F. Ducobu , E. Rivière- Lorphèvre , E. Filippi

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

F. Ducobu , E. Rivière- Lorphèvre , E. Filippi