An inductive measurement is carried out of the distance between a workpiece and a working head, which bears an induction coil, through which an alternating current flows and which is part of a resonance circuit whose oscillation frequency is monitored for changes which occur as a consequence of changes in the distance between the workpiece and working head. The production process comprises a primary carburization step for carburizing a steel product having a predetermined composition at a primary carburization temperature until the surface carbon concentration reaches a predetermined carbon concentration, a cooling step of, after the completion of the primary carburization step, cooling the steel product at a cooling rate of not less than 1\xb0 C. The spring is associated with and extends from the first wall.