In order to overcome the limitations named in the previous section, a new hardware for the voltage supply of the air coil is necessary. As it was mentioned, NDT based on electromagnetic induction usually uses analog amplifiers or induction generators [15]. These converter topologies have the advantage that they can create an output voltage with a low Total Harmonic Distortion (THD). Thus, no additional filter is necessary to create a sinusoidal output voltage. In the present application, where an air coil is used to induce eddy currents in a steel structure, a low THD value does not result in any usable benefits.
Moreover, in order to build a portable system for NDT in real time a small and light system is desirable. Both converters, the analog amplifier and the induction generator, are very bulky and heavy. Hence, they are not suitable to build a portable test setup. Another important criterion for portable systems is the system efficiency because usually only a limited amount of energy is available in situ, such as bridges or off shore structures. Thus, a switched-mode converter topology, the H-Bridge converter, is developed for the given application.
The H-Bridge Converter
There are several requirements for the developed hardware. The initial goal is to achieve a high efficiency so that a battery-based system can be designed. Since a portable system is developed, the used voltage level should below 120 V so that the system is a protective low voltage system and thus no additional safety concepts are necessary. In previous tests with an 1200 V converter, it was shown that a voltage between 80 and 100 V is sufficient for an NDT based on electromagnetic induction [25]. Besides, the size and weight of the system are also important, because a hand-held system should be designed which must be used in areas difficult to access. Furthermore, the coil structure and also the behavior of different materials are part of the investigation, so a variable system must be developed that is able to adjust the output current and frequency as well as the modes of operation. To satisfy all these requirements, an H-Bridge converter is developed according to the schematic shown in Fig. 2. The H-Bridge converter contains three parts: the Human Machine Interface (HMI), the signal processing part and the power electronics part. The power electronics part consists of the MOSFETs \(T_1\)–\(T_4\), the gate-drivers, the heatsink and DC-link capacitors. For the signal processing part a proprietary MAX10 board [26] is used.
On this board, the FPGA 10M08SAE144C8G from Intel is implemented. The FPGA has several tasks: It controls the operation mode of the MOSFET H-Bridge, it communicates via Fiber Optic Cables (FOC) with a central PC to facilitate automatic measurement routines controlled by the PC, it controls the heatsink temperature of the MOSFET H-Bridge and finally it reacts on the commands of the user via the Human Machine Interface (HMI) of the converter. Thus, the H-Bridge converter can be controlled by the PC or manually over the HMI of the converter. By means of the HMI, the user can adjust the frequency of the output voltage, the voltage waveform and the operation mode. The developed prototype with the implemented HMI is shown in Fig. 3. The prototype has a length of \(L = 20\) cm, a width of \(W = 10\) cm and a height of \(H = 7\) cm. The weight of the prototype is 850 g in combination with commercial available 120 V batteries with 360 W h and a weight of 1.9 kg the whole system has only a weight of 2.75 kg.
As can be seen in Fig. 3, the power electronics part is enclosed by the housing of the prototype and only the HMI and the MAX10-board are freely available.
To reach a high system efficiency, the design of this power electronics part is crucial. Therefore, the different operation modes of the converter has to be considered. Hence, the different operation modes are first discussed in the following, before the design of the power electronics part is described.
Operation Modes of the H-Bridge Converter
The H-Bridge converter has two basic parameters: the switching frequency \(f_\mathrm {sw}\) and the phase shift \(\beta \). It operates with a switching frequency \(f_\mathrm {sw}\) between 50 and 100 kHz with fundamental frequency pulse. To adjust the amplitude of the output voltage \(V_\mathrm {out}\) and thus the output current \(I_\mathrm {out}\), a phase shift method with the phase shift \(\beta \) is utilized. In Fig. 4 the output voltage \(V_\mathrm {out}\) and the output current \(I_\mathrm {out}\) for a phase shift \(\beta =\pi /2\) and \(\beta =\pi \) is shown for an ideal air coil with \(R_\mathrm {eq} = {0}\varOmega \). The voltage \(V_\mathrm {a}\) and \(V_\mathrm {b}\) are the voltages of one phase leg, as can be seen in Fig. 2. The highest current occur for \(\beta =\pi \).
Four different operating modes are superimposed on these two basic parameters: continuous mode, pulse mode, sweep mode and combination mode. In the continuous mode, the switching frequency and the phase shift are adjust and the output is activated.
In the pulse mode, the output switches between two different phase shifts \(\beta _1\) and \(\beta _2\). The switching frequency \(f_\mathrm {sw}\) is constant. The time period within the inverter uses one phase shift is defined by the number of switching periods per phase shift. In Fig. 5 the measured output current \(I_\mathrm {out}\) for an exemplary operation in pulse mode is illustrated.
In sweep mode, a phase shift \(\beta \), a start frequency \(f_\mathrm {sw,1}\) and a stop frequency \(f_\mathrm {sw,2}\) are defined. The switching frequency \(f_\mathrm {sw}\) is swept up and down between start and stop frequency with a defined frequency step \(\varDelta f_\mathrm {sw}\). For each frequency, a defined number of periods is used before the inverter makes a frequency step.
