1. technology and computing

Journal of Information & Computational Science 12:2 (2015) 641–656
Available at http://www.joics.com
January 20, 2015
Simulation on the High Frequency Induction Cladding
and Experimental Validation ?
Yancong Liu a,b,∗, Chengkai Li b , Jianghao Xie b , Yongjun Shi b , Peng Yi b
Guidong Sun b , Xianghua Zhan b , Xiaoli Ma b , Lanfang Cui c
a Shengli
b College
College, China University of Petroleum, Dongying 257097, China
of Mech. and Elec. Engineering, China University of Petroleum, Qingdao 266580, China
c National
Center of Quality Supervision and Inspection for Automobile Fittings of China, Yantai
Products Quality Supervision and Testing Institute, Yantai 264001, China
Abstract
The simulation model of the High Frequency Induction Cladding (HFIC) is built using three-dimensional
(3D) and its dependability is validated by the experimental measurement result. Firstly, a mathematical
3D model with respect to the HFIC process is established with corresponding assumptions and border
condition. Secondly, the 3D model of the FEM simulation is validated by comparing the calculation
results and the experimental results. Thirdly, the thermal distributions at vary time are investigated by
the 3D model simulation. The results show that the 3D model simulation has significant effect on the
analysis of the thermal distribution, optimal cladding process, and crystal phase transition. It is possible
to obtain an ideal temperature distribution for the HFIC process using the 3D simulation calculation.
Keywords: Induction Cladding; Experimental Measurement; Three-dimensional Model; FEM; Thermal
Field
1
Introduction
Induction heating has become quite popular now in industry due to its fast heating rate, good
reproducibility and low energy consumption [1, 2], It is a technique of heating electrically conductive materials such as metals and alloys, and is commonly used in process heating prior to
metalworking, heat treatment, welding, and melting [3], Recently, a newly-emerging application
of the induction heating technique, known as the high-frequency induction cladding, has attracted
much attention from process engineers [4]-[13].
?
Project supported by the Fundamental Research Funds for the Central Universities (14CX06061A), Fundamental Research Funds for the Central Universities, China (No. 13CX02076A), and Shandong Province Science
and Technology Development Plans, China (No. 2011GGX10329).
∗
Corresponding author.
Email address: liuyc@upc.edu.cn (Yancong Liu).
1548–7741 / Copyright © 2015 Binary Information Press
DOI: 10.12733/jics20105297
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Y. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 641–656
The induction cladding process is a representative induction heat process [4, 5], including
electromagnetic, thermal and metallurgic phenomena. In this process, an alternating electric
current induces electromagnetic field, which in turn induces eddy currents in the substrate of
the conductor. Making use of inductive skin effect is helpful to utilize heat source efficiently
and to reduce heat influence on the bulk material. Then, the released heat from the induced
eddy currents melts the surface self-fused alloy coat, and the alloy is coated on the surface of the
substrate. The surface alloy coatings usually play an important role in resisting high temperature
wear and corrosion for a variety of applications [6]. In the particular case where wear and corrosion
resistance at low and moderate temperature are required, it can be expected that the induction
cladding will be widely used in the future [7].
The high frequency is the first choice for induction cladding process duo to getting the best
thermal distribution using the skin effect. Besides, the application of the high frequency has many
merits comparing the medium and low frequency, such as more high efficiency and more saving
energy [8]. Therefore, it is indispensable for the study on the induction cladding to adopting the
high frequency as the inductive heat source.
Many studies have been carried out on the induction heat model to investigate the effects of the
process parameters in recent years. Naar and Bay [9] achieved an accurate control of temperature
distribution and evolution in the heat affected zone by formulating a classical optimization problem. Shokouhm and Ghaffari [10] analyzed the effects of process parameters on moving induction
heat from a hollow cylinder. Luozzo et al. [11] made use of the finite element method to conduct
the numerical simulations of the heating stage of the bonding process. Yi Han et al. [12] analyzed
the influences of the current frequency, the current density and the distance between the coil and
the weld seam on the heating efficiency and the temperature difference across the thickness of
weld seam using the finite element method. S. Hansson and Fisk [13] simulated the manufacturing
process chain at glass-lubricated extrusion of stainless steel tubing by the finite element method.
