jheat

Simulation
Methods
for Inductive
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Annealing of Steel
Jürgen Wibbeler, CADFEM GmbH, Berlin
© CADFEM 2015
ANSYS Conference & 33rd CADFEM Users' Meeting 2014, 24.-26.06.2015, Bremen
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Simulation Methods for Inductive Annealing of Steel
• Introduction
• Technical Challenges of the Coupled-field Simulation
• Reducing Solution Time by Adaptive Harmonic Analysis
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Introduction
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Introduction
• Physics: Joule heat by eddy currents
• Current of kAmps in the inductor
• Fast surface heating with control
on heated region and achieved
temperature
• Target temperatures: >1000°C
• Process duration: <1 s ... 10 s
• Most common application:
Induction hardening of surfaces
www.eldec.de
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Introduction
Benefit of FEM-simulation:
• Identifying lateral area and depth of hardened region
• Finding the optimum geometrical design of an inductor
• Configuring process parameters (effective power, frequency, time, application
of coolant, ...)
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Technical
Challenges
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Coupled-field Simulation
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Technical Challenges of the Coupled-field Simulation
Iterative Simulation Loop:
Electromagnetic
Simulation
Joule
. heat density
q(x,y,z) = ρ·|J|²
Thermal
Simulation
Temperature field T(x,y,z)
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Technical Challenges of the Coupled-field Simulation
Example:
Hair pin
inductor
Band motion
Continuous
steel band
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Technical Challenges of the Coupled-field Simulation
Technical Challenges for a Simulation Environment:
• Temperature range above TCurie (for steel ≈740°C)
 Loss of BH-curve
• Phase transitions of steel (Ferrite, Austenite, Martensite, Perlite, Bainite)
 Material properties depending on temperature AND phase proportions
• Motion of workpiece or inductors and spray units
 Changing electromagnetic model geometry
• Multiple inductors, multiple spray units
 Thermal interaction
• Simulation time
 90% for electromagnetic, only 10% for thermal analyses
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Technical Challenges of the Coupled-field Simulation
Solutions:
• Individual control of material properties for each finite element
• Evaluation of phase transition in each thermal step
• Parameter-based re-modeling of
electromagnetic geometry
• Field interpolation between different
meshes
• Electromagnetics:
Fast adaptive harmonic analysis
of nonlinear fields
Annealing
"Toolbox"
• Modular tool structure for a variety
of process configurations
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Reducing
Solutiondurch
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Adaptive Harmonic Analysis
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Reducing Solution Time by Adaptive Harmonic Analysis
Situation:
• Nonlinear electromagnetic problem
with strong magnetic saturation
• Transient electromagnetic analysis:
Inductor
current
• at least one electric cycle
• about 20 substeps per cycle
 ≈150 equation system solutions
CSG Convergence
• Example: 62500 elem., 172000 nodes
(SOLID236/237)
207400 equations
 ca. 35 min on 12 cores
(single el.-mag. solution!)
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Reducing Solution Time by Adaptive Harmonic Analysis
Alternative:
H=0 or H=Ht-1
• Single linear harmonic solution
of the same model: 31 sec
H(x,y,z)
µr,eff
Concept:
1.0
H
• Use a linear harmonic solution with
effective µr,eff in each finite element.
Set µr,eff = f(H)
• Adapt µr,eff iteratively depending on
local magnetic saturation.
Harmonic
solution
 "Adaptive harmonic analysis"
H, B converged?
No
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
Yes
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Reducing Solution Time by Adaptive Harmonic Analysis
Empirical definition of µr,eff(H) from the original B1(H)-curve:
5.0
Original curve
Area-based curve
4.5
B2(H)
 r, eff 
2000
4.0
3.5
A2
2.5
B1(H)
2.0
µ_r,eff
1500
3.0
B [T]
1
wB1  (1  w) B2 
0 H
1000
w = 1.0
w = 0.0
1.5
A1
1.0
w = 2/3
500
A1 = A2
0.5
0
0.0
0
50000
100000
H [A/m]
150000
200000
• Secant on B1(H) seems insufficient.
 B2(H) based on identical area
below the secant triangle.
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0
2000
4000
6000
H [A/m]
8000
10000
H
2
B2 ( H )   B1 ( H ) dH
H 0
Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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 Compare adaptive harmonic with
a transient solution as reference.
