Theoretical Analysis of Current Distribution in

Electric Resistance Welding*

By Michio SAI T 0, * * Hiroji KASAHARA, * * * Hirotomo

and Shuxo WA TANABE * * *

TOMINAGA***

Synopsis In order to manufacture a fairly heavy walled pipe, the distribution of

the electric current in the strip edge of Vee apex zone was analyzed by comparing the measured and calculated electric circuit constants in Vee apex zone.

From the result of the analysis it can be concluded that the current in strip edges has a tendency to flow uniformly as the strip thickness increases and, also, that the overheat at the corner of strip edges can be reduced to an allowable level by employing a small apex angle and mild welding condition. In addition, it is found that the large amount of upset is needed to ob-tain a sound quality of welding. So, the proper welding conditions of heavy wall are selected to be as follows, mild welding condition, i.e., slow welding speed, small apex angle and large amount o f upset. A fairly heavy walled ERW pipe with large outside diameter of 2I inch c x 19.05 are manufactured by applying the proper conditions. The toughness of the weld part is proved to have excellent toughness.

I. Introduction

Recently, the demand of High Frequency Electric Resistance Welding (HFERW) pipes for line pipe and OCTG has been expanded to large out diameter, heavier wall thickness and higher grade pipe. One of the best idea to cope with this problem is to inves-tigate forming and welding processes in order to pre-vent edge wave, weld defects, etc.

In ERW process, high frequency current is intro-duced through sliding contact electrodes to edges of a strip, which is formed into a tubular shape. The edges are selectively heated to a welding temperature by skin effect and proximity effect of high frequency current. The heated edges of the strip are pressed together by the squeeze rolls to form a welded pipe.

In the process, the welding phenomena was dif. ficult to be analyzed, because the measurement of the parameters such as temperature, welding current, etc., was interrupted by the noise due to high frequency, high voltage, bad atmosphere with cooling water and high welding velocity.

However, the welding phenomena have recently been clarified by various methods. It has been con-sidered that the corners of the strip edges are more easily heated than the middle surface of the strip edges, because the high frequency current is concen-trated at the corners of edges. Haga et a1.' pointedd out that the selective heating at the corner of the strip edges was proportional to the wall thickness of pipes. The available wall thickness has been about 16 mm so far. However, the demand for line pipes has re-

cently increased toward heavier walls over 16 mm. Authors have made it possible to manufacture pipes

of fairly heavy wall thickness by investigating the basic characteristic of ERW and applying the results to the manufacturing process.

This report deals with the welding phenomena and the weld quality of fairly heavy walled pipes.

II. Investigation Method

The self inductance and resistance of Vee apex zone in ERW changes depending on the current distribu-tion in the zone, so the current distribution can be

presumed through the measurement of self inductance and resistance by taking them the other way round.

The self inductance and the resistance were mea-sured at 400 kHz by LCR meter, using quasi Vee apex specimens with various thickness and Vee apex angle, as shown in Fig. 1.

Though Vee apex zone in making a pipe shows three-dim.entional shape, it is considered that Vee apex zone as shown in Fig. 1 is validly used in order to investigate the effect of the shape on the current dis-tribution in the zone. Vee apex angle is 3 to 6 deg.

The self inductance (L) and resistance (R) of Vee apex zone under various current distribution were cal-culated respectively by Eqs. (1) and (2). Equation

(1) is derived by assuming that the electric current is concentrated in the corners of strip edges, as is shown in Fig. 2. The deviation of the equation is explained in detail at Chap. III.

Fig. 1. Quasi Vee apex zone specimen.

*

**

***

Based on the papers presented to the 105th ISIJ Meeting, April 1983, S369, at The University of Tokyo in Tokyo and to the 106th ISIJ Meeting, October 1983, S1220, at Akita University in Akita. Manuscript received on August 26, 1985; accepted in the final form on March 4, 1986. © 19861SIJ Chita Research Department, Iron & Steel Research Laboratories, Kawasaki Steel Corporation, Kawasaki-cho, Chita 475.

Chita Works, Kawasaki Steel Corporation, Kawasaki-cho, Handa 475.