Besides, many investigations have been done with respect to the induction heat process parameters using the numerical model. However, by far, the simulation of the high frequency induction
cladding has not been investigated. As there is no single universal computational method that
can optimally fit all cases and be optimum for modeling all induction heating applications [14],
it is necessary to study an appropriative computational model of the high frequency induction
cladding (FHIC) process.
The objective of this study is to build three-dimensional (3D) model of the induction cladding
process and to validate the dependability of the 3D model. Firstly, the 3D geometry numerical
model of the shaft workpiece of 45 Steel is established for the HFIC process. Secondly, the
validation of the 3D Finite Element Method (FEM) model is carried out by using the experiment
measurement results. Thirdly, based on the results of the simulation calculation, the thermal
distribution is investigated in detail.
2
Numerical Modeling
Generally, for the axisymmetrical geometry, the 3D geometry models with FEM method are simplified into two-dimensional (2D) geometry model or even one-dimensional geometry model. This
can be attributed to the following reasons [15]. Firstly, the skin effect of thermal distribution
in the low and medium frequency induction heating process is not remarkable, so the simplification of axisymmetric geometry models is applicable on that condition. Secondly, the precision of
Y. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 641–656
643
controlling thermal distribution with two-dimensional or one-dimensional geometry model is not
demanded rigorously for some induction heating applications. Thirdly, it takes much more calculation time using the 3D geometry model than using the two-dimensional or the one-dimensional
geometry model. Therefore, the accurate 3D geometry model with FEM method is rarely adopted
in induction heating numerical simulation.
In our case, because the high-frequency current is employed in the induction heating cladding
process, the contribution of skin effect is remarkable. Besides, technical requirements for the
induction cladding are needed that metallic coating on the surface is melted by the induction
Joule heat and the temperature from the inner part of the shaft workpiece is less than 600◦ C as
far as possible [16]. Thus, the more accurate calculation requires the adoption of the 3D geometry
model. Since the state-of-the-art computer technology provides more efficient ability in numerical
calculation, the calculation time when the 3D geometry model is used can be readily neglected.
Therefore, in this case, the 3D geometry model is adopted to the HFIC process for achieving more
accurate numerical solution.
2.1
Assumptions
The generating heat of the coating needs no consideration for the reason that HFIC coating
thickness is about one to two millimeters, so the generating heat of the coating is ignored on
the FHIC process and the heat conduction is only considerate into the process. Meanwhile, the
assumptions made for the numerical modeling in the process are as follows:
(1) The steel material is homogeneous and isotropic;
(2) The heat conduction and eddy currents effect for the helix coil are not considered in the
process;
(3) Hysteresis loss of the high-frequency induction process is ignored;
(4) The magnetic saturation for the steel material is neglected.
2.2
Domain Dividing
The whole domain for the HFIC process is shown in Fig. 1 (a). Considering the symmetry of
revolution and the symmetry shaft workpiece, in this case, the whole domain is divided into three
model domain zones, including shaft substrate, coating, inductor coil and air. The model domains
zones are shown in Fig. 1 (b) and provided in detail as follow:
Ω1: Shaft substrate zone. It is a heat-generating region by electric conduction and induction,
where induced magnetic field and induced electric field can be stimulated. Free electricity exist
duo to the conductor of shaft workpiece, so Joule heat of induction process can be generated by
induced current in this region.
Ω2: Coating zone. It is a magnetic conduction and heat conduction region. In this case, it
mainly receives the heat by the heat conduction of the shaft substrate.
Ω3: Induction coil zone. It is an inducing eddy current drive region, where driving current AC
is enforced. As Joule heat of the induction coil conducting is taken away by the cooling water
inside coil, Free electricity is not taken into account.
