XXIV Symposium
Electromagnetic Phenomena in Nonlinear Circuits
June 28 - July 1, 2016 Helsinki, FINLAND
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FIELD-CIRCUIT MODELLING OF THE RESISTANCE SPOT
WELDING TRANSFORMERS
L. Sakhno, O. Sakhno, D. Likhachev, P. Fedorov
St. Petersburg State Polytechnic University, Department of Theoretical Electroengineering,
Polytechnicheskaya 29, St. Petersburg, 190251, RUSSIA,
LSAHNO2010@yandex.ru
Abstract - Transformers of high frequency resistance spot
welding systems are considered. The study of the transformers
includes both 2D eddy-current FEA analysis for estimation the
leakage impedances and the circuit simulation, which gives the
output current. The results are used to design economical
welding transformers.
details.The load is given by the conductor with a DC
resistance RL of 100 μΩ and the inductance LL of 700 nH .
I. INTRODUCTION
Resistance spot welding (RSW) are mainly used in
automotive industry in welding systems. The RSW system
size and mass are limited due to use on a robotic arm. In order
to achieve the required compact design and high welding
current, the high frequency RSM system (Fig.1) consists of an
input H-bridge inverter, welding transformer (TR) and a fullwave centre tapped output rectifier that consists of diodes (D1,
D2 ).
a)
Fig.2. Design of the transformer
b)
III. CIRCUIT MODELLING OF HIGH FREQUENCY RSW SYSTEM
Fig.1.
The transformer impedance affects the load current and power
consumption. In this regard, in the literature a lot of attention
is paid to calculation of the transformer impedance and the
equivalent circuit of the RSW transformer [1-3]. The current
in the massive conductors is not uniformly distributed due
to skin effect and proximity effect. In [4] power losses of the
transformers with the parallel-connected secondary windings
are analyzed. A method of optimizing copper winding
dimensions in order to reduce copper losses and design were
proposed in [5].
II. RSW TRANSFORMER
The article deals with the transformers which have armored
magnetic cores, primary winding and two secondary windings
Figure 2 shows one of the transformer designs. The primary
winding consists of four series-connected coils made.of wire
with rectangular cross-section. The two secondary coils are
made of copper tubes through which cooling water flows. The
primary winding consists of 36 turns. The transformers
considered differ in the number of coils of the primary
winding and interleaving of primary and secondary windings.
The frequency is 10 kHz. Frequency of the H- bridge inverter
is defined production requirements when welding some
For high RSW system simulation the equivalent circuit of the
three-winding transformer is needed. The circuit given in
fig.3a allows to study influence of the transformer design on
the load current of RSW system. This circuit differs from
well-known circuit of the three-winding transformer [6] and it
was succesfully used for studing transformers of doublebridge rectifiers [7,8]. The two secondary windings of the
transformer are not condactively coupled. All inductances in
the circuit are always positive. Therefore, the circuit is
suitable for the standard simulation program (P-Spice) [9]. It
is important that the circuit parameters have the clear physical
sense and can be easily evaluated by FEA [10]. This circuit is
based on replacing the three-winding transformer with two
transformers: one with windings 1, 2 and the second with
windings 1, 3 (further denoted as transformers 1-2 and 1-3).
The mutual impact of transformers 1-2 and 1-3 is modelled as
a change of EMF on the terminals of their secondary
windings by magnetic leakage fields.
Equations of three-winding transformer, referred to the
secondary windings, for sinusoidal currents and voltages are:
r

