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Heat transfer and temperature distribution during high-frequency induction cladding of 45 steel plate
Applied Thermal Engineering 139 (2018) 1–10
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Research Paper
Heat transfer and temperature distribution during high-frequency induction cladding of 45 steel plate
T
⁎
Rui Sun, Yongjun Shi , Zhengfu Pei, Qi Li, Ruihai Wang College of Mechanical & Electronic Engineering, China University of Petroleum, Qingdao, Shandong 266580, China
H I GH L IG H T S
electromagnetic–thermal multifield coupling finite element model for HFIC was built. • AThethree-dimensional heat used to melt the powder coating originates from the substrate–coating interface. • Influence of different parameters on temperature distribution has been studied. • The dissolution of WC particles corresponds with the temperature distribution. •
A R T I C LE I N FO
A B S T R A C T
Keywords: High-frequency induction cladding Heat transfer Temperature distribution Finite element analysis Electromagnetic-thermal multifield coupling Microstructure analysis
High-frequency induction cladding, a new surface-modification technology with high thermal efficiency and good formability, can be used to improve the surface mechanical properties of metal components. In this study, a three-dimensional electromagnetic–thermal multifield coupling model was developed to investigate heat transfer and temperature distribution in high-frequency induction cladding. Results showed that the heat used to melt the powder coating originates from the substrate–coating interface and that melting proceeds from the interior to the exterior of the coating. The effects of current density, current frequency, and air–gap spacing on temperature distribution were analyzed by using the effective size of the cladding area and the maximum temperature difference in the coating as reflections of temperature distribution. Microstructure analysis indicated that the dissolution of WC particles corresponds with temperature distribution, and a temperature field with low temperature difference in the coating is helpful for obtaining uniform microhardness distribution.
1. Introduction Surface cladding methods, such as arc spraying, plasma spraying, and laser cladding, have been widely applied to repair and strengthen the surfaces of critical machinery components [1–3]. Nonetheless, the further applications of these methods are limited by some essential drawbacks, such as low energy conversion efficiency and high cracking susceptibility. High-frequency induction cladding (HFIC) is a relatively newly developed surface cladding method based on induction-heating technology. During HFIC, an alternative electric current is applied to produce an electromagnetic field, which induces eddy current in the workpiece. The heat released from the eddy current melts and bonds coatings with the substrate. HFIC has lower energy consumption and higher heating rates than other surface-modification methods and can be used to fabricate coatings with superior surface characteristics and excellent metallurgical bonding with substrates [4–6]. Numerous studies have been conducted to investigate the
⁎
microstructure and mechanical behaviors of coatings prepared through HFIC. Wang et al. [7] prepared TiC/Ni composite coating from prealloyed Ni60, titanium, and graphite powders through HFIC. They obtained coatings reinforced with in-situ synthesized TiC particles and microhardness values of 1000–1100 HV. He et al. [8] investigated the mechanical properties of induction-melted Ni-based alloy coatings with different WC particle contents and found that increasing WC particle contents improves microhardness and wear resistance. Zhang [9] and Hu [10] obtained NiCrBSi and Fe-based alloy coatings through HFIC and intensively investigated the friction and wear behavior of the coatings. HFIC is a complex thermal process that involves electric and magnetic fields. However, relatively few studies have examined temperature evolution in HFIC. Currently available investigations do not fully discuss the relationship between microstructure properties and the temperature field. Cen et al. [11] performed numerical simulations and experiments on the HFIC of boiler tubes and investigated the effects of
Corresponding author. E-mail address: [email protected] (Y. Shi).
https://doi.org/10.1016/j.applthermaleng.2018.04.100 Received 23 August 2017; Received in revised form 20 February 2018; Accepted 20 April 2018 Available online 23 April 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.
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current frequency and density on heating speed. Nevertheless, their simulations did not account for the nonlinearity of material properties. Given that HFIC was developed on the basis of induction heating, the temperature evolution of induction heating should also be investigated. Luozzo et al. [12] used the finite element method to analyze the temperature evolution of carbon steel tubes during induction heating and experimentally validated the simulated model. Han et al. [13] designed a profile coil to heat heavy-duty sprocket coils and numerically compared the differences in the heat transfer process between profile and normal circular coils. Song and Moon [14] considered the temperature dependency of material properties when simulating temperature distribution in induction heating for the forging of marine crankshafts. Temperature distribution has important effects on the microstructure and mechanical properties of coatings processed through HFIC. Controlling the distribution of the temperature field is helpful in improving cladding efficiency and quality. In addition, the metallurgical bonding between two materials with different properties is affected by the process of heat transfer. Therefore, the objective of this study was to build a three-dimensional electromagnetic–thermal multifield coupling model and investigate the characteristics of heat transfer and temperature distribution in the process of HFIC. The influence of key process parameters on temperature distribution was investigated to provide the theoretical basis for temperature field control. A cladding experiment was conducted to verify the finite element model and evaluate the effect of temperature distribution on the microstructure and microhardness of coatings.
45 steel plate
Induction coil Induction heating power Flux concentrator
Refractory brick Cooling system
(a)
2. Description of the mathematical model 2.1. Description of the electromagnetic field model
(b)
The eddy current generated in the workpiece during induction heating is dependent on the alternative magnetic field. The governing equations of electromagnetic induction heating are Maxwell's equations, which can be described as follows:
∇×H=J+ ∇×E=−
∂D ∂t
∂B ∂t
Fig. 1. Experimental device and induction coil applied in high-frequency induction cladding. (a) Experimental device. (b) Induction coil.
The electric scalar potential φ is introduced because ∇ × (∇φ) = 0 meets Helmholtz theorem. Eq. (8) can be further described as follows:
(1)
E=−
(2)
∇·B = 0
(3)
∇·D = ρ
(4)
∂A −∇φ ∂t
(9)
In accordance with Eqs. (1), (5), and (6), and (7), the governing equation in the eddy current domain is derived as:
1 ∂A ∇×A+σ + σ ∇φ = 0 μ ∂t
where H is the magnetic field intensity, J is the electric current density associated with free charges, D is the electric displacement vector, E is the electric field intensity, B is the magnetic flux density, and ρ is the electric charge density. In HFIC, displacement current density ∂D / ∂t is not the main contributor of joule heat that melts the alloy powders, and induced conduction current J is considerably greater than the displacement current density ∂D / ∂t ; therefore, ∂D / ∂t in the equations should be negligible [15]. Moreover, the physical parameters H, J, B, and E obey the following auxiliary equations:
∇×
B = μH
(5)
2.2. Description of the temperature field model
J = σE
(6)
The boundary conditions of continuity between regions with different properties are as follows:
n × (H1−H2) = 0
(11)
n·(B1−B2) = 0
(12)
Moreover, in the outermost boundary of the model, the magnetic vector potential A is 0.
Induction heating is a process that occurs with drastic temperature increase, and an extreme temperature gradient will exist in the surface layer of the workpiece because of the skin effect. Thus, this nonlinear transient heat transfer process can be expressed by the Fourier equation as follows:
where μ is magnetic permeability, and σ is electrical conductivity. The magnetic vector potential A is introduced on the basis of the Helmholtz theorem, and the following equation is obtained:
B=∇×A
(10)
(7)
Thus, the electric field intensity E can be described as follows from Eqs. (2) and (7):
∂ 2T ∂ 2T ∂ 2T ⎞ ∂T k⎛ 2 + + + Q = ρc 2 2 ∂ x ∂ y ∂ z ∂t ⎝ ⎠
∂A ⎤ ∇ × ⎡E + =0 ∂t ⎦ ⎣
where k is the thermal conductivity coefficient, Q is internal heat source intensity due to the eddy current, c is specific heat capacity, and ρ is
⎜
(8) 2
⎟
(13)
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Substrate Coating Flux Concentrator Induction Coil
Air
Air
z
z
y
y x
x
(a)
(b)
Fig. 2. Finite element model of the high-frequency induction cladding of 45 steel plate. (a) Without air. (b) With air. 250
Table 1 Specific process and geometrical parameters of the high-frequency induction cladding of 45 steel plate. Parameter
Unit
Size of 45 steel plate Size of metal alloy coating Section size of induction coil Wall thickness of induction coil Air-gap spacing (distance between induction coil and coating) Length of induction coil Current frequency Current density Heating time
80 × 80 × 10 40 × 12 × 2 4×4 1 1
mm3 mm3 mm2 mm mm
40 200 1.10 × 108 30
mm kHz A/m2 s
200
Material properties
Item
Relative permeability -8 Electrical resistivity /( 10 m) -1 -1 Thermal conductivity /(W m K ) -1 -1 Specific heat /(10J kg K )
150
100
50
0
120
0
Relative permeability -8 Electrical resistivity /( 10 m) -1 -1 Thermal conductivity /(W m K ) -1 -1 Specific heat /( 10J kg K )
Material properties
100
80
200
400
600
800
1000
Temperature ( C) Fig. 4. Electromagnetic and thermal physical property curves of 45 steel.
