This paper presents a comprehensive study of 3D magnetic field modeling for a Hall effect-based electromagnetic transducer designed for high-precision, non-contact measurement of ferromagnetic film thickness. The transducer features a solenoidal coil and a sensitive gold Hall plate, with the test material placed between them. Magnetic field interaction with the material causes measurable changes in Hall voltage, correlating with layer thickness. A simulation model was developed in ANSYS Maxwell to visualize magnetic field distribution and study its dependence on geometry, material properties, and sensor positioning. Simulations with and without the specimen allowed analysis of system sensitivity and resolution, leading to the identification of optimal design parameters. The study demonstrates improved es the importance of computational methods in the development, optimization, and validation of electromagnetic measurement systems. The integration of simulation tools enhances predictive capability and reduces reliance on costly experimental testing, making the approach valuable for industrial applications requiring precise, real-time thickness control.
Modern industrial production increasingly requires accurate and reliable sensors and quality assessment systems that are vital for productivity [1, 2]. The development of surface engineering technologies, in particular gas-thermal methods such as plasma and arc spraying, has led to the emergence of advanced coatings that require non-destructive and accurate thickness measurement. Among the most effective approaches are electromagnetic methods that provide high accuracy, operational reliability and seamless integration with automated production systems [3].
High-performance sectors such as aerospace and automotive often rely on multilayer coatings with distinct properties, making it essential to discriminate between layers while maintaining overall measurement accuracy. As these industries adopt Industry 4.0 strategies, the need for intelligent measurement systems with real-time feedback, predictive maintenance capabilities, and automated decision-making has grown. Electromagnetic approaches especially those based on the Hall effect are becoming indispensable in this evolving context.
The Hall effect, discovered by Edwin Hall in 1879, forms the physical basis for many modern electromagnetic sensors. When current flows through a conductor in a magnetic field, a voltage is generated that reflects the magnetic field strength. This measurement principle provides exceptional sensitivity to changes in coating thickness, while remaining robust to environmental influences and surface contamination that typically affect other measurement approaches. Modern Hall sensor technologies have achieved significant improvements in sensitivity, stability, and operating range through advanced semiconductor fabrication techniques and intelligent signal processing algorithms, as presented in the following publications [4, 5].
Advanced Hall sensor configurations employ differential measurement techniques and temperature compensation algorithms to minimize environmental effects and enhance measurement accuracy across varying operational conditions. The development of integrated Hall sensor arrays has enabled spatially resolved thickness mapping, providing comprehensive assessment of coating uniformity and identifying localized variations that may affect component performance.
The evolution of electromagnetic computer modeling began in the 1950s when growing system complexity led engineers to adopt computers for design and virtual testing. Early modeling tools design verification, optimization, and predictive modeling. The Finite Element Method (FEM) became 7]. FEM handles nonlinear magnetic behavior, thermal effects, and multiphysics interactions. Techniques like adaptive meshing and efficient solvers enable accurate modeling, validated experimentally for sensor optimization [8, 9]. Electromagnetic coating measurement systems are widely used in aerospace, automotive, marine, and energy industries. For example, aerospace relies on these systems to control thermal barrier coating thickness on turbine blades, directly affecting durability [10], while the automotive sector uses them for corrosion protection assessment [11]. Current research focuses on enhancing measurement range, resolution, and layer discrimination. Multi-element Hall sensors and intelligent signal processing improve accuracy and robustness [12, 13]. Adaptive calibration and machine learning allow systems to compensate for material variability and environmental factors [14, 15]. Signal processing advances, including digital filtering, noise suppression, and real-time data interpretation, enhance performance in harsh conditions. 3D field modeling reveals how coatings redistribute magnetic flux, aiding both transducer optimization and algorithm development [16]. Parametric studies and cloud-based optimization facilitate efficient design exploration [17, 18]. Challenges remain in measuring ultra-thick or ultra-thin coatings and distinguishing multilayer structures. These are addressed by combining advanced hardware with hybrid electromagnetic measurement techniques [19 21].
The primary objective of this research is to develop a comprehensive three-dimensional magnetic field model of an electromagnetic transducer utilizing Hall effect principles for precise measurement of ferromagnetic coating thickness. This investigation aims to establish optimal design parameters for the Hall sensor element through detailed computational analysis, enabling enhanced measurement accuracy for heat-resistant protective films in industrial applications. The modeling approach seeks to characterize the complex electromagnetic interactions within the sensor system and determine the functional relationships between transducer geometry, material properties, and measurement sensitivity.
The main objective of this study is to simulate the operation of a Hall effect electromagnetic transducer specifically designed for accurate measurement of ferromagnetic coating thickness. This study aims to establish optimal design parameters through detailed computational analysis using advanced finite element methods, characterize complex electromagnetic field distributions in the transducer system, and determine functional relationships.
3. Mathematical analysis and simulation modeling of the operation of the Hall sensor , . = /
, = =
, , (
) ( 2
) ( 3
) ( 4
) ( 5
) ( 6
) ( 7
) ( a b a b 4. Conclusions