As published in Heat Processing (March 2015). Depending on workpiece and process parameters, induction heating of components requires a certain amount of power. By simulation, experiments and experience, this needed energy can be well anticipated and enables the dimensioning of the converter. Basically, cost of the converter increases with rising provided power. Due to increasing energy expenses, efficiency of the system plays an important role. In this article, the influences of different process parameters on the efficiency of an example are investigated and valuable potential for improvement is demonstrated, so that the heating process is implemented with minimum converter power.

1. 713-2015 heat processing
Induction technology REPORTS
Optimization potential of
­induction heating systems
by Stefan Schubotz, Hansjürg Stiele
Depending on workpiece and process parameters, induction heating of components requires a certain amount of power.
By simulation, experiments and experience, this needed energy can be well anticipated and enables the dimensioning
of the converter. Basically, cost of the converter increases with rising provided power. Due to increasing energy expenses,
efficiency of the system plays an important role. In this article, the influences of different process parameters on the
efficiency of an example are investigated and valuable potential for improvement is demonstrated, so that the heating
process is implemented with minimum converter power.
W
hen a converter is designed for an induction
heating process, many simplifications have to
be taken into account since the exact know-
ledge of the application parameters doesn’t exist in this
development stage. Based on workpiece and duration
of heating time, the required workpiece energy can be
calculated. However, many additional parameters have a
decisive influence on the overall efficiency and thus on the
necessary converter power.
The essential and examined parameters in this report are:
■■ coil leads,
■■ coupling distance, i.e. distance between coil surface
(workpiece-facing side) and the workpiece surface,
■■ field guiding elements (concentrators),
■■ process frequency.
In contrast to other parameters which also often have a high
impact on the efficiency (such as the converter or the match-
ing transformer), these physical quantities can be changed to
a certain extent afterwards and they offer a high optimization
potential. Hence, a simplified application example is presented
and subsequently, the different application parameters with
potential of improvement are demonstrated.
APPLICATION EXAMPLE
A workpiece made of magnetic steel (C45) shall be heated
from 20 °C (room temperature) to homogeneous 300 °C.
The heating process must be carried out in 1 s and the
workpiece shall reach the uniform target temperature by
heat conduction. The construction of coil and workpiece
is shown in Fig. 1.
For accomplishing the task by using the model shown,
a power of 122 kW at the coil is required. The heating pro-
cess has been modelled by the help of the 1D simulation
program Elta [1]. Here, the maximum surface temperature
of the workpiece amounts to 720 °C which is still below the
Curie temperature (approximately 770 °C). The simulated
heating process of this model has an efficiency of only 18 %.
The influence of the application parameters on the overall
efficiency and to what extent it can be improved will be
explained in the following sections. For this purpose, the
model will be optimized step by step.
Fig. 1: Setup of application example

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COIL LEADS
Due to the skin effect, the current in the coil and the leads
only flows at the surface or in low surface depth. Besides
that, the proximity effect also causes the current to flow
only at the workpiece-facing sides of the coil and at the
inner sides of the leads. The highest current flows directly
on the surface, whereas the curve shape to the outside of
the leads is exponentially decreasing (Fig. 2).
The unit of the width of the surface layer in which a sig-
nificant current is flowing is referred to current penetration
depth δ. This can be calculated by the formula:
δ =
ρ
π⋅ ⋅μ ⋅μf 0 r
ρ = spec. electrical resistance
f = frequency
μ0 = magn. field constant
μr = relative permeability of the material
This parameter indicates the profile depth at which the
current density has decreased to 1
e = 0,37 ⇒ 37 % of the
surface value. For the application example shown in Fig. 1,
surface depth refers to
δ =
Ω
π⋅ ⋅ π⋅ ⋅
=
−
0,01786
mm
m
2000Hz 4 10
N
A
1
H
m
1,5mm
2
7
2
.
With the help of the current density, the volume power
density can be derived by the basic relationship P = I2 ∙ R
which leads to the correlation 1 – 1
e2 = 0,86 , i.e. 86 % of
the induced power in the workpiece is converted in the
layer between the surface and current penetration depth.
Thus, the area in which the substantial amount of power
is induced can be calculated by using the formula A = h · δ,
wherein h represents the height of the coil profile.
Therefore, power losses in the coil leads are calculated
as follows:
= ⋅ = ⋅
⋅ρ
⋅δ
= ⋅
⋅ρ
⋅
ρ
π⋅ ⋅μ
= ⋅ ⋅ ρ⋅π⋅ ⋅μP I R I
2l
h
I
2l
h
f
2l
l
h
floss
2 2 2 2
The term
l
h
represents the proportional relationship
between the power losses Ploss, the length l and the height
h of the coil leads. Accordingly, both geometric dimensions
have a significant influence on the power dissipation.
In the model shown in Fig. 1, for optimization, the length
of the leads has been shortened from 100 to 50 mm while
the height of the leads has been increased from 10 to 30 mm.
Fig. 2: Current distribution in the leads of a coil
Fig. 3: Coil head of the example of Fig. 1 with associated curve about the efficiency 𝜂 at different coupling ­distances
coupling distance [mm]
efficiency[%]

