Proceedings of IDMME - Virtual Concept 2010 Bordeaux, France, October 20 – 22, 2010

Original Article

Machining Advanced Simulation: Distortion Prediction of Prestressed Machined Parts in NCSIMUL environment Habib Karaouni1, Benoit Souvestre1, Yves Ahipo1

(1) : SPRING Technologies Immeuble Le Méliès, 261 rue de Paris, 93556 Montreuil Cedex, FRANCE +33 (0)1436025 39 /01 E-mail : hkaraouni,bsouvestre,[email protected]

Abstract: We discuss machining simulation of high valueadded revolution parts which may deviate from the nominal shape because of residual stresses relaxation initially induced by primary manufacturing processes. Today, NC machinetools simulation software, such as NCSIMUL from SPRING Technologies, is able to simulate the whole numerical command in the virtual machine environment. Nevertheless, it is not possible to take into account part distortions during machining, even if it is assumed rigid. We could use finite element analysis to study this problem. This solution is not easy because it is necessary to match continually the workpiece’s mesh along the cutting interfaces. Also, continuum’s issue of the numerical chain remains a big problem as long as a gap still exists between the world of NC machining simulation and the physical machining behaviour one. This paper describes an integrated industrial-driven approach for predicting distortions in pre-stressed machined parts. Key words: CAD/CAM, Machining simulation, Residual stresses, FEA, Reverse engineering. 1- Introduction

In many machining applications, residual stresses and part distortion are obstacles to time-to-market and high part quality. That is particularly true in aerospace domain for large airframes or turbine disks for example. Without any simulation tool, it leads to long and expensive machining iterations on real parts (parts generally manufactured with high value-added material). Residual stresses in machined parts result from two sources. At first, almost all applications, bulk residual stresses are generated during previous operations such as forging and heat treatments [HO1]. Then, secondary residual stresses induced by the machining process are superimposed. Significant distortions can arise from both sources, particularly on thin parts or on “big” machining (when a large amount of material is removed). This contribution focuses on the first source. Considering the highest level of distortions comes from relaxation of residual

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stresses, a global scale simulation (i.e.: without taking into account chip forming and tool/workpiece interactions) is enough powerful for the shape error prediction. Finite element analysis is very often used to study this problem [MA1,PI1,HO1]. This solution needs to follow cutting interfaces with great precision, to control dynamically mesh quality, to manage fields mapping and to update automatically the numerical definition of the machined part. This FE-centred solution has a significant limitation: flexibility, due to systematic remeshing, which can be very expensive for 3D modelling. Some authors attempt to circumvent this limitation by decreasing (or even eliminating) the remeshing step. Techniques using level-set method are used to match the boundary during machining [PI1]. The level-set function is a signed distance function defined at the nodes of finite element mesh. Sometimes, local mesh adaptations are necessary because cutted elements can be highly distorted. Also, because of models variety and software modules interactions, integration requires the use of a data model as a common data exchange medium. This data model includes CAD geometry, complete FE mesh and analysis information such as nodes, elements connectivity, material properties, boundary conditions, forces, initial stresses and output control to predict the distortion of the part during machining. In this research, a CAD/CAM-centred approach is carried out. We propose to show a machining advanced simulation in the NCSIMUL environment coupled dynamically to a FEM based distortion service. 2- Machining Classical Simulation

We call Machining Classical Simulation (MCS) simulation such as what it is still perform today by NC machine-tools simulation software like NCSIMUL. By extension, we call Machining Advanced Simulation (MAS) simulation enriched by physical behaviour computations. Physical aspects can be of any kind [RA1]: part deflection, part/tool vibrations, residual stresses relaxation, residual stresses induced by the

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machining process, thermal effects... NCSIMUL software is dedicated for developing, optimizing and running machining programs. Unlike CAM software, which are in fact simple viewers displaying a tool path, NCSIMUL simulates really the tool path within the machine environment and checks it: secured and optimized machining operations are thus guaranteed. The MCS positioning within the numerical chain is described in figure 1. It takes place precisely between the virtual world of CAM and the physical world of production.

