Induction hardening of complex geometry and geared parts - eldec

International Magazine for Industrial Furnaces
Heat Treatment & Equipment
www.heatprocessing-online.com
10 th - 12 th October 2012
Wiesbaden, Germany
03 I 2012
ISSN 1611-616X
Vulkan-Verlag
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Induction hardening of complex
geometry and geared parts
by Fabio Biasutti, Christian Krause, Sergio Lupi
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Published in heat processing 3/2012 - Vulkan Verlag GmbH Essen (Germany)
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REPORTS Induction Technology
Induction hardening of complex
geometry and geared parts
by Fabio Biasutti, Christian Krause, Sergio Lupi
Mechanical gear parts for automotive or aeronautical industry are highly stressed toothed workpieces, which need to be
heat treated in order to improve their mechanical properties. Up to now the most common heat treatment technology
is carburizing. This method permits to achieve strength and wear resistance but cannot be integrated in a production
line. Moreover, the carburizing process takes several hours and the workpiece must be completed heated up to the
austenization temperature, resulting in extensive deformation. The induction contour hardening process is an alternative
to carburizing. The purpose of this paper is to present the induction contour hardening process with particular reference
to geared parts. In the paper are first recalled the basic laws of induction heating and is given an historical overview of
the induction hardening process of gears. Induction hardening involves electromagnetic and metallurgical phenomena,
which are described in the third and fourth paragraph. Some practical industrial applications of the induction hardening
are presented in the fifth paragraph.
BASICS OF INDUCTION HEATING
The induction hardening process consists of two steps:
�rst the heating above the austenization temperature of
the surface layer that has to be hardened, and second the
quenching below a de�ned temperature (martensite �nish
or room temperature).
The heating is performed by electromagnetic induction, in
which are involved di�erent physical phenomena and laws, i.e.:
Electromagnetic
Induction
Electromagnetic
�eld distribution
Conversion of electromagnetic
energy into heat
Temperature �eld
distribution
Faraday, Neumann,
Lenz laws
Maxwell laws
Joule law
Fourier equation
With reference to the system of Fig. 1, in which an alternative
current I �ows in the exciting coil and produces
a magnetic �ux Ф variable in time, according to the law
of the electromagnetic induction an e.m.f. is induced in
every closed path inside the work piece. This e.m.f. causes
induced currents Ik (eddy or Foucault currents) to �ow
within the mass of the body which, in turn, generates
power according to the Joule’s law, thus heating the body.
Like the coil current, the induced currents Ik also produce
an alternating magnetic �eld which, in accordance
with Lenz’s principle, is in opposition to the exciting �eld.
The two �elds are superimposed, and the result is a radial
reduction of the magnetic �eld towards the inside of the
work piece and the outside of the inductor. This is known
as “skin e�ect”, because the resulting induced current and
power density distributions (the heating sources) are not
uniform inside the work piece and concentrate in a surface
(or “skin”) layer.
This surface layer has radial dimensions comparable with
the so called “penetration depth”, given by:
2 ρ
mm][
2π
f µ
60 heat processing 3-2012
δ =
0
with: ρ - resistivity [Ωm]; μ0 = 4 π ·10 -7 - magnetic permeability
of vacuum [H/m]; m - relative magnetic permeability;
f – frequency of the inductor and workpiece currents [Hz].
The heating sources cause the heating of the workpiece,
and the temperature increase follows the law of thermal
conduction (Fourier equation).
HISTORICAL OVERVIEW
Since the beginning of the development of induction heating,
the induction hardening of gears has been at the attention
of researchers and engineers because of the advantages of
(1)

3-2012 heat processing
Fig. 1:
Sketch of the inductor coilwork
piece system: a current
I [A] � owing in the coil produces
a magnetic � ux Ф [Wb]
which induces eddy currents
Ik [A] in the work piece.
Fig. 2:
Classi� cation of the di� erent
spin hardening methods [14]
this technique, such as short heating times, strict process
control, low distortion of the heat treated parts. An historical
document is, in this sense, the patent US1687656 of Brown
[1] as much as the work of Hogel [2] in 1938 and the work of
Vologdin [3] 1939. In the 1940s many researches and publications
related to the improvement of the gear hardening were
developed in several countries around the world [15]. It was
found relatively early that the best service properties could be
obtained by a hardness layer more or less uniform along all the
surface of the gear, following its contour (“contour hardening”).
At the end of the 40 s the basic in� uence of the main
process parameters was known and the main results were
available, e.g. in the book of prof. V. Vologdin; examples of
the in� uence of frequency and heating time on the hardening
pattern are reported in the 2 nd edition of this book [4].
But the industrial application of the process to mass
production took place only later, � rst for the needs of the
military production during the II World War and then for
the development of the automotive industry, starting from
the beginning of the 50 s.
