Electrothermal Analysis OfElectric Resistance Spot Welding Processes by a 3-D Finite Element

8/17/2019 Electrothermal Analysis OfElectric Resistance Spot Welding Processes by a 3-D Finite Element

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ELSEVIER

Joumal

of

Materials Pro eSSing Te..imology 63 1997) 672-677

JournaJof

aterials

rocessing

Technology

Electrothermal Analysis ofElectric Resistance Spot Welding Processes by a 3-D Finite Element

Method

H Huhand W J Kang

Dept.

of

Mechanical Engineering

Korea Advanced Institute

of

Science

n

Technology

373 1 Kusongdong Yusonggu Taejon 305 701 Korea

bstract

Electric resistance spot welding which is an important process in auto-body assembly is simulated by a 3-D finite element code

developed. The main interest in the simulation is the quality

of

welding and the durability of electrodes, which needs electrothermal

analysis for temperature distribution in both electrodes and welded sheets. A finite element formulation is derived for both electric

analysis and thermal analysis that are coupled together. The contact resistance between electrodes and sheets is especially treated with

artificial interface elements in which the material properties for electric and thermal analysis are artificially imposed for physically

reasonable simulation.

1. Introduction

Electric resistance spot welding is an important process in the

industry.

In

electric resistance spot welding, the overlapping

work is positioned between the water-cooled electrodes, then the

heat is obtained

by

passing a large electrical current for a shot

period of time. Auto-body assembly needs 7000 to 12000 spots

of welding according

to

the size of a car, so the spot welding is

an important process in auto-body assembly. Each spot welding

is not performed on the same condition because of the alignment

of sheets and electrodes as well as the surface condition. For that

reason, a spot welding process needs the optimum process

condition that can afford allowance in parametric values for good

quality of welding. The optimum condition has to consider the

amount and duration

of

electric current, the shape and material

properties of electrode, and the surface condition and alignment

of sheets. The main interest in spot welding process is the

quality of welding and the durability of electrodes, which needs

electrothermal analysis for temperature distribution in both

electrodes and welded sheets[IJ[2J[3]. The shape

of

electrode is

an important parameter determining the shape and size of the

nugget which has large effects on the stress concentration and

fatigue strength of welding parts. The stress distribution in the

lap joint of spot-welded steel is calculated by finite element

method[4]. The effect of a space angle of line contact is

analytically calculated[5].

In this paper, a finite element formulation is derived for both

electric analysis and thermal analysis that are coupled together.

Two sets of formulation are uncoupled after finite dimensional

approximation to a time-incremental analysis. First, the electric

0924-0136/97/ 15.00

1997 Elsevier Science S All rights reserved

PII S0924-0136 96)02705-7

potential is obtained for the entire field and scaled according to

the given electric current. The electric field obtained is used to

calculate the energy dissipation due

to

the electric resistance of

materials. The energy dissipation calculated from the electric

analysis is substituted for the heat generation in the heat

conduction equation to calculate the temperature distribution in

the entire domain. After the calculation, all material properties

are updated element-wise for the next step according

to the

calculated temperature. The finite element code developed

simulates electric resistance spot welding processes with the

variation of process parameters such as the electric current, the

contact resistance, and the material properties

of

electrodes and

sheets. The contact resistance between electrodes and sheets is

especially treated with artificial interface elements in which the

material properties for electric and thermal analysis are

r t i f i i ~ l l y imposed for physically reasonable simulation. The

numerical result provides the electric potential field, the electric

current distribution, and the temperature distribution. Elliptic

electrodes are studied with the variation

of ellipticities on

condition of the same tip area. The results informs that the shape

of electrodes is important in distribution

of

the electric current

and thus the heat generation. On the same welding condition

such as the welding current, the weldtime and the pressure, the

size of nuggets obtained

by

various shapes

of

electrodes which

have the same contact area are different from each other.

Relation between the shape

of

nugget and the shape of electrode

is important for the purpose of obtaining necessary nuggets

which appropriate to the various stress condition and the number

of

spots can be reduced

by

selecting an adequate elliptic

electrode.


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H Huh W J Kang / Journal Materials Processing Technology 63 (1997) 672-677 673

where P is the density, cp is the specific heat per unit volume,

kij is

the heat conductivity, and f id heat generation calculated

form Eqn (6).

2. ormul tion for electrotherm l analysis

The heat lOr electric resistance spot welding is obtained

by

passing a large electric current through workpieces which have

electric resistance in the domain and contact surfaces. The

amount of heat generation per unit volume can be calculated by

the electric potential in the domain and then it can be applied

to

the heat transfer equation

to

calculate the temperature

distribution in the electrode and workpieces. The maximum

temperature in electrodes and workpieces approaches the phase

change temperature and the effect of latent heat is considered by

increasing a specific heat in the temperature range

of

phase

change as Eqn

1 .