residual stresses. We consider a 2D-axisymmetric modelling of the problem even if the real boundary conditions do not satisfy revolution hypothesis. We also suppose that the level of residual stresses don’t exceed the yield stress of the material in order to allow purely elastic response of the structure during material removal. We recall that secondary surfacing residual stresses induced by the machining are ignored. Finite element analysis with conforming mesh is used. This means that in the finite element representation of a Cm-1 variational problem, the displacements and their (m-1)st derivatives are continuous across the elements boundaries. However, this continuity does not mean that the element stresses are continuous across element boundaries, unless very fine element mesh is used. 3.1 – Machining modelling

The main idea is to be able to invoke the distortion service from NCSIMUL to update the workpiece deformation at any time. On figure 2, the kth updating request is done at the end of block N. Prior request was at block M. Two times are thus defined: t1k and t2k .

Ω (t1k )

Figure 1: MCS positioning.

Typically, the main functionalities of MCS are: - NC program analysis - Material removal and machine simulation - Dimensional analysis - Analysis and optimisation of cutting conditions

t1k = t2k −1 Block M

t2k Block N

Ω(t2k )

MCS inputs are: - Machine environment definition (3D geometry, kinematic...) - Tool path (trajectory and tool definition) via ISO code or APT format - Raw part (in-process workpiece) - Fixture conditions - Target finished part MCS outputs are: - Machined part - Real cumulated cycle times of machining

t

NC program

Figure 2: Definition of the machining times.

Also, figures 3 and 4 show the different domains to update during the machining.

NCSIMUL integrates powerful material removal algorithm and advanced library for CAD geometries handling and exchanging [NC1]. These capabilities will be strongly put in contribution in this current work for building the MAS process. Another interesting feature deals with the capability to catch at any time the machined and removed volumes between two any blocks of the NC program. However, the main limitation is that all is assumed rigid. To take into account the distortion of the part, we are thus considering that the workpiece becomes flexible (tool remains rigid).

Vsweep (t1k , t2k ) = Sweeping ( Γ cut (t ) )

(1)

Ω(t2k ) = Ω(t1k ) − Ω r (t1k , t2k )

(2)

Ω r (t1k , t2k ) = Ω(t1k ) ∩ Vsweep (t1k , t2k )

(3)

t∈⎡⎣t1k ,t2k ⎤⎦

in which Vsweep (t1k , t2k ) is the volume swept by the effective cutting edge Γ cut (t ) between time t1k and t2k ; k k Ω r (t1k , t2k ) is the removed volume between time t1 and t2 ;

Ω(t1k ) and Ω(t2k ) are respectively the part domains before and after a material removal ;

3- Part distortion Modelling

In this research, we focus on turning of revolution parts which may deform because of the relaxation of the bulk

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Ω r (t1k , t2k )

Initial stresses as stated above do not create deformation unless element killing technique is used.

Ω(t2k )

3.3 – Fields mapping

When the part distortion service is involved, a new meshing of the current geometry is done. All physical fields, in particular residual stress field, have to be mapped from previous mesh to current one. In other formulation, plastic strain field can be concerned too. In this work, P0-mapping is used. Indeed, two kinds of variables are distinguished: - P1-variable : it is calculated and stored at the nodes of the mesh (such as displacement, pressure, temperature, velocity) - P0-variable : it is calculated and stored at the elements of the mesh, usually at Gauss points (such as stress and strain)

Figure 3: Machining domains Maximal cutting edge Maximal cutting volume Effective cutting edge

Figure 4: Cutting edge path representation

A special focus is put on the fact that when the tool path is defined, we consider that the NC program is validated by NCSIMUL. We have thereby the guarantee to prevent any error such as collision with fixture and undercutting. This integration is very cost-effective since it reduces iterations between NC machine-tools and FE simulation software. 3.2 – Initial stress capability

