# Methods and Means of Eddy Current Testing of Soldered Lap Joints of Electrical Machines
## 2 Materials and Methods
### Finite Element Model of ECP and TO Interaction  
Designing the ECP is generally conducted using different methods: analytical calculation and modeling by the finite difference method and finite element method, each of which has its own features [39; 40; 41]. In order to obtain a precise model of the ECP and TO interaction, the finite element method (FE) was chosen to calculate the parameters of the sensor for testing solder joints [42]. The model of the TO is a horizontally located soldered lap joint of two plates. The overlapping area of the two plates is the tested zone. The test parameter is the soldering integrity of the joint, expressed as the ratio of the actual area of electrical contact between the plates to the overlapping area of the plates. The expected defect is dry solder in the tested zone, whereas both the size and position of the defect within the tested zone are important. For this reason, two types of defects are considered: a defect along the side wall (Figure 3a) and a defect along the end (Figure 3b) [4]. Based on the presented idea, an ECP for testing the soldered lap joints was designed, consisting of two elements located on different sides of the TO symmetrically relative to solder plane (Figure 4). Each element includes four main tangentially positioned coils: excitation, measuring, shielding, and compensation coils. Figure 3: Models of defect simulators: (**a**)—TO with a model of a soldering defect along the side wall; (**b**)—TO with a model of a soldering defect along the end. The electrical circuit of the ECP is shown in Figure 5. The excitation signal in a sine waveform goes from the outputs of the digital-to-analog converter to the amplifiers of the circuit, with the excitation coils and shielding coils connected in series. In the circuit, the measuring coils and compensation coils connected in series are connected to the measuring signal amplifier. Figure 4: Close-up of ECP coils and TO: 1—excitation coils; 2—measuring coils; 3—shielding coils; 4—compensation coils; 5—TO [4]. Figure 5: Electrical schematic diagram of ECP [4]. The synchronous detector receives a signal from the measuring signal amplifier and the phase-shifting circuit, in which, by shifting the phase of the excitation signal by \(-45^{\circ}\) and \(+45^{\circ}\), a reference signal is formed. In the synchronous detector, real and imaginary components extracted from the measurement signal pass through low-pass filters for the removal of harmonics at the excitation frequency. The amplitude values of the filtered real and imaginary components of the measurement signal are fed to the microcontroller via analog-to-digital converters. The excitation winding consists of 8 coils connected in series. Between the excitation coils are gaps designed to generate magnetic flux leakage, which, penetrating the test object, induces eddy currents in it. Without these gaps, the magnetic field of the excitation and shielding coils would mostly penetrate the coils themselves, similar to how the magnetic field inside a toroidal coil does not extend beyond its dimensions. In the gaps between the excitation coils and coaxially to them are placed 7 measuring coils connected in series. Compensation coils are wound on top of the shielding coils to separate the informative parameter of the ECP signal on the TO from the ECP signal in the air. To solve the problem of shielding from the influence of adjacent current-carrying busbars on ECP measurement results, the classical method of coil shielding using a ferromagnetic shield is not applicable because coils are positioned tangentially relative to the installation plane of the ECP. Shielding is achieved by using additional shielding coils located on the outer sides of the ECP. In each element of the ECP, a shielding coil is placed above an array of excitation and measuring coils and is connected inversely to excitation coils. Excitation coils create tangential magnetic field, inducing eddy currents in the TO.