# Stress modeling of a superconducting solenoid for a novel MRI machine

Winding stress

During the manufacturing process of the superconducting solenoid, the wires are wounded around the mandrel with pretension. This application of winding stress helps compensate the tensile stress at the time of electromagnetic operation and assist in restraining the developed strains within the design criteria. It also helps to encounter the transverse shear stress at the time of magnet operation resulting from developed Lorentz force which prevents sliding of the layers. Another important phenomenon ‘training’ of superconducting magnet is attributed to the plastic deformation of epoxy. Applying pretension on the wire provides comparatively large room for the strain development before the deformation starts reaching plastic region and critical current limit. Researchers has shown that it is possible to control the total stress development more precisely at the time of electromagnet charging if the applied pretension is varied along the radial distance. These findings underscore the importance of controlling of pretension on the wire during winding process of a superconducting solenoid.

Finite Element Analysis

Commercial Finite Element Analysis (FEA) software ANSYS can be used to model the winding process of superconducting magnet system. The basic driving equation for finite element is summarized with the equation in compact form as,

[F] =[K]{u}

In the equation, [K] is the stiffness matrix, {u} represents the vector displacement of each of the node points, and [Fnode] indicates the forces acting on each nodes of the modeled geometry. To imitate the winding process the element birth and death technique is employed. The geometry is considered 2D axisymmetric for simplification. Initial state condition is used to apply the pretension on each layer. After modeling the geometry, pretension is applied on the coil bundle and all corresponding layer elements are killed by setting the stiffness to a very low value. Then to imitate the winding process, each layer is made alive by returning the stiffness values to the desired material property values. 