In order to investigate the effect of machining states and cutting parameters on the surface roughness of slender shafts in turning operations,based on the geometrical mapping relationship between cutting edge of tool and surface morphology of workpiece,the contour curve equation of axial section was derived，the theoretical surface roughness values under different cutting parameters were obtained.The surface roughness data of slender shaft turning under different machining states and cutting parameters were compared and analyzed.The results show that during stable turning,the vibration of slender shaft workpiece is mainly caused by spindle rotation frequency and its frequency multiplication.During this process,the roughness of machined surface is greatly affected by feed,and the roughness increases with feed.The error between theoretical roughness and measured results is small when the rigidity of workpiece is large.When chatter occurs,a high frequency vibration component appears in the vibration signal of the workpiece which is close to its natural frequency,at this time,the error between the theoretical prediction of roughness and the measured result is large.Vibration information of process system should be fully integrated in theoretical model to further improve the accuracy and applicability of prediction model.