Abstract In turning, tool wear and cutting vibration are inevitable, which have great influence on surface quality. Analyzing the influence mechanism of tool wear and cutting vibration on surface quality is important to achieve the accurate prediction of surface roughness before machining and improve machining quality. In this paper, a turning vibration experiment is conducted to reveal that the diameter of shafts is an important factor affecting the vibration amplitude and frequency. In addition, based on machining parameters, tool wear and workpiece diameter, this empirical model, the response surface method and a support vector machine are used to model and predict surface roughness. The fitting accuracy, prediction accuracy and generalization performance of the proposed methods are compared in detail. The results show that the response surface modeling method has the highest fitting accuracy, but the exponential empirical modeling method has the highest prediction accuracy and best generalization performance. Additionally, the prediction results indicate that the surface roughness increases with the increase in tool wear and decreases with the increase in workpiece diameter. Keywords: surface roughness; tool wear; workpiece diameter; response surface method; support vector machine