A 3-D Closed-Form Cutting Force Model for End Milling With Application to Sculptured Surface Milling

Abstract

A comprehensive, 3D mathematical model of desired/optimal cutting force for end milling of free-form surfaces is proposed in this paper. The closed-form predictive model is developed based on a perceptive cutting approach resulting in a cutting force model having a comprehensive set of essential cutting parameters. In particular, the normal rake angle usually missing in most existing models of the same sort is included in the developed model. The model also enables quantitative analyses of the effect of any parameters on the cutting performance of the tool, providing a guideline to improving the tool performance. Since the axial depth of cut varies with time when milling sculptured surface parts, an innovative axial depth of cut estimation scheme is proposed for the generation of 3-D cutting forces. This estimation scheme improves the practicality of most existing predictive cutting force model for milling in which the major attention has been focused on planar milling surface generation. In addition, the proposed model takes the rake surface on the flute of mills as an osculating plane to yield 3-D cutting force expressions with only two steps. This approach greatly reduces the time-consuming mathematical work normally required for obtaining the cutting force expressions. A series of milling simulations for machining free-form parts under scenario cutting conditions have been performed to verify the effectiveness of the proposed cutting force model. The simulation results demonstrate accurate estimating capability of the proposed method for the axial depth of cut estimation. The cutting force responses from the simulation exhibit the same trends as what can be obtained using the empirical mechanic’s model referenced in the literature. Finally, through the simulation results it is also learned that designing a tool with a combination of different helix angles having cutting force signatures similar to that of the single helix angle counterparts is particularly advantageous.