Ω4: Air zone. It is a heat convection and heat radiation region. Phenomenon of convection
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Axis of symmetry Γ0e
Ω1 shaft substrate
Ω2 coating
Ω3 induction coil
Ω4 air
Artificial surrounding box
e
Γe−Γ0
(a) Whole domain
(b) Model domains
Fig. 1: Domain dividing in the HFIC process
and radiation takes place in this zone.
For using the standard finite element method, it is necessary that a closed domain with an
artificial border is taken into account. Considering that shaft workpiece is axis-symmetrical
geometric profile, a null Dirichlet boundary condition on the symmetry axis Γe0 is prescribed for
the electrical field. Avoiding artificial reflections or external borders Γe − Γe0 an absorbing-type
Robin-like condition is prescribed [17, 18], as shown in Fig. 1 (b).
The numerical models are summarized below, which of proper continuous equations are written
with proper applied boundary conditions.
2.3
Electromagnetic Model
The global system in the electromagnetic fields can be described by the following four Maxwell
equations:
∇·D=ρ
∇·B=0
∂B
∇×E=−
∂t
∂D
∇×H=J+
∂t
(1)
(2)
(3)
(4)
where D is the electric flux density, B is the magnetic flux density, E is the electric field intensity,
H is the magnetic field intensity, J is the electric current density associated with free charges,
and is the electric charge density. ∇× and ∇· denote the curl operator and divergence operator,
respectively.
Joule heat of conductor is the focus of analysis, which is produced by free charge directional
migration in induction heating process. Besides, since displacement current density ∂D/∂t of
conductor is no reason of generating the Joule heat, and when the frequency of the current
is less than 10 MHz, the induced conduction current J is much greater than the displacement
current density ∂D/∂t, the displacement current density ∂D/∂t is negligible compared with the
conduction current density [19]. Thus, the Maxwell equations can be written as:
∇·B=0
(5)
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∂B
∂t
∇×H=J
645
(6)
∇×E=−
(7)
There are constitutive relations for the intrinsic material properties:
B = µH
(8)
J = σE(Ohm0 slaw)
(9)
where µ and σ are the magnetic permeability and electrical conductivity, respectively. They are
temperature independent parameters.
Since the magnetic flux density B satisfies the zero divergence condition Eq. (5), a magnetic
vector potential A is given in accordance with Helmholtz theorem.
B=∇×A
(10)
Substituting Eq. (10) into Eq. (6), it can be obtained:
³
∂A ´
∇× E+
∂t
(11)
Electric scalar potential ϕ is introduced due to the reason that ∇ × (∇ϕ) = 0 satisfies Helmholtz
theorem. Then, Eq. (11) can be further derived as:
E=−
∂A
− ∇ϕ or
∂t
E=
∂A
+ ∇ϕ
∂t
(12)
Eq. (10) and Eq. (12) ensure that Eq. (5) and Eq. (6) can be satisfied. The constitutive relations
Eq. (8) and Eq. (9) are taken account in conjunction with Eq. (7). Thus, substituting Eq. (5) to
Eq. (9) into Eq. (7), it can be obtained:
∇×
1
∂A
∇×A+σ
+ σ∇ϕ = 0
µ
∂t
(13)
Electric scalar potential ϕ and magnetic vector potential A are not unique, for different gauges
have various values. Furthermore, Lorentz gauge and Coulomb gauge are usually employed to
solve the electromagnet analysis formula. However, in our case, on magneto-quasi-static approximation condition, the utilization of Coulomb gauge can simplify the model equations compared
with that of Lorentz gauge, since scalar potential and vector potential are controlled by electric
scalar potential ϕ and magnetic vector potential A, respectively. ThereforeCoulomb gauge expressed as ∇ · A = 0 is put into use. The penalty function ∇ µ1 (∇ · A) is added to Eq. (13) and
the following expression can be acquired:
∇×
1
∂A
1
∇ × A − ∇ (∇ · A) + σ
+ σ∇ϕ = 0
µ
µ
∂t
(14)
Introducing the formula of curl ∇ × ∇ × A = ∇(∇ · A) − ∇2 A, and substituting it into Eq. (14),
it can be obtained:
1 2
∂A
∇ A+σ
+ σ∇ϕ = 0
(15)
µ
∂t
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Substituting Eq. (9) into Eq. (11), it can be obtained:
J = −σ
∂A
− σ∇ϕ = Je + Js
∂t
(16)
where Je and Js are eddy induction current density and source current density, respectively.