The di� erent techniques developed for contour hardening
of gears are summarised in the scheme of Fig. 2.
The � rst technique proposed and used for gear contour
hardening is the “single frequency” one, i.e. the simultaneous
hardening of the whole contour with an inductor
encircling the gear, excited with current at a convenient
optimal frequency. It corresponds to the process cycle
of Fig. 3 left.
But since the beginning it was clear that, for obtaining
comparable penetration depths in gear regions characterised
by very di� erent geometrical dimensions (i.e. the teeth
and the part of the gear below the roots, as schematically
shown in Fig. 4a, it would be useful to use two di� erent
frequency values.
Induction Technology REPORTS
The optimal single frequency represents therefore a
compromise, which gives relatively good results for modules
between 4 and 10, if used in connection with high
power densities and short heating times, as shown in Fig.
4b which gives the process parameters suggested in [9].
For these modules, frequencies up to 30 kHz can be
used in practice. But for gears with module lower than
3 to 4 mm, peak power densities above 5 to 6 kW/cm 2 ,
heating times of few hundreds of milliseconds and
frequencies in the range of few hundreds kHz are required.
Additional � exibility in the selection of the single frequency
process parameters may be achieved by a preheating
stage at lower power, followed by one or more pulses;
this technique, so called also “Pulsing Single Frequency”,
allows to expand the possibility to achieve results close to
contour hardening for di� erent gears.
As shown in Fig. 3 right, the process comprises a preheat
stage with a reduced power to approximately 500 to
750 º C (dependent on the material), a soaking stage, and
a short � nal heating to the hardening temperature with
higher speci� c power, followed by the quenching and a
� nal low-power heating stage for tempering [12].
To overcome the limits of the single frequency technique,
dual frequency processes have been proposed since
the middle of the 20 th century [5,6,8].
In these processes (named “Pulsing dual-frequency processes”)
two frequencies are applied separately in sequence
to the same work piece for realizing the heating cycle of
Fig. 5: pre-heat is accomplished in the � rst step of the heating
cycle by applying a low power density at MF (usually in
the range 3 to 10 kHz), while during the � nal heating stage,
which is much shorter than the � rst one, a high power
density at HF is used for contour hardening. The selection
of suitable values of the frequency of the � nal pulse, in the
61

REPORTS Induction Technology
range 30 to 450 kHz - depending on the type of gear, its
size and material – and the heating time allows to obtain
the desired contour hardened depth.
The MF and HF frequency converters can be connected
to two di� erent coils which are spatially separated, as
shown in Fig. 6.
The dual frequency process can also be carried out without
transferring the gear wheel from one inductor into
another. In this case the inductor is made in the form of
two half rings connected to a MF transformer and a HF
transformer, as shown in Fig. 7. A limit of this technique is
the time required for switching the power from one generator
to the other.
As in the single frequency process, the heating cycle
can comprise a pre-quenching and tempering stage of
the tooth area before the actual hardening step; this stage
Fig. 3: Single-frequency hardening processes [12] Fig. 4a: Schematic of a gear highlighting two di� erent
geometrical dimension;
Fig. 4b: Process parameters suggested for single shot hardening
[average surface speci� c power; heating time;
frequency]
is used for improving the � nal metallurgical results also
when the prior microstructure of the steel is not particularly
suitable for hardening.
Though the “Simultaneous Dual Frequency” (SDF) process
is a still emerging technique, it has been already successfully
introduced in the automotive, airspace and other
industries. This technique also uses both medium frequency
and high frequency currents, but they � ow simultaneously
in the same coil.
The idea of this process is also very old, since it was
patented in 1948 in USA by J. Jordan, General Electric
Company [5]. According to this patent, medium and high
frequency currents were supplied to the same inductor by
two power supplies, such as spark or tube generators for
HF and motor-generators for MF. The power supplies were
connected in parallel via a system of � lters.
Fig. 5: Pulsing dual-frequency cycle [11] Fig. 6: Inverters connected to separate
coils for pulsing dual- frequency
process [11]
Fig. 7: Dual frequency scheme using one coil and two inverters [11]
62 heat processing 3-2012

However at that time there were no e�ective generators
producing simultaneously two signi�cantly di�erent
frequencies with su�cient power. The situation changed
later with the development of solid state generators in the
range 20 to 300 kHz, which have made possible to improve
the dual-frequency hardening process and, in particular,
to avoid the need for switching frequencies, supplying
simultaneously a single inductor with medium and high
frequency energy.
The frequency mixture at the inductor current consists
of a high-frequency oscillation superimposed to a fundamental
medium frequency, as shown in the example
of Fig. 8.
TECHNOLOGY
The hardening treatment of steel parts, gears in particular,
is performed in order to improve their mechanical
properties. Sometimes it is required to improve only the
wear resistance and the contact fatigue strength, other
times the goal can be to increase the compressive residual
stress in a sub-surface layer of the workpiece, to the end
of increasing the applicable load on the mechanical component,
maintaining or reducing its volume and weight
(economical savings).