Start 60
Establishment of finite element model
40
20
Electromagnetic field calculation
0 0
200
400
600
800
1000
Update thermal parameters
1200
Temperature ( C) Fig. 3. Electromagnetic and thermal physical property curves of Ni60 alloy.
Adjust the sub time increment Δtsub
density. Considering thermal convection and radiation between material surfaces and the ambient environment, the boundary condition of the temperature field can be described as follows:
∂T 4 = h (T −Tair ) + εemi σb (T 4−Tair −k ) ∂n
No
Joule heat Temperature field calculation
Update electromagnetic parameters
t = t+Δt Result converged Yes
t = tsum
(14)
No
Yes
where n is the outward unit normal vector; h is the heat-convection coefficient; εemi is material emissivity; and σb is the Stefan–Boltzmann constant, which is equal to 5.67 × 10−8 W/m2 K4. In this model, the heat-convection coefficient is 50 W/m2 K, and the emissivity is 0.68. The ambient temperature is 20 °C, and the initial temperature of 45 steel plate and alloy powder is 20 °C.
End Fig. 5. Flow chart of the calculation process of high-frequency induction cladding.
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800
Calculated temperature Measured temperature
T2 (0.012,0.04,0.01) T1 (-0.028,0.03,0.01)
Temperature ( C)
700
Point T2
600 500 400 300 200
Point T1
100 0 0
5
10
15
20
25
30
Time (s)
(a)
(b)
Fig. 6. Comparison between experimental measurements and simulated calculations. (a) Locations of selected points (b) Temperature curves of selected points.
comprises an induction coil, flux concentrator, induction-heating power source, and refractory brick. The flux concentrator is used to concentrate magnetic flux to improve heating efficiency. The experimental device is equipped with a cooling system. A 45 steel plate precoated with metal alloy powder is placed on the refractory brick, and the induction coil is directly above the precoated alloy powder. The induction coil is a rectangular coil fabricated from a square-sectioned copper tube, as shown in Fig. 1b. The finite element model of HFIC is established on the basis of ANSYS software. As illustrated in Fig. 2a, the model is composed of substrate, induction coil, flux concentrator, coating and air. It should be noted that the substrate, induction coil, flux concentrator and coating are wrapped in the air, thus the air is not shown in Fig. 2a to provide a clear view of the internal geometry of the model. The finite element model with air is additionally shown in Fig. 2b. The induction coil used in this experiment is a planar rectangular coil with two lifted ends. According to the proximity effect, the main part of the coil that is used to heat the workpiece is the concave section. Therefore, the induction coil in this model is simplified as two separated leads with opposite electrical currents flowing in, as shown in Fig. 2a [16]. The specific process and geometrical parameters of the model are shown in Table 1. As depicted in Fig. 2a and b, a hexahedral mesh is applied to discretize
Middle cross- section
y x
Fig. 7. Temperature distribution in the surface and middle cross-section of the substrate and coating at 15 s of heating.
3. Establishment of the finite element model and experimental validation 3.1. Establishment of the finite element model The experimental HFIC device is shown in Fig. 1a. The device
t=5s Low-temperature zone in middle area
t=10s High-temperature zone in two sides
t=15s
Experiment observation
t=20s
Fig. 8. Temperature distribution in the middle cross-section of the coating at 5–20 s of heating. 4
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Fig. 9. Melting state of the coating at different time points.
model of HFIC is reliable and can be employed to further study the heat transfer and temperature distribution during HFIC.
the whole model, and the elemental size of this model varies from its heating center to its outmost layer. A fine mesh with an elemental size of 1 × 2 × 0.5 mm3 is carried in the coating and in the central part of the substrate, and a coarse mesh with a size of 5 × 5 × 2.5 mm3 is used in the outmost layer of the model. The finite element model with air, as shown in Fig. 2b, contains 80,000 hexahedral elements and 314,364 nodes. Considering the temperature dependency of the electromagnetic and thermal physical properties of Ni60A and 45 steel, which are shown in Figs. 3 and 4, respectively, a coupled electromagnetic-thermal analysis should be conducted. The relative permeability of the flux concentrator is 60. The calculation process of HFIC coupled with electromagnetic and temperature fields is shown in Fig. 5. Sequential coupling is adopted in consideration of calculation efficiency and accuracy. The coupling method can be described as follows. The electromagnetic field is calculated when the initial parameters are specified, and then magnetic flux density and eddy current intensity are calculated. Afterwards, the joule heat generated by the induced eddy current is used as the load of the temperature field. Δt refers to the time increment within which the electromagnetic parameters remain constant and temperature-field calculation is conducted. During temperature-field calculation, time increment Δt will be divided into several subtime increments Δtsub , which can be adjusted automatically by the simulation package. Once temperature-field analysis converges, the electromagnetic parameters will be updated and electromagnetic analysis restarts [14]. In this study, the total heating time tsum is set to 30 s, and the procedures described above are recycled until heating is completed. Time increment Δt and minimum subtime increment Δtsub are defined as 1 and 0.01 s, respectively. The convergence of the calculation is based on heat flow. L2 norm is selected as the convergence norm, and the tolerance is 0.001. The total number of calculation iterations is 412.
4. Results and discussion 4.1. Characteristics of heat transfer and temperature distribution Temperature distribution in the surface and middle cross-section of the substrate and coating after 15 s of heating is shown in Fig. 7. The parameters are selected as follows: Current density of 1.2 × 108 A/m2 , current frequency of 200 kHz, and air–gap spacing of 1 mm. As seen in the figure, temperature is symmetrically distributed in the surface, and a high-temperature zone (HTZ) exists in both sides of the coating directly underneath the induction coil. The origin of the HTZ indicates the location where the eddy current, the main contributor to temperature increase, occurs during heating. Fig. 8 shows the variation in temperature distribution in the middle cross-section over the period of 5–20 s. In accordance with experimentally observed phenomenon (shown in Fig. 8), the temperature in the middle area of the coating is lower than that at the two sides of the coating. This phenomenon is largely attributed to the geometry of the coil, which is displayed in Fig. 1b. At the beginning of heating, the HTZ first appears in the substrate–coating interface. Comparing the HTZ at different time points revealed that the HTZ develops around the substrate–coating interface and extends into the internal substrate and coating as heating continues because the relative permeability of the substrate is higher than that of the coating. Moreover, the relative permeability of the coating is reduced to 1 in the initial period as the temperature exceeds the Curie point of the coating. Eddy current in this condition is mainly induced in the substrate–coating interface. Subsequently, Joule heat generated by the eddy current transfers into the surrounding cold area, and the HTZ expands continually, revealing that the heat used to melt the coating originates from the interface between substrate and coating, and the temperature increment of coating is mainly dependent on thermal conduction. On the other hand, this kind of temperature distribution also indicates that melting proceeds from the interior to the exterior of the coating, experimental observation corresponding to the melting characteristic is depicted in Fig. 9. This phenomenon is significantly different from that observed in other surface coating technologies, such as laser cladding or plasma cladding. After 20 s of heating, the temperature of the coating reached 1100 °C, which exceeds the melting temperature of the Ni60 alloy powder. Given that heat originates from the substrate–coating interface, temperature distribution in the substrate surface was analyzed to identify the variation characteristics of the temperature field in the x–y plane. The temperature distributions in the surface of the substrate at 10, 20, and 30 s of heating are shown in Fig. 10. Fig. 10a and b show that the temperature distribution in the HTZ exhibits a twin-peak
3.2. Experimental validation The results calculated by the finite element model for the HFIC of 45 steel plate are experimentally validated. The experimental process parameters are listed in Table 1. The coating is composed of Ni60A alloy powder mixed with 30% WC particles. During preparation, the alloy powder is mixed with adhesive and then coated onto the surface of 45 steel plate, which is polished and cleaned to eliminate rust and oil stains. After drying, the workpiece is heated using the experimental device. The temperature of selected points is measured by K-type thermocouples. The accuracy of the thermocouples is ± 1 °C, and the interval for data collection is 1 s. As shown in Fig. 6, the calculated temperature curves of selected points match well with the measured temperature curves. The maximum difference between the calculated temperature and the measured temperature is 13 °C, which is within the error range [12,17]. That is to say, the three-dimensional finite element 5
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1600
Point A Point B Point C Point D Point E
1400
3.5 mm 3.5 mm
Temperature ( C)
24 mm
1200 1000 800
Z
400
X
200 0
(a)
A B C D E
600
0
5
10
15
20
25
30
Time (s) Fig. 11. Temperature variation curve with time of feature points.