T=T

o

at

t=O

D

on aD

7

(8)

9

(1)

where H

L

is a latent heat, T

L

is a melting temperature, and Ts is

solidifying temperature.

3. inite element formul tion

When the principle of

the first variation is applied

to

Eqn

(2)

and Eqn (7), respectively, weakforms can be obtained

as

Eqn

10 and Eqn 11 .

2 Formulation relectric analysis

The electric potentia] can be expressed by Quasi-Laplace

equation. The governing equation and its boundary condition are

as

follows.

C lV - -

Clx; Oij Clxj Vdn =0,


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Huh W J Kang / Journal Materials Processing Technology 63 1997) 672-677

of

matrix equations are obtained for electrothermal analysis

For finite e lement simulation Eqn 16) is first solved

to

calculate heat generation from the electric potential. The heat

generation calculated is substituted in Eqn 18), which is solved

for temperature distribution at the specific time. According to the

temperature distribution obtained, all electrothermal properties

are updated element-wise for the next time increment step. This

procedure continues until a desired temperature distribution is

obtained.

Fig. 2 through Fig. 5 show the electric and thermal properties

for the present analysis with the variation of the temperature.

As

shown in Fig. 2, the electric resistance in contact interface

between workpieces is larger than that between

an

electrode and

a workpiece. Both values are decreased

as

the temperature

increases[7]. The electric resistivity and Heat conductivity

of

a

steel workpiece is much larger than those

of

a copper electrode

as

shown in Fig. 3 and 4.

As

the t emperature goes up, a steel

workpiece experiences phase changes absorbing the heat

energy[9]. In order to describe the phenomenon, the specific heat

per unit volume is modified

by

the enthalpy method thus the

heat capacitance is represented as shown in Fig.

5

Fig. 6- a) through Fig. 8- b) explains temperature

distributions in

an

electrode and a workpiece with respect to

each ellipticity. The shape

of

nuggets in the faying surface is

nearly the same

as

the shape

of an

electrode tip. However, the

amount

of

temperature rise and the nugget growth closely

depends on the ellipticity. The comparison has made for various

ellipticity in Fig. 9 to Fig. II

Fig. 9 represents relation between the electrode ellipticity and

the nugget ellipticity. In this curve the nugget ellipticity nearly

follows that

of an

electrode except when the ellipticity is 0.25.

Fig. 10 and Fig.

represents relation between the electrode

ellipticity and the nugget area and thickness obtained

respectively. In contrast to the nugget ellipticity, the nugget area

and thickness shows asymptotic behavior demonstrating the poor

nugget growth when the ellipticity is smaller than a certain value.

Fig. 2 represents dynamic resistance curves vs. time with

the variation

of

the ellipticity. The figure shows the global

electric resistance decreases with the decrease of the ellipticity,

which indicates the amount

of

the heat energy generated. The

efficiency

of

welding decreases

as

the ellipticity decreases.

When an elliptic nugget is needed for a strength purpose,

an

elliptic electrode

of

the ellipticity more than 0.4 can be selected

to

maintain the welding efficiency and nugget size.

18)

17)

16)

the Crank-

with the first and initial boundary conditions.

Eqn 17) can be integrated in time

by

applying

Nicholson s

e-

Method

as

shown in Eqn 18).

Results and discussion

The shape and size

of

nuggets are calculated with a 3-D

electrothermal finite element code developed. In the computation,

the electric current

of

12000 amperes passes through the

electrodes and workpieces during the time

of

l2cycles

0.2second). The material

of

sheets is steel and the size is

assumed 30mm x 30mm x 1.6mm which is sufficient for good

simulation

of

a real process. The ell ipti ci ties

of

the elliptic

electrodes are

1 0 0 75 0 5

0.4, and 0.25 with its tip area being

constant

as

38.44mm

so that the electric contact resistance

in

each case assumed the same.

Fig. 1 represents typical finite element meshes used in this

analysis. Because the welding system is symmetric, one eighth of

the system can be modeled in the analysis. To consider the

electric contact resistance, one-layered artificial interface

elements is used on each contact surfaces. The electrothermal

properties

of

artificial interface elements are carefully chosen to

have reasonable physical meaning considering complicated

contact phenomena[6-9]. Fig. 1 Finite element mesh

of an

elliptic electrode and a sheet.


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H

Huh

W

J Kang / Journal Materials Processing Technology 63 1997 672-677

675

2000

1 e l e c t o d ~

,- -

- workpIece

1\

o

500

1000

1500

Tempera ture DC

Fig. 5 Heat capacitance in an electrode and a workpiece with

respect to the temperature.

