A unified ternary-mechanism model for the calibration of cutting force coefficients and prediction of ploughing-based process damping in flank milling process

Exciting ternary-mechanism model considers the effects of flank shearing, flank ploughing and bottom ploughing and suits for the calibration of cutting force coefficients with a relatively lower axial depth of cuts in which the cutting force proportion of bottom edge gradually increases. Since the vibration velocities are not formulated in the empirical rubbing formulae, the process damping effect in chatter stability can not be modelled. In order to simultaneously guarantee the calibration accuracy of the cutting force coefficients and solve the chatter stability with process damping, a unified ternary-mechanism model is established in this article. First, the ploughing forces corresponding to the flank edge and bottom edge are formulated as the function of the indented area and the corresponding proportion factors based on Hertz contact theory. And the static and dynamic ternary cutting forces are explicitly formulated. Second, with the aid of the static equilibrium equation together with the expression of small disturbance, the dynamic model including ploughing-based process damping is established. Third, a fast procedure to calibrate the real-time cutting force coefficients is also derived based on the inverse process of static cutting force modelling. A series of test platforms are built to verify the correctness of the calibration method and the ploughing-based process damping model. Good consistency between the predicted and experimental results in both static cutting forces and dynamic chatter tests proves that above models have better accuracy.