Simulation of Machining Mesoscopic and Macroscopic Scales Gérard Coffignal* Philippe Lorong*, Christian Le Calvez** *Laboratoire de Mécanique des Systèmes et des Procédés UMR CNRS 8106 / ENSAM Paris / Polytech'Orléans
** Snecma Groupe SAFRAN
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Introduction
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Complex pieces : necessity to get them good at the first attempt Many industries have to face the problem of getting a good piece at the first attempt : mass production (high cost of the manufacturing environment : automotive industry…) small series : complex piece like in aeronautic or space industry SNECMA (Groupe SAFRAN) is a designer and a manufacturer of whole, or part of, airplane turbo-reactors : production of small series of complex pieces (geometry, tolerances, material integrity) : very high cost of each piece
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The first piece must be good The first manufactured piece of the set must be included in a motor which is used for qualification : it is not possible to adjust or perfect it before. The first manufactured piece must be produced in the conditions the other will be : industrial validation has to be achieved too. To get an idea : 600 Computer Numerically Controlled machine tools are used in Snecma's Corbeil plant.
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Virtual manufacturing : to anticipate Concurrent engineering is the only way to master the complexity of turbo reactor pieces Virtual manufacturing is an inescapable link in the chain of concurrent engineering. target piece design specifications expected piece : geometry, properties, costs
virtual manufacturing
analysis
virtual piece : geometry, properties, costs
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Virtual machining : missing in the link Fully operational simulation are now available for casting, forging and heat treatments. The lack of fully operational simulations in machining breaks the simulation link. virtual casting
virtual manufacturing
intermediate virtual piece
virtual forging
virtual heat treatment virtual machining final virtual piece
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intermediate virtual piece
The simulation link exists in forging
in the case of forging, the goal is achieved : metallurgical microstructure can be predicted 7
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Machining
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Machining : examples of tools and workpieces MILLING active parts of the tool active parts of the tool
active part of the tool
tool
chip
TURNING
workpiece 9
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Industrial example 1 ( turning ) Without a simulator : several weeks to reach a "good solution" and get the prescribed accuracy. among possible reasons : An important proportion of matter to remove from the initial workpiece and presence of "residual stresses" in the initial state of the workpiece. Bending under the action of cutting forces, supports, clamping and unclamping. Vibrations. 10
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Industrial example 2 ( turning )
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Aim : prediction of the piece geometry ++ • Theoretical tool path, velocity along the path
physical properties of tool and workpiece
• Kinematics and Dynamic models of the machine • Model of the Numerical Control of the machine • Initial geometry of the workpiece + "initial stress field" (after forging…) Collision tool/parts : unexpected machining (machine itself,…)
Global
Theoretical tool path / Actual tool path (due to imperfect NC) Static deformation of the workpiece and tool + machine Vibrations of the workpiece and tool + machine
Macro
Deformations induced by "relaxation" of initial stresses (new equilibrium) Deformations induced by workpiece heating
Meso
Residual mechanical state in the workpiece after machining (damage, residual stresses, material changes) ), tool wear…
Micro
machining is possible or not 12
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Challenges in Computational Mechanics
mechanical state
Different scales
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at least 4 Scales microscopic scale : vision of the grains, metallurgical and chemical aspects, possibility of some homogeneization to get constitutive relations at the mesoscopic scale. mesoscopic scale : study at the level of the chip formation. few physical observations may be done (very difficult by nature : tool and/or workpiece moves quickly and the interesting part is between tool and workpiece!) today, lots of simulations can be done at this level : • coupled thermomechanics, • non linear, viscoplasticity, temperature dependant, large deformations, friction, damage, rupture… • mesh adaptivity needed, complex geometry… 14
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Mesoscopic scale ALE, Radioss Touratier, Pantalé, Rakotomalala (96)
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mesoscopic scale it appears that long tool paths (>10^4 times chip thickness) are not realistic objectives today short tool paths can allow to understand accurately what physically occurs, this can be used to set up simplified global interaction models to get densities of equivalent cutting forces along cutting edges.
Challenges in Computational Mechanics
Mesoscopic scale : CNEM tomorrow ? CNEM : easier adaptivity but still a lot of work to get "industrial simulations"
the very begining with CNEM !!!!
