Deflection modeling of permanent magnet spherical chains in the presence of external magnetic fields

• Published in: Journal of magnetism and magnetic materials 2013-10, Vol.343, p.251-256
• Main Authors: O'Donoghue, Kilian, Cantillon-Murphy, Pádraig
• Format: Article
• Language: English
• Subjects: Catheter deflection; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Corners; Deflection; End effectors; Exact sciences and technology; Gravitational effects; Magnetic anisotropy; Magnetic fields; Magnetic guidance; Magnetic properties and materials; Magnetically ordered materials: other intrinsic properties; Mathematical analysis; Mathematical models; Navigation; Permanent magnet; Permanent magnets; Physics; Sphere; Spherical chain; Studies of specific magnetic materials
• ISSN: 0304-8853
• DOI: 10.1016/j.jmmm.2013.05.006

This work examines the interaction of permanently magnetised spheres in the presence of external magnetic fields at the millimetre scale. Static chain formation and deflection models are described for N spheres in the presence of an external magnetic field. Analytical models are presented for the two sphere case by neglecting the effects of magnetocrystalline anisotropy while details of a numerical approach to solve a chain of N spheres are shown. The model is experimentally validated using chain deflections in 4.5mm diameter spheres in groups of 2, 3 and 4 magnets in the presence of uniform magnetic fields, neglecting gravitational effects, with good agreement between the theoretical model and experimental results. This spherical chain structure could be used as an end effector for catheters as a deflection mechanism for magnetic guidance. The spherical point contacts result in large deflections for navigation around tight corners in endoluminal minimally invasive clinical applications. •We model the interaction of magnetic spheres with uniform external fields.•Analytical models are presented for two spheres interacting with an external field.•Numerical methods are used to model the interaction of N spheres in chain formations.•These models are tested experimentally.•We report good agreement between experiment and theory.