50 Elements/mm
Excitation
of CSGZ
(unit: Amps)
Air (1 mm)
One-dimensional Test Model:
Steel (1 mm)
Adaptive Harmonic Analysis
Air (1 mm)
Criterion:
Distribution of Joule heat generation
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Reducing Solution Time by Adaptive Harmonic Analysis
One-dimensional Test Model: Total Joule Heat
40
w = 1.0 (B1(H))
w = 0.0 (B2(H))
w = 2/3
30
Relative error [%]
• Relative
error to
transient
reference
Saturation through
full metal thickness
20
10
Linear range
0
0.001
-10
CSGZ excitation [A]
0.01
0.1
1
10
100
1000
-20
• Based on B1(H)  JHEAT too low
• Based on B2(H)  JHEAT too high
© CADFEM 2015
 w = 2/3 seems to be optimum.
Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
Reducing Solution Time by Adaptive Harmonic Analysis
JHEAT [W/m³]
One-dimensional Test Model: Distribution of Joule Heat Density
1.8E+10
1.6E+10
1.4E+10
1.2E+10
1.0E+10
8.0E+09
6.0E+09
4.0E+09
2.0E+09
0.0E+00
0.00
CSGZ = 10 A
Transient reference
w = 1.0 (B1(H))
w = 0.0 (B2(H))
w = 2/3
0.20
0.40
Depth [mm]
0.60
 w = 2/3 seems to be optimum also here.
© CADFEM 2015
Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
0.80
Reducing Solution Time by Adaptive Harmonic Analysis
One-dimensional Test Model: Adaptive Harmonic Converged Solution
B [T] (Magnitude)
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µr,eff = B/H/µ0
Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
JHEAT [W/m³]
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Reducing Solution Time by Adaptive Harmonic Analysis
"Hot Test" at the Inductor Model:
• Extension: Exact inductor current is typically unknown.
Effective power (= total heat) is given instead by power sources.
 Use µr,eff-iterations for simultaneously adjusting inductor current
to achieve a given total heat setpoint.
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Reducing Solution Time by Adaptive Harmonic Analysis
"Hot Test" (cont.):
• Transient:
• I = 5000 A (setpoint)
• P = 8130 W (result)
• JHEATmax
= 3.00E+10 W/m³
JHEAT [W/m³]
• Adaptive harm.:
• P = 8130 W (setpt.)
• I = 5175 A (result)
• JHEATmax
= 3.09E+10 W/m³
Cut (see next page)
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Reducing Solution Time by Adaptive Harmonic Analysis
"Hot Test" (cont.): Cut View
• Transient:
• Adaptive harmonic:
[W/m³]
 Result: Very similar JHEAT distributions
© CADFEM 2015
Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Reducing Solution Time by Adaptive Harmonic Analysis
"Hot Test" (cont.): Cut View (Adaptive Harmonic Solution Only)
• Flux density (magnitude):
[Tesla]
(NOTE: Calculated flux density is higher than in a transient solution.)
• Distribution of µr,eff:
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Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Reducing Solution Time by Adaptive Harmonic Analysis
"Hot Test" (cont.): Electromagnetic-thermal Coupled Simulation
• Temperature fields at equal heat power
(P = 7205 W = total heat at I = 5000 A and high temperature, transient)
Transient solution
Adaptive harmonic solution
 Tmax = 661°
 Tmax = 663°C, I = 5149 A
© CADFEM 2015
Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
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Reducing Solution Time by Adaptive Harmonic Analysis
"Hot Test" (cont.): Iterations, Simulation Time
• Single or initial EM-simulation starting from zero magnetic field:
• transient:
47 min / 24 time steps
• adaptive harm.: 18 min / 21 µr,eff-iterations
(ΔBconv = 10 mT)
 Acceleration factor 2.6
• Coupled-field band process:
 Calculating a steady-state thermal field
 Re-use of the previously converged
H-field in each new thermal step
• transient:
738 min
• adaptiv harm.: 145 min (ΔBconv = 10 mT)
 Acceleration factor 5
© CADFEM 2015
Simulation Methods for Inductive Annealing of Steel. J. Wibbeler
Thermal iteration
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µr,eff-iterations
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Thank you!
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