PDF
Induction Hardening of a Cylindrical Pin
Introduction
Induction hardening is a heat treatment process that is used to increase hardness and wear resistance of steel parts. The process uses a copper coil with a high frequency alternating current to induce eddy currents on the surface layer of the part. These eddy currents heat the material rapidly above the austenitization temperature, and the part is then rapidly quenched in water, oil, or similar. This typically produces a hard and durable martensitic surface, while retaining the softer base composition inside.
This example shows how to perform an induction hardening simulation for a small steel pin. The pin is made from a hypoeutectoid ferritic–pearlitic steel and is positioned inside a multiturn coil, where it is rapidly heated and then quickly cooled using a water spray.
Model Definition
This section describes the various aspects involved in setting up and performing an induction hardening simulation.
Geometry
The pin is 30 mm in length and 10 mm in diameter, and has a 1 mm chamfer at its ends; see Figure 1.
Figure 1: The pin used in the simulation.
As the pin is axisymmetric as well as symmetric across its center, half the pin is modeled in 2D axisymmetry.
Material Properties
Material properties for the phases austenite, ferrite, pearlite, bainite, and martensite are imported from JMatPro® (Ref. 1). They include thermal properties, mechanical properties, and electrical properties, and they are in general temperature dependent. Elastoplastic properties additionally depend on plastic strain and plastic strain rate. Magnetic permeability is treated separately in JMatPro®. It is imported into COMSOL Multiphysics as a single, compound material with averaged properties, rather than as separate phase-specific materials.
Phase Transformations and Initial Composition
Phase-transformation data for austenite decomposition are imported from JMatPro® (Ref. 1). Four phase transformation models are automatically configured to represent the decomposition into ferrite, pearlite, bainite, and martensite, respectively. For austenitization, a simple linear phase-transformation model is used. This model is based on the simple idea that the rate of formation of the destination phase (austenite) is proportional to the heating rate. The upper and lower temperature limits Tu and Tl in the denominator are taken as 900 and 723 degrees Celsius, respectively. The rate equation is given by
For a more accurate description of the austenitization process, a more sophisticated phase-transformation model is required, but for the present example the linear model will suffice. The base (starting) composition of the steel is taken to be 50% ferrite and 50% pearlite.
Thermal Boundary Conditions
The surface of the pin will transfer heat to its surroundings during the induction hardening process. The model considers three mechanisms for heat transfer: Convection to the surrounding air, thermal radiation to the surrounding air, and convection to the water during the water spray cooling.
Convection to Air
For simplicity, this mode of heat transfer is modeled using a constant heat transfer coefficient of 15 W/(m2·K), considering the ambient air to be 20 degrees Celsius.
Thermal Radiation
When the pin is heated it becomes increasingly important to account for thermal radiation. Here, the emissivity of the steel surface is 0.8.
Water Spray Cooling
The water spray cooling is modeled using a temperature-dependent heat transfer coefficient; see Figure 2. The water temperature is taken to be 60 degrees Celsius, and this convection mechanism is active only when the induction current has been turned off. This represents rapidly removing the inductor from the pin, and spraying water on its surface.
Figure 2: The temperature dependent heat transfer coefficient for the water spray cooling.
Mechanical Boundary Conditions
Because only half the pin is modeled, a symmetry boundary condition is applied at the center plane.
Electromagnetic Boundary Conditions and Loading
Because only half the pin is modeled, an antisymmetry condition is applied to the magnetic flux density across the geometric symmetry plane. The computational domain is chosen large compared to the pin itself, and it is magnetically insulated along its perimeter.
The twenty-turn induction coil is made from copper and the alternating current is increasing linearly over half a second to a peak value of 175 A and then down linearly again for a total excitation time of one second. The frequency of the induction current is 120 kHz.
Results and Discussion
The purpose of using induction heating compared to, for example, a furnace, is that it is possible to essentially heat only the surface of the part. This means that the interior of the part remains at its ferritic–pearlitic base composition, and only the surface is austenitized. After quenching the part, here using water spray cooling, the austenitic surface transforms into hard martensite; see Figure 3. Because of the lower density of martensite compared to austenite, the phase transformation produces volumetric expansion, and this results in compressive stresses near the surface. Figure 4 shows the axial stress component after hardening. Stresses are compressive near the surface, and balanced by tensile stresses on the inside of the pin. From a durability standpoint, compressive residual surface stresses are usually desired.
