An assembly that includes a rotating shaft supported with respect to a stationary housing by at least one active magnetic bearing presenting a mean radial air gap and at least one auxiliary bearing having a bushing fixed to the housing and a sleeve fixed on the rotating shaft. The bushing and the sleeve have opposite surfaces that define a clearance (E2) which is less than the mean radial air gap (E1). The bushing and the sleeve each exhibit symmetry around a longitudinal axis of the shaft and have different profiles in a longitudinal cross-section including the longitudinal axis to optimize the contact pressure distribution when the rotating shaft lands on the auxiliary bearing.