E02  r12 I 2  jL12 I 2  1 I 3  jMI 3  U LOAD 2 
k12 k13
 (1)

r1
E03  r13 I 3  jL13 I 3 
I 2  jMI 2  U LOAD 3 

k12 k13
where I 2 , I 3 are complex currents in windings 2 and 3,
  2f ,
f
is frequency,
j   1 , E02 , E03 are open
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circuit EMF in windings 2 and 3, L12 , r12 are leakage
inductance and active resistance of transformer 1-2, L13 , r13
are leakage inductance and active resistance of transformer 13, r 1 is active resistance of winding 1, M - the mutual
inductance of the leakage fluxes of transformers 1-2 and 1-3,
U LOAD 2 is complex voltage on the terminal of winding 2,
U LOAD 3 is complex voltage on the terminal of winding 3.
The mutual inductance of the leakage fluxes can be found:
L  L13  L23 , (2)
M  12
2k12 k13
where L23 is the leakage inductance of transformer 2–3. All
the leakage inductances in (2) are referred to winding 1.
The magnetic leakage fields in transformers 1-2 and 1-3
(short-circuit tests for transformers 1-2, 1-3) have been
modelled by 2D FEA software QuickField [9]. The leakage
flux of the transformer 1-2 in the window is shown in Fig.2b.
In Figure The circuits parameters L12, L13, r12, r13 evaluate by
2D FEA model. For evaluating the magnetic leakage mutual
inductance M we have made the FEA simulation of another
short-circuit field in transformer 2- 3.
a)
b)
Fig.3. Equivalent circuit of three-winding transformer and the model of
RSW system
The model for the high frequency RSW system
simulation is shown in Fig. 3b. Calculation of transient in the
circuit in Fig.3b have been made using the Microcap [10]
software.
IV. THE CALCULATION RESULTS
Due to the centre tapped rectifier (Fig.1) the current only
flows in one of the secondary windings at the same time. It
causes the increased leakage inductances of the transformers
1-2 and 1-3. Calculations have shown that it is necessary to
reduce the leakage inductances of transformers 1-2 and 1-3
for increasing the operating current if open circuit voltage is
constant. The magnetic coupling factor for the leakage fluxes:
M
(3)
k
L12 L13
has a great influence on the operating current. The mutual
inductance M can be either positive, when the leakage flux in
winding 3 caused by the transformer 1-2 is directed opposite
to the main core flux, or negative , if above fluxes have the
same direction. Dependence of the operating current on the
magnetic coupling factor for the leakage fluxes is
approximately the same for any value of the leakage
inductances of transformers 1-2 and 1-3. In this regard, the
dependence of the relative operating current (IL/IL0 , IL0 – load
current at k=0) on the coupling factor is shown in Fig.4.
Fig.4. The influence of the coupling factor on the load current
It shows that when k > 0 the load current is less than when k<
0. This effect can be explained by the appearance of
additional EMF at the terminals of winding 2 when current
flows in winding 3 caused by leakage flux. Increased EMF
reduces diodes switching times, which in turn leads to an
increase load current. We investigated several transformer
designs for RSW system with frequency of 10 kHz. Designs
differs interleaving of primary and secondary windings and
the number of primary winding coils. They have different
leakage inductance and different coupling factors for the
leakage flux. All options have the same number of turns of
the primary winding. For example, the transformer in Fig.2
has L12 = L13 =83 μH (referred to the primary windings),
coupling factor k= -0.5. The field-circuit modelling of RSW
transformer allowed us to optimize the transformer. The
transformer with two coils of primary winding and secondary
windings located between them appeared to be the most
economical.
REFERENCES
[1] X. Margueron, A. Besi, Y. Lembeye , J.P. Keradec “ Current sharing
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transfer in a two-winding transformer from 1-D propogation to an equivalent
circuit”, IEEE Trans. on Magn., vol.32, no.1, pp. 274-280, Jan. 1996.
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[6] Sakhno L.I., An investigations of double-bridge rectifiers with steeply
falling external characteristics for supplying an electric arc. Electrical
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[7] Sakhno L.I., Two-bridge welding rectifiers with single-phase
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[8] L. Sakhno , O. Sakhno, S. Dubitsky. Field-Circuit Modelling of an
Advanced Welding Transformer with Two Parallel Rectifiers. Archives of
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Proceedings of EPNC 2016, June 28 - July 1, 2016 Helsinki, FINLAND