12th ESAFORM 2008
conference on material forming
Enschede, The Netherlands
27, 28 and 29 april 2009
Comparison of experimental and simulation distortions of
quenched C-ring test parts
C. NICOLAS, Ph.D. Student
C. BAUDOUIN, Assistant-professor
R. BIGOT, Professor
LCFC
L. LELEU, Assistant-professor
M. TEODORESCU, Research engineer
1
Methodology
Presentation content
 Methodology applied to quantify distortions
The C-ring
 Introducing C-ring test part
The methodology applied on on C-rings
 Application of the methodology on C-ring test parts
Conclusion &
Outlook
 Conclusion and outlook
2
Methodology
Methodology applied to quantify distortions
The C-ring
The methodology applied on on C-rings
Conclusion &
Outlook
3
Methodology
Introducing C-ring test part
Eccentricity
Geometry
The C-ring
11
11
Ø 45 Inner cylinder
16
Gap
Pincer
The methodology applied on on C-rings
100
100
Ø 70 Outer cylinder
Values in mm
Manufacturing process
Machining
Stress relieving
Heating (930°C)
+ oil/gas quench (20°C)
Conclusion &
Outlook
4
Gradients of
temperature
microstructure
stress
Heterogeneity
Distortions
The C-ring
CCT diagram
The methodology applied on on C-rings
Gradients of
heating/cooling
rate
100% martensite
50% ferrite +
45% bainite +
5% martensite
65% bainite +
35% martensite
3 gradients of thickness
Radial 
Conclusion &
Outlook
Circumferencial 
3
Core
2
Longitudinal 
Case (surface)
1
Pincers extremity
Methodology
C-ring geometry & quench distortions
5
Methodology
Experimental data for simulation
The C-ring
 Steel grade: thermo-elasto-visco-plastic behaviour
 Mechanical data: yield stress, flow stress, hardness, …
 Thermal data: dilatation coefficients, conductivity, …
 Metallurgical data: TTT/CCT diagram
For each
metallurgical
phase
 Process modelling: temperature evolution (thermo couples)
The methodology applied on on C-rings

Heating 20° to 930°  Thermal law

Quench 930° to 20°C  Thermal law inner/outer cylinders
Nominal
geometry
Conclusion &
Outlook
Simulation sofware:
Forge 2008 TTT
Distortions & temperatures
Distortions & temperatures
6
Methodology
Measurement of
real and simulated parts
 For real parts  probing with a CMM
The C-ring
overall uncertainty : 1.6 μm
Upper plane
110 points
Right generatrix
Outer cylinder
1722 points
21 points
The methodology applied on on C-rings
 For f.e.m. parts  algorithm for virtual
1722 points
probing [1]
21 points
38 points
Inner cylinder
overall uncertainty : 0.5 μm
with 217 500 nodes for a C-ring
Left generatrix
Bottom plane
Measurement meshing
Conclusion &
Outlook
Same gaps fields for real and virtual C-ring
7
[1] C. Nicolas and al., “Dimensional control strategy and products distortions identification”, International Journal of Material Forming (Springer), vol. 1, pp. 1039-1042, 2008.
 Gaps fields analysis for real and simulated C-rings

Gap generatrixes
(topside view)
Cylinders (topside and iso views)
Barrel effect
The methodology applied on on C-rings

Planes (left view)
Height variation

Pincers and gap opening
Barrel/bobbin effect of rear generatrixes
Lip effect of front generatrixes
Height variation
Bobbin effect

Lip effect
The C-ring
 Significant distortion phenomena
Lip effect
Methodology
Modelling distortion phenomena
Conclusion &
Outlook
Gap opening
Pincers opening
8
Scale factor: x50
Nominal geometry
Quenched geometry of
real C-ring
Quenched geometry of
virtual C-ring
Methodology
Modelling distortion phenomena
Significant distortion
phenomena
The C-ring
Choose the mathematical
expressions for each one
The methodology applied on on C-rings
Physical origin
• known  literature
e.g. pincers opening [2] [3] [4] [5]
• unknow  experimental and
f.e.m. tests
e.g. lip effect
Relevance
• linearity
• independence
Conclusion &
Outlook
[2] R.A. Hardin and al., “Simulation of Heat Treatment Distortion”, In the Proceedings of: 59th Technical and Operating Conference, Chicago, 2005.
[3] Z. Li and al., “Experiment and Simulation of Heat Treatment Results of C-Ring Test Specimen”, In the Proceedings of: 23rd ASM Heat Treating Society Conference,
Pittsburgh, pp. 245-252, 2005.
[4] D.O. Northwood and al., “Retained austenite - Residual stress - Distortion relationships in carburized SAE 8620 steel”, Materials Science Forum, vol. 539-543, pp.
4464-4469, 2007.
[5] B.E. Brooks and al., “Prediction of Heat Treatment Distortion of Cast Steel C-Rings”, In the proceedings of: 61th Technical and Operating Conference, Chicago, 2007.
9
Methodology
Modelling distortion phenomena

