An axial flux machine, in particular a single-sided axial flux motor, for an electrical machining device, includes a machine shaft, in particular a motor shaft, a disc-shaped stator, and a disc-shaped rotor which is arranged adjacent to the stator in the axial direction of the machine shaft. The stator is formed as a winding carrier with a plurality of stator teeth for at least one stator winding and the rotor, which is connected to the machine shaft in a rotationally fixed manner, can be set in a rotational movement relative to the stator. The rotor of the axial flux machine has a rotor yoke configured as a bidirectional fan or which is permanently connected to a bidirectional fan by a joining process, the bidirectional fan having at least one radial and one axial air flow direction for cooling the axial flux machine, in particular the stator and the rotor.