A drilling device with automatic or controlled feed speed. The drilling device includes a casing that houses a drilling spindle that is to drive a cutting tool in motion to drill a workpiece having a target surface. The spindle is tiltable inside the casing relative to the axis of the casing. The device has a self-alignment, which self-aligns the spindle relative to the target surface. The self-alignment moves the spindle into a position in which its axis is essentially perpendicular to the target surface under the effect of an application of a thrust force of the drilling device against the target surface essentially along the axis of the casing.