17 mm
Given that the melting point of Ni60A is between 980 °C and 1020 °C, the powders in contact with the substrate–coating interface where the temperature exceeds 1000 °C will be melted. Here, the surface area where the temperature is above 1000 °C is defined as the effective cladding area. The length of the effective cladding area in the xand y-directions is used to measure the size of the effective cladding area. Comparing the effective cladding areas shown in Fig. 10a and b revealed that length in the x- and y-directions increases dramatically, and the maximum temperature significantly increases. Fig. 10c shows that size only slightly increases in the x direction, and the size of the effective cladding area is approximately 18 mm × 45 mm. Fig. 11 shows the temperature variation curves with time of feature points in the middle cross-section of the model, and the coordinates of these points are shown in Table 2. The temperature of point B, which is located in the substrate–coating interface, is higher than those of other points. Temperature gradually decreases with increasing distance from the interface. Although points A and C are equidistant from point B, the temperature of point A is higher than that of point C. Temperature increases rapidly during the initial period of heating. After 5 s, the heating speed slows down significantly because the temperature of the substrate surface increases to 800 °C, which exceeds the Curie point. The relative permeability of the surface layer of the substrate is suddenly reduced to 1.
45 mm
(b) 18 mm
45 mm
4.2. Influence of different parameters on temperature distribution Temperature distribution has a great influence on the microstructure and processing efficiency of coatings during cladding. The processing efficiency and quality of HFIC can be improved by analyzing the effects of different parameters on temperature distribution. In this study, changes in the size of the effective cladding area and maximum temperature difference ΔT (Δ T= TB−TA ) between points A and B (located in the surface and the bottom of coating, respectively) in the coatings are used to evaluate the influence of different parameters. The parameters investigated in this study include current density, current frequency, and air-gap spacing (distance between induction coil and coating).
(c) Fig. 10. Temperature distribution in the substrate surface during 10–30 s of heating. (a) t = 10 s; (b) t = 20 s; (c) t = 30 s.
4.2.1. Influence of different parameters on the size of the effective cladding area Within the same processing time, a large effective cladding area indicates that a large amount of alloy powder has been melted, which in turn reflects high cladding efficiency. Fig. 12a shows the effect of current density on the size of the effective cladding area. The current
pattern, and the temperature in the center of the HTZ is lower than that in the two sides of the coating. As shown in Fig. 10c, the HTZ is oval, and the temperature difference in the HTZ is eliminated when heating is terminated.
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Table 2 Coordinates of selected feature points. Point
A
B
C
D
E
Coordinate
(0.003,0.04,0.012)
(0.003,0.04,0.010)
(0.003,0.04,0.008)
(0.003,0.04,0.006)
(0.003,0.04,0.004)
200
0.04
0.03
0.02
180
1600
140 1500
120 1400
100 1300
80
1200
60
1100
40 1.00 10
8
1.10 10
8
1.20 10
8
8
1.00 10
8
8
1.20 10
1.10 10
8
1.30 10
8
1.40 10
1.30 10
2
1.40 10
8
1.50 10
(a)
8
60
Maximum temperature difference (°C)
(a)
X direction Y direction
0.030 0.025 0.020
58
Temperature of point B Maximum temperature difference
56
1250
54 1200
52 50
1150
48 46
1100
44 42
1050
40 38
170
0.015
1300
180
190
200
210
220
230
240
250
1000 260
Current frequency (kHz)
(b)
0.010 90
190
200
210
220
230
240
250
Current frequency (kHz)
(b) 0.05
X direction Y direction
0.04
1600
260
0.03
Temperature of point B Maximum temperature difference
80
1500 1400
70
1300
60
1200 50 1100 40
1000
30
900
20
Temperature of point B (°C)
180
Maximum temperature difference (°C)
170
Size of effective cladding area (m)
8
1.50 10
Current density (A/m2)
0.035
8
Current density (A/m )
0.01
Size of effective cladding area (m)
1700
160
Temperature of point B (°C)
0.05
1800
Temperature of point B Maximum temperature difference
Temperature of point B (°C)
X direction Y direction
Maximum temperature difference (°C)
Size of effective cladding area (m)
0.06
800
0.02 10
1.0
1.5
2.0
2.5
3.0
700
Air-gap spacing (mm)
0.01
(c) Fig. 13. Variation curves of maximum temperature difference ΔT and temperature of point B under different parameters (a) Current density. (b) Current frequency. (c) Air-gap spacing.
0.00 1.0
1.5
2.0
2.5
3.0
Air-gap spacing (mm) frequency is 200 kHz with an air–gap spacing of 1 mm. As shown in Fig. 12a, when the current density increases from 1.0 × 108 A/m2 to 1.50 × 108 A/m2 , the size in the x-direction of the effective cladding area gradually increases from 0.01 m to 0.025 m. The size of the
(c) Fig. 12. Variation in the size of the effective cladding area under different parameters. (a) Current density. (b) Current frequency. (c) Air-gap spacing.
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density are specified as 200 kHz and 1.2 × 108 A/m2 , respectively. The figure shows that the size of the effective cladding area and air-gap spacing are negatively correlated. In the case of a 1.5 mm air-spacing gap, the size in the y-direction is 0.042 m, which has decreased by 6.7% compared with 0.045 m in the case of 1 mm air spacing gap. In the xdirection, the size of the effective cladding area increases slightly from 0.017 m to 0.018 m as the air-spacing gap decreases from 1.5 mm to 1 mm. When the air–gap spacing increases to 3 mm, the size of the effective cladding area is 0, indicating that no metallurgical bonding exists between the substrate and coatings.
WC particles
Coating Interface
Transition region Substrate
4.2.2. Influence of different parameters on maximum temperature difference ΔT Maximum temperature difference ΔT is a reflection of temperature uniformity in coatings. A uniform temperature distribution is important for obtaining high-quality coating. In fact, alloy powders in the surface of the coating require a longer time to reach the melting point than those in the bottom of the coating because heat is generated from the substrate–coating interface. Given that eliminating the temperature difference between the surface and the bottom of the coating is difficult, the practical method to obtain temperature uniformity is to control the temperature difference within a reasonable range. The influence of different processing parameters on the maximum temperature difference ΔT is shown in Fig. 13. To provide an intuitive understanding of temperature variations in the coating, the temperature of point B when the maximum temperature difference appears is listed in Fig. 13. The maximum temperature difference ΔT with different current densities is shown in Fig. 13a. When the current density varies between 1.0 × 108 and 1.1 × 108 A/m2 , the maximum temperature difference ΔT is approximately 50–60 °C. The temperature of point B is 1130 °C and 1291 °C, respectively. As the current density increases to 1.5 × 108 A/m2 , the maximum temperature difference increases to 184 °C. This variation can be attributed to the increase in coating temperature with
Fig. 14. Microstructural morphology of the substrate–coating interface.
effective cladding area in the y-direction also increases with current density. However, the rate of increase gradually slows down. Size in the y-direction slightly changes from 0.045 m to 0.05 m as the current density increases from 1.20 × 108 A/m2 to 1.50 × 108 A/m2 , indicating that size expansion is limited in the y-direction. Fig. 12b shows the variation in effective cladding area with current frequency. The size of the effective cladding area in the y-direction increases almost linearly with current frequency. In this case, the current density is 1.0 × 108 A/m2 , and the air-gap spacing is 1 mm. The largest effective cladding area is obtained at the frequency of 250 kHz, and the sizes in the x- and y-directions under this condition are 0.035 and 0.021 m, respectively. Moreover, the size in the x-direction does not significantly increase when the current frequency varies between 180 and 220 kHz. The variation in effective cladding area with air-gap spacing is depicted in Fig. 12c. The current frequency and current
Bottom of coating
Middle of coating
Top of coating
(a) 90 80
Elements content (%)
70
C Cr W Ni Si
18 16 14 12 10 8 6 4 2 0 Bottom of coating
Middle of coating
Top of coating
(b) Fig. 15. Morphology and composition of WC particles in different positions of the coating. (a) Morphology. (b) Composition. 8
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50±m
50±m
50±m
Side Part
Intermediate part
Side Part
(a) 65 C Cr W Ni Si
60
Element contents (%)
55 50 45 40 35 30 25 20 15 10 5 0
Intermediate part
Side part
Side part
(b) Fig. 16. Morphology and composition of WC particles in the intermediate and side parts of the coating. (a) Morphology. (b) Composition. 900
current frequency has a relatively small effect on the uniformity of temperature distribution in the coating. The temperature of point B slightly changes with current frequency, showing that current frequency has a limited influence on the temperature field. Fig. 13c shows that a negative relationship exists between maximum temperature difference and air-gap spacing. When the air-gap spacing is 3 mm, the maximum temperature difference is 16 °C, which has decreased by 81% relative to the maximum temperature difference of 84 °C obtained with the air–gap spacing of 1 mm. As a result of proximity effect, temperature of point B decreases from 1423 °C to 825 °C when the air gap spacing increases from 1 mm to 3 mm. Therefore, the reason for the variation in maximum temperature difference with different air-gap spacing is that under high temperature in coating surface, there is a high heat loss caused by thermal radiation, which in turn leads to high maximum temperature difference between the surface and bottom of coating. Notably, the effective cladding area under an air-gap spacing of 3 mm is 0, and the processing parameter in this case is invalid.