The work of Sigwart [7] has shown, from a qualitative
point of view, how the compressive residual stress and the
hardness pattern are related, and that higher values of the
compressive residual stress can be achieved with contour
true hardening of the gear.
Such contour hardening pattern is achievable by thermo-chemical
processes like carburizing, nitro-carburizing,
nitriding or pure thermal processes like �ame, laser, electron
beam or electromagnetic induction heating.
In the thermo-chemical processes the whole volume of
the work piece has to be heated during several hours in an
oven, with consequent waste of energy and high distortion
levels of the component.
Among the thermal process, induction heating is interesting
from the economical and technological point of
view, in particular for hardening geared work pieces with
modules between 1.5 and 5 [10]. This technology allows on
one side to achieve contour hardening of the component
in order to improve its mechanical properties, on the other
hand to concentrate the heating sources directly into the
outer surface layer to be hardened.
The possibility of concentrating the heating sources
where they are needed, implies a reduction of the heating
times and leads to a minimal distortion produced
by the heat treatment, thus allowing to reduce/eliminate
expensive post-treatment hard machining. A comparison
between gas carburizing and induction contour hardening
is presented, for automotive industry, in the work of Jenhert
[16] and for aeronautical industry by Jones [19].
3-2012 heat processing
Induction Technology REPORTS
Process
This paragraph highlights the electromagnetic phenomena
relevant for the induction hardening process. The geared
steel workpiece to be treated is placed inside or in front the
inductor coil where an alternating current �ows (Fig. 9).
As previously mentioned, the depth of the outer layer, in
which the induced currents and practically all the induced
power concentrate, has a dimension comparable with the
so-called skin depth d (eqn. 1), which as a consequence
– due to the short heating time which prevents heat di�usion
– can be considered the parameter that de�nes how
deep will be the heated layer.
For a cylindrical workpiece the coupling distance between
coil and work piece is constant along the circumference
and it is possible to control the depth of the heated
layer and its hardness only by choosing suitable values of
frequency, heating time and power density.
The achievement of a uniform hardness pattern is much
more complicated in case of mechanical workpieces having
an irregular or complex contour such as pinions, gears,
toothed racks and screws. In fact, in the case of toothed
mechanical parts, the root area does not have the same
good coupling with the inductor as the tips; moreover,
roots and teeth are characterized by very di�erent surface
areas and thermal capacities. Therefore it is di�cult to induce
the proper amount of energy into the gear roots and
teeth, required for obtaining a uniform heated layer, which
in turn is strongly a�ected by the frequency of the exciting
current and the geometry of the inductor.
Influence of the frequency on the skin depth
In the work of Slukhotsky [9] is presented a parameter m is
de�ned as follows, for characterising the induction heating
of cylindrical workpieces:
D
m =
2δ
(2)
where D is the diameter and δ is the skin depth.
This parameter, describing the current and power distribution
inside the workpiece, depends on its geometrical
dimensions and the applied frequency. It is known that, in
order to achieve a good energy transfer from the coil to
the workpiece, relatively high values of m are necessary. As
published by Di Pieri [29] and showed in Fig. 4a, two different
geometrical dimensions R1 and R2 characterise the
gear; since R1 is much smaller than R2, in order to achieve
a good energy transfer m1 and m 2 should be both high
enough, thus δ1 should be much smaller than δ2 or f1
much higher than f2.
If we consider the two regions independent one from
the other, it is easy to understand that two independent
frequencies would lead to an optimum energy transfer
between the coil and these two regions.
63

REPORTS Induction Technology
Fig. 8: Shape of the inductor supply voltage with HF
superimposed on MF
Fig. 9: Section of the coil – work piece system
Fig. 10 left: Heating e� ect of MF frequency current in the teeth of a
gear (A: coil current, B: induced currents path, C: heating
zone, D: tooth dimension) [28]
Fig. 10 right: Heating e� ect of HF frequency current in the teeth of a gear
(A: coil current, B: heating zone, C: induced currents path) [28]
Fig. 11: Hardness patterns achieved with di� erent applied power
density and constant energy; A) 3 kW/cm 2 , B) 5 kW/cm 2 , C)
8kW/cm 2 . The values of the “contour” parameter are respectively
A) 47 %, B) 67 % and C) 88.3 %.
Fig. 10 left, Fig. 10 right illustrate the heating e� ect
of medium frequency MF (left) and high frequency HF
(right) currents in gears with module between 1.5 and 5.
As schematically shown in the � gures, the current direction
in the coil is normal to the teeth axis, while the induced
current will � ow in the opposite direction within a layer δ
that depends on the frequency (eqn. 1).
