Theoretical estimation of machined surface profile based on cutting edge movement and tool orientation in ball-nosed end milling

This paper presents the theoretical estimation method of machined surface profile without actual machining in ballnosed end milling. The fundamental simultaneous equations of identifying the cusp height at any point of a workpiece in the simulated surface have been successfully derived from the geometric relationship between the cutting edge movement and the normal line at the point. By the numerical calculation, the machined surface profile can be estimated and illustrated graphically. It was found that the maximum and minimum cusp heights exist in a narrow range of tool orientation less than 3 degrees near the normal direction.