Simulation
Simulations and numerical calculations
We use targeted calculation methods and numerical simulation tools to optimize the design of inductors, induction hardening processes and frequency converters as an energy source. Among other things, we use these to advise you on the feasibility of the induction heating process for your heat treatment requirements and to evaluate and optimize it in terms of efficiency and practical feasibility.
In the following, we explain the possible applications of our calculation methods and their advantages in connection with induction heating.
Take advantage of our expertise in simulations and numerical calculations. We offer these as a service – even independently of system-related inquiries and orders.
Overview: The principle of
induction heating
In heat treatment, heating using induction technology offers many advantages, including the fact that the heat is generated directly in the respective component. In comparison, heat treatment with ‘classic’ industrial furnaces requires a carrier medium in the furnace atmosphere in order to transfer the energy to the component by means of heat transfer.
There is one material requirement for induction heating: the component must be made of electrically conductive material. As many components are made of metal and almost all metals are electrically conductive, many components are suitable for induction heating. Other applications can also be found with non-metallic conductive materials such as glass or graphite.
To put it simply, inductive heating works like this:
- When an electrically conductive component is exposed to an alternating magnetic field, an electric current flows in it.
- As the material has a resistance, the induced current flow generates frictional losses and thus the desired component heating.
- Alternating current is used to increase the heating effect – and thus the efficiency of the current – in the component.
- The more often the current changes direction, the stronger the heating effect.
In addition to the shape of the inductor, the parameters used to tailor the heating effect to the desired result are, for example, the distance between the workpiece and the inductor (coupling distance), the use of concentrator material (field-conducting material for local amplification of the magnetic field), the frequency and the current intensity.
Excursus: Structure of an inductor
Every current-carrying conductor generates a magnetic field (see Fig. 1). This magnetic field can be represented using the so-called ‘three-finger rule’ (or ‘right-hand rule’): If you grasp the conductor with your right hand, the thumb points in the direction of the current and the curved fingers indicate the direction of the magnetic field lines.
To concentrate the magnetic field, for example, a copper conductor is wound into a cylindrical coil (see Fig. 2). The magnetic field is in the center of the coil and therefore the heating effect is particularly strong there.
Fig. 1: Every current-carrying conductor builds up a magnetic field.
Fig. 2: The magnetic field is amplified within a coil.
This inductor cylinder shape is particularly suitable for cylindrical workpieces such as shafts, pipes etc. due to its good coupling properties and high efficiency.
With inductive heating, the heating in the component results from
- the component itself – depending on its structure/geometry and
- the geometry of the inductor in combination with
- the frequency, the current strength and the time in which the current flows.
Numerical calculations using CAE
The type of heating described above is a complex and highly non-linear process. Various parameters and side effects must be taken into account, e.g. the generation of the magnetic field, the interaction with the component, also known as “coupling” of the magnetic field, the generation of induction currents in the component, the consideration of the current displacement effect (skin effect) as well as the penetration depth and temperature-dependent material properties.
These influences can be estimated using the empirical knowledge of process experts. Due to their complexity, however, these methods reach their limits. Modern calculation methods such as Computer Aided Engineering (CAE) offer the possibility of taking these complex relationships into account. For this purpose, a mathematical model of the induction process is created based on the CAD data and the process boundary conditions are defined for each component, such as
- Currents,
- Frequencies,
- electrical voltages and
- Material data.
The model is then meshed using the finite element method (FEM). Meshing (also known as discretization) is of great importance for a realistic calculation. In the process
- the element type,
- depending on the frequency, the refinement levels
- the outgoing and incoming electrical power lines and
- the airspace is discretized.
The induction process can then be calculated, taking heating and transport times into account (see Fig. 3).
Based on the model created, the strengths and advantages of CAE simulation come into play: time-, personnel- and material-intensive test series, such as achieving the optimum in terms of
- process efficiency,
- the frequency selection,
- of the coupling distance,
- of the concentrator material and
- the load on the inductor and
- the current density
can be carried out virtually with little effort. On the one hand, this leads to a deeper understanding of the processes and, on the other, to new insights and possibilities and a way of thinking “out of the box”. The questions of the
- Feasibility of the process
- Reasonableness of implementation by means of induction
- Optimization with regard to energy efficiency
- Homogeneous temperature distribution
- are also the focus here.
