Numerical Insights and Optimization of Magnetic Pulse ...

© Fraunhofer IWS 26.04.2012

Numerical Simulation of Magnetic Pulse Welding: Insights and Useful Simplifications J. Körner, G. Göbel, B. Brenner, E. Beyer


Numerical Simulation of Magnetic Pulse Welding: Insights and Useful Simplifications Julia Körner

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Content

1. Magnetic Pressure Evaluation

1.1 Model

1.2 Electric Result

1.3 Magnetic Result

2. Timeharmonic vs. Transient Calculation

3. The Influence of Meshing

3.1 Model

3.2 Calculation Time and Variation in Currents

4. Conclusions



3

Motivation

Insights and Useful Simplifications

Hidden aspects of Magnetic

Pulse Welding Minimal simulation time

Manner of calculation

Optimized meshing

Fast. Accurate. Easy.

Minimal simulation time


Optimized meshing




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1.1 Model

x

z y


Model consists of:

Flat coil with one turn

Field shaper

Tubular workpiece

Boundary conditions:

Right port: Ground

Left port: Potential

Calculation Method:

Comsol Multiphysics

t700033 et)10cos(2π102.5U(t) ⋅−⋅⋅⋅⋅⋅=



5

1.2 Electric Result: Current in coil


0 50 100 150 200 250 300 350 400

-8x105

-4x105

0

4x105

8x105

1x106

Resulting current in coil Potential at coil's port

Time [µs]

Curr

ent i

n co

il [A

]

-2x103

-1x103

0

1x103

2x103

3x103

Po

tent

ial [

V]

u(t)

i(t)



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1.3 Magnetic Result: Magnetic pressure in workpiece


( )20

B(t)μ21p(t) ⋅⋅

=

Radially from all directions onto the workpiece

Difference in pressure on the inside and outside of the workpiece

Magnetic pressure at the position of the field shaper



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0 50 100 150 200 250 300 350 4000

50

100

150

200

250

300

magnetic pressure on the outside of steel workpiece magnetic pressure on the inside of steel workpiece

Time [µs]

p mag

,out

[MPa

]

0

5

10

15

20

25

30

p mag

,in [M

Pa]


The resulting difference in the magnetic pressure is the quantity which deforms the workpiece

Small negative amount due to the phase shift between inner and outer pressure evolution most significant in the first period

negative pressure

Deng et al: Numerical simulation of magnetic flux and force in electromagnetic forming with attractive force



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The resulting difference in the magnetic pressure is the quantity which deforms the workpiece

Small negative amount due to the phase shift between inner and outer pressure evolution most significant in the first period

0 50 100 150 200 250 300 350 400-50

0

50

100

150

200

250

300

p mag

,eff

[MPa

]

Time [µs]

Difference in magnetic pressure (pmag,out - pmag,in)

negative pressure

Deng et al: Numerical simulation of magnetic flux and force in electromagnetic forming with attractive force



9

Motivation

Insights and Useful Simplifications

Hidden aspects of Magnetic Pulse

Welding Minimal simulation time


Optimized meshing




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2. Transient vs. Time-Harmonic Calculation

Transient

Differential equations solved for each predefined time-step

Arbitrary excitation function

Time-harmonic

System only solved once

Excitation function approximated as a continuous sine wave

All parameters equal zero

Continuous process

+ Accurate solution

- Time-consuming

+ Fast

- May disregard highly transient aspects at the beginning of a pulse

Initial conditions

Advantages / Disadvantages

-4 -2 0 2 4 6 8 10 12 14 16 18 20

-1,0

-0,5

0,0

0,5

1,0

sin(x

)

x-10 0 10 20 30 40 50 60 70

-1,0

-0,5

0,0

0,5

1,0

Y Ax

is Ti

tle

X Axis Title



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2.1 Comparison of currents

0 25 50 75 100 125 150 175 200

-100-80-60-40-20

020406080

100Forming coil

Curr

ent [

kA]

Time [µs]

coil transient coil time-harmonic

No significant error Fast time-harmonic approach applicable Is this assumption always correct?



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0 25 50 75 100 125 150 175 200

-80

-60

-40

-20

0

20

40

60

80Workpiece

Curr

ent [

kA]

Time [µs]

workpiece transient workpiece time-harmonic


0 25 50 75 100 125 150 175 2000

50100150200250300350400450500550600

Workpiece

p mag

, out

side

[M

Pa]

Time [µs]


Inaccuracy or real fact?



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2.2 Idea: Analytical description for the workpiece

Solution of differential equation

Transient Steady-state

i



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0 25 50 75 100 125 150 175 200-125-100-75-50-25

0255075

100125

Time [µs]

Curr

ent [

kA]

F1: Steady-state function F2: Transient function F3: Resulting current of network


0 25 50 75 100 125 150 175 200

-80

-60

-40

-20

0

20

40

60

80Workpiece

Curr

ent [

kA]

Time [µs]




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3.1 Model

A B

x

z

y x

Flat coil with one turn 2 planes were inserted for the meshing simulation



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3.2 Calculation time and variation of currents

0 10 20 30 40 50 60 70 80 900,00,20,40,60,81,01,21,41,61,82,0

Ideality of meshing [%]

Varia

tion

of th

e cu

rren

ts in

the

plan

es [%

]

0200400600800100012001400160018002000

Calc

ulat

ion

time

[s]



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4. Conclusions

Negative parts of the magnetic pressure visible

- Dependent on material and frequency - Influenced by adjusting forming current

Time-harmonic calculations: fast and fairly accurate in some cases

- Knowledge about highly transient aspects necessary

Only one mesh element per skin depth sufficient

- For a certain geometry - Significant reduction of calculation time



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Thank you for your

attention!



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Comsol Multiphyiscs

From the COMSOL website: The COMSOL Multiphysics engineering simulation software environment facilitates all steps in the modeling process − defining your geometry, meshing, specifying your physics, solving, and then visualizing your results.

From: http://www.comsol.com



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Deng: Numerical simulation of magnetic flux and force in electromagnetic forming with attractive force

“[…] In this paper, the principle of electromagnetic attractive force forming is proposed and the effect of the discharge current wave-form on the direction of magnetic force acting on the workpiece is discussed. […]“



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Deng: Numerical simulation of magnetic flux and force in electromagnetic forming with attractive force


„[…] Accordingly, the improved discharge current which ascends slowly, descends quickly, and descends slowly is more suitable for the process of electromagnetic attractive force forming. […]“



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Proposes negative magnetic pressure as a way to remove driver materials

Uses a sine wave as current in coil

Damped current

Derivation of current Magnetic pressure

Steingröver: Patent DE 196 02 951 C 2 Verfahren und Vorrichtung zum Aufweiten von Rohren oder rohrförmigen Teilen durch das Magnetfeld eines Stromimpulses



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1. Magnetic Pressure Evaluation Steingröver: Patent DE 196 02 951 C 2 Verfahren und Vorrichtung zum Aufweiten von Rohren oder rohrförmigen Teilen durch das Magnetfeld eines Stromimpulses

1 Coil

2 Outer part of workpiece

2a Inner part of workpiece

4 Driver ring



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Solution of differential equation

(1)

Homogeneous solution

Right side of eq. (1) is set to zero

,

Special solution

Formulation according to cosine-function of ue(t)

Differentiation and use in eq. (1) leads to special solution

Sum

Numerical Insights and Optimization of Magnetic Pulse ...

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