Coating
Substrate
Microhardness (HV)
800
700
600
500
1.10e8A/m^2 1.20e8A/m^2 1.50e8A/m^2
400
300 -1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Distance from interface (mm) Fig. 17. Microhardness of the coating and substrate surface under different current densities.
5. Microstructural morphology and microhardness of the coating Measuring the internal temperature distribution of coatings is difficult; however, the microstructure of the coating would change significantly in accordance with temperature distribution in the coating. Thus, temperature distribution can be evaluated by researching and comparing the microstructural morphologies of coatings. Fig. 14 shows the microstructural morphology of the area around the interface. The current density, current frequency, and air-gap spacing selected in the experiment is 1.2 × 108 A/m2 , 200 kHz, and 1 mm, respectively. The area comprises three primary regions, including substrate, transition region, and coating. The grey pieces dispersed in the coating are WC particles. A white bright band that appears in the interface indicates metal-element diffusion and metallurgical bonding between substrate
increasing current density, leading to high thermal radiation in the coating surface that in turn increases the temperature difference between the surface and the bottom of the coating. The temperature of point B under this condition is 1698 °C, and the coating may become overheated. When the sizes of the effective cladding areas are almost the same under different parameters, the parameters with low temperature difference should be selected. Therefore, the suitable current density should be 1.0 × 108–1.2 × 108 A/m2 . The influence of current frequency on maximum temperature difference is shown in Fig. 13b. The maximum temperature difference ΔT varies between 40 °C and 60 °C in these four cases, indicating that
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stages of heating. 2. The size of the effective cladding area and maximum temperature difference in the coating are directly proportional to current density and inversely proportional to the air-gap spacing. The variation in current frequency minimally influences the maximum temperature difference in the coating. When the air-gap spacing is increased to 3 mm, no effective cladding area is observed although the maximum temperature difference in the coating is only 16 °C. 3. The dissolution of WC particles in the bottom of the coating is more severe than that in the top of the coating. This result indicates that the temperature in the bottom of the coating is higher than that in the top of the coating and corresponds to the temperature distribution simulated by the finite element model established in this study. A uniform microhardness distribution is obtained under a temperature field with low temperature difference in the coating.
and coating. WC particles will dissolve into the bonding metal and precipitate carbides around their edges at high temperature [18]. Therefore, the morphology of WC particles in different locations may reflect temperature distribution in a specific location. The morphology of WC particles at different coating locations is shown in Fig. 15a. Flocculent carbides have precipitated around WC particles in the bottom of the coating. The flocculent carbides that precipitated around the edges of WC particles gradually disappear as the distance from the interface increases. Subjecting the selected areas marked in Fig. 15a to EDS analysis revealed the elemental content of the areas surrounding WC particles at different locations. As seen in Fig. 15b, the area near the WC particle in the bottom of the coating is rich in tungsten, and with the increase of distance from the interface, the amount of tungsten in the selected area is greatly reduced, indicating that less tungsten is dissolved into the coating. Chromium and silicon contents also decrease with increasing distance from the interface. This is mainly because that with the dissolution level of WC particle reduced, less carbon is released into the coating. Furthermore, the amount of carbon is insufficient for the synthesis of chromic carbide and silicon carbide, thus leading to the reduction of chromium and silicon contents. The above analysis indicated that the dissolution of WC particles in the bottom of the coating is more severe than that in the top of the coating. This result indicated that the temperature in the bottom of the coating is higher than that in the top of the coating and corresponds to the temperature distribution shown in Figs. 8 and 11. In addition, in the discussion of temperature distribution in the middle cross-section of the coating, the temperature in the intermediate part of the coating is lower than those in the two sides of the coating because of the coil shadow effect, as shown in Fig. 8. Therefore, the morphology and composition of WC particles in the intermediate and side part of the coatings are also compared, as shown in Fig. 16. The tungsten contents in the side area of WC particles increase from the intermediate part to the side part of the coating, indicating that temperature is higher in the side part than that in the intermediate part. Fig. 17 shows the microhardness of the coating and substrate surface under different current densities. The microhardness of the coating is higher than that of the substrate under these conditions. Comparing the microhardness of the coatings reveals that the average microhardness of the bottom of the coatings is lower than that of the top of the coatings because of the different amounts of dissolved WC particles. In addition, previous research on temperature differences under different current densities demonstrated that microhardness distribution under low maximum temperature difference ΔT is relatively uniform than that under high temperature difference. When the current density increases to 1.5 × 108 A/m2 , the microhardness of the coatings decreases significantly because the temperature under this parameter is too high, and the coating is over-heated.
Acknowledgments The author gratefully acknowledges that the work presented in this paper was supported by the National Natural Science Foundation of China (No. 51175515) and Fundamental Research Funds for the Central Universities, China (No. 17CX06003). References [1] J.J. Fang, Z.X. Li, Y.W. Shi, Microstructure and properties of TiB 2-containing coatings prepared by arc spraying, Appl. Surf. Sci. 254 (13) (2008) 3849–3858. [2] L.M. Zhang, D.B. Sun, H.Y. Yu, Characteristics of plasma cladding Fe-based alloy coatings with rare earth metal elements, Mater. Sci. Eng. A s 452–453(452) (2007) 619–624. [3] A. Emamian, S.F. Corbin, A. Khajepour, Effect of laser cladding process parameters on clad quality and in-situ formed microstructure of Fe–TiC composite coatings, Surf. Coat. Technol. 205 (7) (2010) 2007–2015. [4] J.H. Chang, S.K. Tzeng, J.M. Chou, et al., Effect of dry sliding wear conditions on a vacuum induction melted Ni alloy, Wear 270 (3–4) (2011) 294–301. [5] Z.Z. Zhang, G.Q. Han, Y.W. Fu, et al., A study on properties of GNi-WC25 coating by high frequency induction cladding, laser cladding and oxygen-acetylene sprayingfusing, J. Mater. Eng. 3 (2003) 3–6. [6] G. Hu, H.M. Meng, J.Y. Liu, Microstructure and corrosion resistance of induction melted Fe-based alloy coating, Surf. Coat. Technol. 251 (29) (2014) 300–306. [7] Z.T. Wang, J.S. Meng, L.L. Chen, et al., Microstructure and forming mechanism of TiC/Ni composite coating in situ synthesized by induction cladding, Trans. Mater. Heat Treat. 28 (6) (2007) 99–103. [8] D.Y. He, J. Xu, R. Ma, et al., Wear resistance properties of micron-WC reinforced Ni60 coating by high frequency induction cladding, Trans. China Welding Inst. 29 (2008) 138–141. [9] M.Q. Zhang, W. Zhang, H.L. Yu, et al., Microstructure and tribological properties of NiCrBSi coatings prepared by different methods, China Surf. Eng. 27 (6) (2014) 75–81. [10] G. Hu, H.M. Meng, J.Y. Liu, Friction and sliding wear behavior of induction melted FeCrB metamorphic alloy coating, Appl. Surf. Sci. 308 (308) (2014) 363–371. [11] H. Cen, Y.S. Wang, J.B. Lei, et al., Numerical simulation on temperature field of boiler tube coating fabricated by high frequency induction cladding, Mater. Sci. Eng. Powder Metall. 18 (5) (2013) 639–646. [12] N.D. Luozzo, M. Fontana, B. Arcondo, Modelling of induction heating of carbon steel tubes: mathematical analysis, numerical simulation and validation, J. Alloys Comp. 536 (4) (2012) S564–S568. [13] Y. Han, H.Y. Wen, E.L. Yu, Study on electromagnetic heating process of heavy-duty sprockets with circular coils and profile coils, Appl. Therm. Eng. 100 (2016) 861–868. [14] M.C. Song, Y.H. Moon, Coupled electromagnetic and thermal analysis of induction heating for the forging of marine crankshafts, Appl. Therm. Eng. 98 (2016) 98–109. [15] H.S. Park, X.P. Dang, Optimization of the in-line induction heating process for hot forging in terms of saving operating energy, Int. J. Precision Eng. Manuf. 13 (7) (2012) 1085–1093. [16] X.B. Zhang, C. Chen, Y.J. Liu, Numerical analysis and experimental research of triangle induction heating of the rolled plate, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 10 (3) (2015) 1–16. [17] V.I. Rudnev, D. Loveless, R. Cook, et al., Handbook of Induction Heating, Mracel Dekker, New York, 2003. [18] S.F. Zhou, Y.J. Huang, X.Y. Zeng, A study of Ni-based WC composite coatings by laser induction hybrid rapid cladding with elliptical spot, Appl. Surf. Sci. 254 (10) (2008) 3110–3119.
