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Paper   IPM / Cognitive Sciences / 14226
School of Cognitive Sciences
  Title:   Torque and Translational Force Estimation for Ferromagnetic Objects: the Saturation Effect
1.  V. Ghodrati
2.  A. Nasiraei Moghaddam
  Status:   In Proceedings
  Proceeding: Proc. Intl. Soc. Mag. Reson. Med. 23 (2015)
  Year:  2015
  Supported by:  IPM
Introduction: Translational force and torque that acts on the ferromagnetic object in the magnetic field depends on the shape and volume of object, magnetic field strength and spatial gradient of the static magnetic field1. Ferromagnetic objects in the MR-environment experienced linear magnetic region or saturation region. conventional approximation of the force and torque on the ferromagnetic ellipsoid of revolution are based on the linear magnetic region2. However, almost ferromagnetic objects placed in the saturation region in the commercial MR-scanners. Therefore, it is necessary to considered saturation region for these objects. Here, the approximated strength for the magnetic field that can be saturated the almost ferromagnetic objects will be presented. a simple simulation with Ansoft Maxwell 3D will be performed to show the Cast-Iron as a ferromagnetic object placed in the highly saturation region. Also, it will show that just by using the linear region, the approximation of force will be 1.5 times overestimated in comparison by considering of real states for these objects.
Methods: Analytical approaches, shows if a ferromagnetic spherical object exposed to a magneto-static field, total intensity of the magnetic field inside it, is 3 times greater than the applied field2. This approximation is just valid for the ferromagnetic objects in the linear region. Therefore, the threshold strength for the external magnetic field to saturated the ferromagnetic object is 1⁄3 times of the Bs, where Bs is the threshold for the saturation value for the inside of the object’s magnetic field and can be obtained from the B-H curve of the object. for example for the soft Iron, Bs=2.13T or for the high permeability iron alloys is Bs= 1.6 - 2.2 T. therefore almost ferromagnetic materials such as iron, nickel, cobalt and their alloys saturated if the applied field is greater than .7 Tesla. Conventional approximation formula for the magnetic energy of the ferromagnetic ellipsoid of revolution are based on the (Eq.1)1,3 Where n􀭟 , n􀭰 are the demagnetization factors along the axis of symmetry and radial axis, also, V is the volume of the objects, m􀭱, M and B are the saturation value for the magnetization, magnetization and external applied magnetic field, respectively. Also, θand φ are the angle between the external field with axis of symmetry and dipole moment angle with the mentioned axis, respectively. In the strong saturation state for the objects approximately θ ≃ φ.With using the virtual works methods, the closed form formula can be simply obtained for these objects in 2 regions (Eq.2),(Eq.3).

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