Heating Time
The heating time is a fundamental parameter which determines
the hardening result. If the heating process is not short
enough, the heat will be transmitted from the surface layer
to the core of the tooth, resulting in the through hardening
of the teeth. The smaller is the gear module the shorter as to
be the heating time, so that for gears of module between 1.5
and 5, the heating times should not be longer than 250 ms.
Heating a mechanical part to the austenization temperature
means to transfer a certain amount of energy. If short
heating times are needed, as a consequence high power
densities must be applied.
Infl uence of the power density on the hardness
pattern
The applied power density has a strong in� uence on the
“quality” of the hardness contour, as shown by the experimental
results of Fig. 11, obtained on the same gear with
3, 5, and 8 kW/cm 2 [20].
The higher is the power density the better is the quality
of the contour hardness pattern, which can be evaluated
through the “contour parameter” C% [20], de� ned as:
TH − SHDT + SHDR
%C =
TH
64 heat processing 3-2012
* 100
where: TH - height of the teeth, SHDT - hardness depth in
the tooth tip and SHDR - hardness depth in the tooth root.
Ring and proximity e� ects
If we consider a straight electrical conductor, like a copper
tube, where an alternating current � ows, it is well know that
the current distribution in the conductor cross-section is
generally not homogeneous and it concentrates on the
external surface layer due to the skin e� ect.
In case of two adjacent current � owing conductors, the
current distribution in their cross-sections will depend also
on the distance between the conductors and the currents
directions. If the currents have opposite directions, the
currents will concentrate towards the adjacent surfaces
and vice versa (proximity e� ect).
If we consider � nally a bent conductor, e.g. a turn of a
circular inductor coil, again the distribution of the current will
be non-uniform in the cross section of the conductor. In fact,
the magnetic � eld intensity is considerably higher in the inner
(3)

space of the coil turn, this will give rise to a concentration of
the current towards the inner coil cross section, and the current
will � ow through the lowest impedance path (ring e� ect).
In an induction heating system, where the work piece
is encircled by the inductor coil, both ring-e� ect and proximity
e� ect will take place: in particular, since the induced
currents have a direction opposite to the coil current, in
the work piece they will be concentrated in the outer layer
while in the coil conductor in the internal one .
On the contrary, if the surface to be hardened is the
internal diameter of the work piece and the inductor coil is
internal to it, the current in the coil conductor will distributed
both on the external layer of the cross-section (due to proximity
e� ect between coil and work piece) and the internal
one (due to the ring e� ect). In this case the coil e� ciency
would be drastically reduced because of the lower coupling
between the inductor current and load; for this reason the
coils for hardening the inside diameter of a workpiece (ID)
should always be equipped with � eld concentrators.
This e� ect depends on the frequency of the applied
current; in particular, the lower is the frequency, the more
prominent it is. This means that for hardening ID, high
frequency currents must be preferred.
An analogous phenomenon arise in case of hardening
bevel gears or similar workpieces, where the conductor of
the inductor coil is bent to a circular form and the inductor is
placed in front of the work piece (Fig. 12, left). Here again,
due to the simultaneous ring- and proximity-e� ects, the distribution
of the current will be non-uniform in the cross section
of the coil conductor. The e� ect will be more evident in case
of medium frequency supply, and the hardening results will
be di� erent in the outside diameter (OD) and inside diameter
(ID) cases. The choice of a suitable variable distance between
coil and work piece along the coil cross section (Fig. 12, right)
allows to control the heating pattern in both cases.
End and Edge e� ect
The end e� ect is a phenomenon present in the hardening
inductors, due to their geometry, where, usually, the coil
diameter is much larger than its axial length. Inside such coils
the lines of the electromagnetic � eld are non uniform in the
axial direction; in particular, at the coil ends the lines are not
anymore straight and this leads to an axial variation of the
induced power density. This e� ect can lead to the reduction
of the heating of the workpiece near the ends of the coil.
At the workpiece edges another e� ect takes place,
which is known as “edge e� ect”. In these regions the work
piece is in� uenced at the same time by the longitudinal
component of the magnetic � eld along the axial direction
and by the radial magnetic � eld component on the edge
surface. This leads to an increase of the induced power
density at the workpiece corner.
The experience has shown that the above e� ects
3-2012 heat processing
Induction Technology REPORTS
depend on the choice of the process parameters, i.e. frequency,
power density and coil geometry, which in turn
strongly in� uence the � nal hardening pattern.
Uniform heating along the axial length of a gear can
be achieved by the use of magnetic � ux concentrators,
placed at the top and bottom of the work piece. They
allow to achieve a quite uniform hardening pattern along
the axial direction while, without them, the root edges
tend to be overheated. When the use of this solution is
not possible, excellent results along the axial length of
the gear can be achieved by the use of the SDF® process,
through a suitable coil design and applying high power
density levels [17, 18, 20].