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In simulation, lowering lead length to 50 mm reduces
the process power requirement from 122 to 100 kW. Fur-
thermore, increasing the height of the profile from 10 to
30 mm reduces the power demand by additional 16 to
84 kW. This power saving of more than 30 % reveals that
the optimized design of the coil leads is an extremely
important aspect.
COUPLING DISTANCE
At induction heating systems, it is very important that the
coupling distance, i.e. distance between coil workpiece-
facing side and workpiece itself (Fig. 1), is minimized to
achieve a high efficiency. However, this is often hard to
realize. First of all, it is often the objective in industrial appli-
cations that workpieces of different diameters / geometries
shall be heated by the same coil. While this saves time and
costs, it results to a correspondingly high coupling distance
at some workpieces.
Secondly, there are often induction applications where
no centred workpiece or coil construction exists, so the user
heats the workpiece with the hand-guided coil. Instead of
providing the inside of the coil with insulating material, a
big coupling distance is often selected to avoid a contact
between coil and workpiece. However, increasing coupling
distance causes a lower efficiency.
To determine the change of efficiency in dependence
of coupling distance, various simulations have been per-
formed. The coil head with the workpiece from Fig. 1 was
used and the efficiency at various coupling distance inter-
vals has been determined. The efficiency is calculated by
the expression
η=efficiency
workpiece power
coil power
A diagram of the relationship between efficiency and cou-
pling distance at 2 kHz process frequency with associated
simulation setup is shown in Fig. 3. There, it can be seen
that the efficiency drops almost linear (small exponen-
tially decreasing) when the coupling distance increases. In
this isolated view of the coil head, the efficiency has been
increased by 0,436
0,293 – 1 = 49 % due to a reduction of coupling
distance from 10 to 2 mm. Therefore, a small coupling dis-
tance which is still reasonable regarding the process should
be selected. Concerning the already improved (regarding
the leads) application example of Fig. 1, only 57 instead
of 84 kW power is needed in the coil after reducing the
coupling distance from 10 to 2 mm.
FIELD GUIDING ELEMENTS
By using field guiding elements (also called concentrators),
the efficiency can also be significantly increased. Then, the
magnetic field is guided and focused in a certain direction
and allows a reduction of stray fields. Usually, concentra-
tors are U-shaped and attached to a profile side of the
coil which focusses the magnetic field on the averted side
(Fig. 4).
Fig. 5: Extract of a coil with transformer sheets of ironFig. 4: Influence of concentrators on heat distribution caused
by induction at same coil current [3]

