A new 3D finite element (FE) model of the cold hole expansion process by means of spherical mandrelling (SM) has been developed. The model has the following characteristics: the spherical motion of the tool has been defined by means of decomposition along static axes; interactions (normal and tangential contact with friction) defined in the tool-workpiece-supports system; nonlinear kinematic hardening of the workpiece material, defined on the basis of symmetric test with strain-controlled deformation to achieve a stabilized cycle. The actual spherical motion of the tool and the optimal value of the angle of nutation have been found through numerical minimization of the lost available work functional, which is equivalent to the minimum generated entropy. The FE model authenticity has been proved by means of comparison of the results for axial force variation with those obtained by experiment. The optimized FE model has been used for investigation of the residual displacements and stresses around cold expanded holes by means of SM. The FE results obtained have been compared with those obtained from other FE models.
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