Fig. 13: Iron-Carbon-Diagram [26]
Fig. 12:
Typical heating pattern:
left – with constant gap
between inductor and
workpiece; right - with
variable coupling distance
between work
piece and coil [27]
65

REPORTS Induction Technology
METALLURGICAL ASPECTS
Induction hardening is based on the martensitic transformation
of steels and cast irons. The possibility of the
martensitic hardening of steel is due to the allotropy of
iron. At room temperature iron has a cubic body centred
lattice, called ferrite. At a temperature of 911 °C a solid state
transformation starts and the lattice transforms to a cubic
face centred structure, austenite. In the cubic face centred
lattice 100 times more carbon is soluble compared to the
cubic body centred lattice. Fig. 13 presents the iron-carbon
diagram [26].
For the martensitic transformation it is necessary to
heat the alloy up to the austenising temperature, in order
to solute the carbon in the cubic face centred lattice, holding
it at a this temperature for a time long enough for
completetion of the formation of austenite. In case that a
fast cooling follows, the solid state transformation into the
cubic body centred lattice takes place without di�usion of
carbon and the hard martensitic structure with a tetragonal
distorted cubic body centred lattice is created.
There is one principle necessary to understand to increase
hardness of metals. A higher hardness always occurs
because of a restraint or limitation of the movement of dislocations
during a mechanical load. By the heat treatment
we can change the microstructure in a way that limits the
movement of dislocations. Thus there are di�erent mechanisms
in steels that can lead to an increase of hardness.
The mechanism that leads to limit the dislocation movements
are:
■ Formation of a tetragonal distorted cubic body centred
lattice (martensite)
■ Grain re�nement
■ Precipitations (depends on dimension and distribution)
■ Increase of density of dislocations.
The data of hardenability of induction hardenable materials
in most cases are published for a full martensitic structure,
where during heating nearly all the carbon is solved
in the austenite. In some cases, when the austenitization
times are short, the cooling rates are high and the carbon
is not completely solved in the austenite, it is possible to
reach an increase of hardness (up to 2 or 3 HRC). This increase
occurs, in addition to the contribution of martensite, if
a re�nement of grains takes place (shorter heating times
leads to a �ne grained austenite and with a fast cooling
rate to a �ne grained martensite) and, additionally, if some
carbides are retained. This phenomenon is sometimes
described as “super hardening e�ect” [31].
The two main requirements to realize a martensitic
hardening process are the austenitic transformation and
the right carbon content. For induction surface hardening
processes normally carbon contents between 0.3 and 0.6
weight percent are used.
The solid state transformations as well as the solution
of the carbon in the austenite are processes controlled by
di�usion. We can activate these processes by the heating
to a speci�c temperature and, like all di�usion processes,
they need a de�ned holding time, which also depends
on temperature. The temperature acts like a mainspring.
Within speci�c limits we can use higher temperature to
shorten the time necessary to complete the transformation
into austenite and to solve the carbon in the cubic face
centred lattice. Formation of austenite is a function of the
starting microstructure. Austenite starts to form ferrite/
cementite interfaces. To continue the austenite formation,
cementite dissolves and supplies the carbon (via di�usion)
to the austenite/ferrite interface in order to activate the
transformation from low carbon ferrite to austenite [25].
Heating times for induction gear hardening are between
100 ms and 3s; in some cases more, by the use of preheating.
Short heating times can in the worst case scenario lead
to incomplete martensitic transformation. This depends on:
■ Chemical composition / Bond of carbon at room temperature
■ Starting microstructure / Dispersion of carbon
■ Austenitization temperature
■ Heating rate / time.
Counteractive measures are [22]:
■ Higher austenising temperature
■ Focus the sources of heat into the critical area
■ Preheating
■ Use of di�erent material and/or initial microstructure.
A bene�t of induction hardening is that the heat sources
are located inside the part itself. It is not necessary to bring
in the heat from outside. Moreover, the use of di�erent
frequencies gives the possibility to focus the heat sources
into the critical area. Skin e�ect and the dependence of
the induced heat sources from the relative coil-workpiece
position are thereby crucial factors of in�uence.
If the carbides are �ne distributed in the material, the distance
to cover the di�usion processes is shorter. Thus �ne
grained microstructures with �ne distributed carbides are
the most suitable materials for short austenitisation times.
Also the stability of the bond of carbon plays a major role.
The higher the stability the higher energies and temperatures
are necessary to dissolve the carbides [21].
Depending on the geometry of the tooth of the gear,
temperature di�erences occur from the �anks to the tooth
axis and from the tip to the root [20]. As a consequence,
this leads to di�erent microstructures in the heat treated
gear. In many cases the reached austenitisation temperature
in the tip is lower then in the root; in these cases, a
short preheating time with high frequency power leads
to a higher temperature, specially in the tooth tip, and
66 heat processing 3-2012

therewith to a more homogeneous austenite and � nally
to a better transformation into martensite.
