# The Design of a System for the Induction Hardening of Steels Using Simulation Parameters
## 3 Results and Discussion  
It was concluded that the initial parameters were satisfactory for a relatively faithful representation of the waveforms from the experiment, using the iterative method of changing the value of the resistance and inductance of the series branch in the simulation model. A further increase in the resistive load would reduce the voltage on the inductor. A further increase in the inductive load would change the resonant frequency of the oscillator circuit vitally, and the waveforms would change their appearance more drastically. The experiments were performed at different voltage values on the DC link and the same inductor, as described previously, but the optimization was performed at V\({}_{\text{DC}}\) = 250 V. Firstly, the experimental results will be presented, followed by the simulation results for the same experimental conditions. The additional measuring equipment is shown in Table 1.  
A corresponding graph of the voltage and current waveforms of the inductor at a DC link voltage of 250 V, with the values of the relevant parameters, is shown in Figure 8. \begin{table}
\begin{tabular}{c c} \hline \hline
**Measurement** & **Equipment** \\ \hline V, I, R, L & 0.1\% class instruments \\ Waveform, frequency & Oscilloscope ROHDE \& CHWARZ RTB2004 (Munich, Germany) \\ Power (active, reactive) & Digital Energy meter Saving Electronics DTSU 1218 (Jiangsu, China) \\ Temperature & Thermography camera FLIR T420, FLIR Systems, Inc., \\  & (Santa Barbara, CA, USA) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The additional measuring equipment. Figure 7: Simplified diagram of a half-bridge resonant inverter. The yellow line indicates the voltage and the green line indicates the current. The circuit operated at a frequency of 11.22 kHz. In Figure 8, perceptibly, the amplitude of the voltage on the inductor was about 610 V, while the amplitude of the current was about 155 A. Under the mentioned conditions in the experiment, the current from the network was 36 A, and the measured active power was P = 3360 W.  
Figure 8 also shows that the circuit in the experiment was operating at a frequency lower than the resonant frequency. Due to the fact that the DC link voltage is constant, setting the operating frequency closer or further from the resonant frequency is an efficient way to control the output power. The results of the transient analysis of the simulated circuit under the same conditions as in the experiment are shown in Figure 9.  
Figure 8: Measured voltage and current waveforms from the experiment. Figure 9: Simulated waveforms of the voltage and current of the inductor at the voltage of the DC intermediate circuit (250 V) and the pulse width modulation frequency (11.22 kHz \(<\) freez = 11.68 kHz). In addition to the qualitative comparison (signal shape, for example), a quantitative comparison of the characteristic values was performed, and they are shown in Table 2.  
Assuming that the actual resistance of the batch is equal to the calculated one, the efficiency coefficient of the system would be about 76.6%. Parasitic effects significantly influence that factor, so the actual value lies in the interval between 75.3% and 95.1%. Maximum efficiency is achieved in optimal conditions, as described in 2.3. The parameters obtained in this research in comparison with related research results are shown in Table 3[35; 37]. A series of images were taken with a thermal imaging camera in order to form the heating curves of the batch. One of the images from the thermal imaging camera is shown in Figure 10, showing that the steel reached a temperature of 680 \({}^{\circ}\)C. The temperature ranged from 211.4 \({}^{\circ}\)C to 904.2 \({}^{\circ}\)C (Figure 11). Based on the graph, it can be estimated that the temperature would enter a stationary state under the mentioned conditions. After a few minutes, it would remain at a value of about 1000 \({}^{\circ}\)C. A photo of the red-hot steel in the process of hardening is given in Figure 12.