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Two methods are presented for the estimation of tangential, radial and axial cutting coefficients for the shearing and ploughing mechanisms from a single set of cutting forces in ball-end milling. These estimation methods are based upon the invertibility of the analytical milling force model, which considers both the shearing and the ploughing mechanisms by incorporating their respective cutting constants in the local force model. The periodic milling forces are established as the convolution integral of the differential local cutting forces and their Fourier coefficients are derived and expressed in a matrix expression as a linear function of the unknown cutting constants in terms of cutting conditions and cutter geometry. This linear expression thus leads to a systematic formulation of the estimation methods allowing the six unknown cutting constants to be determined from the measured milling forces. The first method uses the first harmonic forces as the source signal while the second method extracts the six cutting constants from the average force as well as the first harmonics. Limitations of both estimation methods are discussed. The consistency and accuracy of the estimated cutting constants are confirmed by the experimental results.

This paper extends analytical modeling of the milling process to include process damping effects. Two cutting mechanisms (shearing and plowing mechanisms) and two process damping effects (directional and magnitude effects) are included. The directional effect is related to vibration energy dissipation due to directional variation of cutter∕workpiece relative motion. The magnitude effect is associated with change in force magnitude due to variation of rake angle and clearance angle. Process damping is summarized as containing these separate components: direction-shearing, direction-plowing, magnitude-shearing, and magnitude-plowing. The total force model including the process damping effect is obtained through convolution integration of the local forces. The analytical nature of this model makes it possible to determine two unknown dynamic cutting factors from measured vibration signal during milling. The effects of cutting conditions (cutting speed, feed, axial and radial depths of cut) on process damping are systematically examined. It is shown that total process damping increases with increasing feed, axial and radial depths of cut, but decreases with increasing cutting velocity. Predictions based on the analytical model are verified by experiment. Results show that plowing mechanism contributes more to the total damping effect than the shearing mechanism, and magnitude-plowing effect has by far the greatest influence on total damping.