An important fact is that, during a correct induction surface
hardening, the mechanical properties of the core will
not be a� ected. This means that the required core properties
of the mechanical parts (i.e. hardness and core strength)
must be already reached before the part are heat treated.
In Fig. 14 is shown a typical hardness pro� le, from the
surface to the core, after a successful induction surface
hardening process.
Some important factors can in� uence the shape of the
hardness pro� le. These factors and the characteristics on
which, in turn, they have in� uence are:
Austenitization time and temperature:
■ surface hardness in terms of grain size, carbon distribution
and carbon bond
■ width (b) of the transition zone
■ width (c) of over tempered zone
■ hardness collapse (d) in over tempered zone
Starting microstructure:
■ core hardness
■ hardness collapse (d) in over tempered zone
Carbon content:
■ level of surface- and core hardness
Fraction and content of alloys:
■ hardenability
Cooling rate:
■ width (b) of the transition zone
■ level of surface hardness
■ width (c) of over tempered zone
■ hardness collapse (d) in over tempered zone
Fig. 14: Hardening pro� le after induction surface hardening
3-2012 heat processing
Induction Technology REPORTS
Therefore the hardness pro� le depends on material
starting microstructure as well as heating and cooling parameters.
This means that the design of the heat treatment
process has a big in� uence on the � nal hardness pattern.
All the above described factors/parameters determine
also the residual stress after heat treatment. In most cases
a compressive residual stress on the surface is desired after
the heat treatment of geared parts [7]. A small hardness
penetration depth and a low cooling rate give bene� ts
for reaching high compressive residual stresses. Therefore
it is important that the cooling rate is as high as possible
to form the necessary amount of martensite. However, it is
di� cult to foresee the amount of residual stress after hardening,
since this amount depends also on the workpiece
geometry and the residual stresses before heat treatment.
Thus the whole process chain, for one speci� c workpiece,
leads to a speci� c pattern of � nal residual stress.
In most cases a tempering process is done after hardening
to give more ductility to the material. Tempering of
steel is a di� usion process. In the martensite the carbon is
trapped in the cubic body centred lattice. If we heat up the
martensite the di� usion of carbon is activated.
The tempering process is composed of � ve stages, described
in the reference [23]. In each stage de� nite transformation
processes are activated as a function of temperature.
In the � rst tempering stage, from 100 to 150 °C, the precipitation
of ε-carbides Fe 2C begins for carbon content over 0.2 %.
According to [23], the second stage (150 to 300 °C) is
characterised by transformation from retained austenite
in bainite or martensite.
The third tempering stage (325 to 400 °C) is denoted
by the precipitation of cementite (Fe 3C) and the disappearance
of carbide Fe 2C. The fourth stage, above 400 °C, is
characterised by the recovery and recrystallisation of the
martensitic microstructure, where defects such as vacancies
and dislocations are removed.
Fig. 15:
Worm gear true contour
surface hardened with total
power 566 kW and heating
time 0.35 s
Fig. 16:
Bevel gear true contour surface
hardened with total power 580kW
and heating time 0.2 s [30]
67

REPORTS Induction Technology
In the �fth tempering stage special carbides develop in
high-alloy steels above 450 °C. The temperature at which
the Ostwald ripening occurs is reported at approx. 500 °C.
All these stages can be found, during tempering of
the steels used in the induction hardening of gears. They
occur at di�erent temperature ranges for each material,
in dependence of its chemical composition. An example
of the tempering process on microscopic scale, for the
42CrMo4 steel, is described in [24].
Tempering is a di�usion process, which is controlled
by temperature and time. That means that it is possible,
within speci�c limits, to compensate temperature by time
and time by temperature in order to reach the desired
material requirements. For low alloyed carbon steels the
temperature is the mainspring [25], time plays a secondary
role. The more alloyed is the material, the more the time
has in�uence on the tempering result. Thus tempering with
short heating times can lead to the desired results also by
using induction heating. The authors of [25] suggest the
use of heating rates not exceeding 50 K/s.
APPLICATIONS
In this paragraph are presented some practical applications
of induction contour hardening of geared parts. As explained
in the historical overview, the idea to contour harden
geared parts by mean of induction is not new, since from
the beginning of induction industrial application hardening
of gears was a main topic.
The range of application of induction hardening has
being increasing during the last 15 years due to developments
in power electronic components. In particular, the
development of solid state generators, which can deliver
a higher power level and two di�erent frequencies to the
same coil, allows today to harden by induction parts, which
were carburized before. Typical power densities for these
processes are in the range 5 to 15 kW/cm².
In this paragraph some examples are discussed were
the heat treatment has been switched from carburizing
to induction or were this change is an actual topic. Why
changing the kind of heat treatment?
