Analytical Modeling for Mechanical Straightening Process of Case-Hardened Circular Shaft

Straightening has to be carried out in order to ensure the straightness of a shaft, as distortions exceed the tolerance limit. Since the straightening load is typically large enough to produce plastic and residual deformation, repeated straightening loading cycles are very likely to induce cracks or fractures on the case-hardened shaft surface. In this study, in order to minimize repeated straightening cycles, an analytical straightening model is developed which calculates optimum stroke displacements corresponding to measured straightness errors so as to achieve the desired residual deflections and eliminate straightness errors. First, the hardness variation in the shaft radial direction is considered in the analytical model. Then, the proposed theoretical model is validated by numerical simulations. The results suggest that the analytically predicted stroke displacements and residual deflections agree very well with the numerical results when using induction-hardened SAE 4140 steel, and this signifies that the analytical straightening model developed in this study is capable of providing predictions of straightening stokes.