f. ducobu , e. rivière- lorphèvre , e. filippi

Faculté Polytechnique

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

Machine Design and Production Engineering DepartmentSIMULIA Academic Seminar 2013

[email protected]

Université de Mons

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 materialsFormation of a chip or not?Study of the influence of the depth of cut on

Chip morphologyChip formation mechanismCutting forces

Context

2François 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

Université de Mons 3François Ducobu | Machine Design and Production Engineering Department

IntroductionMiniaturisation increasing demand for micro-components

development of micro-manufacturing techniquesMicro-milling = one of themMicro-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 speedApplications 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.


Université de Mons

Plan

4François Ducobu | Machine Design and Production Engineering Department

A. Chip formation specificities in micro-cutting

B. Model presentation

C. Results in macro-cutting

D. Influence of the depth of cut

E. 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



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

1. Minimum chip thickness

Chae, J., Park, S., Freiheit, T., 2006, Investigation of micro-cutting operations, Int. J. Machine Tools and Manufacture, 45: 313-332.



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

2. Size effect

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.


B. Model presentationCHIP FORMATION SPECIFICITIES IN MICRO-CUTTING | MODEL PRESENTATION | RESULTS IN MACRO-CUTTING | INFLUENCE OF THE DEPTH OF

CUT | CONCLUSIONS

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-cuttingAllows 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



Modeling = complex problem

Formation physicsBehavior law

Cutting edge radius

Separation criterion

Contact + Friction

Thermal aspects



2D plane strain modelTake 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.

1. Formulation



Tool: Rake angle: 15° Clearance angle: 2° Edge radius: 20 µm

Cutting speed: 75 m/min Initial workpiece shape = rectangular box

2. Boundary conditions



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 chipTool material: tungsten carbide described by a linear elastic law

3. Materials constitutive laws

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.

Université de Mons

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

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François Ducobu | Machine Design and Production Engineering Department

4. Contact and friction model

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Friction at the chip – workpiece interface: Coulomb’s friction law

14

= 0,05

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.

All of the friction energy converted into heat

25% of this heat flow into the workpiece

This heat fraction: calculated with the thermal effusivities



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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%

15

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.



5. Thermal aspects



Lagrangian formulation chip separation criterion neededChip formation possible thanks to an “eroding element” methodCriterion based on the temperature dependent tensile failure of

Ti6Al4V

6. Separation criterion

[ASM Handbook]

Temperature

Te

nsile

failu

re



Tensile failure value reached in an element deleted from the visualisationand 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



Upper area: small elements (5 µm < 20 µm) to take the cutting edge radius of the tool (20 µm) into account

4 nodes plane strain elements with linear formulation in displacement and temperature (CPE4RT) disposed in a structured way

Workpiece ≈ 21 500 elementsTool ≈ 400 elementsReduced integration elementsHourglass control method: Relax Stiffness (default one)

7. Mesh


C. Results in macro-cuttingCHIP FORMATION SPECIFICITIES IN MICRO-CUTTING | MODEL PRESENTATION | RESULTS IN MACRO-CUTTING | INFLUENCE OF THE DEPTH OF

CUT | CONCLUSIONS

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



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


CHIP FORMATION SPECIFICITIES IN MICRO-CUTTING | MODEL PRESENTATION | RESULTS IN MACRO-CUTTING | INFLUENCE OF THE DEPTH OF CUT | CONCLUSIONSCyclic 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 teethSimulated force of the same order but smaller than experiments

choice of TANH parameters?Same observations for FFSimulated 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


D. Influence of the depth of cutCHIP FORMATION SPECIFICITIES IN MICRO-CUTTING | MODEL PRESENTATION | RESULTS IN MACRO-CUTTING | INFLUENCE OF THE DEPTH OF

CUT | CONCLUSIONS

For a determined material, minimum chip thickness depends ondepth 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)

h (µm) 280 100 40 20 10 5 2.5 1h/r 14 5 2 1 0.5 0.25 0.125 0.05



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 = 2 h/r = 1

h/r = 14

h/r = 0.05

h/r = 0.25h/r = 0.5

h/r = 0.125

h/r = 5



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 = 0.05

h/r = 0.25h/r = 0.5

h/r = 0.125

103 Pa



2. Cutting forcesh/r decreases teeth are less deep then disappearSame observation for the cyclic evolutions of the forces

Forces ratio = FF/CF h/r decreases forces ratio increases When forces ratio > 1: change in the cutting phenomenon: FF > CF If critical ratio value = 2 minimum chip thickness value between 5 µm and 10 µm

Experiments



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)



4. Elastic recoveryElastic 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)



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.


E. ConclusionsCHIP FORMATION SPECIFICITIES IN MICRO-CUTTING | MODEL PRESENTATION | RESULTS IN MACRO-CUTTING | INFLUENCE OF THE DEPTH OF

CUT | 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 listA minimum chip thickness prediction has been performed


Thank you for your attention



Lagrangian ExperimentsALE

103 Pa

f. ducobu , e. rivière- lorphèvre , e. filippi

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