Research Article ( 461)

( 462) Transactions ISIJ, Vol. 26, 1986

L = - P0 -a2 tan-i li tan fl +ali tan O 2~rb' tan 0 a

+ (li tan 0)2 tan' li tan -a11 tan U

a

(li tan 0)2 -li tan l x In + 1 + (a-b')2 tani a2 a-b'

-(a-b')li tan 0-(li tan 0)2 tan-i li tan 0 a-b'

ll tan2 0 +(a-b')litandln +l (b')2 ...............(1)

where, Po : the magnetic permeability (=1.26 x 10 H/m)

b' : the current separate depth from inner or outer surface

0 : Vee apex angle 2a: wall thickness

1, : the distance from V convergency point to contact tip.

2li R =pbxb' ........................(2)

where, S: cross sectional area of current path b : current penetration depth from strip

edges p: specific resistance.

The current distribution was discussed by cornpar-ing the measured results with the calculated results.

III. Theoretical Analysis of Self Inductance in Vee Apex Zone

To derive the equation of self inductance, both edges of Vee apex zone were subdivided along the longitudinal direction and the subdivided portion was assumed parallel as is shown in Fig. 3. Magnetic field Hx of point P at distance r from one side of strip edge in the subdivided portion is represented by Eq.

(3),2) on the assumption that the current in strip edge flows separately within depth b' from both surface and the current penetration depth b from. strip edges is considerably small as compared with wall thickness.

Hx=-_!(01_02) (3)

where, I0: total current

D1: angle L PAB

02: angle L PBC. Magnetic flux d~b0, caused by the current in one

side of the strip edges in an infinitesimal part dr of Fig. 3 is given by Eq. (4).

-1i010d1 dJ0 _ 2

rb' (0i - U2) • dr ...............(4)

where, dl: length of parallel edge dr : infinitesimal part at distance r from one

side edge. Therefore, total magnetic flux `YO in the subdivided

portion, generated by the current in one side of the strip edges can be derived by summing up d~b0 gen-erated by each infinitesimal part. Equation (5) gives the results.

p010dl R c5° _ 2Trb' (O1- H2) • dr

1i010d1 R a R 2 = - 2ir6, R tan' a - 2 In 1 + -a

2

-R tan-i R + a In 1 + R a-b' 2 a-b'

...........................(5)

r where, tan 0i = -a

tan B2 = r - -

a-b'

R : distance between both strip edges. Magnetic flux d¢, caused by the current in one side

of the strip edges in a subdivided portion dl of Fig. 4 is given by Eq. (6), on the assumption that the Vee

Fig. 3. Vee apex zone subdivided in the longitudinal direc-

tion.

Fig. 2. Quasi current path of Vee apex zone. Fig. 4. Vee apex zone.

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apex angle B is very small.

2 do _ P0;° • x x•tan-1 - a In 1 + x 2

2rb tan B a 2 a

x -x tan-1ab, + a In 1 + x , - 2 a-b

...........................(6)

(R=x=lltanO)

Total magnetic flux ~b in Vee apex zone, generated by the current in one side of the strip edges can be derived by summing up d~b generated by each sub-divided zone. Equation (7) gives the results.

010 li tan d x a x tan-1-- ~'- _ 2rrb' tan © o a 2

'x2 x a-b' X In 1+ a )J_xtanl - a-b' + 2- x 2

x In 1+ b,dx ...........................(7)

Therefore, the self inductance L of Vee apex zone is represented by above-mentioned Eq. (1), because L is 201.

Iv. Results and Discussion

1. Current Distribution in Vee Apex Zone

The measured self inductance (Lm) by LCR meter and the calculated self inductance (Lc1, Lc2) by Eq. (1) are shown in Fig. 5, when Vee apex angle (B) is 3 deg and the distance from Vee apex point to con-tact tip (l1) is 300 mm. Lc1 is calculated on the as-sumption that the current in strip edge flows uni-formly (b' = a). Lc2 is calculated on the assumption that the current in strip edge flows separately within one-fourth of strip thickness from both surface (b'= 2a). Lm is approximate to Lc2, which is smaller than Lc1. Therefore, it is supposed that the current in the Vee apex zone flows separately in the corner of strip edge. This phenomenon is confirmed by four heated lines in Photo. 1, which shows the appearance of Vee