6. Conclusions An electromagnetic–thermal-coupled finite element model was established to analyze the characteristics of heat transfer and temperature distribution in the HFIC of 45 steel plate. The influences of different parameters on effective cladding area and temperature distribution in coatings were also discussed. The primary conclusions are summarized as follows: 1. The heat used to melt the alloy powder originates from the substrate–coating interface. HTZ expands from the interface to the interior of the substrate and coating, and the coating melts from the interior to the exterior. Temperature increases rapidly during the early stages of heating and then increases slowly during the later
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Heat transfer and temperature distribution during high-frequency induction cladding of 45 steel plate
T
⁎
Rui Sun, Yongjun Shi , Zhengfu Pei, Qi Li, Ruihai Wang College of Mechanical & Electronic Engineering, China University of Petroleum, Qingdao, Shandong 266580, China
H I GH L IG H T S
electromagnetic–thermal multifield coupling finite element model for HFIC was built. • AThethree-dimensional heat used to melt the powder coating originates from the substrate–coating interface. • Influence of different parameters on temperature distribution has been studied. • The dissolution of WC particles corresponds with the temperature distribution. •
A R T I C LE I N FO
A B S T R A C T
Keywords: High-frequency induction cladding Heat transfer Temperature distribution Finite element analysis Electromagnetic-thermal multifield coupling Microstructure analysis
High-frequency induction cladding, a new surface-modification technology with high thermal efficiency and good formability, can be used to improve the surface mechanical properties of metal components. In this study, a three-dimensional electromagnetic–thermal multifield coupling model was developed to investigate heat transfer and temperature distribution in high-frequency induction cladding. Results showed that the heat used to melt the powder coating originates from the substrate–coating interface and that melting proceeds from the interior to the exterior of the coating. The effects of current density, current frequency, and air–gap spacing on temperature distribution were analyzed by using the effective size of the cladding area and the maximum temperature difference in the coating as reflections of temperature distribution. Microstructure analysis indicated that the dissolution of WC particles corresponds with temperature distribution, and a temperature field with low temperature difference in the coating is helpful for obtaining uniform microhardness distribution.
1. Introduction Surface cladding methods, such as arc spraying, plasma spraying, and laser cladding, have been widely applied to repair and strengthen the surfaces of critical machinery components [1–3]. Nonetheless, the further applications of these methods are limited by some essential drawbacks, such as low energy conversion efficiency and high cracking susceptibility. High-frequency induction cladding (HFIC) is a relatively newly developed surface cladding method based on induction-heating technology. During HFIC, an alternative electric current is applied to produce an electromagnetic field, which induces eddy current in the workpiece. The heat released from the eddy current melts and bonds coatings with the substrate. HFIC has lower energy consumption and higher heating rates than other surface-modification methods and can be used to fabricate coatings with superior surface characteristics and excellent metallurgical bonding with substrates [4–6]. Numerous studies have been conducted to investigate the
⁎
microstructure and mechanical behaviors of coatings prepared through HFIC. Wang et al. [7] prepared TiC/Ni composite coating from prealloyed Ni60, titanium, and graphite powders through HFIC. They obtained coatings reinforced with in-situ synthesized TiC particles and microhardness values of 1000–1100 HV. He et al. [8] investigated the mechanical properties of induction-melted Ni-based alloy coatings with different WC particle contents and found that increasing WC particle contents improves microhardness and wear resistance. Zhang [9] and Hu [10] obtained NiCrBSi and Fe-based alloy coatings through HFIC and intensively investigated the friction and wear behavior of the coatings. HFIC is a complex thermal process that involves electric and magnetic fields. However, relatively few studies have examined temperature evolution in HFIC. Currently available investigations do not fully discuss the relationship between microstructure properties and the temperature field. Cen et al. [11] performed numerical simulations and experiments on the HFIC of boiler tubes and investigated the effects of
Corresponding author. E-mail address: [email protected] (Y. Shi).
https://doi.org/10.1016/j.applthermaleng.2018.04.100 Received 23 August 2017; Received in revised form 20 February 2018; Accepted 20 April 2018 Available online 23 April 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.
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current frequency and density on heating speed. Nevertheless, their simulations did not account for the nonlinearity of material properties. Given that HFIC was developed on the basis of induction heating, the temperature evolution of induction heating should also be investigated. Luozzo et al. [12] used the finite element method to analyze the temperature evolution of carbon steel tubes during induction heating and experimentally validated the simulated model. Han et al. [13] designed a profile coil to heat heavy-duty sprocket coils and numerically compared the differences in the heat transfer process between profile and normal circular coils. Song and Moon [14] considered the temperature dependency of material properties when simulating temperature distribution in induction heating for the forging of marine crankshafts. Temperature distribution has important effects on the microstructure and mechanical properties of coatings processed through HFIC. Controlling the distribution of the temperature field is helpful in improving cladding efficiency and quality. In addition, the metallurgical bonding between two materials with different properties is affected by the process of heat transfer. Therefore, the objective of this study was to build a three-dimensional electromagnetic–thermal multifield coupling model and investigate the characteristics of heat transfer and temperature distribution in the process of HFIC. The influence of key process parameters on temperature distribution was investigated to provide the theoretical basis for temperature field control. A cladding experiment was conducted to verify the finite element model and evaluate the effect of temperature distribution on the microstructure and microhardness of coatings.
45 steel plate
Induction coil Induction heating power Flux concentrator
Refractory brick Cooling system
(a)
2. Description of the mathematical model 2.1. Description of the electromagnetic field model
(b)
The eddy current generated in the workpiece during induction heating is dependent on the alternative magnetic field. The governing equations of electromagnetic induction heating are Maxwell's equations, which can be described as follows:
∇×H=J+ ∇×E=−
∂D ∂t
∂B ∂t
Fig. 1. Experimental device and induction coil applied in high-frequency induction cladding. (a) Experimental device. (b) Induction coil.
The electric scalar potential φ is introduced because ∇ × (∇φ) = 0 meets Helmholtz theorem. Eq. (8) can be further described as follows:
(1)
E=−
(2)
∇·B = 0
(3)
∇·D = ρ
(4)
∂A −∇φ ∂t
(9)
In accordance with Eqs. (1), (5), and (6), and (7), the governing equation in the eddy current domain is derived as:
1 ∂A ∇×A+σ + σ ∇φ = 0 μ ∂t
where H is the magnetic field intensity, J is the electric current density associated with free charges, D is the electric displacement vector, E is the electric field intensity, B is the magnetic flux density, and ρ is the electric charge density. In HFIC, displacement current density ∂D / ∂t is not the main contributor of joule heat that melts the alloy powders, and induced conduction current J is considerably greater than the displacement current density ∂D / ∂t ; therefore, ∂D / ∂t in the equations should be negligible [15]. Moreover, the physical parameters H, J, B, and E obey the following auxiliary equations:
∇×
B = μH
(5)
2.2. Description of the temperature field model
J = σE
(6)
The boundary conditions of continuity between regions with different properties are as follows:
n × (H1−H2) = 0
(11)
n·(B1−B2) = 0
(12)
Moreover, in the outermost boundary of the model, the magnetic vector potential A is 0.
Induction heating is a process that occurs with drastic temperature increase, and an extreme temperature gradient will exist in the surface layer of the workpiece because of the skin effect. Thus, this nonlinear transient heat transfer process can be expressed by the Fourier equation as follows:
where μ is magnetic permeability, and σ is electrical conductivity. The magnetic vector potential A is introduced on the basis of the Helmholtz theorem, and the following equation is obtained:
B=∇×A
(10)
(7)
Thus, the electric field intensity E can be described as follows from Eqs. (2) and (7):
∂ 2T ∂ 2T ∂ 2T ⎞ ∂T k⎛ 2 + + + Q = ρc 2 2 ∂ x ∂ y ∂ z ∂t ⎝ ⎠
∂A ⎤ ∇ × ⎡E + =0 ∂t ⎦ ⎣
where k is the thermal conductivity coefficient, Q is internal heat source intensity due to the eddy current, c is specific heat capacity, and ρ is
⎜
(8) 2
⎟
(13)
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Substrate Coating Flux Concentrator Induction Coil
Air
Air
z
z
y
y x
x
(a)
(b)
Fig. 2. Finite element model of the high-frequency induction cladding of 45 steel plate. (a) Without air. (b) With air. 250
Table 1 Specific process and geometrical parameters of the high-frequency induction cladding of 45 steel plate. Parameter
Unit
Size of 45 steel plate Size of metal alloy coating Section size of induction coil Wall thickness of induction coil Air-gap spacing (distance between induction coil and coating) Length of induction coil Current frequency Current density Heating time
80 × 80 × 10 40 × 12 × 2 4×4 1 1
mm3 mm3 mm2 mm mm
40 200 1.10 × 108 30
mm kHz A/m2 s
200
Material properties
Item
Relative permeability -8 Electrical resistivity /( 10 m) -1 -1 Thermal conductivity /(W m K ) -1 -1 Specific heat /(10J kg K )
150
100
50
0
120
0
Relative permeability -8 Electrical resistivity /( 10 m) -1 -1 Thermal conductivity /(W m K ) -1 -1 Specific heat /( 10J kg K )
Material properties
100
80
200
400
600
800
1000
Temperature ( C) Fig. 4. Electromagnetic and thermal physical property curves of 45 steel.