Therefore, equation Js = σ∇ϕ can be described.
For time harmonic analysis, electromagnetic field quantities are oscillating functions of a single
frequency. Thus, A can be expressed as:
A = A0 ejωt
(17)
Js = J0 ejωt
(18)
where J0 and A0 are the amplitude of source current density and magnetic vector potential,
respectively, and ω is the angular frequency expressed as ω = 2πf .
Substituting A and Js into Eq. (15), it can be obtained:
1 2
∇ A0 + J0 + jωσA0 = 0
µ
(19)
When dealing with axi-symmetrical configurations, Eq. (19) can be transformed into the equation of cylindrical coordinate (R, ϕ, Z). Then, Eq. (19) is rewritten as:
1 ∂A0 ∂ 2 A0 A0 i
1 h ∂ 2 A0
+
+
− 2 = −J0 − jωσA0
µ ∂R2
R ∂R
∂Z2
R
(20)
The above presented equations are employed to describe different mediums in electromagnetic
fields, including dielectric, conductor and magnetic medium. In our case, three different regions
with various mediums, i.e. the workpiece, the coil, and the surrounding air, can be analyzed as
follows.
For the workpiece Ω1 region, there is no source term. The equation for this region can be
written as:
∂A
1 2
∇ A+σ
=0
(21)
µ
∂t
For the coil Ω2 region, because the coil is linked to an external source current, the current
density of the induction coil is composed of two components: induced part and impressed part.
The induced part is stimulated by the time harmonic magnetic field B, while the impressed part
is defined by the gradient of the electric scalar potential Js = σE = σ∇ϕ and is connected to an
external source. Thus, for the coil, it can be obtained:
∂A
1 2
∇ A+σ
+ Js = 0
µ
∂t
(22)
For the air Ω3 region, there is no current density and electrical conductivity is zero. Then,
Eq. (15) can be simplified as:
1 2
∇ A=0
(23)
µ
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647
The source current density Js must be input into Eq. (22). When the induction coil loads an
alternating voltage source, Js is unknown. In this case, it is necessary to compute the equivalent
impedance of the coil-workpiece by circuit analysis.
Finally, the boundary condition is either Dirichlet or Neumanntype along with a given surface
depending on whether B · n = 0 or B × n = 0 has to be satisfied. Continuity conditions between
regions of different properties are also provided as follows [20]:
Ω1: Normal direction:
n · (D2 − D1 ) = σeo
(24)
n · (B2 − B1 ) = 0
(25)
n · (J2 − J1 ) = −
∂σeo
∂t
(26)
Tangent direction:
n × Hout
n × (E2 − E1 ) = 0
= i0 or n × (H2 − H1 ) = 0
(27)
(28)
Ω2: Normal direction:
n × (J2 − J1 ) = 0
(29)
n · (B2 − B1 ) = 0
(30)
n × (H2 − H1 ) = 0
(31)
Ω3: Normal direction:
Ω3: Tangent direction:
where Di , Bi , Ji and Ei (i = 1, 2) are the electric flux density, the magnetic flux density and eddy
induction current density on both sides of the boundary, respectively, n is unit normal vector,
σe0 is free charge surface density, i0 is surface current density on the surface of the conductor
boundary, and Hout is magnetic field intensity, of which direction is point to the outside along
the interface. Especially, under the condition of the Ultrahigh Frequency (UHF), n × Hout = i0
is used as the substitution for n × (H2 − H1 ) = 0 as tangent direction boundary condition. In
our study, the high frequency induction eddy is laid upon the workpiece, so n × (H2 − H1 ) = 0 is
employed to the boundary condition.