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Depending on frequency range and application, differ-
ent types of field guiding elements are used. A distinction
is made between
■■ laminated soft iron sheets (so-called transformer sheets)
and
■■ magneto-dielectric materials (e.g. Ferrotron™ and Flux-
trol™)
Laminated soft iron sheets are thin (usually 0.1 mm)
U-shaped plates, which are lined up on the coil and nor-
mally glued (Fig. 5). Using these types of concentrators
largely take place in a frequency range of 1 to 50 kHz and
the insulation of the sheets can withstand temperatures
up to 500 °C.
Magneto-dielectric concentrators (differently shaped)
are made of high-performance thermoplastic material with
embedded iron particles. Due to these thermoplastics, the
maximum allowed upper temperature is usually limited to
250 °C; however, this material provides various conceivable
design possibilities which can also be handled in compli-
cated coils.
Known products of these magneto-dielectric materials
are Ferrotron and Fluxtrol of the company Polytron [2].
Fluxtrol is used in a similar frequency band as laminated
soft iron sheets (mainly 1 to 50 kHz). Due to lower perme-
ability, Ferrotron is applied at a higher frequency range
(mostly 50 to 500 kHz). Depending on the structure of the
workpiece and the associated coil, field guiding elements
have a different influence on the efficiency.
Especially at outfield heating applications (Fig. 6a), the
efficiency of concentrators can be significantly improved.
Due to physical reasons, the magnetic field is created par-
ticularly in the interior of an induction coil. But even at
induction infield applications (Fig. 6b) which usually own a
high efficiency, the effectiveness can be improved crucially
by concentrators.
In the optimized (regarding leads and coupling distance)
example of Fig. 1, the efficiency determined by simulation
increases from 40 to 65 % when field guiding elements
are used. The total power requirement decreases from 57
to 34 kW if concentrators are applied. This represents an
enormous energy saving potential of about 40 %.
However, the usage of field guiding elements is also
associated with disadvantages. First, the construction of
the coil gets more complex, time-consuming and accord-
ingly expensive. In addition, concentrators own another
disadvantage, which especially occurs in hardening applica-
tions. There, the workpieces which are heated up to very
high temperatures produce such a high heat radiation
energy that the bonded field guiding elements are also
strongly heated up and the use of a cover made of high-
temperature materials is required.
Besides that, the thermal conductivity of concentrators
is significantly lower than from copper; correspondingly,
the heat transport to cooling water might be insufficient.
Both circumstances may lead to a destruction of the adhe-
sive material of the laminated transformer sheets or of the
thermoplastics at magneto-dielectric materials. Therefore,
lifetime of coils can be reduced extensively if field guiding
elements are used.
PROCESS FREQUENCY
Another parameter that has a big influence on the effi-
ciency is the frequency. Basically, the highest priority in
dimensioning the frequency is the fulfilment of the pro-
cess. In general, a converter can create frequencies in a
Fig. 6a, b: Different induction heating principles
a) induction outfield heating b) induction infield heating

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very high bandwidth while the desired frequency may be
configured exactly by the control system; certainly, almost
all converters for induction heating adjust the predeter-
mined frequency of the resonant circuit in order to avoid
the converter creating reactive power.
This frequency is set by the external resonant circuit
(consisting of matching transformer, capacitors for reactive
power compensation and coil) and it is slightly determined
by the process and thus, continually adjusted by the con-
verter. Consequently, an adjustment of the oscillation circuit
is necessary to change the frequency.
This is usually realized by changing the ratio level of the
matching transformer, by connecting or disconnecting the
resonant circuit capacitors or it is achieved by changing the
design of the coil. Concerning the efficiency, it is important
for cylindrical workpieces to consider the ratio between
workpiece diameter d and current penetration depth δ.
If this is chosen too small
(d
δ 3,5),
the efficiency decreases rapidly since the magnetic fields
overlap each other and thus interfere [4].
In practice, in some cases it is also recommended that
the workpiece diameter should be at least six times higher
than the current penetration depth [5]. In addition, when
choosing a low application frequency, the basic math-
ematical background of the induction phenomenon is
not negligible.
The relationship between the generated magnetic field
(B: magn. flux density) and induced voltage (Uind) is:
Uind = −
∂
!
B
∂tA∫ ⋅∂
!
A
The component
∂
!
B
∂t explains that the created average
amount of voltage rises with increasing frequency.
This shows that the principle of induction is based on
alternating fields. To visualize the influence of frequency
on the efficiency, the setup of Fig. 3 has been used but
with a constant coupling distance (2 mm) and different
frequencies. In addition, the coil power was significantly
reduced to 10 kW because at very high frequencies, the
surface temperature would rise above Curie temperature
which would decrease the efficiency and falsify the results.
Therefore, for illustrating the pure frequency influence, the
model has been adjusted and the absorbed workpiece
power has been determined at varying frequencies. Based
on these results, the efficiency has been calculated and is
shown in Fig. 7.
Fig. 7: Frequency effect on the efficiency of the application example (Fig. 1, Fig. 3) with reduced coil
power and ­different coupling distances

