Modelling, Linearity Analysis and Optimization of an Inductive Angular Displacement Sensor Based on Magnetic Focusing in Ships

Abstract

A sensor for measuring the crankshaft angle of the main engine in ships is designed. Compared with the existing crankshaft angle encoder, this design’s advantage is that there is no need to add a gear system at the free end of the crankshaft, reducing machining complexity. The purpose of providing high angle resolution over a wide speed range is achieved. Inductive angular displacement sensors (IADSs) require an eddy current magnetic field as a medium to generate the induced voltage. The induced voltage also requires a complex linearization calculation to obtain a linear relationship between angle and voltage. Therefore, a model of the inductive angular displacement sensor based on magnetic focusing (IADSMF) is proposed. Magnetic focusing is introduced into the IADS to replace the eddy current magnetic field with a focusing magnetic field. The main disadvantage of traditional IADSs, which is that they cannot reduce the eddy current magnetic field, is mitigated. An approximate square−shaped focusing magnetic field (12.4 × 12.4 mm2) is formed using the magnetic field constraint of the magnetic conductor. When the receiving coil undergoes a position change relative to the square−shaped focusing magnetic field, the voltage generated via the receiving coil is measured using the electromagnetic induction principle to achieve angular displacement measurement. A mathematical model of the IADSMF is derived. Induced voltages at different frequencies and rotational speeds are simulated and analyzed via MATLAB. The results show that frequency is the main factor affecting the induced voltage amplitude. The sensitivity of the IADSMF is 0.2023 mV/°. The resolution and measurement of the IADSMF range from 0.06° and 0–360°. Compared with a conventional planar coil−based IADS, the eddy current loss is reduced from 2.1304 to 0.3625 W. Direct linearization of the angular displacement with the induced voltage is achieved through designing a square−shaped focusing field and receiving coil. After optimizing the sensor structure with the optimization algorithm, the linearity error is 0.6012%. Finally, this sensor provides a theoretical basis and research ideas for IADS development in ships and navigation.