Let assume that the bulk residual stress field generated from primary processes such as forging and/or heat treatments is provided as a stress map on a given mesh. At time 0, this residual stress field has to be introduced as initial stresses. Unfortunately, this ability is not always implemented in FE software. Initial stress capability allows initial stresses corresponding to an unknown loading to be input. These stresses are generally provided as nodal point initial stresses or element initial stresses. Whenever the constitutive relation is used, the initial stresses are added to the current stresses t Σ caused by externally applied loading. The following equations [BA1] are used: t

F=∫ B t

T

( Σ + Σ )d V t

t

The principle of the P0-mapping is the following one: - A first operation consists in extrapolating at nodes of the old mesh the variables stored by the element of this one (generally, least squares method is used) [BA1] - The second operation consists in transporting the new nodal variables on the new mesh (via P1mapping) The transport of P1-variables is a two-step process: - Step 1: Each node h for the new mesh is projected into the old one. It’s about to find the element e of the old mesh containing the node h (figure 5) - Step 2: Interpolation of the nodal values of node h within the previous found element e.  

Element of the new mesh

Node of the old mesh Node of the new mesh ξ1 

(4)

i

ξ 3  h 

v

ξ2 

in which Σi are the initial stresses (corresponding to Cauchy

Element e of the old mesh  containing the node h of the  new mesh  

t

stresses), t F is the nodal point force vector at time t, B is the Figure 5: Transport of P1-variable

strain-displacement matrix, and t Σ are the current stresses and calculated as usual from the mechanical strains. Equation (4) yields at time 0: Ri =

∫B

T

Σi dV

The nodal interpolation is done by using the interpolation functions associated to the element e of the old mesh. Let Vh′ be the nodal variable to transport:

(5)

∀h ∈ Th′, Vh′ =

V

The step-by-step incrementation is then carried out using: t +Δt

in which

t +Δt

K (i −1) Δ U

(i)

=

t +Δt

R−

t +Δt

F (i −1) + R i

R is the externally applied load vector,

i

(7)

variable to calculate at the node h of the new mesh Th′ ,

(Vi )i =1.. N

K is

the stiffness matrix, and U is the displacement vector.

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i

in which e is the current element of the old mesh, Vh′ is the

(6) t +Δt

∑ V N (ξ )

i∈e i =1.. N e

is the known variables at node i of the old mesh e

and Ne is the number of nodes of the element e.

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P0-mapping tends to smooth the results and the new calculated field is no longer equilibrated at singular zones. The projection step on the new mesh is in principle slightly error-diffusive if mesh densities are comparable. Sophisticated techniques can be used to ensure continuous stresses between two connected elements [OD1]. 3.4 – Modelling process

still desirable to check the meshing quality in order to ensure accurate solution of the problem. 4- Machining Advanced Simulation

The machining advanced simulation (MAS) process is encompassed within a hat service, NCManager, which is in charge of managing the coupling between NCSIMUL and HyperMAS (figure 7, 8). Classically  Machined part

The part distortion modelling consists in: - Getting the geometry of the intermediate raw part Ω(t1k ) at time t1k

Machine Environment

MCS  process

Meshing the domain Ω(t1k ) with respect of cutting

-

NCManager

interface between time t1k and t2k . This mesh is

-

M (t1k ) -

Launching the elastic computation by using element killing technique Upgrading the (deformed) part Ω(t2k ) and storage of the new map of the residual stress field.

-

A dedicated service, HyperMAS, has been developed for embedding the part distortion modelling. Pre‐treatment Template

Ω(t2k )

Ω( t )

GEO

GEO

M (t2k )

k 1

Ω r (t , t ) k 2

RS

M (t2k −1 ) RS : Residual Stresses

Figure 6: Part distortion process

Elastic computations can be done by any FEA software including initial stress and element killing technique capabilities. HyperMAS in/out is displayed in figure 6. Once FE pre-treatment templates are defined, the whole process is fully automatic Each step can also be validated on demand by the user. Actually, although the system proposes mesh densities by analysing the current geometry and the first user-meshing, it

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Raw part Initial Residual  Stresses

Figure 7: MAS process

4.1 Initialization In this present work, a step for initializing the MAS process has to be done by the user. It consists mainly in: - Splitting the NC code into Nr sets (Nr is the number of requests of deformation updating) - Preparing the FE pre-treatment templates for HyperMAS by defining material properties, default mesh densities, boundary conditions…

4.2 Geometry Beautification

RS Mapping

RS

Final Residual  Stresses

Ω(t2k )

In a future work, this step will be assisted by NCManager to decrease the manual interventions of the user.