Figure 3: Phase fraction of martensite after hardening.
Figure 4: Stress in the Z direction after hardening.
Notes About the COMSOL Implementation
•
When material properties are imported from JMatPro®, the relative permeability is not provided per metallurgical phase. Instead, it is imported as an effective quantity for the material. It is therefore merged into the compound material after import.
•
Because the induction frequency is rather high (125 kHz), it may be necessary to mesh the surface of the pin even finer to adequately resolve the skin effect.
•
Phase-transformation data is imported by selecting Import Phase Transformations in the physics interface’s context menu.
•
Phase material properties are imported by selecting Import Materials from the Materials context menu under Global Definitions or under Materials at the component level (not available in 0D).
Reference
1. Sente Software, Ltd., United Kingdom.
Application Library path: Metal_Processing_Module/Induction_Hardening/induction_hardening_of_a_cylindrical_pin
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D Axisymmetric.
2
In the Select Physics tree, select Heat Transfer > Metal Processing > Induction Hardening.
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select Preset Studies for Selected Multiphysics > Frequency–Transient.
6
Click  Done.
Geometry 1
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 0.005.
4
In the Height text field, type 0.015.
5
In the Width text field, type 0.1.
6
In the Height text field, type 0.1.
Rectangle 2 (r2)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 0.005.
4
In the Height text field, type 0.015.
Chamfer 1 (cha1)
1
In the Geometry toolbar, click  Chamfer.
2
On the object r2, select Point 3 only.
3
In the Settings window for Chamfer, locate the Distance section.
4
In the Distance from vertex text field, type 0.001.
Rectangle 3 (r3)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type 0.002.
4
In the Height text field, type 0.017.
5
Locate the Position section. In the r text field, type 0.006.
Form Union (fin)
In the Geometry toolbar, click  Build All.
Pin
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Pin in the Label text field.
3
On the object fin, select Domain 1 only.
Coil
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Coil in the Label text field.
3
On the object fin, select Domain 3 only.
Air
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, type Air in the Label text field.
3
On the object fin, select Domain 2 only.
Pin Surface
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, locate the Entities to Select section.
3
From the Geometric entity level list, choose Boundary.
4
On the object fin, select Boundaries 4, 6, and 7 only.
5
In the Label text field, type Pin Surface.
Symmetry Plane
1
In the Geometry toolbar, click  Selections and choose Explicit Selection.
2
In the Settings window for Explicit Selection, locate the Entities to Select section.
3
From the Geometric entity level list, choose Boundary.
4
On the object fin, select Boundaries 2, 8, 10, and 13 only.
5
In the Label text field, type Symmetry Plane.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in > Air.
4
Click the Add to Component button in the window toolbar.
Materials
Air (mat1)
1
Select Domain 3 only.
2
Click the  Zoom In button in the Graphics toolbar.
3
Select Domain 2 only.
Add Material
1
Go to the Add Material window.
2
In the tree, select Built-in > Copper.
3
Click the Add to Component button in the window toolbar.
4
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Copper (mat2)
1
Select Domain 3 only.
2
In the Materials toolbar, click Import Materials and choose Import Materials.
3
In the Import Materials dialog, click  Browse.
4
Browse to the model’s Application Libraries folder and double-click the file induction_hardening_of_a_cylindrical_pin_JMatPro_general_steel.xml.
5
Click OK.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
tEnd
1[s]
1 s
End of induction
Interpolation 1 (int1)
1
In the Home toolbar, click  Functions and choose Global > Interpolation.
2
In the Settings window for Interpolation, locate the Definition section.
3
In the Function name text field, type htc.
4
In the table, enter the following settings:
t
f(t)
20
35
200
40
600
5
1000
1
5
Locate the Units section. In the Function table, enter the following settings:
Function
Unit
htc
kW/(m^2*K)
6
In the Argument table, enter the following settings:
Argument
Unit
t
degC
Interpolation 2 (int2)
1
In the Home toolbar, click  Functions and choose Global > Interpolation.