1.5

30

0

u

x

electrode

;>--

1.2

Mel

.....

- workpiece

u

:>

.....

8 20 0


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676

Huh J Kang / Journal Materials Processing Technology 63 1997 672-677

A

. 170E 04

0

150E 04

0

160E 04

9

. 140E+04

9 . 150E 04 8

.

130E 04

8

. 140E 04

7

120E 04

7

.

130E 04

6

. 110E+04

6

. 120E 04

5

100E 04

5

. 110E 04

4

900E 03

4

100E 04

3

800E 03

3

900E 03

2

700E 03

2

800E 03

1

600E 03

1 700E 03

Min=25°c

Max= I733°C

Fig. 7- a Temperature distribution in the xy plane when the

ellipticity is

0.5.

Fig. 8- b Temperature distribution in the yz plane when the

ellipticity is

0.25.

Electrode ellipticity

. 170E 04

0

160E 04

9

. 150E 04

8

.

140E 04

7

130E 04

6

120E 04

5

. 110E 04

4

100E 04

3

900E 03

2

800E 03

1

700E 03

[

2

;>-,

1.0

u

O 8

-

0.6

Q

0.4

£l

l

O 2

0.0

O

0

O

2

O

4 0.6

O

8

1.0

2

Fig. 7- b Temperature distribution in the yz plane when the

ellipticity is

0.5.

Fig. 9 Relation between nugget ellipticity and electrode

ellipticity.

20

Electrode area =38 44mm

2

2 2 O 4

O

6

O

8

0

Electrode

ellipticity

15

< J

l l

10

o

O 0

o 150E 04

9 .

140E 04

8 130E 04

7 120E 04

6 . 110E 04

5 100E 04

4

900E 03

3 800E 03

2 7 0 0 E 0 ~

1

600E 03

Min=25°c

Fig. 8- a Temperature distribution in

xy

plane when the

ellipticity is

0.25.

Fig. 10 Relation between nugget area and electrode ellipticity.


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uh W Kang / Journal Materials Processing Technology 63 (1997) 672-677

677

Fig. 11 Relation between nugget thickness and electrode

ellipticity.

1.0

O

8

..

j)

s

j ) . - 4

s u

.- 4

O

6

c:

.c:

j)

u

0.4

j)

j .-

00 p .

00 .- 4

::>

H

z

0

O 2

o

0

0.0

O 2 O 4 O 6 O 8

I

0

Electrode ellipticity

I

2

5. Conclusion

Electric resistance spot welding is simulated

by

a 3-D

electrothermal finite element code developed considering the

temperature dependent electrical and thermal properties.

In

this

simulation elliptic electrodes are adopted and the effects of the

variation

of

their ellipticities on the acquired nuggets are

calculated. Among simulated electrodes,

an

circular-shaped

electrode can produce the largest nugget under the same welding

condition. The welding efficiency shows asymptotic relation

to

the ellipticity

of an

electrode. When

an

elliptic nugget is needed

for a strength purpose, an elliptic electrode

of

the ellipticity

larger than 0.4 can be selected

to

maintain the welding efficiency

and nugget size. An elliptic electrode is used in this range then

the obtained nugget have smaller stress concentration than that

of

circular nugget at the short edge

of

nugget.

References

150

140

j)

u

l:1

oj

130

j)

120

u

-x-e=1.0

110

Q e=O.75

s

e=O. 5

.

C l

e=O. 4

00

e=O. 25

90

O 00

O

05

O

10

O

15

O

20

O

25

Time (sec.)

Fig. 12 Variation

of

the dynamic resistance with respect

to

time

for various ellipticity.

[1]

F. Houchens,

R. E.

Page and

W. H.

Yang,

In

Numerical

modeling

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by R.

F. Jones, H.

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[3]

W. Rice and E.

J.

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(1967)175.

[4]

D.

H.

Bae, J. Niisawa and

A.

Koiso, KSME, spring

conference, (1987)7.

[5] Y .

Sano, IEEE Trans., vol. CHMT-8, (1985)228.

[6] S. R. Robertson, IEEE Trans., VoI.CHMT-5, No.1, (1982)3.

[7] W . L

Roberts, The Welding Journal, Nov. (1951)1004.

[8] J. Greenwood, Brit. J. Appl. phys., Vol.17 (1966)1621

[9]

C.

Bonacina, G. Comini,

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Fasano and

M.

Primicerio, Int.

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Electrothermal Analysis OfElectric Resistance Spot Welding Processes by a 3-D Finite Element