Simulations in the 3D printing use case
In additive manufacturing – i.e. the production of inductors using the 3D printing process – simulations also offer added value: a particularly promising inductor variant can be determined in advance of 3D printing using simulation. In addition to process reliability, this offers great advantages for targeted development “to the point” for both the energy supply and the process.
Simulations in the hardening application
In order to achieve a certain hardness in the component, the geometric penetration/heating depth is of decisive importance: only where the microstructure is austenitized (phase transformation from ferrite to austenite) and then cooled down considerably can the martensite microstructure be formed at all. Heating itself does not yet produce hardness, but it is the prerequisite for a hardening zone. The combination of strong heating and strong cooling can result in hardening (martensite structure). The geometric shape of the martensite zone and the absolute hardness are highly dependent on the application.
Martensite is characterized by high hardness and is often used in components that are exposed to tribological loads. Martensite-hardened components have excellent hardness values, which in turn enable high wear resistance.
Use of CAE for the design of the energy supply
The frequency is not a direct setting variable on the frequency inverter. It results from the resonant frequency of the resonant circuit, consisting of the inductance in the heating process and the installed capacitance in the power supply.
The frequency has a decisive influence on the position of the induced current and therefore on the generation of heat in the component. If the material of the component is known, the current penetration depth δ can be calculated using this calculation formula.
In addition to the material-specific parameters p and µr, the frequency is the only free variable. This means that the penetration depth decreases at high frequencies.
Fig. 4: Calculation formula for the current penetration depth; source: Schreiner, A; Irretier, O (ed.): Praxishandbuch Härtereitechnik; Vulkan-Verlag GmbH, 2013; p. 223
This can be seen schematically in Figure 5:
The field lines at low frequency are shown on the left and the field lines at high frequency in the center.
(Source: Schreiner, A; Irretier, O (ed.): Praxishandbuch Härtereitechnik; Vulkan-Verlag GmbH, 2013; p. 223)
The penetration depth can also be visualized in the calculation using CAE:
- Fig. 6 (left): Electromagnetic field at low frequency => Large penetration depth
- Fig. 7 (right): Electromagnetic field at high frequency => Small penetration depth
High frequency
Fig. 8:
Small penetration depth, current flows close to the contour
=> Heating of the tooth heads and tooth flanks
Low frequency
Fig. 9:
Large penetration depth, current flows at the base of the tooth
=> Heating at the base of the tooth
This means: For every
- Gear diameter,
- Gear height,
- Inductor shape and
- Inductor position
results are different for different heating times. This is where the strengths of the CAE come into play again.
The following example – an external field inductor fitted with a concentrator – can be used to illustrate the principle explained above in color in the CAE simulation for internal gearing:
For the relatively high frequency of 1,000 Hz, the tooth base is heated to the maximum. However, the tooth tip and tooth flank would not be hardened. This may be intentional.
Fig. 10: CAE / temperature at 1,000 Hz
If the frequency is increased to 200 kHz, the temperature pattern is mathematically different: Here, the tooth heads show the highest temperatures. In combination with prompt quenching, a hard martensitic structure could also be achieved at the high temperature. This temperature pattern would be much more suitable for high tribological loads, i.e. high forces and relative movements on the tooth flanks.
Fig. 11: CAE / temperature at 200 kHz
Experimental tests are of great importance for verifying the calculation results. Only when the experiment covers the calculated correlations can a “correct” CAE analysis be assumed in further analogous analyses. Fundamental verification tests are therefore necessary, especially for new types of calculations, new materials or innovative inductor shapes.
The penetration depth, depending on the frequency, was carried out on identical gearwheels for 20 kHz and 200 kHz respectively. The hardness zones visible in the figure below (see dark areas) were set using the same rapid cooling method.
In the example of 20 kHz (left), hardening close to the contour was achieved along the outer contour of the tooth.
On the right, only the tooth tips were hardened at a tenfold frequency of 200 kHz.
Fig. 12: Influence of frequency on the hardening zone using the example of a gear wheel
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Do you have questions about simulation processes or would you like to use our expertise for the optimum design of inductors and frequency converters? We will be happy to support you with your challenges. Contact us with your requirements.