Method and apparatus for truing or straightening out of true work pieces

A method for straightening a work piece having different cross-sections along its length with fillets forming transition areas between neighboring different cross-sections, said work piece having a rotational axis and a bend relative to said rotational axis, said bend being determined by three values, namely as to its location by an axial coordinate value, as to its direction by an angular coordinate value, and as to its size by an eccentricity magnitude value, comprising the following steps:

• (a) performing a first heating operation in at least one of said fillets for introducing into a work piece first residual compressive stresses in a surface layer zone for increasing a fatigue strength of said work piece,
• (b) determining from said three values a respective control signal representing a circumferentially limited angular range (.beta.1) around a portion of said at least one of said fillets, and
• (c) performing a second heating operation on said at least one fillet of said fillets for introducing in response to said control signal, in addition to said first residual compressive stresses in said surface layer zone, second residual compressive stresses in that part of said surface layer zone determined by said limited angular range (.beta.1) of said at least one fillet, whereby said first residual compressive stresses are increased by said second residual compressive stresses in said surface layer zone of said at least one fillet determined by said limited angular range (.beta.1) so that said bend is at least reduced or removed and any fatigue strength caused by said first residual compressive stresses is maintained without relieving said first residual compressive stresses by said second residual compressive stresses, and wherein said first and second heating operations are performed by heating said surface layer zone, said second heating operation applying heat only in said limited angular range (.beta.1) of said at least one fillet, and then cooling the heated surface layer zone for hardening, whereby exclusively compressive residual stresses remain in said surface layer zone.