Geometric Modeling of Serrated Cutters for Endmilling Forces using Local Oblique Cutting and Rake Normal Correspondence

Abstract

For nonstandard endmills with sinusoidal and circular serrations on nominally helical cutting edges, the edge space curve was subdivided into straight edge elements for constant increments of arc length. To calculate the local normal rake angle at the serrated edge point, Local Rake Normal Correspondence used the normal vector on the rake face of the corresponding unserrated helical edge point at the same axial cross section. Uncut chip thickness h was computed under Local Oblique Cutting Correspondence published earlier. Stabler’s rule specified chip flow direction and Lazoglu mechanistic normal and friction force coefficients completed the straight edge cutting element forces. Local force contribution vectors summed over the tool engagement resulted in global tool forces. Number of straight edge element computations were minimized with the hypotheses (a) cutting predominantly occurs at the vicinity of serration tips and (b) only the stock surfaces swept by flutes immediately prior and following the current flute need be considered for h. Interaction of axial cross sections at a significant fraction of the serration wavelength was noted. Thus, treating tool axial subdivisions in relative isolation for h is untenable. However, local normal rake angle on the serrated edges followed earlier published trends. For a square endmill, sinusoidally serrated, cutting with low axial depth of cut ADOC, modeled forces showed idle periods and unbalance fluctuations during a full rotation, but not the data; modeled forces for an identical unserrated helical cutter were lower than the serrated. For the same endmill with circular serrations cutting at high ADOC, no idle periods or unbalance were predicted and the agreement with published data was better.