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On machined parts, major indication of surface quality is surface roughness and also surface quality is one of the most specified customer requirements. In the turning process, the importance of machining parameter choice is enhancing, as it controls the required surface quality. To obtain the better surface quality, the most essential control parameters are tool overhang and tool geometry in turning operations. The goal of this study was to develop an empirical multiple regression models for prediction of surface roughness (Ra) from the input variables in finishing turning of 42CrMo4 steel. The main input parameters of this model are tool overhang and tool geometry such as tool nose radius, approaching angle, and rake angle in negative direction. Regression analysis with linear, quadratic and exponential data transformation is applied so as to find the best suitable model. The best results according to comparison of models considering determination coefficient (R 2 ) are achieved with quadratic regression model. In addition, tool nose radius was determined as the most effective parameter on turning by variance analysis (ANOVA). Cutting experiments and statistical analysis demonstrate that the model developed in this work produces smaller errors than those from some of the existing models and have a satisfactory goodness in all three models construction and verification .

Surface Roughness Estimation for Turning Operation Based on Different Regression Models Using Vibration Signals