Equation of the cross-sectional profile of a groove produced by helical milling with a ball-end mill

Abstract

Description of surfaces produced by cutting tools that have complex tool paths is demanding. However, it is usually difficult to derive the expressions to represent the machined surfaces because higher-order geometric forms result from the combination of the cutting tool and tool path, even though they have simple geometries. To illustrate this, the tool can be considered as a sphere, and the tool path is a helix in this work. An analytical model with three parameters was introduced to derive the cross-sectional profile of a groove machined using helical milling. A ball-end mill that can machine undercuts was considered. Variation of the cross-sectional profile of the groove was investigated depending on the radius of the tool and the pitch of the helix. A simulation was performed by using a commercial computer-aided design program to validate the analytical model. Experimental work was also carried out to support the findings. According to the results, the model gives the exact cross-sectional profile of the groove and thus provides the whole set of points on the created surface. The most important contribution of the introduced model is that the equation of the cross-sectional profile of the groove can be obtained immediately after entering the numerical values for three parameters.