Determination of the Equivalent Diameter of an End Mill Based on its Compliance

The deflection of the end mill was studied both experimentally with strain gauges and on a finite element model of the cutter using CAE software. The “equivalent diameter” D e , i.e. the diameter of a solid cylinder yielding the same deflection under identical loading conditions as the cutter, and having, therefore, the same moment of inertia, was then calculated. It was found that D e is approximately 80% of the cutter diameter for both two- and four-flute end mills and that D e /D ratio can be considered a shape factor of the end mill. The equivalent diameter provides a simple way to calculate the end mill deflection, particularly for other than four-flute cutters, for which the inscribed square method cannot be used.