Role of surface temperature
in laser forming
Zygmunt Mucha 1,2, Jacek Widłaszewski 2,
Marek Cabaj 1, Ryszard Gradoń 1
1
Center for Laser Technology of Metals, The Kielce University of
Technology and Polish Academy of Sciences, Kielce, Poland
2
Institute of Fundamental Technological Research, PASc,
Warsaw, Poland
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Programme
• Introduction. Thermal bending – macro and ... nano
• Surface temperature aspect in studies
• On the FEM simulations
• Analytical modeling
• Experimental verification
• Conclusions
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Flame bending
Legs of the Space Needle (Seattle, USA) bent by
heating with gas torches.
[Holt R. E., Flame straightening basics. Welding Engineer, Sept. 1965]
[Holt R. E., Primary concepts of flame bending. Welding Journal, June 1971]
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Laser micro-bending
IBM has developed and implemented in manufacturing of hard disk
drives a process called Laser Curvature Adjust Technique (LCAT).
This closed-loop microscopic laser-shaping process can produce
desired slider curvatures, particularly, crown and camber, to
accuracies of a few nanometers.
[http://www.almaden.ibm.com/sst/html/lpro/microbending.htm]
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Surface temperature aspect in studies
• Magee, Watkins et al. 1997:
the dimensions of the final part and the rate of bending can
be controlled primarily from the temperature field
• Casalino, Ludovico et al. 2001:
experiments in which melting of the treated materials was
not allowed. Maximal value of the bend angle turned out to
result from processing with the maximal surface
temperature close to the melting point.
• Li, Yao 1999:
analysis of the laser bending process in conditions of
constant maximal surface temperature. Laser beam power
for a given maximal temperature and beam velocity was
estimated iteratively with the use of FEM simulations.
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FEM simulations of
laser forming and line heating
Full three-dimensional FEM
simulation of forming with
moving heat source typically
takes hours or days for
computation, and therefore is
impractical for real-time
applications [Yu, Masubuchi et
al. 2001], [Yu, Anderson et al.
2001]
Computing time with CRAY YMP-EL: 5.5 h
[Holzer S., Berührungslose Formgebung mit
Laserstrahlung. Reihe Fertigungstechnik Erlangen,
Bd. 57. Meisenbach Bamberg 1996]
Simplified modelling
methods are sought
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Analytical modelling
v
x
zpl
Tpl
Assumptions:
• The heat source moves fast
• Rectangular inherent strain zone is
produced under the heat source path
• Depth of the zone is determined by the
range of the critical temperature Tpl, at
which material does not resist to the load
• The temperature field is quasi-stationary
in a coordinate system related to the heat
source
• Distribution of temperature in the inherent
strain zone is taken into account
z
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Nondimensional / normalized parameters
Temperature
θ=
Q=
Power
S=
Velocity
T − T0
T pl − T0
Notation:
A – the absorption coefficient
AP
2πλ (T pl − T0 )h
λ – the thermal conductivity coefficient
vh
2κ
κ
Bend angle
αB =
Depth
Z=
Beam length
l
L=
h
Beam breadth
B=
αb
h – plate thickness
– the thermal diffusivity
α th – the thermal expansion coefficient
α th (Tpl − T0 )
z
h
b
h
The Fourier number:
Fo =
τ
κτ
h2
=
κb
vh 2
=
B
2S
- beam-material interaction time
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Temperature field
v
x
zpl
T ( x, z ) =
Tpl
z
Fast heat source (SB>>1)
θ=
θ=
Ashby, Easterling 1984:
the real heat source on the material θ =
surface is replaced by an apparent
source above the surface
AP  r v 
-xv
K o   exp
 + To
πλ l  2κ   2κ 
2Q
K o ( SR) exp(− SX )
L
π 2Q
2e LSZ
π
1 B
2Q
, Z0 =
2 eS
2e LS ( Z + Z 0 )
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Surface temperature - analytical
Circular heat source
θS =
TS =
8Q
θS =
2 SD 3
4 AP
κ
πλ
vd 3
D=3
20
15
10
5
10
15
2 AP
κ
+ T0
lλ π vb
L=3.67 B=2.17
30
25
5
20
25
DIMENSIONLESS VELOCITY S
8π Q
SB L
DIMENSIONLESS TEMPERATURE θ
S
DIMENSIONLESS POWER Q
DIMENSIONLESS POWER Q
TS =
+ T0
DIMENSIONLESS TEMPERATURE θ
30
Rectangular heat source
30
S
25
20
15
10
5
5
10
15
20
25
DIMENSIONLESS VELOCITY S
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Deformation
Plate is modelled as the Bernoulli-Euler beam
with imposed inherent strain field
Elasticity problem
with inherent strain
σ yy ( z ) = E (ε 0 + zC + α th ∆T ( z ) H ( z pl − z ) )
h
h
∫σ
Equilibrium conditions
yy
( z ) dz = 0
α B = 3 Lθ S
yy
( z ) z dz = 0
0
0
Solution for the angle
of bend (rectangular
beam)
valid for
∫σ