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Mesoscopic scale : CNEM tomorrow ? CNEM : shape functions
φi (X ) =
Norm(VorCell ( X ) I VorCell (ni )) Norm(VorCell ( X ))
2D 17
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NEM Sibson
3D
Challenges in Computational Mechanics
FEM
macroscopic vision : the chip is omitted
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Macroscopic scale macroscopic scale : at this scale, a simplified vision of the physical phenomena is chosen in order to be able to simulate long tool paths. Both static and dynamic analyses are possible. The interaction between tool and workpiece is simplified : • the tool is seen as a 3D eraser of matter, • the chip and its formation is not considered, • the interaction is modeled via a relation giving force densities along "cutting edges" as a function of instantaneous parameters (depth of cut, relative velocity,…) and materials in presence. Stiffness and mass of the machine are supposed to be constant and a perfect control is assumed for the relative movement tool frame versus workpiece frame. 19
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Equivalent forces
3D eraser
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Global scale global scale : at this scale, takes place optimization of tool paths, verification of collisions, and the axis control is taken into account. main assumptions are the same as at the macroscopic scale. today, in most situations (in milling) • the tool is assumed to rotate with an infinite angular velocity (teeth are not seen), geometry simulations are limited to this case, • only static deformations of the tool are taken into account the control algorithm can be taken into acount => simulation may include control loops and inertial effects (direction changes…)
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Global scale : tool paths and geometry
Example : industrial software Vericut Example : industrial software NCSIMUL 22
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Macroscopic Scale : More Details
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Macroscopic scale : main objectives Numerical simulation of machining to predict : • the vibrational behaviour during machining, instabilities, chatter, excessive vibrations ... => it is necessary to follow the evolution of the surface •
the cutting forces, forces applied to tool and workpiece (and machine)
•
the resulting final surface of the workpiece. geometry, roughness ...
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4 models modèle de coupe
modèle EF finite element models
piece geometry BREP model or Dexel model 25
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Nsy Usinage 3D
2 modèles géométriques BREP Challenges in Computational Mechanics
cutting force model
BREP model of the tool and its swept volume
Tool = eraser in material space
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Example of a workpiece designed to make experimental or numerical tests
N=14000trs/min
Ap=4mm
Ae=0,3mm
(Lapujoulade)
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fz=0,13mm
Cas STABLE
Simulation : academic example Young modulus: 2.1 1011 Pa Poisson’s ratio: 0.3 Density: 7,800 kg/m3 First natural frequency: 2,134Hz Damping ratio: 0.005 (1st freq.)
Nb. teeth: 3 Pitch angle: 30° Diameter: 12mm Feed per tooth: 0.3mm Angular velocity: 43100rpm Frequency excitation: 2,155Hz
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Surface : final geometry simulation Rigid Workpiece:
waviness height = Cste = 0.1mm
Flexible Workpiece :
waviness height = 0.88 mm
waviness height = 0.3 mm
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Macro : main features of our approach Non-linear dynamics : tool/worpiece interaction regeneration phenomenon (variation of cutting forces at time t is dependant upon the geometry history of the surface) The workpiece undergoes deformations a (set of) finite element model is used (linear, elastic) the geometry model of the workpiece is linked to it (BREP or Dexels) The domain swept by the active faces of the tool erases the geometry model of the piece. Interaction => "cutting forces" Time domain simulation
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Equation
finite element model
M C
mass matrix
ω
angular velocity (tool or workpiece)
K
stiffness matrix
q
degrees of freedom
Cutting Law Geometry Models
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Coriolis and damping matrix
cutting force : non-linear part of the equation interaction surface Challenges in Computational Mechanics
Solution process • For all the time interval of the study incremental approach (step by step integration : Newmark’s method) • For each time increment iterations are needed non-linear problem • For each iteration evaluation of the cutting force intersection between the current domain of the workpiece and the domain generated (swept) by the active faces must be calculated • At the end of each time increment : updating workpiece geometry (volume) 32