Start 60
Establishment of finite element model
40
20
Electromagnetic field calculation
0 0
200
400
600
800
1000
Update thermal parameters
1200
Temperature ( C) Fig. 3. Electromagnetic and thermal physical property curves of Ni60 alloy.
Adjust the sub time increment Δtsub
density. Considering thermal convection and radiation between material surfaces and the ambient environment, the boundary condition of the temperature field can be described as follows:
∂T 4 = h (T −Tair ) + εemi σb (T 4−Tair −k ) ∂n
No
Joule heat Temperature field calculation
Update electromagnetic parameters
t = t+Δt Result converged Yes
t = tsum
(14)
No
Yes
where n is the outward unit normal vector; h is the heat-convection coefficient; εemi is material emissivity; and σb is the Stefan–Boltzmann constant, which is equal to 5.67 × 10−8 W/m2 K4. In this model, the heat-convection coefficient is 50 W/m2 K, and the emissivity is 0.68. The ambient temperature is 20 °C, and the initial temperature of 45 steel plate and alloy powder is 20 °C.
End Fig. 5. Flow chart of the calculation process of high-frequency induction cladding.
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800
Calculated temperature Measured temperature
T2 (0.012,0.04,0.01) T1 (-0.028,0.03,0.01)
Temperature ( C)
700
Point T2
600 500 400 300 200
Point T1
100 0 0
5
10
15
20
25
30
Time (s)
(a)
(b)
Fig. 6. Comparison between experimental measurements and simulated calculations. (a) Locations of selected points (b) Temperature curves of selected points.
comprises an induction coil, flux concentrator, induction-heating power source, and refractory brick. The flux concentrator is used to concentrate magnetic flux to improve heating efficiency. The experimental device is equipped with a cooling system. A 45 steel plate precoated with metal alloy powder is placed on the refractory brick, and the induction coil is directly above the precoated alloy powder. The induction coil is a rectangular coil fabricated from a square-sectioned copper tube, as shown in Fig. 1b. The finite element model of HFIC is established on the basis of ANSYS software. As illustrated in Fig. 2a, the model is composed of substrate, induction coil, flux concentrator, coating and air. It should be noted that the substrate, induction coil, flux concentrator and coating are wrapped in the air, thus the air is not shown in Fig. 2a to provide a clear view of the internal geometry of the model. The finite element model with air is additionally shown in Fig. 2b. The induction coil used in this experiment is a planar rectangular coil with two lifted ends. According to the proximity effect, the main part of the coil that is used to heat the workpiece is the concave section. Therefore, the induction coil in this model is simplified as two separated leads with opposite electrical currents flowing in, as shown in Fig. 2a [16]. The specific process and geometrical parameters of the model are shown in Table 1. As depicted in Fig. 2a and b, a hexahedral mesh is applied to discretize
Middle cross- section
y x
Fig. 7. Temperature distribution in the surface and middle cross-section of the substrate and coating at 15 s of heating.
3. Establishment of the finite element model and experimental validation 3.1. Establishment of the finite element model The experimental HFIC device is shown in Fig. 1a. The device
t=5s Low-temperature zone in middle area
t=10s High-temperature zone in two sides
t=15s
Experiment observation
t=20s
Fig. 8. Temperature distribution in the middle cross-section of the coating at 5–20 s of heating. 4
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Fig. 9. Melting state of the coating at different time points.
model of HFIC is reliable and can be employed to further study the heat transfer and temperature distribution during HFIC.
the whole model, and the elemental size of this model varies from its heating center to its outmost layer. A fine mesh with an elemental size of 1 × 2 × 0.5 mm3 is carried in the coating and in the central part of the substrate, and a coarse mesh with a size of 5 × 5 × 2.5 mm3 is used in the outmost layer of the model. The finite element model with air, as shown in Fig. 2b, contains 80,000 hexahedral elements and 314,364 nodes. Considering the temperature dependency of the electromagnetic and thermal physical properties of Ni60A and 45 steel, which are shown in Figs. 3 and 4, respectively, a coupled electromagnetic-thermal analysis should be conducted. The relative permeability of the flux concentrator is 60. The calculation process of HFIC coupled with electromagnetic and temperature fields is shown in Fig. 5. Sequential coupling is adopted in consideration of calculation efficiency and accuracy. The coupling method can be described as follows. The electromagnetic field is calculated when the initial parameters are specified, and then magnetic flux density and eddy current intensity are calculated. Afterwards, the joule heat generated by the induced eddy current is used as the load of the temperature field. Δt refers to the time increment within which the electromagnetic parameters remain constant and temperature-field calculation is conducted. During temperature-field calculation, time increment Δt will be divided into several subtime increments Δtsub , which can be adjusted automatically by the simulation package. Once temperature-field analysis converges, the electromagnetic parameters will be updated and electromagnetic analysis restarts [14]. In this study, the total heating time tsum is set to 30 s, and the procedures described above are recycled until heating is completed. Time increment Δt and minimum subtime increment Δtsub are defined as 1 and 0.01 s, respectively. The convergence of the calculation is based on heat flow. L2 norm is selected as the convergence norm, and the tolerance is 0.001. The total number of calculation iterations is 412.
4. Results and discussion 4.1. Characteristics of heat transfer and temperature distribution Temperature distribution in the surface and middle cross-section of the substrate and coating after 15 s of heating is shown in Fig. 7. The parameters are selected as follows: Current density of 1.2 × 108 A/m2 , current frequency of 200 kHz, and air–gap spacing of 1 mm. As seen in the figure, temperature is symmetrically distributed in the surface, and a high-temperature zone (HTZ) exists in both sides of the coating directly underneath the induction coil. The origin of the HTZ indicates the location where the eddy current, the main contributor to temperature increase, occurs during heating. Fig. 8 shows the variation in temperature distribution in the middle cross-section over the period of 5–20 s. In accordance with experimentally observed phenomenon (shown in Fig. 8), the temperature in the middle area of the coating is lower than that at the two sides of the coating. This phenomenon is largely attributed to the geometry of the coil, which is displayed in Fig. 1b. At the beginning of heating, the HTZ first appears in the substrate–coating interface. Comparing the HTZ at different time points revealed that the HTZ develops around the substrate–coating interface and extends into the internal substrate and coating as heating continues because the relative permeability of the substrate is higher than that of the coating. Moreover, the relative permeability of the coating is reduced to 1 in the initial period as the temperature exceeds the Curie point of the coating. Eddy current in this condition is mainly induced in the substrate–coating interface. Subsequently, Joule heat generated by the eddy current transfers into the surrounding cold area, and the HTZ expands continually, revealing that the heat used to melt the coating originates from the interface between substrate and coating, and the temperature increment of coating is mainly dependent on thermal conduction. On the other hand, this kind of temperature distribution also indicates that melting proceeds from the interior to the exterior of the coating, experimental observation corresponding to the melting characteristic is depicted in Fig. 9. This phenomenon is significantly different from that observed in other surface coating technologies, such as laser cladding or plasma cladding. After 20 s of heating, the temperature of the coating reached 1100 °C, which exceeds the melting temperature of the Ni60 alloy powder. Given that heat originates from the substrate–coating interface, temperature distribution in the substrate surface was analyzed to identify the variation characteristics of the temperature field in the x–y plane. The temperature distributions in the surface of the substrate at 10, 20, and 30 s of heating are shown in Fig. 10. Fig. 10a and b show that the temperature distribution in the HTZ exhibits a twin-peak
3.2. Experimental validation The results calculated by the finite element model for the HFIC of 45 steel plate are experimentally validated. The experimental process parameters are listed in Table 1. The coating is composed of Ni60A alloy powder mixed with 30% WC particles. During preparation, the alloy powder is mixed with adhesive and then coated onto the surface of 45 steel plate, which is polished and cleaned to eliminate rust and oil stains. After drying, the workpiece is heated using the experimental device. The temperature of selected points is measured by K-type thermocouples. The accuracy of the thermocouples is ± 1 °C, and the interval for data collection is 1 s. As shown in Fig. 6, the calculated temperature curves of selected points match well with the measured temperature curves. The maximum difference between the calculated temperature and the measured temperature is 13 °C, which is within the error range [12,17]. That is to say, the three-dimensional finite element 5
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1600
Point A Point B Point C Point D Point E
1400
3.5 mm 3.5 mm
Temperature ( C)
24 mm
1200 1000 800
Z
400
X
200 0
(a)
A B C D E
600
0
5
10
15
20
25
30
Time (s) Fig. 11. Temperature variation curve with time of feature points.
