Influence mechanism of machining angles on force induced error and their selection in five axis bullnose end milling

In the machining of complicated surfaces, the cutters with large length/diameter ratios are used widely and the deformation of the machining system is one of the principal error sources. During the process planning stage, the cutting direction angle, the cutter lead and tilt angles are usually optimized to minimize the force induced error. It may lead to a low machining efficiency for bullnose end mills, as the material removal rates are different largely for different machining angles. In this paper, the influence mechanism of the machining angles on the force induced error is studied based on the models of the instantaneous cutting force when the cutter flute traveling through the cutting contact point and the stiffness of the machining system. In order to evaluate the machining angles, the force induced error/efficiency indicator (FEI) is defined as the division of the force induced error and the equal volume sphere of the removed material. FEI is dimensionless, with the lower FEI, the lower force induced error and the higher machining efficiency. For optimal selection of the machining angles, the critical FEI is calculated with the constraint of force induced error and the desired material removal rate, and the critical FEI separate the set of the machining angles into two subsets. After the feed rate scheduling process, the machining angles in the optimal subset would have higher machining accuracy and efficiency, while the machining angles in the other subset have lower machining accuracy and efficiency. Through the machining experiment of five axis machining and freeform surface machining, the effectiveness and superiority of the proposed FEI method is verified with a bullnose end mill, which can improve the machining efficiency with the constraint of force induced error.