The last mode is the combination mode. In this mode a phase shift \(\beta \) for one time interval is defined, in the second time interval \(\beta = 0\). Also, a start frequency \(f_\mathrm {sw,1}\) and a stop frequency \(f_\mathrm {sw,2}\) are specified. For each pulse period a different switching frequency is used. As in sweep mode, the number of periods per frequency and the frequency step \(\varDelta f_\mathrm {sw}\) are specified. This mode is used to find the optimal switching frequency for the given steel specimen and coil configuration.
Design of the Power Electronics Part
For the design of the power electronics, the working point with the highest current must considered. As mentioned above, the highest current occur for a phase shift of \(\beta = \pi \). In addition to the phase shift, the switching frequency \(f_\mathrm {sw}\), the distance between air coil and the steel specimen \(h_\mathrm {c,s}\), the material of the specimen and the coil configuration must also be taken into account. The coil configuration itself has the following parameter: coil diameter \(d_\mathrm {cl}\), the number of windings \(w_\mathrm {cl}\) and wire diameter \(d_\mathrm {w}\). To identify the worst case operation point, a magnetic analysis of the test scenario is performed with Flux2D, varying the distance between specimen and coil \(h_\mathrm {c,s}\), the coil diameter \(d_\mathrm {cl}\) and the specimen material, i.e. the specific electrical resistance \(\rho \) and the relative permeability \(\mu _\mathrm {r}\). The number of windings \(w_\mathrm {cl}\) is defined to the minimum of ten. The distance \(h_\mathrm {c,s}\) is varying between 4 and 40 mm, the coil diameter \(d_\mathrm {cl}\) between 100 and 250 mm, the specific electrical resistance between 0.4 and 0.8 \(\Omega \) mm\(^2\)/m and the relative permeability between 500 and 1500 which are typical values for used steel types. The modification of the distance \(h_\mathrm {c,s}\) has no crucial impact on the maximum current value since the inductive behavior is dominant. The variation of the coil diameter \(d_\mathrm {cl}\) strongly influences the maximum current, with the smallest diameter causing the highest current, as be shown in Fig. 6b. Thus, the material modification is analyzed with the smallest distance \(h_\mathrm {c,s}\) and smallest coil diameter \(d_\mathrm {cl}\). In Fig. 6a the analyzed test scenario in Flux2D, in Fig. 6c the resulting current for different specific electrical resistance \(\rho \) and in Fig. 6d for different relative permeability \(\mu _\mathrm {r}\) are illustrated. As can be seen, the current is nearly triangular and the maximum amplitude of the output current \(\hat{I}_\mathrm {out}\) is 26 A for an specific electrical resistance \(\rho \) of 0.4 \(\Omega \) mm\(^2\)/m and a relative permeability \(\mu _\mathrm {r}\) of 1500.
According to Fig. 6c, d, the change in electrical resistance \(\rho \) and relative permeability \(\mu _\mathrm {r}\) has almost no effect on the current. This can be explained by the fact that the path of the magnetic field is mainly in the air and thus the magnetic resistance of the air \(R_{m,a}\) is dominant. Hence, a change of the material or rather the magnetic resistance of the material \(R_{m,m}\) does not have a crucial impact on the resulting current.
With the knowledge of the output current, a loss analysis of the MOSFETs is possible. The losses are calculated according to [27]. The analysis is done with two Si-MOSFETs and one SiC-MOSFETs. The 150 V Si-MOSFET “FDH055N15A” generates total power losses of 25 W, the 200 V Si-MOSFET “IXTP150N15X4” 26 W and the 650 V SiC-MOSFET “C3M0015065D” 37 W. Hence, the system is build with the 150 V Si-MOSFET “FDH055N15A”. Besides the MOSFETs, also the DC-link capacitor is crucial, because the main part of the output current \(I_\mathrm {out}\) is reactive current and oscillated between the DC-link capacitor and the air coil. The RMS-current of the DC-link capacitor is about 20 A. Hence, four 200 V aluminum electrolytic capacitors with a maximum RMS current of 5.25 A are used.
By means of the developed H-Bridge converter in combination with the 360 W h battery and assuming that the average power consumption of the specimen is 200 W, a portable system is available that can be used for about one hour on one charge.
Steel Specimens
In order to prevent structural damages and to reduce the cost of maintenance, it is very important to detect small cracks or defects in weld seams and geometrical notches of fatigue loaded steel structures.
During the experiments one specimen made of steel S355J2+N has been used, its geometry shown in Fig. 7 is the same as the specimen used in the research presented in [28].
The specimen is 10 mm thick and has a small fatigue crack at the notch. The crack was generated by a high cycle fatigue test, and it has a length of 24 mm and has a CMODFootnote 1 of around 25 \(\upmu \)m, see Fig. 8.