Extended classification of surface errors shapes in peripheral end-milling operations

The prediction of form surface error represents the basis of many approaches, which aims at increasing the productivity and reducing the costs of a milling operation. In peripheral end-milling the form error caused by the tool/workpiece static deflection is not constant along the axial depth of cut, and it presents different shapes due to the cutting forces, which change according to the cutting strategy, end-mill geometry and cutting parameters, making the surface error prediction complex and time consuming. This paper presents a comprehensive classification of the shape of the cutting forces which cause the surface form errors, in both up and down-milling. The proposed classification includes analytical equations to obtain the axial position of key points (also known as kinks) defining the surface error shape in any cutting condition and tool geometry. The results given by the developed classification were experimentally validated trough different cutting tests to prove the reliability and the effectiveness of the proposed approach. The proposed classification and formulations manage to identify the surface error shapes both when several flutes are involved in the process and aggressive axial depths of cut are adopted, extending the knowledge about surface errors in peripheral milling. Furthermore, the proposed formulations could be exploited to ease error prediction methods based on simulations or drastically reduce the surface measuring time in quality control.