Modeling and measurement of non-uniform magnetic fields of a diametrically magnetized annular permanent magnet

Permanent magnet (PM) driven capsule robots represent a significant advancement in the real-time diagnosis and treatment of gastrointestinal issues. Permanent magnets are advantageous due to their small size, simple structure, and high magnetic field strength. Their non-uniform magnetic fields can generate torque on the capsule robot, allowing for precise control over its position and orientation to navigate the complexities of human stomach and intestines. In this study, we employed the equivalent magnetic charge method to create a model for calculating and analyzing the spatial magnetic field distribution of a diametrically magnetized annular permanent magnet, which can be used appropriately to drive capsule robots. Additionally, a Hall-type magnetic flux density measurement system was set up to gauge the radial magnetic flux density of a rotating annular permanent magnet. We also established a three-dimensional (3D) finite element analysis model within Maxwell software to conduct numerical simulations of the magnetic field of the annular permanent magnet. The results from our theoretical calculation align closely with both the measured and finite element analysis results, confirming the accuracy and reliability of our model. Furthermore, we quantitatively analyzed the three-dimensional magnetic flux density at various points in the external space surrounding the permanent magnet and influencing factors. The results of this research will offer valuable theoretical support for designing and developing magnetic materials and devices, and serve as a reference for the driving methods of magnetically driven capsule endoscopes, magnetic soft continuum robots, and other medical devices.