Advantages of induction surface hardening are:
■ one piece control, i.e. the possibility to follow and monitor
the heat treatment of each single workpiece,
■ intelligent use of the energy, since the heating sources
are only placed were they are need,
■ low distortion,
■ repeatability, since the process parameters are the same
for each work piece both during the heating (i.e. not
depending on the position in the carburizing oven) and
the quenching,
■ increase of productivity, due to heating times shorter
than one second, with consequent reduction of the
total cycle time.
Another very important factor, that increases the utility
of induction technology, is the possibility to have a full
automated process. The process parameters, like transferred
energy, input current and power, can be monitored
and/or regulated by the generator controller.
The evaluation of the advantages is speci�c for every
application. It has to be determined if it is possible to
achieve a cost reduction in the heat treatment process
and/or in the whole process chain, maintaining
or improving the quality standards of the produced
workpieces.
A typical workpiece that can be conveniently heat treated
by induction is worm gear (Fig. 15). By the simultaneous
dual frequency process it is possible to reach a
contour true austenitisation and therewith a contour true
hardening pattern. These parts can be hardened in single
shot operation under rotation inside a coil that induces
currents in the workpiece �owing at 90 degrees to the
teeth direction.
Another interesting example of application is the contour
induction hardening of the bevel gear shown in Fig. 16.
By using of `single shot` simultaneous dual frequency
induction hardening minimal distortion of the workpiece
was achieved. This bevel gear processed by SDF was
compared with a case hardened bevel gear in terms of
distortion. Induction hardening allows much closer control
of surface distortion (less distortion) than conventional
carburizing, as explained in [19], this implies a signi�cant
reduction of production costs.
Another new �eld of application of induction hardening
is the treatment of ring gears and pinions used in
the automotive industry. Fig. 17 shows an induction
hardened ring gear. Major savings in the process chain are
due to the energy costs and reduced distortion. The lower
distortion leads to a signi�cant shorter lapping process of
the induction hardened workpiece. The economical and
heat treatment quality comparison between the induction
hardening and the carburizing processes has been
presented in paper [16].
Up to now, steering parts - in particular steering pinions
and steering racks - are induction hardened by a
scanning process using low power density. This process
is well known but has some drawbacks since it gives rise
to the through hardening of the teeth, resulting in high
mechanical distortion. An actual topic is the hardening of
these parts by a `single shot` process, using simultaneous
dual frequency and a high power density (5 to 15 kW/
cm²). Fig. 18 presents a hardening example heated by
the SDF process, with 500 kW power and 200 ms heating
time. The switching to the `single shot` process leads
to the reduction of the mechanical distortion and the
consequent lowering of the heat treatment and whole
process chain costs.
68 heat processing 3-2012

Fig. 17: Ring gear contour true surface hardened with
total power 1.5 kW and heating time 0.4 s [16]
CONCLUSION
This paper describes state of the art of induction hardening
of complex geometry and geared parts. The electromagnetic
and metallurgical aspects which are involved in the
induction hardening process have been highlighted. In
particular has been pointed out the advantages of using
the simultaneous dual frequency process combined with
high power densities applied to the workpiece.
LITERATURE
[1] Brown W.J.: Patent USA n. 1 687 656, �led July 1926
[2] Hogel L.: Induction hardening cuts distortion in worm gears,
Steel 103, 57, 1938
[3] Volgdin V.P.: Method of surface gear hardening by means of
induction, Patent USA n. 61 405, �led Sept. 1939
[4] Vologdin V.P.: Surface induction hardening, 1st ed.: Metallurgizdat,
Moskow-Leningrad, 236 pp., 1939; 2nd ed.: Oborongiz,
Moskow, 291 pp., 1947, (in Russian)
[5] Jordan J.: Patent USA n. 2 444 259, June 29, 1948
[6] Knolwlton H.B., Kincaid H.F.: Induction-hardening gears, Soc.
Autom. Eng. Quart. Trans, 4, n.1, 1950
[7] Sigwart H.: Direkthärtung von Zahnrädern., HTM J. Heat
Treatm. Mat., 12 (1958), 9-22
[8] Reboux J.: Die Zhanradober�aechenhaertung, eine typische
Anwendung der Induktions erwaermung, Deut. Elektrotechnik,
11, 375, 1957
[9] Slukhotsky A.E., Ryskin S.E.: Inductors for induction heating,
Ed. Energhia, Leningrad, pp.263, 1974, (in Russian)
[10] Schwenk W.: Simultaneous Dual-Frequency Induction Hardening,
Heat treating Progress, April/May 2003,35 - 38
[11] Rudnev V., Loveless D., Cook R., Black M.:”Handbook of Induction
Heating”, Ed. Marcel Dekker, Inc., New York, 2003, 777
pp., ISBN: 0-8247-0848-2
[12] Rudnev V., Loveless D., Cook R., Black M.: ”Induction Hardening
of Gears: a Review”, Heat Treatment of Metals, Wolfson
Heat Treatment Centre, Aston University, UK, Part 1: 97-103
(2003); Part 2: 11-15 (2004)
3-2012 heat processing
Induction Technology REPORTS
Fig. 18: Steering pinion contour true surface hardened with
total power 500 kW and heating time 0.25 s
[13] Wrona E.: Numerische Simulation des Erwärmungsprozesses
für das induktive Randschithärten komplexer Geometrien,
Ed. Cuvillier- Verlag, Göttingen (Germany), 2005
[14] Stiele H., Marquis F.:”An Overview of inductive gear spin hardening”,
Conf. Proc. of HES-07 – Heating by Electromagnetic
Sources, Padua (Italy), June 19-22, 2007, 183-190, ISBN
88-86281-92-7
[15] Mühlbauer A.: History of induction heating and melting, Ed.
