Prediction of cutting forces in flexible micro milling processes by considering the change of instantaneous cutting direction

The characteristic of low stiffness of the micro mills usually leads to instantaneously changeable tool deflections, and as a result, actual in-process cutting parameters such as the instantaneous cutting directions and trajectories of the cutting edges will deviate from their designed values. Existing works seldom studied the influence of this fact on the cutting forces. This article presents a theoretical method to predict the micro milling forces by introducing the effects of the tool's deflections on the process. Analytical formulae for determining the actual in-process cutting edge position and instantaneous cutting direction are originally derived based on the tool deflections, which are calculated by using the cantilever beam theory. At the same time, other actual in-process parameters such as rake angle, shearing angle and uncut chip thickness are subsequently formulated to detect their influences on the cutting. Based on the obtained actual in-process parameters and tool deflections, the shearing and ploughing forces, which constitute the total micro milling forces, are then formulated separately. An iterative algorithm, which integrates the above derivations with the material piling up effect, is developed to capture the coupling effect between the cutting forces and tool deflections during the micro milling process. A series of experimental tests are conducted, and the results prove that the accuracies of cutting forces and the cutting edge's moving trajectories predicted by the proposed method are better than those obtained from the classic models without including the changes of cutting directions caused by the tool deflections.