2.4
Heat Transfer Model
The induction heating processes involve conservation of energy and Fourier law. Energy transferring in the induction heating process is governed by the classical heat transfer equation, which
can be expressed as:
∂T
ρC
− ∇ · (k∇T ) = Q
(32)
∂t
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where ρ is the material density, C is the specific heat, T is temperature time function, k is the
thermal conductivity, and Q is the heat source term due to eddy currents [21]. In our induction
heating process, the specific heat C and the thermal conductivity k are assumed to be isotropic
with temperature dependence.
In this case, with regard to the axi-symmetrical workpiece, the classical heat transfer equation
Eq. (25) in the cylindrical coordinate (R, ϕ, Z) can be rewritten as:
∂T
∂T ³ ∂T ´ 1 ∂ ³ ∂T ´
ρC
−
k
−
kR
=Q
(33)
∂t
∂Z
∂t
R ∂R
∂R
The heat source of the workpiece is generated by the eddy current. Connecting to the Joule
heat theorem, by substituting Eq. (18), it can be obtained:
³ ∂A ´2
h ∂(A ejωt ) i2
0
2
Q = J · E = σE = σ
=σ
= σ(jωσA0 ejωt )2
(34)
∂t
∂t
In our case, boundary conditions of the workpiece for temperature can be described through its
normal derivative at interfaces. Therefore, modeling function with respect to heat flux, convection
(− T )
k = k0 + (k0 − k∞ )e T0 and radiation between the part and the air, and it can be expressed as:
−k
∂T
4
= h(T − Tair ) + εemi σb (T 4 − Tair
)
∂n
(35)
where n is the outward unit normal vector, Tair is the environment temperature of the workpiece,
and h, εemi and σb are the convection coefficient, the material emissivity, and the Stephan constant,
respectively.
2.5
Material Properties Model
Material properties, including the thermal conductivity, specific heat, magnetic permeability and
electric resistivity, are nonlinearly correlated with temperature in the heating process. The models
of material properties can be obtained through the mathematical methods.
The temperature-dependent thermal conductivity and specific heat are expressed as follows
[22]:
(− T )
(36)
k = k0 + (k0 − k∞ )e T0
where k0 , k∞ and T0 is thermal conductivity value for zero degree centigrade, thermal conductivity
value for ∞ degree centigrade and initial temperature constant, respectively.
h 1 ³ T − T ´2 i
Eb
b
(− T )
ρCP = √ e −
+ (V0 − V∞ )e T0 + V∞
(37)
2
S0
S0 2π
where V0 , V∞ , s0 , Eb and Tb is ρCp value for zero degree centigrade, ρCp value for ∞ degree
centigrade, ferrite to austenite temperature transition, transition energy for the ferrite to austenite
transition and standard deviation of the Gaussian part of equation in temperature, respectively.
The studies of workpieces are made of carbon steel, which is the ferromagnetic material. The
temperature-dependent magnetic permeability and electric resistivity are described as follows [23]:
h (µ − 1)πµ |H| i³
T´
2Ms
r0
0
arctan
1−
(38)
µ=
π
2Ms
Tc
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ρe = ρ0 + ρ1 arctan
³T − T ´
c
Tr
(39)
where Ms is the saturation magnetization at zero degree centigrade, µr0 is the initial relative
permeability, µr0 is vacuum magnetic permeability(4π×107 H/m) and Tc is the Curie temperature,
and ρe is electric resistivity.
3
FEM Simulation
Based on the electromagnetic model, heat transfer model, and material properties model, the
Finite Element Method (FEM) is adopted to carry out the different stages of the numerical
simulation and ANSYS software is employed to establish the 3D simulation model.
