Annealing of Steel. Jürgen Wibbeler, CADFEM GmbH, Berlin CADFEM ANSYS Conference & 33 rd CADFEM Users' Meeting 2014,

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1 Titelmasterformat Simulation Methods durch for Inductive Klicken bearbeiten Annealing of Steel Jürgen Wibbeler, CADFEM GmbH, Berlin ANSYS Conference & 33 rd CADFEM Users' Meeting 2014, , Bremen 1

2 Simulation Methods for Inductive Annealing of Steel Introduction Technical Challenges of the Coupled-field Simulation Reducing Solution Time by Adaptive Harmonic Analysis Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 2

3 Titelmasterformat Introduction durch Klicken bearbeiten Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 3

4 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 s Most common application: Induction hardening of surfaces Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 4

5 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,...) Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 5

6 Titelmasterformat Technical Challenges durch of Klicken the bearbeiten Coupled-field Simulation Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 6

7 Technical Challenges of the Coupled-field Simulation Iterative Simulation Loop: Electromagnetic Simulation Joule. heat density q(x,y,z) = ρ J ² Temperature field T(x,y,z) Thermal Simulation Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 7

8 Technical Challenges of the Coupled-field Simulation Example: Hair pin inductor Band motion Continuous steel band Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 8

9 Technical Challenges of the Coupled-field Simulation Technical Challenges for a Simulation Environment: Temperature range above T Curie (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 Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 9

10 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 Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 10

11 Titelmasterformat Reducing Solution durch Time Klicken by bearbeiten Adaptive Harmonic Analysis Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 11

12 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 Example: elem., nodes (SOLID236/237) equations CSG Convergence ca. 35 min on 12 cores (single el.-mag. solution!) Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 12

13 Reducing Solution Time by Adaptive Harmonic Analysis Alternative: Single linear harmonic solution of the same model: 31 sec H(x,y,z) H=0 or H=H t-1 µ r,eff Concept: Use a linear harmonic solution with effective µ r,eff in each finite element. 1.0 Set µ r,eff = f(h) H Adapt µ r,eff iteratively depending on local magnetic saturation. "Adaptive harmonic analysis" Harmonic solution H, B converged? Yes Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 13 No

14 B [T] µ_r,eff Reducing Solution Time by Adaptive Harmonic Analysis Empirical definition of µ r,eff (H) from the original B 1 (H)-curve: Original curve Area-based curve A 1 A 2 B 2 (H) B 1 (H) A 1 = A r,eff 0 1 H wb 1 (1 w) B w = 1.0 w = 0.0 w = 2/ H [A/m] H [A/m] Secant on B 1 (H) seems insufficient. B 2 (H) based on identical area below the secant triangle. 2 B2 ( H) B1 ( H) dh H H 0 Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 14

15 Air (1 mm) Steel (1 mm) Air (1 mm) 50 Elements/mm Adaptive Harmonic Analysis One-dimensional Test Model: Excitation of CSGZ (unit: Amps) Compare adaptive harmonic with a transient solution as reference. Criterion: Distribution of Joule heat generation Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 15

16 Relative error [%] Reducing Solution Time by Adaptive Harmonic Analysis One-dimensional Test Model: Total Joule Heat Relative error to transient reference CSGZ excitation [A] w = 1.0 (B1(H)) w = 0.0 (B2(H)) w = 2/3 Linear range Saturation through full metal thickness Based on B 1 (H) JHEAT too low Based on B 2 (H) JHEAT too high w = 2/3 seems to be optimum. Simulation Methods for Inductive Annealing of Steel. J. Wibbeler

17 JHEAT [W/m³] Reducing Solution Time by Adaptive Harmonic Analysis One-dimensional Test Model: Distribution of Joule Heat Density 1.8E E E E E E E E E E Depth [mm] w = 2/3 seems to be optimum also here. CSGZ = 10 A Transient reference w = 1.0 (B1(H)) w = 0.0 (B2(H)) w = 2/3 Simulation Methods for Inductive Annealing of Steel. J. Wibbeler

18 Reducing Solution Time by Adaptive Harmonic Analysis One-dimensional Test Model: Adaptive Harmonic Converged Solution B [T] (Magnitude) µ r,eff = B/H/µ 0 JHEAT [W/m³] Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 18

19 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 µ r,eff -iterations for simultaneously adjusting inductor current to achieve a given total heat setpoint. Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 19

20 Reducing Solution Time by Adaptive Harmonic Analysis "Hot Test" (cont.): Transient: I = 5000 A (setpoint) P = 8130 W (result) JHEAT max = 3.00E+10 W/m³ JHEAT [W/m³] Adaptive harm.: P = 8130 W (setpt.) I = 5175 A (result) JHEAT max = 3.09E+10 W/m³ Cut (see next page) Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 20

21 Reducing Solution Time by Adaptive Harmonic Analysis "Hot Test" (cont.): Cut View Transient: Adaptive harmonic: [W/m³] Result: Very similar JHEAT distributions Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 21

22 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 µ r,eff : Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 22

23 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 T max = 661 Adaptive harmonic solution T max = 663 C, I = 5149 A Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 23

24 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 µ r,eff -iterations (ΔB conv = 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 (ΔB conv = 10 mt) Acceleration factor 5 Thermal iteration µ r,eff -iterations Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 24

25 Titelmasterformat Thank you! durch Klicken bearbeiten Simulation Methods for Inductive Annealing of Steel. J. Wibbeler 25