In this research, workpiece studied minimum surface roughness Ra, minimum Amp for vibration and maximum material-removal rate MRR of Manganese steel Hadfield steel investigated. The turning processes were carried out on a center lathe machine. The machining conditions selected in this work are rotational speed, feed rate, depth of cut, and tool overhang. Taguchi’s L16 (44) Orthogonal array applied for the design of experiments. The parameter processes significance quality estimated using analysis of variance ANOVA. Gray relation analysis utilised as a multi-response optimisation method. The results obtained by grey relation analysis (GRA) indicated that the Amplitude of vibration improved by 108%the material removal rate MRR was improved by 69.03%, while surface roughness Ra recorded a deviation of 7.30% from considering initial cutting conditions.