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Material removal : geometry models • Geometry model of the workpiece : changing (less and less matter) and moving (linked to finite element displacements in its frame). - B-Rep : a set of plane triangular facets Fine description - problems of robustness - Volume : dexels (multi-level Z-map *) - Fine description in Z direction -Other directions: follows grid coarseness -possibility : dexels in 3 directions • Geometry model of the active faces : moving, (linked to finite element displacements in its frame) •BREP of the swept domain : a set of plane triangular facets
* B.K. Choi and R.B. Jerard, Kluwer Academic, 1998 33
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Dexels • several dexels can take place on one support ( i, j ) • a dexel is defined by its support and its position on the support (zMin, zMax)
cross section Z
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Material removal : flexible workpiece Difficulty: simultaneous motion of workpiece and tool Solution: Define and compute material erasing in a fixed configuration for the workpiece
Reference (or Material) configuration Using dexels: configuration where dexels are undeformed (straight) The motion of the rake faces has to be sent into the workpiece reference configuration: • to build the domain swept by rake faces in material domain • to update the workpiece volume and to calculate cutting forces
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Domain transformations
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The extended mapping and its mesh Only a part
of the rake faces is included in an extension of verifying : : finite element description
Structured regular mesh (hexahedrons) fully linked to the FE shell mesh
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Definition of material removal Domain generated by the displacement of the active faces
Domain machined (erased)
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Aim : prediction of the piece geometry ++ Meso
• Theoretical tool path, velocity along the path • Kinematics and Dynamic models of the machine • Model of the Numerical Control of the machine • Initial geometry of the workpiece + "initial stress field" (after forging…)
cutting forces models
physical properties of tool and workpiece
Collision tool/parts : unexpected machining (machine itself,…) Theoretical tool path / Actual tool path (due to imperfect NC)
Global
Static deformation of the workpiece and tool + machine
Macro
Vibrations of the workpiece and tool + machine Deformations induced by "relaxation" of initial stresses (new equilibrium)
Meso
Deformations induced by workpiece heating Residual mechanical state in the workpiece after machining (damage, residual stresses, material changes), tool wear… machining is possible or not 39
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accuracy of the geometry
Challenges in Computational Mechanics
Micro
mechanical state
Another academic example Plate (140/90/6.2): Steel Insert (35/11(3)/0.5): Aluminium
First natural frequency: 936Hz
Second natural frequency: 2425Hz Nb. teeth: 2 Pitch angle: 20° Diameter: 12mm Feed per tooth: 0.2mm Angular velocity: Simul. A : 241 rev/s Simul. B : 468 rev/s 40
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Excitation Frequency : 482 Hz 936 Hz Challenges in Computational Mechanics
3mm
35 mm
Surface description: 280,000 Dexels
3m m
Rigid Workpiece (ampl.=10.)
0.5mm Rigid Workpiece (ampl.=1.): begining
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Rigid Workpiece (ampl.=100.): begining
Challenges in Computational Mechanics
Rigid Workpiece (ampl.=10.): Surface description: 280,000 Dexels
Flexible Workpiece (ampl.=10.): 241 rev/s
Flexible Workpiece (ampl.=10.): 468 rev/s 42
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Conclusion : the challenges
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Couplings between levels Meso
• Theoretical tool path, velocity along the path • Kinematics and Dynamic models of the machine • Model of the Numerical Control of the machine • Initial geometry of the workpiece + "initial stress field" (after forging…)
cutting forces models
physical properties of tool and workpiece
Collision tool/parts : unexpected machining (machine itself,…) Theoretical tool path / Actual tool path (due to imperfect NC)
Global
Static deformation of the workpiece and tool + machine
Macro
Vibrations of the workpiece and tool + machine Deformations induced by "relaxation" of initial stresses (new equilibrium)
Meso
Deformations induced by workpiece heating Residual mechanical state in the workpiece after machining (damage, residual stresses, material changes) ), tool wear… machining is possible or not 44
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accuracy of the geometry
Challenges in Computational Mechanics
Micro
mechanical state
Need for an integrated software A very complex problem Several scales Many topics of interest for the engineer at different levels Users usually very far from computational mechanics… Need for an integrated tool taking advantage of up-to date simulation capabilities different levels of expertise in its use Problem of model coupling and succession (transfer of fields and information), pre and post processors… Robustness, accuracy, feasibility, efficiency… Industry would like it for yesterday !!!!!!!! And free …
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~~~ The End ~~~
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