2
In the Settings window for Interpolation, locate the Definition section.
3
In the Function name text field, type current.
4
In the table, enter the following settings:
t
f(t)
0
0
tEnd/2
175
tEnd
1
5
Locate the Units section. In the Function table, enter the following settings:
Function
Unit
current
A
6
In the Argument table, enter the following settings:
Argument
Unit
t
s
Heat Transfer in Solids (ht)
1
In the Model Builder window, under Component 1 (comp1) click Heat Transfer in Solids (ht).
2
In the Settings window for Heat Transfer in Solids, locate the Domain Selection section.
3
From the Selection list, choose Pin.
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Boundary Selection section.
3
From the Selection list, choose Pin Surface.
4
Locate the Heat Flux section. From the Flux type list, choose Convective heat flux.
5
In the h text field, type htc(T)*(t>tEnd).
6
In the Text text field, type 60[degC].
Heat Flux 2
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
In the Settings window for Heat Flux, locate the Heat Flux section.
3
From the Flux type list, choose Convective heat flux.
4
Locate the Boundary Selection section. From the Selection list, choose Pin Surface.
5
Locate the Heat Flux section. In the h text field, type 15.
6
In the Text text field, type 20[degC].
Surface-to-Ambient Radiation 1
1
In the Physics toolbar, click  Boundaries and choose Surface-to-Ambient Radiation.
2
In the Settings window for Surface-to-Ambient Radiation, locate the Boundary Selection section.
3
From the Selection list, choose Pin Surface.
4
Locate the Surface-to-Ambient Radiation section. From the ε list, choose User defined. In the associated text field, type 0.8.
5
In the Tamb text field, type 20[degC].
Solid Mechanics (solid)
1
In the Model Builder window, under Component 1 (comp1) click Solid Mechanics (solid).
2
In the Settings window for Solid Mechanics, locate the Domain Selection section.
3
From the Selection list, choose Pin.
Linear Elastic Material 1
In the Model Builder window, under Component 1 (comp1) > Solid Mechanics (solid) click Linear Elastic Material 1.
Plasticity 1
1
In the Physics toolbar, click  Attributes and choose Plasticity.
2
In the Settings window for Plasticity, locate the Plasticity Model section.
3
Find the Isotropic hardening model subsection. From the list, choose Hardening function.
Symmetry Plane 1
1
In the Physics toolbar, click  Boundaries and choose Symmetry Plane.
2
Select Boundary 2 only.
Austenite Decomposition (audc)
1
In the Model Builder window, under Component 1 (comp1) click Austenite Decomposition (audc).
2
In the Settings window for Austenite Decomposition, locate the Domain Selection section.
3
From the Selection list, choose Pin.
4
Locate the Solid Mechanics section. Select the Enable phase plasticity checkbox.
5
From the Thermal strain formulation list, choose Density based.
6
Locate the Material Properties section. Click Create Compound Material in the upper-right corner of the section.
Materials
Air (mat1)
1
In the Model Builder window, under Component 1 (comp1) > Materials click Air (mat1).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Air.
Copper (mat2)
1
In the Model Builder window, click Copper (mat2).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Coil.
Compound Material (mat9)
1
In the Model Builder window, click Compound Material (mat9).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Pin.
General Steel, Effective Properties (mat8)
In the Model Builder window, under Component 1 (comp1) > Materials right-click General Steel, Effective Properties (mat8) and choose Merge Into > Compound Material (mat9).
Austenite Decomposition (audc)
Austenite
1
In the Model Builder window, under Component 1 (comp1) > Austenite Decomposition (audc) click Austenite.
2
In the Settings window for Metallurgical Phase, locate the Initial Phase Fraction section.
3
In the ξ0 text field, type 0.
4
Locate the Phase Material section. From the Phase material list, choose General Steel, Austenite (mat3).
5
Locate the Electromagnetic Properties section. From the εr list, choose User defined. Locate the Mechanical Properties section. From the Isotropic hardening model list, choose Hardening function.
Ferrite
1
In the Model Builder window, click Ferrite.
2
In the Settings window for Metallurgical Phase, locate the Initial Phase Fraction section.
3
In the ξ0 text field, type 0.5.
4
Locate the Phase Material section. From the Phase material list, choose General Steel, Ferrite (mat4).
