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Hardening of sphere by induction heating

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Induction heating explained

Induction heating is an accurate, fast, repeatable, efficient, non-contact technique for heating metals or any other electrically-conductive materials. By applying a high-frequency alternating current to an induction coil, a time-varying magnetic field is generated. The material to be heated is placed inside the magnetic field, without any contact to the coil. The alternating electromagnetic field induces eddy currents in the workpiece (material to be heated), resulting in resistive losses, which will be converted to heat inside the workpiece. Ferrous metals are heated by induction more easily than other materials due to the generated heat by hysterisis loss. Figure 1 shows a typical induction heating setup.
In this example, we show you how to simulate hardening of a sphere inside a coil using EMS coupled to thermal analysis.

Induction heating setup

Figure 1 - Induction heating setup

Electromagnetic-Thermal coupling capability of EMS 

EMS ensures a Multi-physics simulation by the capability of coupling between electro-magnetic- structural- thermal field. In our case, an electro-magnetic- thermal simulation was carried on. To solve an induction heating problem in time varying domain, a transient magnetic study coupled to thermal analysis in EMS is needed.                   

Problem description 

In this example, a sphere inside a coil will be heated by induction heating phenomenon. Figure 3 shows a 3D CAD of simulated model. The excitation waveform is sinusoidal and the frequency is 60 Hz. 

The simulated model

Figure 3 - The simulated model

Simulation setup

After creating an Transient Magnetic study coupled to thermal analysis in EMS, four important steps shall always be followed:

  1. apply the proper material for all solid bodies
  2. apply the necessary electromagnetic inputs
  3. apply the necessary thermal inputs
  4. mesh the entire model and run the solver


Both coil and sphere are made of copper.

Table1 -  Material properties

Components / Bodies Relative Permeability Electrical Conductivity Thermal Conductivity (W/m*K) Specific Heat (J/Kg*K) Masse Density (Kg/m^3)
Sphere/ Coil 1 5.840e+7 401 384 8960

Electromagnetic inputs

In this study, only a wound coil is assigned as electromagnetic input.

Table 2 -  Coil information
  Number of turns RMS total current
Wound coil 1000 6.468 A


Meshing is a very crucial step in any FEA simulation. EMS estimates a global element size for the model taking into consideration its volume, surface area, and other geometric details. The size of the generated mesh (number of nodes and elements) depends on the geometry and dimensions of the model, element size, mesh tolerance, and mesh control. In the early stages of design analysis where approximate results may suffice, you can specify a larger element size for a faster solution. For a more accurate solution, a smaller element size may be required.

Meshed model
Figure 4 - Meshed model

Electromagnetic-thermal results 

After finishing the setup, a successful run of Transient Magnetic simulation coupled to thermal analysis generates both magnetic and thermal transient results.

In the figure below is a 3D plot of magnetic flux density in the sphere at 50 ms. 

Magnetic flux density in the sphere at 50 ms.
Figure 5 - Magnetic flux density in the sphere at 50 ms.


In the figure 6,7, 3D plot of current density distribution shows the circulation of eddy current in the surface of sphere and figure 8 shows the temperature distribution in the sphere after 1.6 hour. 

Current density distribution in the sphere, section plot
Figure 6 - Current density distribution in the sphere, section plot

Eddy current animation in the sphere at 0.044 second
Figure 7 - Eddy current animation in the sphere at 0.044 second

Temperature in the sphere at 1.6 hour
Figure 8 - Temperature in the sphere at 1.6 hour 
Temperature evolution
Figure 9 - Temperature evolution 


The electro-thermal simulation capability in EMS enables users to effectively test their coil designs for induction heating application. Engineers can now simulate multiple designs of their coils and choose the most effective coil based on the component to be heated. By studying the temperature distribution inside the heated component, one can complete understand the heating profile.