Force reduction is one of the most important benefit of applying ultrasonic vibration on milling. However, most of studies so far are limited to experimental investigation. In the current study, an analytical predictive model on cutting forces in ultrasonic vibration-assisted milling is proposed. The three types of tool-workpiece criteria are considered based on the instantaneous position and velocity of tool center. Type I criterion indicates that there is no contact if the instantaneous velocity is opposite to tool rotation direction. Type II criterion checks whether the vibration displacement is larger than the instantaneous uncut chip thickness. Type III criterion considers the overlaps between current and previous tool paths due to vibration. If none of these criteria is satisfied, milling forces are nonzero. Then the calculation is performed by transforming milling and tool geometry configuration to orthogonal cutting at each instant. The orthogonal cutting forces are predicted through the exhaustive search of shear angle and calculation of shear flow stress on tool-chip interface. The axial force is then calculated based on tool geometry, and the milling forces in feed, cutting, and axial directions are calculated after coordinate transformation. The proposed predictive force model in ultrasonic vibration-assisted milling is validated through comparison to experimental measurements on Aluminum alloy 2A12. The predicted values are able to match the measured milling forces with high accuracy of average difference of 13.6% in feed direction and 13.8% in cutting direction.
force; ultrasonic vibration; modeling; milling
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