Mathematical expression
Geometrical prints

For each section:
Pincers
opening
The methodology applied on on C-rings
Heterogeneity of
cooling rate (faster near
pincers)


e ouverturei  1  cos i

2
 i  Atan2(OTi .x; OTi .y)
x5
Barrel effect
For each rear generatrix:
e bombé  1  z i 2

i


z i  1  0.1  k, k  0,20 
Heterogeneity of cooling
rate inside/outside
x5
For each front generatrix:
Lip effect
Conclusion &
Outlook


2
e lèvrei  sin (  i  2 )  e ouverturei





  i   6  k  30 , k  0,20 
Unknown  f.e.m.
approach needed
Time-dependent combination
between thermal metallurgical and
mechanical stresses
The C-ring
Distortion
phenomena
Physical origin
For the two cylinders
10
x5
Theoretical points
Points of a geometrical print
Methodology
Modelling distortion phenomena
Physical origin
Geometrical prints
For each point of planes:
The methodology applied on on C-rings
Height
variation of
planes
e
 dila _ plansi   i .z  z i ,

Nz i  1  e dila _ plansi  1


Volume change
x5
Gap opening
Pour each generatrix:
e
 dilai    i .x   x i ,

 Nx i  1  e dilai  1
Volume change
x5
Conclusion &
Outlook
Barrel effect
Pour each generatrix:
of the two 
e bombéi  1  z i 2
generatrixes z  1  0.1  k, k  0,20 
of the gap  i
Heterogeneity of cooling
rate inside/outside
x5
Theoretical points
Points of a geometrical print
stresses
Mathematical expression
Thermo-mechanical
and metallurgical
The C-ring
Distortion
phenomena
For the planes and the gap
Thermo-mechanical
stresses

11
Methodology
Modelling distortion phenomena
Relevance

The C-ring

linearity  mathematical expressions checked
detection of slight dependence
 by comparing each phenomena uncertainty to the measurement
uncertainty
The methodology applied on on C-rings
When measuring the real C-ring: measurement uncertainty = 1.6 μm
Pincers opening
Barrel effect of
rear generatrixes
Lip effect of front
generatrixes
Height variation
Gap opening
Barrel effect of
gap generatrixes
0.92 µm
0.15 µm
0.36 µm
0.2 µm
0.58 µm
0.93 µm
Phenomena uncertainties < measurement uncertainty
Conclusion &
Outlook
 no great dependence
 distortion phenomena are dissociated by the optimization method
12
 One steel grade - 4 cooling rates - 3 C-rings for experiments - 1
Pincers opening (shape change)
Experiments
The methodology applied on on C-rings
300
250
200
150
100
50
0
-50
-100
Gas12b
Experiments
Simulation
350
Gas3b
Gap opening (volume change)
Gas18b
Oil
Amplitudes of distortion phenomena
in μm
The C-ring
for simulation
 Amplitudes of distortion phenomena
Amplitudes of distortion phenomena
in μm
Methodology
Dissociation of distortion phenoma
Simulation
550
450
350
250
150
50
-50
Gas3b
Gas12b
Gas18b
Oil
Increase in quench cooling rate
Increase in quench cooling rate
Conclusion &
Outlook
Pincers opening  with cooling rate
Pincers closing - simu. - oil quench
Gap opening  with cooling rate
Gap opening  - simu. - oil quench
Same trends excepted for oil quench
Same amplitudes for gap opening (gas quenches)
13
Methodology
Dissociation of distortion phenoma
 Amplitudes of distortion phenomena
0
-50
-100
-150
Inner generatrixes
Outer experiments
generatrixes experiments
Outer generatrixes
simulation experiments
Inner generatrixes
Inner generatrixes
simulation
Outer generatrixes simulation
150
Inner generatrixes simulation
150
100
Amplitudes of distortion phenomena
in μm
50
Amplitudes of distortion phenomena
in μm
The methodology applied on on C-rings
Amplitudes of distortion phenomena
in μm
100
Lip effect of generatrixes
100
50
0
-50
-100
-150
Gas3b
Gas12b
Gas3b
Gas18b
Gas12b
50
0
-50
-100
-150
Oil
Gas18b
Increase in quench cooling rate
Increase in quench cooling rate
Outer generatrixes experiments
Outer generatrixes experiments
Inner generatrixes experiments
Inner generatrixes experiments
Outer generatrixes simulation
Outer generatrixes simulation
Inner generatrixes simulation
Inner generatrixes simulation
Amplitudes of distortion phenomena
in μm
The C-ring
Barrel effect
of generatrixes
Outer generatrixes
experiments
Gas3b
150
100
50
0
-50
-100
Gas12b
-150
Gas18b
Gas3b
Oil
Gas12b
Oil Increase in quench cooling rate
Gas18b
Oil
Increase in quench cooling rate
Conclusion &
Outlook
Barrel  with cooling rate in gas quenches
Lip  with cooling rate in gas quenches
Barrel  in oil quench
Lip  in oil quench
Symmetry of the two effects inner/outer cylinders
14
Same trends & comparable amplitudes for some cooling rate
Methodology
Conclusion
 Methodology closed to physical origin of distortions
The C-ring
 Distortions (volume changes) thermal effect
 Gap opening



