonal cutting. Numerical and experimental approaches for the comprehension of macroscopic and microscopic cutting mechanisms.” • Goal: setting up a finite element model of orthogonal macro-cutting and micro-cutting • Homogeneous materials • Formation of a chip or not? • Study of the influence of the depth of cut on • Chip morphology • Chip formation mechanism • Cutting forces François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting | Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions Introduction • Miniaturisation increasingdemand for micro-components development of micro-manufacturing techniques • Micro-milling = one of them • Micro-milling= the fastest and flexible micro-machining process • to produce complex 3D micro-forms • with sharp edges • and good surface quality • in many materials (metal alloys, polymers and ceramics) • Uses a micro-mill rotating at high speed • Applications quite varied: micro-injection moulds, watch components,… • Chae, J., Park, S., Freiheit, T., 2006, Investigation of micro-cutting operations, Int. J. Machine Tools and Manufacture, 45: 313-332. François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting | Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions Plan • Chip formation specificities in micro-cutting • Model presentation • Results in macro-cutting • Influence of the depth of cut • Conclusions François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting | Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions A. Chip formation specificities in micro-cutting • Micro- and macro-milling concepts are similar • Scaling-down of the process changes in the process micro-cutting phenomenon cannot be considered as a simple scaling of micro-cutting • Lead to several chip formation specificities in micro-cutting François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting | Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions 1. Minimum chip thickness • Depth of cut and feed per tooth very small no chip is formed below a critical value called “minimum chip thickness” • Estimation of its value = one of the present challenges in micro-milling • Moreover machined material and tool geometry greatly affect its value, complicating its estimation • Chae, J., Park, S., Freiheit, T., 2006, Investigation of micro-cutting operations, Int. J. Machine Tools and Manufacture, 45: 313-332. François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting | Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions 2. Size effect • Size effect, at small depth of cut =non-linear increase in the specific cutting energy when the depth of cut decreases • At the microscopic scale, the microstructure of the machined material takes importance • Its granular structure must be taken into account The material can no longer be considered as homogeneous and isotropic ≠macro-cutting 3. Influence of the machined material • Chae, J., Park, S., Freiheit, T., 2006, Investigation of micro-cutting operations, Int. J. Machine Tools and Manufacture, 45: 313-332. • Filiz, S., Conley, C., Wasserman, M., Ozdoganlar, O., 2007, An experimental investigation of micro-machinability of copper 101 using tungsten carbide micro-endmills, Int. J. Machine Tools and Manufacture, 47: 1088-1100. François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions B. Model presentation • Lagrangian Finite Element Method (FEM) model to study the depth of cut influence on chip formation in orthogonal cutting • Numerical simulations performed with ABAQUS/Explicit v6.8 • Important characteristic of the model = its validity in micro-cutting but also in macro-cutting • Allows to study changes in the cutting mechanism from macro- to micro-cutting with one single model • Ability to form saw-toothed chips in macro-cutting= one of the requirements and difficulties introduced by the multi-scale aspect of the model François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions Formation physics Behaviorlaw Cuttingedge radius • Modeling = complexproblem Separationcriterion Contact + Friction Thermal aspects François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions 1. Formulation • 2D plane strain model • Take into account the chip formation area • Explicit Lagrangian formulation because: • Interest focused on • the transient phase of the chip formation • the absence of chip formation • Production of saw-toothed chips morphologically close to experimental ones • Ducobu, F., Filippi, E., Rivière-Lorphèvre, E., 2009, Chip Formation and Minimum Chip Thickness in Micro-milling, Proceedings of the 12th CIRP Conference on Modeling of Machining Operations, 339-346. • Ducobu, F., Rivière-Lorphèvre, E., Filippi, E., 2010, An ALE Model to Study the Depth of Cut Influence on Chip Formation in Orthogonal Cutting, Proceedings of the Eighth International Conference on High Speed Machining, 202-207. • Ducobu, F., Filippi, E., Rivière-Lorphèvre, E., 2009, Investigations on Chip Formation in Micro-milling, Proceedings of the 9th International Conference on Laser Metrology, CMM and Machine Tool Performance, 