17 mm
Given that the melting point of Ni60A is between 980 °C and 1020 °C, the powders in contact with the substrate–coating interface where the temperature exceeds 1000 °C will be melted. Here, the surface area where the temperature is above 1000 °C is defined as the effective cladding area. The length of the effective cladding area in the xand y-directions is used to measure the size of the effective cladding area. Comparing the effective cladding areas shown in Fig. 10a and b revealed that length in the x- and y-directions increases dramatically, and the maximum temperature significantly increases. Fig. 10c shows that size only slightly increases in the x direction, and the size of the effective cladding area is approximately 18 mm × 45 mm. Fig. 11 shows the temperature variation curves with time of feature points in the middle cross-section of the model, and the coordinates of these points are shown in Table 2. The temperature of point B, which is located in the substrate–coating interface, is higher than those of other points. Temperature gradually decreases with increasing distance from the interface. Although points A and C are equidistant from point B, the temperature of point A is higher than that of point C. Temperature increases rapidly during the initial period of heating. After 5 s, the heating speed slows down significantly because the temperature of the substrate surface increases to 800 °C, which exceeds the Curie point. The relative permeability of the surface layer of the substrate is suddenly reduced to 1.
45 mm
(b) 18 mm
45 mm
4.2. Influence of different parameters on temperature distribution Temperature distribution has a great influence on the microstructure and processing efficiency of coatings during cladding. The processing efficiency and quality of HFIC can be improved by analyzing the effects of different parameters on temperature distribution. In this study, changes in the size of the effective cladding area and maximum temperature difference ΔT (Δ T= TB−TA ) between points A and B (located in the surface and the bottom of coating, respectively) in the coatings are used to evaluate the influence of different parameters. The parameters investigated in this study include current density, current frequency, and air-gap spacing (distance between induction coil and coating).
(c) Fig. 10. Temperature distribution in the substrate surface during 10–30 s of heating. (a) t = 10 s; (b) t = 20 s; (c) t = 30 s.
4.2.1. Influence of different parameters on the size of the effective cladding area Within the same processing time, a large effective cladding area indicates that a large amount of alloy powder has been melted, which in turn reflects high cladding efficiency. Fig. 12a shows the effect of current density on the size of the effective cladding area. The current
pattern, and the temperature in the center of the HTZ is lower than that in the two sides of the coating. As shown in Fig. 10c, the HTZ is oval, and the temperature difference in the HTZ is eliminated when heating is terminated.
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Table 2 Coordinates of selected feature points. Point
A
B
C
D
E
Coordinate
(0.003,0.04,0.012)
(0.003,0.04,0.010)
(0.003,0.04,0.008)
(0.003,0.04,0.006)
(0.003,0.04,0.004)
200
0.04
0.03
0.02
180
1600
140 1500
120 1400
100 1300
80
1200
60
1100
40 1.00 10
8
1.10 10
8
1.20 10
8
8
1.00 10
8
8
1.20 10
1.10 10
8
1.30 10
8
1.40 10
1.30 10
2
1.40 10
8
1.50 10
(a)
8
60
Maximum temperature difference (°C)
(a)
X direction Y direction
0.030 0.025 0.020
58
Temperature of point B Maximum temperature difference
56
1250
54 1200
52 50
1150
48 46
1100
44 42
1050
40 38
170
0.015
1300
180
190
200
210
220
230
240
250
1000 260
Current frequency (kHz)
(b)
0.010 90
190
200
210
220
230
240
250
Current frequency (kHz)
(b) 0.05
X direction Y direction
0.04
1600
260
0.03
Temperature of point B Maximum temperature difference
80
1500 1400
70
1300
60
1200 50 1100 40
1000
30
900
20
Temperature of point B (°C)
180
Maximum temperature difference (°C)
170
Size of effective cladding area (m)
8
1.50 10
Current density (A/m2)
0.035
8
Current density (A/m )
0.01
Size of effective cladding area (m)
1700
160
Temperature of point B (°C)
0.05
1800
Temperature of point B Maximum temperature difference
Temperature of point B (°C)
X direction Y direction
Maximum temperature difference (°C)
Size of effective cladding area (m)
0.06
800
0.02 10
1.0
1.5
2.0
2.5
3.0
700
Air-gap spacing (mm)
0.01
(c) Fig. 13. Variation curves of maximum temperature difference ΔT and temperature of point B under different parameters (a) Current density. (b) Current frequency. (c) Air-gap spacing.
0.00 1.0
1.5
2.0
2.5
3.0
Air-gap spacing (mm) frequency is 200 kHz with an air–gap spacing of 1 mm. As shown in Fig. 12a, when the current density increases from 1.0 × 108 A/m2 to 1.50 × 108 A/m2 , the size in the x-direction of the effective cladding area gradually increases from 0.01 m to 0.025 m. The size of the
(c) Fig. 12. Variation in the size of the effective cladding area under different parameters. (a) Current density. (b) Current frequency. (c) Air-gap spacing.
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density are specified as 200 kHz and 1.2 × 108 A/m2 , respectively. The figure shows that the size of the effective cladding area and air-gap spacing are negatively correlated. In the case of a 1.5 mm air-spacing gap, the size in the y-direction is 0.042 m, which has decreased by 6.7% compared with 0.045 m in the case of 1 mm air spacing gap. In the xdirection, the size of the effective cladding area increases slightly from 0.017 m to 0.018 m as the air-spacing gap decreases from 1.5 mm to 1 mm. When the air–gap spacing increases to 3 mm, the size of the effective cladding area is 0, indicating that no metallurgical bonding exists between the substrate and coatings.
WC particles
Coating Interface
Transition region Substrate
4.2.2. Influence of different parameters on maximum temperature difference ΔT Maximum temperature difference ΔT is a reflection of temperature uniformity in coatings. A uniform temperature distribution is important for obtaining high-quality coating. In fact, alloy powders in the surface of the coating require a longer time to reach the melting point than those in the bottom of the coating because heat is generated from the substrate–coating interface. Given that eliminating the temperature difference between the surface and the bottom of the coating is difficult, the practical method to obtain temperature uniformity is to control the temperature difference within a reasonable range. The influence of different processing parameters on the maximum temperature difference ΔT is shown in Fig. 13. To provide an intuitive understanding of temperature variations in the coating, the temperature of point B when the maximum temperature difference appears is listed in Fig. 13. The maximum temperature difference ΔT with different current densities is shown in Fig. 13a. When the current density varies between 1.0 × 108 and 1.1 × 108 A/m2 , the maximum temperature difference ΔT is approximately 50–60 °C. The temperature of point B is 1130 °C and 1291 °C, respectively. As the current density increases to 1.5 × 108 A/m2 , the maximum temperature difference increases to 184 °C. This variation can be attributed to the increase in coating temperature with
Fig. 14. Microstructural morphology of the substrate–coating interface.
effective cladding area in the y-direction also increases with current density. However, the rate of increase gradually slows down. Size in the y-direction slightly changes from 0.045 m to 0.05 m as the current density increases from 1.20 × 108 A/m2 to 1.50 × 108 A/m2 , indicating that size expansion is limited in the y-direction. Fig. 12b shows the variation in effective cladding area with current frequency. The size of the effective cladding area in the y-direction increases almost linearly with current frequency. In this case, the current density is 1.0 × 108 A/m2 , and the air-gap spacing is 1 mm. The largest effective cladding area is obtained at the frequency of 250 kHz, and the sizes in the x- and y-directions under this condition are 0.035 and 0.021 m, respectively. Moreover, the size in the x-direction does not significantly increase when the current frequency varies between 180 and 220 kHz. The variation in effective cladding area with air-gap spacing is depicted in Fig. 12c. The current frequency and current
Bottom of coating
Middle of coating
Top of coating
(a) 90 80
Elements content (%)
70
C Cr W Ni Si
18 16 14 12 10 8 6 4 2 0 Bottom of coating
Middle of coating
Top of coating
(b) Fig. 15. Morphology and composition of WC particles in different positions of the coating. (a) Morphology. (b) Composition. 8
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50±m
50±m
50±m
Side Part
Intermediate part
Side Part
(a) 65 C Cr W Ni Si
60
Element contents (%)
55 50 45 40 35 30 25 20 15 10 5 0
Intermediate part
Side part
Side part
(b) Fig. 16. Morphology and composition of WC particles in the intermediate and side parts of the coating. (a) Morphology. (b) Composition. 900
current frequency has a relatively small effect on the uniformity of temperature distribution in the coating. The temperature of point B slightly changes with current frequency, showing that current frequency has a limited influence on the temperature field. Fig. 13c shows that a negative relationship exists between maximum temperature difference and air-gap spacing. When the air-gap spacing is 3 mm, the maximum temperature difference is 16 °C, which has decreased by 81% relative to the maximum temperature difference of 84 °C obtained with the air–gap spacing of 1 mm. As a result of proximity effect, temperature of point B decreases from 1423 °C to 825 °C when the air gap spacing increases from 1 mm to 3 mm. Therefore, the reason for the variation in maximum temperature difference with different air-gap spacing is that under high temperature in coating surface, there is a high heat loss caused by thermal radiation, which in turn leads to high maximum temperature difference between the surface and bottom of coating. Notably, the effective cladding area under an air-gap spacing of 3 mm is 0, and the processing parameter in this case is invalid.
Coating
Substrate
Microhardness (HV)
800
700
600
500
1.10e8A/m^2 1.20e8A/m^2 1.50e8A/m^2
400
300 -1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Distance from interface (mm) Fig. 17. Microhardness of the coating and substrate surface under different current densities.
