On Cutter Deflection Profile Errors in End Milling: Modeling and Experimental Validation

Abstract

In the present paper three dimensional cutter deflections and the corresponding profile errors during end milling are predicted by finite element and bond graph modeling approach. The deflections have been modeled considering the cutter as a cantilever beam fixed at the collet end. Rayleigh beam model is used for modeling to consider the shear force effect, and Castigliano's theorem of strain energy is used to predict the deflections due to radial, tangential, and axial cutting forces. The tool-workpiece contact region is sliced into small elements to apply the forces on the entire contact region and predict deflections more accurately. The predicted deflections at different parametric settings are compared with experimental measurements by measuring the geometric accuracy of the cut profiles. The depth of cut has the most significant influence on profile deviations, while feed and speed have marginal effects. The results reveal that the predictions by finite elements and the bond graph closely matches with the experimental results, and errors of the machined profile are significantly influenced by the radial and tangential deflections. The axial deflection is negligible and leads to insignificant deviation in depth of the cut profile. The proposed model shows that the bond graph simulation takes significantly less computational time and space as compared to the finite element technique.