327-336. François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions 2. Boundary conditions • Tool: • Rake angle: 15° • Clearance angle: 2° • Edge radius: 20 µm • Cutting speed: 75 m/min • Initial workpiece shape = rectangular box François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions 3. Materials constitutive laws • Workpiece material: Titanium alloy Ti6Al4V: • Homogeneous simplification of its actual granular structure • Behaviour described by the Hyperbolic TANgent (TANH) law [5] = Johnson-Cook law taking account of the strain softening effect • Strain softening could explain the formation of saw-toothed Ti6Al4V chips taking it into account more realistic chip • Tool material: tungsten carbide described by a linear elastic law • Calamaz, M., Coupard, D., Girot, F., 2008, A new material model for 2D numerical simulation of serrated chip formation when machining titanium alloy Ti-6Al-4V, Int. J. Machine Tools and Manufacture, 48: 275-288. François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions 4. Contact and friction model • The nodes of the workpiece that are going to be in contact with the tool during the chip formation are not known at the beginning of the calculation • Kinematic contact pair between the exterior surface of the tool (master)and all the nodes of the workpiece (slave) Prevent the penetration of the slave surface in the master surface François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions • Friction at the chip – workpiece interface: Coulomb’s friction law • = 0,05 • All of the friction energy converted into heat • 25% of this heat flow into the workpiece • This heat fraction: calculated with the thermal effusivities T. Özel et E. Zeren : Numerical modelling of meso-scale finish machining with finite edge radius tools. International Journal of Machining and Machinability of Materials, 2:451–768, 2007. François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions 5. Thermal aspects • 2 parts initial temperature = 25°C • Only conduction is considered • All the workpiece faces are adiabatic • Simulation time is short (1 ms – 2 ms) • Interest for the chip – tool contact area • Efficiency of deformation to heat transformation = 90% T. Özel et E. Zeren : Numerical modelling of meso-scale finish machining with finite edge radius tools. International Journal of Machining and Machinability of Materials, 2:451–768, 2007. François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions 6. Separation criterion • Lagrangian formulation chip separation criterion needed • Chip formation possible thanks to an “eroding element” method • Criterion based on the temperature dependent tensile failure of Ti6Al4V Tensilefailure Temperature [ASM Handbook] François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions • Tensile failure value reached in an element deleted from the visualisation and all its stress components are set to zero • Suppression of a finite element introduction of a crack in the workpiece making it possible for the chip to come off François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions 7. Mesh • Upper area: smallelements(5 µm < 20 µm) to take the cuttingedge radius of the tool (20 µm)intoaccount • 4 nodes plane strain elements with linear formulation in displacement and temperature (CPE4RT) disposed in a structured way • Workpiece≈21 500 elements • Tool≈400 elements • Reduced integration elements • Hourglass control method: Relax Stiffness (default one) François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions C. Results in macro-cutting • Validation of the model: comparison of the modelled saw-toothed macro-chip (h = 280 µm) and cutting forces to experimental cutting results • Experiments performed on a lathe • Workpiece= shaft comporting flanges in the form of successive slices of equal thickness • Tool width larger than disks • Cutting process: plunge condition ≈ orthogonal cutting • Fixation of the tool high rigidity • Use of a tailstock to avoid workpiece displacements and vibrations François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions • Morphology of the modelled chip very close to the experimental one • For each tooth a slipping band is formed in the primary shear zone, as expected • It vanishes as the tool moves forward, initiating the tooth formation François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting | Influence of the depth of cut | Conclusions • Cyclic evolution of the cutting force = typical of saw-toothed chip formation: a drop in the force = formation of a tooth • Link between force evolution and teeth formation, 7 teeth • Simulated force of the same order but smaller than experiments choice of TANH parameters? • Same observations for FF • Simulated force smaller than experiments influence of the friction, difficult to measure and model • The model is able to model qualitatively the chip formation of Ti6Al4V in orthogonal cutting • Suitable for the study of the depth of cut influence on chip formation François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions D. Influence of the depth of cut • For a determined