2 Fo 
2 Fo 
2 Fo


(θ S − 1)
ln θ S −
 1+
e 
e 
e

θ S ≥ 1 and
Z pl = Z 0 (θ S − 1) ≤ 1
Notation:
E – the Young’s modulus
ε 0 – uniform contraction strain component
C – plate curvature
H(z) – the Heaviside’s function
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Experimental set-up
Laser: CO2 TLF6000 TRUMPF 6 kW
Beam intensity distribution:
circular cross-section – TEM01*,
rectangular - uniform (segmented mirror)
Absorber: graphite
Scanning: CNC table
Displacement sensor: inductive LVDT
Bend angle: calculated from linear displacement
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Temperature measurements
1500
Irradiation 1
Irradiation 2
Irradiation 3
Two-color fiberoptic pyrometer Raytek FR1A CF1
TEMPERATURE [oC]
1400
Nominal spectral response:
0.75 – 1.1 µm, 0.95 – 1.1 µm
1300
Special filter required due to disturbance from
10.6 µm radiation (CO2 laser beam)
1200
Material: St3
h = 3 mm
d = 9.9 mm
P = 3410 W
v = 3500 mm/min
1100
1000
900
Directly under laser beam
//
//
TIME
1 [s]
Recalibration; measurement range shift
Contact sensor – constant initial material
temperature
Mean temperature during first irradiation was
considered
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Surface temperature - experimental
Circular beam
8Q
θS =
= const
3
2 SD
TS =
κ
4 AP
πλ
vd
3
Rectangular beam
+ T0 = const
TS =
1600
2 AP
κ
+ T0 = const
lλ π vb
1400
1400
1200
1200
TEMPERATURE [oC]
TEMPERATURE [oC]
8π Q
= const
SB L
θS =
1000
Material: St3
h = 3 mm
d = 9.9 mm
P = 2230 ... 5150 W
v = 1.5 ... 8 m/min
experiment
linear approx.
800
600
400
200
1000
Material: St3
h = 3 mm
l = 11 mm
b = 6.5 mm
P = 670...6000 W
v = 0.1 ... 8 m/min
experiment
linear approx.
800
600
400
v max
8
=
= 40
v min 0.2
200
0
1
2
3
4
5
v [m/min]
6
7
8
0
0
2
4
v [m/min]
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6
8
Bend angle - experimental
Analytical solution for the rectangular beam
α B = 3 Lθ S
DIMENSIONLESS BEND ANGLE α Β
Example of the bend angle time run
during 3 scans with the circular beam
9
Material: St3, h = 3 mm
Laser beam: 11 x 6.5 mm
Power: 670 ... 6000 W
experimental
analytical (SB>>1)
8
7
6
5
4
3
θ S = const
2
1
0
0
Negligible bending away from the laser
beam (counter-bending, convex bending)