apex zone. As may be seen from Fig. 5, Lm has a tendency to approach to Lc1, as wall thickness in-creases. The measured and calculated self inductance are shown in Figs. 6(a) and (b), when B is 3 deg and l1 is 200 mm. The self inductance is calculated by changing b' and 2a. The mean depth of b' can be estimated by comparing the measured self inductance with the calculated. Figure 6(b) shows the com-

parison of the measured and calculated results. As is shown in Fig. 7, the mean value of b' has a tendency to increase with an increase in wall thickness.

Therefore, it is quite all right to conclude that the separation rate (b'/a) of current in strip edge varies with the wall thickness of pipe, and namely current shows a tendency to flow uniformly in the strip edge, as wall thickness increases.

Photograph 2 shows the cross section of Vee apex specimens which are picked up directly after welding. From the shape of the HAZ, it is confirmed that the current in thicker strip edge has a tendency to flow more uniform and wider near the Vee apex point, but

Photo. 1. Heating and weldin g phenomenon (165.2x11 .Ot).

Fig. 5. Relationship between wall thickness an

ance of Vee apex zone.

d self-in duct- Fig. 6. Relationship between wall thic

ance of Vee apex zone.

kness an d self-in duct-

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(464) Transactions ISIJ, Vol. 26, 1986

the edge corner is overheated. Also, Haga et al.3~ re-

ported that the melt layer width at edge corner in-creased with an increase in wall thickness, as is shown in Fig. 8.

The measured resistance (Rm2, Rm5) by LCR meter and the calculated resistance (Rc2, Rc5, Rmc5) by Eq. (2) are shown in Fig. 9, when Vee apex angle e is 3 deg and the distance from Vee apex point to contact tip (l,) is 300 mm.

Rm2 and Rc2 is the resistance at 20 °C, and Rm5,

Fig . 7. Relationship between

separate depth.

wall thickness and current

Fig. 8. Influence of frequency and plate

amount of the melt layer at edge

between current

point.

supplying point

thickness on an

corner produced

and Vee apex Fig. 9. Relationship among wall thickness, specimen

perature and resistance of Vee apex zone.

tern-

Photo. 2. Macrostructure of Vee apex zone.

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Transactions ISIJ, Vol. 26, 1986 (465)

Rc5 and Rmc5 is the resistance at 500 °C. Rm5 is mea-sured by heating the quasi Vee apex specimen to 500 °C in a electric furnace. On the calculation of Rc2 and Rc5 by Eq. (2) the current separate depth

(b') is estimated from Fig. 7 and the current penetra-tion depth (b) at each thickness is assumed equal to that of 6.4 mm thickness.

Rmc5 is calculated as follows. The cross sectional area (b.b') of current path is derived from the Eq. (2) by using the measured resistance (Rm2) at 20 °C. Assuming that the cross sectional area does not change by the temperature, specific resistance at 500 °C is substituted in Eq. (2) to obtain the estimated resis-tance Rmc5.

It is expected that the cross sectional area (b. b') of current path becomes smaller as thickness increases, because Rm2 becomes larger than Rc2. The decrease in the cross sectional area of current path is depend-ing on the current penetration depth from strip edge, because the current separate depth b' becomes larger as the wall thickness increases.

Generally, the Vee apex angle increases with the increase of wall thickness of pipes partly due to the low mill modulus of squeeze stand and, also, to the in-crease of rigidity of formed pipes themselves. Figure 10 shows the measured changes of Vee apex angle with wall thickness. When the Vee apex angle in-creases, the proximity effect decreases which resulted in the large penetration depth (b) and small current separation depth (b') as guessed by Fig. 11. Photo-graph 2 shows the variation of HAZ. The penetra-tion depth (b) increases and the current separation depth (b') decreases with the increase of thickness. In order to reduce the over heating of the corner, it is necessary to increase the current separate depth (b') by making Vee apex angle small.