material, minimum chip thickness depends on • depth of cut (h) • tool edge radius (r) • Study of the influence of the depth of cut on chip formation with 8 decreasing values of the depth of cut for a constant tool edge radius (20 µm) François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions 1. Chip morphology 103 Pa • From saw-toothed chip to the cutting refuse including segmented chip chip morphology evolving away from macro-cutting • From h/r = 0.25: material seems to be pushed, deformed, not sheared anymore h/r = 5 h/r = 14 h/r = 0.5 h/r = 0.25 h/r = 2 h/r = 1 h/r = 0.125 h/r = 0.05 François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions • For h/r values under 0.125: negative effective rake angle + no chip is formed and a small amount of material accumulates in front of the tool • This small amount grows when the tool moves forward until it reaches a thickness greater than the minimum chip thickness • It is then removed from the workpiece Critical h/r concerning the change in the mechanism of chip formation: between 0.125 (2.5 µm) and 0.25 (5 µm) h/r = 0.5 h/r = 0.25 103 Pa h/r = 0.125 h/r = 0.05 François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions 2. Cutting forces • h/r decreases teeth are less deep then disappear • Same observation for the cyclic evolutions of the forces Experiments • Forces ratio = FF/CF • h/r decreases forces ratio increases • Whenforces ratio > 1: change in the cutting phenomenon: FF > CF • If critical ratio value = 2 minimum chip thickness value between 5 µm and 10 µm François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions 3. Specific cutting energy • Specific cutting energy = cutting force on the area of the chip section • Mean normalized = mean simulated for each case divided by experiments • Size effect highlighted: non-linear increase happens when the depth of cut decreases • Critical h/r value: between 0.25 (5 µm) and 0.5 (10 µm) François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions 4. Elastic recovery • Elastic recovery (or elastic spring back ) of the workpiece after the tool tip passage • Increase of its value when the depth of cut decreases: from 0.45% for h = 280 µm to 25% for h = 1 µm • Significant importance for small depths of cut • Large value relatively to the small depths of cut • Contributes to increase: • Feed force • Slipping force • Specific cutting energy • hm < 10 µm (exponential evolution) François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions 5. Minimum chip thickness prediction • It is obvious that the minimum chip thickness is less a precise and single value than a range of values with unclear limits • According to the model results, for Ti6Al4V with the geometry and the cutting conditions considered: • The elastic recovery sets the upper limit of the values range under 10 µm • The lower limit is set around 2.5 µm by the morphological aspect • The 2 others criterions lead to a value between 5 µm and 10 µm • Minimum chip thickness resulting value in these conditions =of the order of 25% of the cutting edge radius of the tool with a lower limit around 12.5% and an upper limit inferior to 50% • This order of magnitude is confirmed in literature • Filiz, S., Conley, C., Wasserman, M., Ozdoganlar, O., 2007, An experimental investigation of micro-machinability of copper 101 using tungsten carbide micro-endmills, Int. J. Machine Tools and Manufacture, 47: 1088-1100. • Vogler, M.P., DeVor, R.E., Kapoor, S.G., 2004, On the modeling and analysis of machining performance in micro endmilling, Part I: surface generation, J. Manufacturing Science and Engineering, 126:685-694. François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions E. Conclusions • Transition from macro- to micro-cutting changes in the cutting phenomenon • Study of the influence of the depth of cut on chip formation with a 2D Lagrangian finite element model • Chip formation evolves away from macro-cutting when the depth of cut decreases • Specific micro-cutting features reported in literature like: • Minimum chip thickness • Negative effective rake angle • Increase of the importance of the feed force • Size effect are highlighted in the results • Importance and role of the elastic recovery of the workpiece is highlighted and added to the micro-cutting features list • A minimum chip thickness prediction has been performed François Ducobu | Machine Design and Production Engineering Department
Thank you for your attention François Ducobu | Machine Design and Production Engineering Department
Introduction| État des connaissances | Modélisation numérique | Voie expérimentale | Apports | Conclusions & perspectives | Q/R • HyperbolicTANgentlaw= J-C +strainsoftening with François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions François Ducobu | Machine Design and Production Engineering Department
Chip formation specificities in micro-cutting| Model presentation | Results in macro-cutting| Influence of the depth of cut | Conclusions Lagrangian ALE Experiments 103 Pa François Ducobu | Machine Design and Production Engineering Department