‐ Mesh ‐ Boundary conditions ‐ Machining modelling ‐ Initial  stresses ‐…

k 1

Ω(t1k )

Tool path

denoted M (t1k ) . Specifying the set position and the fixture (translation in boundary conditions, contact conditions, tightening force...) Mapping of the residual stresses from M (t2k −1 ) to

-

Distorted Machined part

NC Code 

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Beautification consists for us in reworking a rough model in order to render it more beautiful in the sense that it becomes an input with wished quality for another process. For instance, to use most of automatic meshing process, the geometric model should satisfy several quality criteria. CAM-like software has the drawback to alter the quality of the initial CAD geometry during machining simulation. In fact, efficient material removal algorithm works on triangulated models where triangles quality is mainly relative to time-performance goal. This reaches to concurrent objectives in terms of CAM/FEA efficiency. In this work, some developments on an in-house research on intelligent reverse engineering oriented machining are reused. The idea of this project is to use the result of a machining simulation described as a set of triangles and enriched by additional information (SRE file format) to ease the rebuilding of a new “nice” CAD file (Brep, STEP). The “Spring technologies Reverse engineering” or SRE file format is designed for reverse engineering for NC Simulation. The underlying data structure gathers a set of facets (mesh) and for each facet a colour, a cut number and a surface index. In NCSIMUL, there is one colour per tool so

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facets of same colours are generated by the same tool. The cut number is unique for every tool movement which enables to gather facets. The surface index refers to the index of the underlying geometric surface. An index value of “-1” means that the surface is unknown for the facet. The additional information tells us the type of the surface to be constructed and whether two adjacent meshes belong to a same surface. Using this method, we could obtain the Boundary representation of the solid that only contains planes and cylinders, spheres, tori, shear cylinders, swept tori and cones. Also, the system detects warnings such as disconnected removed volumes and dust volumes.

“Usine Numérique 2 (UN2)” funded by “Pôle de compétitivité System@TIC”

4.3 MAS process The MAS detailed process (figure 8), associated to part distortion modelling, is described as below: 0. Reception of the machining job and the initial residual stress field 1. MAS initialization (section 4.1) 2. MAS execution (k=1) 2.1. [NCSIMUL] MCS initialization: introduce the intermediate raw part Ω(t2k −1 ) and the kth set of NC code 2.2. [NCSIMUL] MCS execution 2.3. [NCSIMUL] Geometry export (intermediate raw part Ω(t1k ) and removed part Ω r (t1k , t2k ) ) 2.4. [HyperMAS] Geometry beautification of Ω(t1k ) and Ω r (t1k , t2k ) 2.5. [HyperMAS] Part distortion computation (section 3.4) 2.6. [HyperMAS] Geometry beautification of the upgraded machined part Ω(t2k )

Figure 9: MAS Demonstrator developed in UN2 project

5- Application

The reported application case has been proposed by SNECMA in UN2 project. It’s about a forged and heat treated revolution disk, Figure 10. The associated primary processes have been numerically simulated. Initial residual stress field is shown in figure 12. Upper and lower sides are machined. Only turning operations are considered. Around 75% amount of material is removed. The goal is to play a MAS for distortion predicting of machined part and its associated residual stress field. For each side’s machining, three requests of deformation updating (Nr=3) are chosen. On figure 11, a MCS is performed on an upgraded workpiece. The final machined workpiece is shown on figure 13. An amplification factor of 10 is used. The results show us the ability of MAS process to take into account how the part may deviate from its nominal shape during machining. Total deflection is around 20% error. We emphasize the importance of having accurate initial residual stress field which has a first-order impact. Also, because of the nature of the FE formulation, quality of mesh is crucial. A very fine mesh can be used on 2D models for decreasing the number of checking operations of the element mesh quality. This solution is unrealistic for 3D models due to time-consuming computations.

