INVESTIGATION OF NON IDEALITY EFFECTS ON AN INDUCTIVE POSITION SENSOR BASED ON EDDY CURRENTS USING NUMERICAL METHODS

This research describes methods in investigating non-idealities on Inductive Position Sensors (IPSs) using numerical method casted in the Discrete Geometric Approach (DGA). These sensors are able to provide position information by means of eddy currents generated on a metallic moving object called target. The positions are retrieved by computing the induced voltages picked from two receivers placed at an operative air gap from the moving object. Being the working principle of the sensor based on the eddy currents firstly a Magneto Quasi-Static (MQS) problem has to be solved. We provide a simulation tool based on the Boundary Integral Method (BIM) to predict the performance of the sensor in terms of linearity error. The advantage with respect to the Finite Element Method (FEM) is that the number of Degrees of Freedom (DoFs) concerns only the conductor. The results validate the methodology, showing that measured linearity errors match simulated values. Secondly, the fact that the stiffness matrix is fully populated put a limit in the size of the problem to treat. To overcome this limit, we speed up the solution of the system using the Gauss-Seidel (GS) iterative techniques and the Fast Multipole Method (FMM). The dissipated power computed when the FMM is applied is in agreement with the one computed analytically. Thirdly, a novel methodology to optimize the design of a ratiometric rotary IPS fabricated in Printed Circuit Board (PCB) technology. The optimization aims at reducing the linearity error of the sensor and amplitude mismatch between the voltages on the two receiving (RX) coils. Distinct from other optimization techniques proposed in the literature, the sensor footprint and the target geometry are considered as a nonmodifiable input. This is motivated by the fact that, for sensor replacement purposes, the target has to fit a predefined space. For this reason, the shape of the RX coils is modified in order to reproduce the theoretical coil voltages as much as possible. The optimized RX shape was obtained by means of a non-linear least-square solver. Comparisons between simulations and measurements performed on different prototypes of an absolute rotary sensor show the effectiveness of the optimization tool. The optimized sensors exhibit a linearity error below 0.1% of the Full Scale (FS) without any signal calibration or post-processing manipulation. Then, we show that each target–receiver pair needs the adoption of a different reconstruction formula for the identification of the target position, whereas in the literature the usual inverse tangent function is applied for every possible pair. We seek the target–receiver pair that maximizes the amplitude of the induced voltages on the receivers. The results show that to achieve the maximum value of the induced voltages, the best choice is to have a rectangular target and rectangular receivers. To verify these facts, a simulation and optimization method has been applied to the rectangular receiver coils on two rotary IPS realized with PCB technology. This assures a theoretical increment of the induced voltage of more than 57\% with respect to the commonly used sinusoidal receivers. Finally, we show for the first time that the rotary IPS has the potential to provide information about not only about the position but also deviations from the normal operating region due to physical misalignments. We use supervised learning techniques such as Random Forest (RF) regressor to predict rotor shaft misalignments based on induced voltages on receivers. The model determines both the directions and magnitudes of these anomalies The measurements confirm the effectiveness of this methods showing the detected misalignments and the accuracy of the model.