Improved adapter and rolling assembly comprising such an adapter

An adapter for a rolling assembly, of axis of rotation X-X′, comprising a tire, having two beads and a rim,

• the adapter being intended to provide a junction between one of the beads and the rim,
• the adapter comprising an axially inner end, an axially outer end and a body oriented mainly axially and arranged between the axially outer end and the axially inner end, so that, when mounted within the assembly, the axially inner end is intended to be immobilized on the rim,
• the axially outer end comprising an outer reinforcing element and intended to receive a bead of the tire,
• wherein the outer reinforcing element is a structure substantially of revolution about the axis X-X′ comprising several windings of at least one wire that are arranged axially beside one another over several layers radially superposed on each other, and
• wherein a section of the outer reinforcing element has a ratio of moments of inertia Ix/Iy greater than 1.3 for an axial width of between 6 and 9 mm, where Ix is the moment of inertia around a first axis passing through its center of gravity and parallel to the axis of rotation X-X′, and Iy is the moment of inertia around a second axis passing through its center of gravity and perpendicular to the first axis.