Identification of Polynomial Cutting Coefficients for a Dual-Mechanism Ball-end Milling Force Model

Background: Calibration of cutting coefficients is the key content in modeling a mechanistic cutting force model. Generally, in modeling cutting force for ball end milling, the tangent, radial and binormal cutting force coefficients are each considered as a polynomial, respectively. This fact is due to the dependency between the cutting force coefficients and the cutting edge inclination angle which is variable in ball-end mills. Objective: This paper presents an approach to determine the polynomial cutting force coefficients. Methods: In this approach, the cutting force coefficients are expressed as explicit linear equations about the average slotting forces. After analysis of the least square regression method which is utilized in the cutting coefficients evaluation, the principle of cutting parameters choice in calibration experiment and the relationship between the order of polynomial and the number of experiments are presented. Besides, a lot of patents on identification of polynomial cutting coefficients for milling force model were studied. Results: Finally, a series of semi-slotting verification cutting tests were arranged, the measured force agrees well with the predicted force, which demonstrates the effectiveness of this approach. Conclusion: Based on the calibration method proposed in this paper, the cutting coefficients can be determined through (m+2) slotting experiments for m-degree shearing coefficients polynomial theoretically.