3.1
Temperature-dependent Material
In this study, the shaft parts of the carbon 45 steel are used to perform FEM simulation of the
HFIC process. The chemical composition of the carbon 45 steel is shown in Table 1. In consideration of the chemical composition of the carbon 45 steel, the Curie temperature Tc = 768◦ C is
employed in the induction heating process [25]. Based on an initial relative permeability µro = 700
and a saturation magnetization Ms = 2.2T , by taking Eq. (36) to Eq. (39) into calculation for
the process, we can obtain the temperature-dependent material properties data including electrical resistivity, thermal conductivity, specific heat, and relative permeability. The value of
the temperature-dependent material properties are illustrated in Fig. 2. Relative permeability
gradually reduces with temperature incrementing, and when the temperature is up to the Curie
temperature, relative permeability is down to zero. Electrical resistivity steadily increases and
thermal conductivity slowly reduces along with the temperature varying. Specific heat fiercely
enlarges with the temperature changing. With the temperature up to 756◦ C, the specific heat
rapidly reduces. Therefore, the material properties are non-linear parameters, and it is necessary
to take into account the temperature-dependent properties for the further precise study on the
induction heating process.
Table 1: Chemical composition of carbon 45 steel (mass%) [24]
C
Si
Mn
S
P
Cr
Mo
Ni
Al
Cu
Fe
0.45
0.25
0.65
0.025
0.008
0.4
0.1
0.4
0.01
0.17
Bal.
Table 2: Chemical composition of Ni60 power (mass%) [26]
C
Cr
B
Si
Fe
Ni
1.0 ∼ 0.6
17 ∼ 14
1.5 ∼ 2.5
4.5 ∼ 3
≤ 15
Bal.
A kind of the nickel base alloy Ni60 was used as the surface self-fused alloy coating due to the
most widely used coating with accurately determined physical properties. Its chemical composition is shown in Table 2. From the above assumptions of the mention, the generating heat of the
coating is not taken into account on the HFIC process. Therefore, the temperature-dependent
650
225
200
175
150
125
100
75
50
25
0
100
Electric resistivity (Ω·m)
225
200
175
150
125
100
75
50
25
0
100
1.2×10−6
1.0×10−6
8.0×10−7
6.0×10−7
4.0×10−7
2.0×10−7
0
100
300
500
700
900 1000
Temperature (°C)
(a)
300 500 700 900
Temperature (°C)
(b)
1100
300 500 700 900
Temperature (°C)
(d)
1100
1100
Specific heat (J/Kg·K)
Thermal conductivity (W/m·K)
Relative permeability
Y. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 641–656
1000
900
800
700
600
500
400
100
300
500
700
900 1000
Temperature (°C)
(c)
100
540
90
Specific heat (J/Kg·K)
Thermal conductivity (W/m·K)
Fig. 2: Temperature-dependent material properties of the 45 steel
80
70
60
50
300
500
700
900 1100
Temperature (°C)
(a)
1300
520
500
480
460
440
420
400
300
500
700
900 1100
Temperature (°C)
(b)
1300
Fig. 3: Temperature-dependent material properties of the Ni60
material properties of the coating Ni60 only include the thermal conductivity and the specific
heat and shown in Fig. 3.
3.2
Three-dimensional Model and Meshing
The induction heating is usually applied to the axial symmetry shaft part. Thus, the previous
researches about induction heating often used the 2D model to analyze the temperature distribution and other properties since the 2D model can simplify the simulation process and reduce the
simulation time under certain conditions. In contrast, the 3D model is used relatively less due
Y. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 641–656
651
to the difficulty in establishing the model and the more time for calculation. However, with the
computer technology developing, the simulation time of the 3D model is remarkably shortened
and thus induction heat process can be simulated with the 3D model without difficulty. It is well
known that, the 3D model of induction heating process has many merits comparing with the 2D
model, such as more fine mesh, more accurate results, more conspicuous temperature gradient,
and more explicit normal direction of the heat conduction. Therefore, in this study work, we
establish the 3D model of induction heating process and take advantage of the 3D model’s preponderance to analyze the parameters sensitivity in the process. The outline of 3D model for the
HFIC process is shown in Fig. 4 (a).
