In present paper there is the refinement method of the non-rigid shafts turning work meant to be provided. There are foundations to the axial forces control necessity gained. The unit that outfits structured functional scheme of the selfcentering rests (SCR) is presented. The main source of rests work by tool motion along the operated non-rigid shaft axis while the one is being centered to technologic shaft axis is widely described. There are operations conditions of the SCR hydraulic cylinders which allow one to level the replication of operated blank crosssection form examined. A planar design scheme of the subsystem "detail-support" taking into account the action of axial forces is presented. We also prove importance of the constriction axial forces due to temperature increase while operating. The integrated functional scheme of the Automatic Control Systems (ACS) is developed; it uses dynamometric system of the thermal deformation compensation. The axial sections profile records and non-rigid shaft circular profile records, taken after the turning operating, either with ACS applying or not, are represented here. It is shown that the error of processing is reduced 2-3 times.