good agreement exp. & simu. (like in literature)
Origin: volume variation
Height variation
The methodology applied on on C-rings


same tendancies exp. & simu. but not the amplitudes
Origin: volume variation
 Distortions (shape changes) metallurgical & mechanical effect
Same trends exp. & simu. but not the amplitudes

Pincers opening


Lip effect

Conclusion &
Outlook

Origin: combination between cooling rate gradient and steel phase
transformations gradient inside pincers
Origin: local effect at the end of pincers, to be determined by simulation
Barrel effect

Origin: heterogeneity of cooling rate inner/outer cylinders
15
Methodology
Outlook
 Investigation via simulation:
 chronology of distortions & phases transformations
The C-ring
Quench time
Pincers closing
The methodology applied on on C-rings
End of heating
Pincers opening
Other distortion phenomena
Conclusion &
Outlook
16
Methodology
Outlook
 Investigation via simulation:
The C-ring

chronology of distortions & stresses (related with phases
transformations)
Quench time
Barrel
effect creation
Mise en bombé des génératrices
The methodology applied on on C-rings









t=20s
t=40s
t=50s 
Frange of
de ferrite
(compression)

Start
ferrite

 Frange de bainite (compression)
 Frange
martensite (traction)
Start
ofdebainite
 Start of martensite
Conclusion &
Outlook
Compressive
stress
Tensile stress

t=70s




t=100s

t=150s
t=200s
t=550s



Augmentation effet lèvre

Lip effect creation

17
 Investigation via simulation:
The C-ring

chronology of amplitudes of distortion phenomena
The methodology applied on on C-rings
800
700
600
500
400
300
200
100
0
-100
-200
Amplitudes en µm
Methodology
Outlook
737
401
258
44 42
-27
8
45 14
146
57
41
-23 -32
-42 -74 -54
Barrel effect
Bombé cyl. ext. Bombé cyl.int.
249
115 102
58 35 71
17
Ouverture
pinces
opening
t=0s, end of heating --> begin of quench
t=80s, martensite at middle-pincers
t=250s, martensite inside whole C-ring
49 24
-28 -31
-49
-110 -109 -99
-74
Pincers
88 79 71
Lip effect
Effet lèvre cyl.
ext.
Effet lèvre
cyl.int.
Variation
épaisseur
pinces
t=50s, martensite at pincers extremity
t=150s, martensite inside all pincers
t=550s, end of quench
Conclusion &
Outlook
Critical quench moments  martensite transformation
18
12th ESAFORM 2008
conference on material forming
Enschede, The Netherlands
27, 28 and 29 april 2009
Comparison of experimental and simulation distortions of
quenched C-ring test parts
C. NICOLAS, Ph.D. Student
Thank you for your attention
LCFC
19
Methodology
Dissociation of distortion phenoma
Goal: to separate effects of elementary distortions amoung the
overall deformation
The C-ring
 Existing optimization methods:
 Modal analysis [6] [7]
 Proper Orthogonal Decomposition (POD) [8]
 …
The methodology applied on on C-rings
 Used method in this work [9]:
 Vectorial decomposition method
 Already successfully applied:

to identify distortions:
Shapes modelled with Fourier/Chebyshev
functions or eigenfunctions.
Vector of measurement gaps

 on camshaft
 on bevel gear obtained by net shape forging

Vector of unidentified
distortion
Ph1
to control geometric position of an hexapod
P
Ph2
Vector of identified distortion
phenomena
Orthogonal projection of   least square principle
Conclusion &
Outlook
[6] S. Samper and al., “Form Defects Tolerancing by Natural Modes Analysis”, Journal of Computing and Information Science in Engineering, 2007.
[7] K.D. Summerhays and al., “Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations”,
Precision Engineering, 2002.
[8] L. Vanoverberghe and al., “Detection of deviations origins in a heat treatment process using POD basis”, Int. J. of Material Forming, 2008.
[9] C. Nicolas and al., « Stratégie de contrôle dimensionnel et identification de la déformation d’un produit - Application à une pièce test traitée thermiquement », In the
Proceedings of: Conception et Production Intégrées (CPI), Rabat (Maroc), 2007.
20