# Retractable Wireless Charging Windings for Inspection Robots
## 4 Experimental Setup and Measurements  
A series of laboratory-based experiments were conducted to validate the performance of the proposed retractable WPT system. These experiments aimed to characterize the system's energy transfer efficiency under various alignment conditions and to compare the empirical results with simulation predictions. All measurements were performed in a controlled indoor laboratory environment at a stable ambient temperature of 22 \(\pm\) 1 \({}^{\circ}\)C. The tests were carried out away from metallic infrastructure and high-frequency switching equipment to minimize electromagnetic interference. Both the transmitter and receiver coils were supported on non-conductive platforms to ensure accurate magnetic coupling. For angular misalignment tests, the receiver coil was mounted on a rotatable platform with angular markers, enabling consistent adjustments with a tolerance of \(\pm\)1\({}^{\circ}\). The instrumentation setup included a digital oscilloscope for voltage and current waveform acquisition, combined with a Rogowski coil for current sensing and high-voltage probes. The oscilloscope has an accuracy of \(\pm\)1% for RMS measurements. A precision LCR meter was used to measure the self-inductance and mutual inductance of the coils, with an accuracy of \(\pm\)0.5%. Distance offsets were measured using a digital caliper with \(\pm\)0.01 mm resolution, while the coil positioning was guided by physical alignment jigs to reduce operator error. The ID of the components from manufacturers are listed in Table 4.  
Each measurement was repeated three times under identical boundary conditions. The average values of the repeated measurements were reported, and standard deviations were used to indicate data variability. For results involving critical parameters such as energy efficiency and mutual inductance, error bars representing \(\pm\)1 standard deviation are included in the corresponding figures in the next section. These repetitions were essential for mitigating random variation introduced by minor mechanical instabilities or probe repositioning. Measurement uncertainty was analyzed using a first-order error propagation method. The cumulative uncertainty in energy efficiency was estimated to be approximately \(\pm\)2.5%, considering the voltage, current, and phase measurement accuracies. For coil inductance values, measurement uncertainty remained within \(\pm\)0.5% as reported by the instrument specification. Litz wire was used as the main material of the coil and wrapped around the coil frame in five turns. The gap between each turn of the coil was designed to be approximately 10 mm apart to reduce the skin effect. The coil turn was held together with Kapton tape for coil management, reducing entanglement during extension and retracting the motion of the retractable square coil (SC-WPT). Figure 10 shows the abstract of the experimental setup using a half-bridge driver board connected to the SC-WPT system. Both Tx and Rx are set to be square coils, with Tx being a fixed square coil, while Rx is the retractable square coil. \(C_{p}\), \(C_{s}\), \(L_{p}\), and \(L_{s}\) are the compensation capacitors, and self-inductance for primary and secondary coil, respectively. \(M_{ps}\) is the mutual inductance. The lateral misalignment \(d\) is set to 0.4, 0.6, 0.8 and 1.0 m along the x-axis. The angular misalignment is set to 0\({}^{\circ}\)