2.7. [NCSIMUL] Geometry import of Ω(t2k ) 3. MAS execution (k=2) 4. .... 5. MAS execution (k= Nr)

NCManager

IN MAS  Initialization

MAS  process

MCS

Ω r (t1k , t2k ) GEO

Ω(t2k )

Beautification Beautification

Ω(t1k ) Meshing

Distortion  computation

M ( t2k −1 )

M (t1k ) RS

Mapping

GEO

M (t2k ) RS

RS

TMP

Figure 8: Representation of the coupling between NCSIMUL and HyperMAS managed by NCManager

Figure 10: NCSIMUL machine environment

Figure 9 shows the MAS prototype developed in the project

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modelling which has been managed without additional difficulties. The aim is to take into account better the fixture conditions. We finally emphasize that adhering to non-fully automatic solution means manual tasks can be carried out, especially for critical ones, such as geometry beautification, remeshing and quality assessment. Such machining advanced simulation mainly aims in a first time to optimize upstream the cutting conditions (i.e. within the numerical chain) and in a second time the tool path. 7- Acknowledgements

The reported research is part of the project « Usine Numérique 2 » funded by “Pôle de compétitivité System@TIC”, the support of which is gratefully acknowledged.

Figure 11: Machining Classical Simulation (MCS) after few computations of part deformation

8- References

[BA1] Bathe K.J., Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ, 1996. [OD1] Oden J.T., Brauchli H.J., On the calculation of consistent stress distributions in finite element approximations. International Journal for Numerical Methods in Engineering, 1971, vol. 3, p317-325. Figure 12: Residual stress field within the initial workpiece

[HO1] D. Hornbach and Prevey, Development of machining procedures to minimize distortion. In Proceedings of the 17th Heat Treating Society Conference and Exposition, pages 13– 18. ASM, 1998. [MA1] Marusich T.D., Usui S., Marusich K.J., Finite Element Modeling for Part Distortion, In proceedings of Intercut2008, France.

Figure 13: Residual stress field within the final deformed workpiece

[NC1] NCSIMUL 8.8 User Manual, www.springplm.com, Montreuil, France, 2010.

6- Conclusion

An integrated industrial-driven approach for machining advanced simulation in NCSIMUL environment has been discussed. In this research, the term “advanced” is relative to the ability to take into account physical aspects such as distortion part due to the relaxation of the residual stress field induced by primary processes (forging and heat treatment in particular). In this approach, resmeshing is certainly a brake to a fully automation of the process. But the plus is to give ability to carry out the good mesh at each stage, therefore accuracy of the prediction is increased. In our case, the imparted time for meshing is trivial for 2D-modelling. We underline the fact that it is difficult to believe in a systematic automatic meshing solution whatever studied cases, neither a “no remeshing” solution. Industrialising the discussed approach essentially consists in tooling the whole process in order to avoid wasting time in data handling and exchanging. An automatic mode can be defined for performing a coarse prediction and an expert mode (semi-automatic) for refining the previous solution (by tuning over the updating requests, the good mesh definition, the constitutive laws, the clamping modelling...). A recent development affects the extension toward 3D-periodic

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[PI1] Pierard O., Barboza J., Duflot M. and D’Alvise L., Relaxation of Residual Stresses During Multi-Passes Machining: Simulation with the Level-Set Method and Process Optimization, 8th.World Congress on Computational Mechanics (WCCM8) [RA1] Ratchev S., Liu S., Huang W., A.A. Becker, An advanced machining simulation environment employing workpiece structural analysis, Journal of Achievements in Materials anf Manufacturing Engineering, Volume 16, Issue 1-2, May-June 2006.

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