5
Locate the Electromagnetic Properties section. From the εr list, choose User defined. Locate the Mechanical Properties section. From the Isotropic hardening model list, choose Hardening function.
Pearlite
1
In the Model Builder window, click Pearlite.
2
In the Settings window for Metallurgical Phase, locate the Initial Phase Fraction section.
3
In the ξ0 text field, type 0.5.
4
Locate the Phase Material section. From the Phase material list, choose General Steel, Pearlite (mat5).
5
Locate the Electromagnetic Properties section. From the εr list, choose User defined. Locate the Mechanical Properties section. From the Isotropic hardening model list, choose Hardening function.
Bainite
1
In the Model Builder window, click Bainite.
2
In the Settings window for Metallurgical Phase, locate the Phase Material section.
3
From the Phase material list, choose General Steel, Bainite (mat6).
4
Locate the Electromagnetic Properties section. From the εr list, choose User defined. Locate the Mechanical Properties section. From the Isotropic hardening model list, choose Hardening function.
Martensite
1
In the Model Builder window, click Martensite.
2
In the Settings window for Metallurgical Phase, locate the Phase Material section.
3
From the Phase material list, choose General Steel, Martensite (mat7).
4
Locate the Electromagnetic Properties section. From the εr list, choose User defined. Locate the Mechanical Properties section. From the Isotropic hardening model list, choose Hardening function.
General Steel, Austenite to Ferrite
1
In the Model Builder window, right-click Austenite Decomposition (audc) and choose Import Phase Transformations.
2
Browse to the model’s Application Libraries folder and double-click the file induction_hardening_of_a_cylindrical_pin_JMatPro_general_steel.xml.
3
In the Settings window for Phase Transformation, locate the Phase Transformation section.
4
From the ξs list, choose Austenite.
5
From the ξd list, choose Ferrite.
General Steel, Austenite to Pearlite
1
In the Model Builder window, click General Steel, Austenite to Pearlite.
2
In the Settings window for Phase Transformation, locate the Phase Transformation section.
3
From the ξs list, choose Austenite.
4
From the ξd list, choose Pearlite.
General Steel, Austenite to Bainite
1
In the Model Builder window, click General Steel, Austenite to Bainite.
2
In the Settings window for Phase Transformation, locate the Phase Transformation section.
3
From the ξs list, choose Austenite.
4
From the ξd list, choose Bainite.
General Steel, Austenite to Martensite
1
In the Model Builder window, click General Steel, Austenite to Martensite.
2
In the Settings window for Phase Transformation, locate the Phase Transformation section.
3
From the ξs list, choose Austenite.
4
From the ξd list, choose Martensite.
Austenitization
1
In the Physics toolbar, click  Domains and choose Phase Transformation.
2
In the Settings window for Phase Transformation, type Austenitization in the Label text field.
3
Locate the Phase Transformation section. From the ξs list, choose Ferrite.
4
From the ξd list, choose Austenite.
5
From the Phase transformation model list, choose Linear.
6
In the Tl text field, type 723[degC].
Additional Source Phase 1
1
In the Physics toolbar, click  Attributes and choose Additional Source Phase.
2
In the Settings window for Additional Source Phase, locate the Additional Source Phase section.
3
From the ξs list, choose Pearlite.
Magnetic Fields (mf)
Initial Values 1
1
In the Model Builder window, under Component 1 (comp1) > Magnetic Fields (mf) click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
Specify the A vector as
1e-8*sqrt(r^2+z^2)
phi
Coil 1
1
In the Model Builder window, click Coil 1.
2
In the Settings window for Coil, locate the Domain Selection section.
3
From the Selection list, choose Coil.
4
Locate the Coil section. From the Conductor model list, choose Homogenized multiturn.
5
In the Icoil text field, type current(t).
6
Locate the Homogenized Conductor section. In the N text field, type 20.
Ampère’s Law in Solids 1
1
In the Physics toolbar, click  Domains and choose Ampère’s Law in Solids.
2
In the Settings window for Ampère’s Law in Solids, locate the Domain Selection section.
3
From the Selection list, choose Pin.
Symmetry Plane 1
1
In the Physics toolbar, click  Boundaries and choose Symmetry Plane.