The solid elements of whole domain are divided into various groups in accordance with different
material properties and thermal distribution. For the surface groups of the axial symmetry shaft
part, dense meshes are set along with the coating line due to the significant skin effect of the highfrequency induction magnetic field intensity distribution. Otherwise, for the remaining groups of
the axial symmetry shaft part, coarser meshes are set along with the radius direction. Then, with
regard to the groups of the air and the coil, homogeneous meshes are set in the region. The mesh
division of the 3D simulation model is shown in Fig. 4 (b). Therefore, through the measures of
the meshing, the results of the simulated the 3D model are more accurate than the simulated the
2D model.
Air
Coil
Surface
Core
(a)
(b)
Fig. 4: 3D simulation model and 3D mesh division
3.3
Numerical Result
Coupling the electromagnetic with thermal fields is a characteristic for simulation of induction
cladding at each time step. With the thermal field by the numerical simulation of the induction
cladding process obtained, the outward contour and inward contour of temperature distribution
of the shaft workpiece are shown in Fig. 5. From the figures of thermal distribution, it is observed
that the skin effect is prominent in the high-frequency range, and the core temperature of the
model thermal field is more lower than that of the model surface.
4
Experiment
In order to validate the above 3D numerical model, a measurement experiment is designed.
The detailed structure of the experiment equipments in the High Frequency Induction Cladding
(HFIC) is illustrated in Fig. 6 (a). The cooling system provides circulating cooling water to take
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(a) The outward contour of temperature
distribution
(b) The inward contour of temperature
distribution
Fig. 5: Temperature distribution of numerical simulation
Thermocouple
Infrared sensor
Coating
Induction coil
A/D
transverter
Substrate
Induction
heating
equipment
Cooling
system
PC
(a) Schematic model of the HFIC equipment
(b) Eddy coil heating in the
experiment process
(c) Thermocouple measurement
Fig. 6: Experimental measurement process
the heat of the induction coil away from the induction heating equipment. Its aim is to sustain
the induction coil temperature. The induction heating equipment supplies the high frequency
Alternating Current (AC) to the induction coil. The AC of the induction coil stimulates the eddy
current on the substrate. To measure the core and the surface temperature in this experiment, a
thermocouple and an infrared sensor are installed. The gathering analog data of the temperature
from the thermocouple and an infrared sensor is transfer to the digital analog (A/D) converter.
Finally, the Personal Computer (PC) receives and saves the experiment measurement data from
the A/D converter.
The induction heating equipment has the rated power of 25 kW and the frequency ranging from
20 to 80 kHz. The recording temperature of the experiment environment is 22◦ C. The current
density of showing on the induction equipment is 554A in the heating cladding process. From
the Fig. 6 (b), we can note that the induction coil heats the shaft workpieces of carbon 45 steel
and then the surface temperatures at different positions is measured by the infrared sensor and
recorded by the PC. As shown in Fig. 6 (c), a core temperature of the shaft workpiece is measured
by the thermocouple that is inserted into cylindrical bore of the shaft workpiece. Geometry data
of the shaft workpiece and the coil are shown in Table 3, respectively.
Y. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 641–656
653
Table 3: Geometry data for the workpiece (mass%)
Size
mm
Outside diameter
20
Number of turns
4
Gap between coil and workpiece (on the radius)
10
Coil length
38.5
Workpiece length
5
55
Validation
The temperature on the surface of the shaft workpiece is obtained by the infrared temperature
measurement instrument, while the temperature at the core of shaft workpiece is gained by the
thermocouple measurement. In the case, the measured and simulated time is 43 s. From Fig. 6,
we can obtain that the maximal temperature is 1312◦ C, which is below the melting point of
45 steel (1350◦ C). When the heating process reaches Curie point, the rising rate of temperature decreases because material properties change. It could be observed that the veracity of
temperature-dependent material properties plays such a significant role in predicting temperature.