Vulkan-Verlag GmbH, Essen (Germany), 2008, pp.202, ISBN
978-3-8027-2946-1
[16] Jenhert H., Peter H.-J.: Einsatzhärten vs. Induktionshärten,
HTM J. Heat Treatm. Mat., 64, 2 (2009), pp 72 – 79
[17] Ulferts A., Nacke.: B Improvements in induction hardening by
adapted �eld guiding. 54th international scienti�c colloquium
IWK 2009, Ilmenau, September 7-11, pp.
[18] Schwenk W., Nacke B., Ulferts A., Häußler A., Biasutti F.: Härteeinrichtung,
Patent DE102008021306A, (2009).
[19] Jones K.T., Newsome M.R., Carter M.D.: Gas carburizing vs.
contour induction hardening in bevel gears, Gear Solutions, 1
(2010), 213 - 233
[20] Biasutti F., Krause C.: Experimental investigation of process
parameters in�uence on contour induction hardening of
gears, Conf. Proc. of HES-10 Heating by Electromagnetic Sources,
May 18-21, 2010, Padua (Italy), 189-199, ISBN 978-88-
89884-13-3
[21] W.C. Roberts-Austen, Fourth Report to Alloys Research Committee,
Proceedings, Istitution of Mechanical Engineers, 1897
[22] Ch. Krause, R. Springer, F. Biasutti, G. Gershteyn, Fr.-W. Bach:
Mikrostrukturelle Untersuchungen an randschichthärtbarem
Stahl Cf53 nach induktiven Hoschgeschwindigkeitsaustenitisierung
mit anschließendem Abschrecken, HTM J. Heat
Treatm. Mat. 65 (2010) 2, S. 96 - 100
[23] Hrsg. Dahl, W.,. Eigenschaften und Anwendung der Stähle,
Verlag der Augustinus Buchhandlung, 5. Au�age, Aachen
1998
[24] Christian Krause 1 | Ronald Springer 1 | Gregory Gershteyn 1 |
Wlodzimierz Dudzinski 2 | Friedrich-Wilhelm Bach 1In-situ
high temperature microstructural analysis during tempering
of 42CrMo4 using transmission electron microscopy;
Appeared in International Journal of Materials Research
2009/07, Page 991-1000.
69

REPORTS Induction Technology
[25] Crafts, W.; Lamont, J.L.: Härtbarkeit und Auswahl von Stählen.
Springer Verlag, 1954
[26] Krauss,G.: Steels: Processing, Structure, and Performance von
George Krauss von A S M Intl (Oh) (Gebundene Ausgabe -30.
August 2005
[27] Benkowski, Induktionserwärmung.5. Au� age Verlag Technik
GmbH Berlin
[28] W. Schwenk, H.-J. Peter. Application for surface induction
hardening using Simultaneous Dual Frequency Induction
Heat Treating. Elektorwärme international Heft 1/2002-März.
Page 14
[29] Di Pieri, C. Moderni impianti di riscaldamento ad induzione.
Vol.LXXV – N.12 – Dicembre 1988 – L´elettrotecnica. Page 1186
[30] Schwenk, M. Substitution/replacement of case hardened
gearbox components in the automotive as well as airplane
industry through contour true induction hardening, Conf.
Proc. of HES-07 Heating by Electromagnetic Sources, June
19-22, 2007, Padua (Italy), 175-182, ISBN 88-89884-07-X
[31] L.C.F. Canale, C.R. Brooks, T.R. Watkins, and V. Rudnev. E� ect
of prior microstructure on the hardness and residual stress
distribution in induction hardened steel, Proc. SAE Intl. O� -
Highway Cong.,Las Vegas, Nev. March 19-21, 2002
23 – 26 OCTOBER 2012
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Dipl.-Ing. Fabio Biasutti
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Dr.-Ing. Christian Krause
eldec Schwenk Induction GmbH
Dorstetten, Germany
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christian.krause@eldec.de
Prof. Eng. Sergio Lupi
University of Padova
Dept. of Industrial Engineering
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