2 Fo 
2 Fo 
2 Fo
 ln θ S −
(
)
1
θ
−
1 +

S
e 
e 
e

4
8
12
16
DIMENSIONLESS VELOCITY S
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Temperature and bend angle
in laser forming
Rectangular laser beam
8π Q
B
θS =
Fo =
DIMENSIONLESS BEND ANGLE α
L = 3.67 B = 2.17
30
DIMENSIONLESS POWER Q
Β
25
α B = 3 Lθ S
20
SB L
2S

2 Fo 
2 Fo 
2 Fo
 ln θ S −
(
)
−
1
θ
1 +

S
e 
e 
e

Melting of a mild steel
θ = 2.5
15
S
10
Tmelt ≈ 1820 K
T pl ≈ 910 K
θ=
Process parameters window
for bending without material
remelting
θ =1
5
S
5
10
15
20
25
DIMENSIONLESS VELOCITY S
30
Temperature threshold for
permanent deformation
producing
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T − T0
Tpl − T0
Conclusions
• Surface temperature is the key parameter of the laser bending
process.
• The highest bend angles are produced for the maximal
allowable surface temperature. The limit can result from the
material melting temperature, in particular.
• Measurements made with two-colour pyrometer in processing
with heat source velocity changing by a factor of 40 and power
changing accordingly by a factor of 6 confirmed possibility of
programming (e.g. maintaining constant) surface temperature.
• Derived analytical dependences for surface temperature can be
applied to different heat treatment processes.
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References
[Ashby, Easterling 1984] Ashby M. F., Easterling K. E., The transformation hardening of
steel surfaces by laser beams – I. Hypo-eutectoid steels. Acta Metall. Vol. 32, No 11,
1935-1948, 1984.
[Casalino, Ludovico et al. 2001] Casalino G., Ludovico A. D., Ancona A., Lugarà P. M.,
Stainless Steel 3D Laser Forming for Rapid Prototyping. International Congress on
Applications of Lasers and Electro Optics, ICALEO 2001, Laser Materials Processing
Proceedings, Section D - Surface Modification, Rapid Prototyping and Laser Forming.
Laser Institute of America, 2001.
[Jang, Seo, Ko 1997] Jang C.D., Seo S.I., Ko, D.E., A Study on the Prediction of
Deformations of Plates Due to Line Heating Using a Simplified Thermal Elastoplastic
Analysis. Journal of Ship Production. Vol. 13, No. 1, 1997, pp. 22-27.
[Li, Yao 1999] Li W., Yao Y. L., Effects of strain rate in laser forming. Proceedings of the
Laser Materials Processing Conference ICALEO ’99, LIA Volume 87 (1999), Section F,
107-116.
[Magee, Watkins et al. 1997] Magee J., Watkins K. G., Steen W. M., Calder N., Sidhu J.
and Kirby J., Laser Forming of Aerospace Alloys. In the Proceedings of the 16th
International Congress of Lasers and Electro Optics, (ICALEO’97), Section E, 1997,
156-165.
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References continued
[Mucha 2003] Mucha Z., Advanced analytical model for laser bending. To be presented at
“Laser Technologies in Welding and Materials Processing” International Conference,
Katsiveli, Ukraine, May 19-23, 2003.
[Watanabe, Satoh 1961] Watanabe M., Satoh K., Effect of Welding Conditions on the
Shrinkage Distortion in Welded Structures. The Welding Journal, Welding Research
Supplement 40 (August 1961) 8, 377-384.
[Yu, Anderson et al. 2001] Yu G., Anderson R. J., Maekawa T., Patrikalakis N. M., Efficient
Simulation of Shell Forming by Line Heating. International Journal of Mechanical
Sciences. Vol. 43, No. 10, 2349-2370, October 2001.
[Yu, Masubuchi et al. 1999] Yu G., Masubuchi K., Maekawa T., Patrikalakis N. M., FEM
simulation of laser forming of metal plates. Journal of Manufacturing Sciences and
Engineering. Vol. 123 (2001), 405-410.
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Thank you for the attention
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