Temperature (°C)
The temperatures of both the surface and the core are acquired for the same locations from the
above FEM numerical simulation results. Therefore, the reliability of the numerical model for
the induction cladding process could be validated by comparing the numerical simulation with
the measurement results. The comparison of temperature distributions between the experimental
measurement and the numerical simulation is shown in Fig. 7. The evolution of the temperature
values on both the surface and the core of the shaft workpiece obtained by the numerical simulation shows a very good matching with that obtained by the experimental measurement. The
discrepancy is within the interval [−25◦ C, 25◦ C]. Thus, referring to the comparison results, it can
be concluded that the 3D model for the induction cladding process using FEM is reliable, and it
can be employed for further study on the induction cladding process.
1500
1400
1300
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
0
Surface
Core
Finite-element solution
Experimental measurment
5
10
15
20 25
Time (s)
30
35
40
45
Fig. 7: Comparison of experimental measurement and numerical simulation of induction temperature
654
6
Y. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 641–656
Discussion
It is well known that the Austenite Start (AS) temperature is approximately 723◦ C for 45 steel
[27], which means that when the temperature at any point of the component exceeds AS during
the heating stage, the material at this point starts to become Austenite [28]. For this case, the
occurrence of phase transformation of Austenite should be avoided so that the inner temperature
of the workpiece is below AS. On the other hand, the ideal induction coating temperature field
is that the temperature of the surface of the shaft is above 1300◦ C and the inner temperature of
the shaft workpiece is below 600◦ C. Thus, to some extent, the layer location temperature 600◦ C
can reflect the quality of the coating in this case, and the bigger thickness ratio is, the better the
quality of induction heating process becomes.
With the 3D simulation model established, the analysis of numerical simulation results with
respect to thermal field can be investigated for the HFIC process. The analysis of thermal field
under the condition above in detail is shown in Fig. 8. The thermal distributions on the threequarter volume are in different induction heat time, including 1 second, 3 second, 8 second, 20
second, 30 second, and 43 second. From Fig. 8 (a) and Fig. 8 (b), we can easy to note that
the surface temperature of the coating is increase and the core temperature for the substrate
remains the initial temperature duo to the skin effect of the induction. When the time is up to
8 second, the core temperature of the substrate raised to 125◦ C. At the time of 20 second, the
core temperature of the substrate is heat up below 600◦ C and the temperature of the coating is
805◦ C. However, at the time of 30 second and 43 second, the core temperatures of the substrate
seriously exceed 600◦ C and the surface temperature is heat up to the ideal coating melting point
of 1200◦ C. The layer location temperature 600◦ C for this case is not exist duo to inductive heating
time too long. Therefore, we can cut down the time of the inductive heat and increase the other
value of the process parameters, such as the electric power.
(a) 1 s
(b) 3 s
(c) 8 s
(d) 20 s
(e) 30 s
(f) 43 s
Fig. 8: Thermal distribution on the three-quarter volume
Y. Liu et al. / Journal of Information & Computational Science 12:2 (2015) 641–656
655
Numerical modeling of the HFIC normally involves three main physical phenomena related to
electromagnetism, heat transfer and solid mechanics. As far as this study is concerned, electromagnetism and heat transfer are described above in detail. Solid mechanics can be indirectly
researched based on the relation with heat transfer. The complete finite elements approach is
chosen to carry out the coupling process in this study. We can take advantage of the 3D simulation model to analyze the thermal distribution, optimal cladding process, and crystal phase
transition in the future research.
7
Conclusions
This study has developed the 3D simulation model to analyze the HFIC process. Firstly, we have
established a mathematical 3D model for the HFIC process by coupling electromagnetism with
heat transfer computation. Secondly, the validation of the constructed model is accomplished
by using the experiment measurement results. Finally, the thermal distribution for the HFIC is
discussed to investigate the quality of induction heating process.
The construction of the 3D geometry model in this case is of significance for the prediction of
thermal field in the HFIC process. The constructed 3D model can be used as a powerful tool to
simulate the induction process for better analyzing the process parameters. Moreover, our future
research will focus on the further analysis of the process parameters by the 3D simulation model.
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