2
In the Settings window for Symmetry Plane, locate the Boundary Selection section.
3
From the Selection list, choose Symmetry Plane.
4
Locate the Symmetry Plane section. From the Symmetry type for the magnetic flux density list, choose Antisymmetry.
Mesh 1
Mapped 1
1
In the Mesh toolbar, click  Mapped.
2
In the Settings window for Mapped, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Coil.
Distribution 1
1
Right-click Mapped 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Distribution section.
3
In the Number of elements text field, type 6.
4
Select Boundary 11 only.
Distribution 2
1
In the Model Builder window, right-click Mapped 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Distribution section.
3
In the Number of elements text field, type 30.
4
Select Boundary 12 only.
Distribution 1
1
In the Model Builder window, right-click Mesh 1 and choose Distribution.
2
Select Boundary 7 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
In the Number of elements text field, type 60.
Distribution 2
1
Right-click Mesh 1 and choose Distribution.
2
Select Boundary 4 only.
3
In the Settings window for Distribution, locate the Distribution section.
4
In the Number of elements text field, type 10.
Size 1
1
Right-click Mesh 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Pin.
5
Locate the Element Size section. From the Predefined list, choose Extremely fine.
Boundary Layers 1
1
In the Mesh toolbar, click  Boundary Layers.
2
In the Settings window for Boundary Layers, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Pin.
Boundary Layer Properties
1
In the Model Builder window, click Boundary Layer Properties.
2
In the Settings window for Boundary Layer Properties, locate the Boundary Selection section.
3
From the Selection list, choose Pin Surface.
4
Locate the Layers section. From the Thickness specification list, choose All layers.
5
In the Total thickness text field, type 0.001.
Free Triangular 1
1
In the Mesh toolbar, click  Free Triangular.
2
In the Settings window for Free Triangular, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
From the Selection list, choose Air.
Study 1
Step 1: Frequency–Transient
1
In the Model Builder window, under Study 1 click Step 1: Frequency–Transient.
2
In the Settings window for Frequency–Transient, locate the Study Settings section.
3
In the Output times text field, type range(0,0.1,tEnd*10).
4
In the Frequency text field, type 120[kHz].
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node, then click Compile Equations: Frequency–Transient.
3
In the Settings window for Compile Equations, locate the Study and Step section.
4
Select the Split complex variables in real and imaginary parts checkbox.
5
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) right-click Time-Dependent Solver 1 and choose Segregated.
6
In the Settings window for Segregated, locate the General section.
7
From the Stabilization and acceleration list, choose Anderson acceleration.
8
In the Maximum number of iterations text field, type 50.
9
In the Model Builder window, expand the Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 > Segregated 1 node, then click Segregated Step.
10
In the Settings window for Segregated Step, locate the General section.
11
In the Variables list, choose Phase Fractions (comp1.audc.phasefractions), Phase Transformation Strains (comp1.ptstr1.ptstrains), Time at Previous Step (comp1.ptstr1.t_old), Temperature (comp1.T), and Displacement Field (comp1.u).
12
Under Variables, click  Delete.
13
Click to expand the Method and Termination section. From the Nonlinear method list, choose Backtracking (Newton).
14
From the Jacobian update list, choose On every iteration.
15
From the Termination technique list, choose Iterations or tolerance.
16
In the Number of iterations text field, type 100.
17
In the Tolerance factor text field, type 1.
18
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 right-click Segregated 1 and choose Segregated Step.
19
In the Settings window for Segregated Step, locate the General section.
20
Under Variables, click  Add.
21
In the Add dialog, in the Variables list, choose Phase Fractions (comp1.audc.phasefractions), Phase Transformation Strains (comp1.ptstr1.ptstrains), Time at Previous Step (comp1.ptstr1.t_old), Temperature (comp1.T), and Displacement Field (comp1.u).
22
Click OK.
23
In the Settings window for Segregated Step, locate the Method and Termination section.
24
From the Nonlinear method list, choose Automatic (Newton).
25
From the Termination technique list, choose Iterations or tolerance.
26
In the Number of iterations text field, type 10.
27
In the Tolerance factor text field, type 1.
28
In the Study toolbar, click  Compute.