An electrical machine having a non-rotating part, a rotating part, at least one bearing supporting said rotating part and having a rotating ring and a non-rotating ring, a fiber grounding brush fixed to said non-rotating part and having a support secured to the non-rotating part and a plurality of conductive fibers having a first end secured to said support and a second free end, opposite to said first end, extending towards the rotating part, and a conductive sleeve having a base fastened to the rotating part or to the rotating ring of the bearing and a conductive layer covering at a portion of a surface of the base, the second free end of the conductive fibers of the fiber grounding brush being in contact with said conductive layer.to