As shown in Fig. 9, Rm5 becomes smaller than Rmc5 as thickness increases, and the ratio of calculated value and measured value (Rc/Rm) at 500 °C is larger than at 20 °C.

Therefore, the cross sectional area (b . b') of current path in Vee apex zone of heavy walled pipe increases

as temperature rises. This can be explained by Eq.

(8). The specific resistance and specific permeability, which affects penetration depth of high frequency cur-rent become larger and smaller, respectively.

P = 5O3/_4- .....................(8)

where, P: penetration depth tel: specific permeability

f : frequency p : specific resistance.

Photograph 3 shows the cross section of Vee apex zone of the pipe (thickness 14.27 mm, diameter 600 mm), which was manufactured at fairly slow welding speed to get a wide HAZ and a high temperature. It is recognized that the strip edge is not overheated at the corner but melted uniformly.

It turns out that even a heavy walled pipe can be welded without any defects owing to the uniform cur-rent: flow and the moderate welding conditions.

2. Design of Squeeze Roll Stand

It is necessary to keep the width of outside bond less than 0.15 mm in order to secure good weld quality from our experience. Figure 12 shows the relation-ships among the wall thickness of pipe, the width of outside bond and the relative amount of upset. I t is understood from Fig. 12 that the large upset is neces-sary for a fairly heavy walled pipe to obtain a con-stant width of outside bond. The width variation near Vee apex point is caused by large bending ri-gidity of formed pipes themselves and a lack of mill modulus to cope with the decrease of necessary set-up gap of squeeze rolls.

Therefore, it is necessary to strengthen the rigidity of squeeze roll stand in order to upset heavy walled pipe and maintain the width of outside bond less than 0.15 mm. As the side rolls were supported only from bottom, the mill spring modulus was small.

So, the design of the squeeze roll stand has im-

proved to support them on both top and bottom sides. As a result, the mill spring modulus was doubled.

Fig. 10. Relationship between wall th

Vee apex zone measured in

mill.

iekness and width of

26 inch ERW pipe Fig. 11. Relationship between Vee apex

inductance of Vee apex zone.

angle D and self-

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3. Quality of ER W Pipe with Fairly Heavy Wall ness4~

Heavy walled pipe of 24 finch x 19.05t mm manufactured by the 26 inch ERW pipe mill.

Thick-

were The

quality of the pipe was examined by 90 deg flattening test, Charpy impact test and DWTT test. The chem-ical composition of used pipe is shown in Table 1.

The result of Charpy impact test is shown in Table 2 and the DWTT transition curve is shown in Fig. 13. It is clear that every pipe has excellent strength and toughness.

V. Conclusions

The welding phenomena and the weld quality heavy walled pipe have been investigated in the lab-oratory and 26 inch ERW pipe mill. The results are as follows :

(1) The current in the strip edge of the Vee apex zone has a tendency to flow uniformly in the strip edge, as thickness increases. However, current pene-tration depth from strip edge become shallower as thickness increases.

(2) The cross sectional area of current path in Vee apex zone of heavy walled pipe increases as tern-perature rises.

Table 1. Chemical composition of used steel.

Fig. 12. Relationship among wall thickness, relative amount

of upset and width of outside bond.

Transactions ISIJ, Vol. 26, 1986 (467)

(3) The strip edges can be heated little overheat at strip edges in the conditions.

(4) The technical improvements squeeze roll stand have enabled the heavy walled pipe with large outside has excellent toughness.

uniformly with moderate heat

in welding and manufacture of

diameter which

Table 2. Results of Charpy im pact tests.

Fig. 13. Relationship between

area of DWTT.

test temperature and shear

REFERENCES

1) H. Haga, Y. Watanabe, S. Yamada and K. Sakurai : Tetsu-to-Hagane, 69 (1983), A73.

2) S. Takeyama : Theory of Electric Magnetic Phenomena, Maruzen, Tokyo, (1962), 253.

3) H. Haga and 51369.

4) H. Tominaga, S. Minamiya 51220.

N. Mizukami :

Y.

and

Yoshimoto,

M. Saito :

T etsu-to-Hagane, 70

S. Watanabe, M.

T etsu-to-Hagane,

(1984),

Shibagaki, 69 (1983),