In five-axis milling, the bottom edge of a flat end mill is probably involved in cutting when the lead angle of tool axis changes to negative. The mechanistic model will lose accuracy if the bottom edge cutting effect is neglected. In this paper, an improved mechanistic model of five-axis machining with a flat end mill is presented to accurately predict cutting forces by combining the cutting effects of both side and bottom edges. Based on the kinematic analysis of the radial line located at the tool bottom part, the feasible contact radial line (FCRL) is analytically extracted. Then, boundaries of the bottom cutter-workpiece engagements (CWEs) are obtained by intersecting the FCRL with workpiece surfaces and identifying the inclusion relation of its endpoints with the workpiece volume. Next, an analytical method is proposed to calculate the cutting width and the chip area by considering five-axis motions of the tool. Finally, the method of calibrating bottom-cutting force coefficients by conducting a series of plunge milling tests at various feedrates is proposed, and the improved mechanistic model is then applied to predict cutting forces. The five-axis milling with a negative lead angle and the rough machining of an aircraft engine blisk are carried out to test the effectiveness and practicability of the proposed model. The results indicate that it is essential to take into account the bottom edge cutting effect for accurate prediction of cutting forces at tool path zones where the tool bottom part engages with the workpiece.
Experimental Investigation of Cutting Forces in High-Feed Milling of Titanium Alloy