One of major problems accompanying metal cutting is the appearing of relative vibrations between tool and the machined work-piece. These vibrations are essentially the result of cutting process itself. They can cause a waved machined surface and limit the process performances, severely. These vibrations can also affect tool life-time and lead to a fast harmful of certain machine tool parts (bearings, slides .....). In the present paper a relationship between vibrations and cut surface roughness in the case of turning, throughout a building of mathematical correlation, is proposed. This allows the prediction of roughness based on the knowledge of tool-nose displacements. The latter evaluated from the gathering of signal accelerations. DOI: http://dx.doi.org/10.5755/j01.mech.19.1.3612