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Fig. 9: Table with associated graph about the influences of the individual optimization steps
Optimization step
Power demand after
optimization [kW]
Savings per ­optimiztion
step [%]
Entire ­savings [%]
Basic state
(no optimization)
122 - -
Reducing length of coil leads
from 100 to 50 mm
100 18 18
Increasing height of coil leads
from 10 to 30 mm
84 16 31
Reduction of coupling ­distance
from 10 to 2 mm
57 32 53
Application of field guiding
elements
34 40 72
Increasing frequency from 2 to
10 kHz
28 18 77
Fig. 8: Optimized coil of Fig. 1

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In the already optimized model (regarding construction,
see Fig. 1), increasing frequency from 2 to 10 kHz results
in a reduction of process power requirement from 34 to
28 kW. This corresponds to an overall efficiency of 80 %.
As mentioned in the explanation of the application
example, the surface temperature amounts to 720 °C at
a process frequency of 2 kHz. This increases to 850 °C at
10 kHz and thus, it significantly exceeds Curie tempera-
ture. Therefore, with regard to the frequency selection, it is
always extremely important to consider what temperatures
in the workpiece or on the surface are allowed.
SUMMARY OF THE RESULTS
The coil of Fig. 1 has been optimized and the result is shown
in Fig. 8. Since the current almost exclusively flows on the
inner sides of the leads, it is not necessary that the whole cop-
per profile is adjusted in height, only thin plates are needed
due to good heat conductivity of copper. An overview of the
individual optimizations on the efficiency and the results with
the associated curve can be seen in Fig. 9.
The table in Fig. 9 indicates that only by constructional
changes of the coil (in this example), about 70 % of power
could be saved. Overall, the efficiency has been enhanced
from 18 to 80 %. This explains the enormous importance of
optimal design of these different parameters which is often
realized fast and with low costs.
CONCLUSION
In this elaboration, it has been explained that there is a
considerable potential for improvement in the application
parameters. High efficiency attracts many cost advantages.
In addition to a lower purchase price for the converter due to
lower power requirements, also a significantly smaller cooling
system may be used. The decreased required converter power
demand also reduces the continuous resource requirements.
Therefore, due to rising cost of electrical energy, the optimum
design of the coil and the process regarding efficiency will
play an increasingly important role.
LITERATURE
[1] http://www.nsgsoft.com/products/elta
[2] http://www.polytron-gmbh.de/ferrotron_und_fluxtrol.aspx
[3] Nemkov, V.; Goldstein, R.: Enhancing Induction Heating
­Processes, in ASM, 1999
[4] Benkowski, G.: Induktionserwärmung, Berlin: Technik, 1990
[5] Ulferts, A.; Andrä, F.: Innovation durch adaptive Frequenzvaria-
tion im Induktionshärten, in ewi – elektrowärme international,
Nr. 3, 2010
AUTHORS
Dipl.-Wirtsch.-Ing. Stefan Schubotz
EFD Induction GmbH
Freiburg, Germany
Tel.: +49 (0) 761 / 8851-174
szs@de.efdgroup.net
Prof. Dr.-Ing. Hansjürg Stiele
Albstadt-Sigmaringen University
Albstadt, Germany
Tel.: +49 (0) 7571 / 732-9583
stiele@hs-albsig.de
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