A machine including: a main frame including at least one functional element and one control unit; an air compressor or water pump integrated in the main frame, including a frame in which are mounted a stator, a rotor interacting with the stator and including a shaft, at least one turbine carried by the shaft, a fluid-supply channel to the turbine, and an outlet channel for compressed fluid, the shaft being mounted rotatably on the frame about an axis by first and second bearings, including respectively first and second spherical elements provided on respective first and second ends of the shaft and centered relative to the axis of the shaft, and respective first and second housings provided in the frame centered relative to the axis of the shaft and to support the respective first and second spherical elements.