5. Microstructural morphology and microhardness of the coating Measuring the internal temperature distribution of coatings is difficult; however, the microstructure of the coating would change significantly in accordance with temperature distribution in the coating. Thus, temperature distribution can be evaluated by researching and comparing the microstructural morphologies of coatings. Fig. 14 shows the microstructural morphology of the area around the interface. The current density, current frequency, and air-gap spacing selected in the experiment is 1.2 × 108 A/m2 , 200 kHz, and 1 mm, respectively. The area comprises three primary regions, including substrate, transition region, and coating. The grey pieces dispersed in the coating are WC particles. A white bright band that appears in the interface indicates metal-element diffusion and metallurgical bonding between substrate
increasing current density, leading to high thermal radiation in the coating surface that in turn increases the temperature difference between the surface and the bottom of the coating. The temperature of point B under this condition is 1698 °C, and the coating may become overheated. When the sizes of the effective cladding areas are almost the same under different parameters, the parameters with low temperature difference should be selected. Therefore, the suitable current density should be 1.0 × 108–1.2 × 108 A/m2 . The influence of current frequency on maximum temperature difference is shown in Fig. 13b. The maximum temperature difference ΔT varies between 40 °C and 60 °C in these four cases, indicating that
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stages of heating. 2. The size of the effective cladding area and maximum temperature difference in the coating are directly proportional to current density and inversely proportional to the air-gap spacing. The variation in current frequency minimally influences the maximum temperature difference in the coating. When the air-gap spacing is increased to 3 mm, no effective cladding area is observed although the maximum temperature difference in the coating is only 16 °C. 3. The dissolution of WC particles in the bottom of the coating is more severe than that in the top of the coating. This result indicates that the temperature in the bottom of the coating is higher than that in the top of the coating and corresponds to the temperature distribution simulated by the finite element model established in this study. A uniform microhardness distribution is obtained under a temperature field with low temperature difference in the coating.
and coating. WC particles will dissolve into the bonding metal and precipitate carbides around their edges at high temperature [18]. Therefore, the morphology of WC particles in different locations may reflect temperature distribution in a specific location. The morphology of WC particles at different coating locations is shown in Fig. 15a. Flocculent carbides have precipitated around WC particles in the bottom of the coating. The flocculent carbides that precipitated around the edges of WC particles gradually disappear as the distance from the interface increases. Subjecting the selected areas marked in Fig. 15a to EDS analysis revealed the elemental content of the areas surrounding WC particles at different locations. As seen in Fig. 15b, the area near the WC particle in the bottom of the coating is rich in tungsten, and with the increase of distance from the interface, the amount of tungsten in the selected area is greatly reduced, indicating that less tungsten is dissolved into the coating. Chromium and silicon contents also decrease with increasing distance from the interface. This is mainly because that with the dissolution level of WC particle reduced, less carbon is released into the coating. Furthermore, the amount of carbon is insufficient for the synthesis of chromic carbide and silicon carbide, thus leading to the reduction of chromium and silicon contents. The above analysis indicated that the dissolution of WC particles in the bottom of the coating is more severe than that in the top of the coating. This result indicated that the temperature in the bottom of the coating is higher than that in the top of the coating and corresponds to the temperature distribution shown in Figs. 8 and 11. In addition, in the discussion of temperature distribution in the middle cross-section of the coating, the temperature in the intermediate part of the coating is lower than those in the two sides of the coating because of the coil shadow effect, as shown in Fig. 8. Therefore, the morphology and composition of WC particles in the intermediate and side part of the coatings are also compared, as shown in Fig. 16. The tungsten contents in the side area of WC particles increase from the intermediate part to the side part of the coating, indicating that temperature is higher in the side part than that in the intermediate part. Fig. 17 shows the microhardness of the coating and substrate surface under different current densities. The microhardness of the coating is higher than that of the substrate under these conditions. Comparing the microhardness of the coatings reveals that the average microhardness of the bottom of the coatings is lower than that of the top of the coatings because of the different amounts of dissolved WC particles. In addition, previous research on temperature differences under different current densities demonstrated that microhardness distribution under low maximum temperature difference ΔT is relatively uniform than that under high temperature difference. When the current density increases to 1.5 × 108 A/m2 , the microhardness of the coatings decreases significantly because the temperature under this parameter is too high, and the coating is over-heated.
Acknowledgments The author gratefully acknowledges that the work presented in this paper was supported by the National Natural Science Foundation of China (No. 51175515) and Fundamental Research Funds for the Central Universities, China (No. 17CX06003). References [1] J.J. Fang, Z.X. Li, Y.W. Shi, Microstructure and properties of TiB 2-containing coatings prepared by arc spraying, Appl. Surf. Sci. 254 (13) (2008) 3849–3858. [2] L.M. Zhang, D.B. Sun, H.Y. Yu, Characteristics of plasma cladding Fe-based alloy coatings with rare earth metal elements, Mater. Sci. Eng. A s 452–453(452) (2007) 619–624. [3] A. Emamian, S.F. Corbin, A. Khajepour, Effect of laser cladding process parameters on clad quality and in-situ formed microstructure of Fe–TiC composite coatings, Surf. Coat. Technol. 205 (7) (2010) 2007–2015. [4] J.H. Chang, S.K. Tzeng, J.M. Chou, et al., Effect of dry sliding wear conditions on a vacuum induction melted Ni alloy, Wear 270 (3–4) (2011) 294–301. [5] Z.Z. Zhang, G.Q. Han, Y.W. Fu, et al., A study on properties of GNi-WC25 coating by high frequency induction cladding, laser cladding and oxygen-acetylene sprayingfusing, J. Mater. Eng. 3 (2003) 3–6. [6] G. Hu, H.M. Meng, J.Y. Liu, Microstructure and corrosion resistance of induction melted Fe-based alloy coating, Surf. Coat. Technol. 251 (29) (2014) 300–306. [7] Z.T. Wang, J.S. Meng, L.L. Chen, et al., Microstructure and forming mechanism of TiC/Ni composite coating in situ synthesized by induction cladding, Trans. Mater. Heat Treat. 28 (6) (2007) 99–103. [8] D.Y. He, J. Xu, R. Ma, et al., Wear resistance properties of micron-WC reinforced Ni60 coating by high frequency induction cladding, Trans. China Welding Inst. 29 (2008) 138–141. [9] M.Q. Zhang, W. Zhang, H.L. Yu, et al., Microstructure and tribological properties of NiCrBSi coatings prepared by different methods, China Surf. Eng. 27 (6) (2014) 75–81. [10] G. Hu, H.M. Meng, J.Y. Liu, Friction and sliding wear behavior of induction melted FeCrB metamorphic alloy coating, Appl. Surf. Sci. 308 (308) (2014) 363–371. [11] H. Cen, Y.S. Wang, J.B. Lei, et al., Numerical simulation on temperature field of boiler tube coating fabricated by high frequency induction cladding, Mater. Sci. Eng. Powder Metall. 18 (5) (2013) 639–646. [12] N.D. Luozzo, M. Fontana, B. Arcondo, Modelling of induction heating of carbon steel tubes: mathematical analysis, numerical simulation and validation, J. Alloys Comp. 536 (4) (2012) S564–S568. [13] Y. Han, H.Y. Wen, E.L. Yu, Study on electromagnetic heating process of heavy-duty sprockets with circular coils and profile coils, Appl. Therm. Eng. 100 (2016) 861–868. [14] M.C. Song, Y.H. Moon, Coupled electromagnetic and thermal analysis of induction heating for the forging of marine crankshafts, Appl. Therm. Eng. 98 (2016) 98–109. [15] H.S. Park, X.P. Dang, Optimization of the in-line induction heating process for hot forging in terms of saving operating energy, Int. J. Precision Eng. Manuf. 13 (7) (2012) 1085–1093. [16] X.B. Zhang, C. Chen, Y.J. Liu, Numerical analysis and experimental research of triangle induction heating of the rolled plate, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 10 (3) (2015) 1–16. [17] V.I. Rudnev, D. Loveless, R. Cook, et al., Handbook of Induction Heating, Mracel Dekker, New York, 2003. [18] S.F. Zhou, Y.J. Huang, X.Y. Zeng, A study of Ni-based WC composite coatings by laser induction hybrid rapid cladding with elliptical spot, Appl. Surf. Sci. 254 (10) (2008) 3110–3119.
6. Conclusions An electromagnetic–thermal-coupled finite element model was established to analyze the characteristics of heat transfer and temperature distribution in the HFIC of 45 steel plate. The influences of different parameters on effective cladding area and temperature distribution in coatings were also discussed. The primary conclusions are summarized as follows: 1. The heat used to melt the alloy powder originates from the substrate–coating interface. HTZ expands from the interface to the interior of the substrate and coating, and the coating melts from the interior to the exterior. Temperature increases rapidly during the early stages of heating and then increases slowly during the later
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