# Feed Rate Variation Strategy for Semi-Conical Shell Workpiece in Ball Head End Milling Process
## 1 Introduction  
The advanced machining technologies of thin-walled parts have generated considerable recent research interest. The semi-conical shell workpiece is a special kind of thin-wall part widely used in aerospace, die and mold industries. Considering the special geometry, stiffness distribution, and thin-wall property of the semi-conical workpiece, the selection of machining parameters like spindle speed and feed rate should be both reasonable and efficient. In general, constant conservative parameters are chosen to ensure the workpiece deformation and surface quality, which will reduce the machining efficiency. In order to achieve harmony between machining quality and efficiency, many researchers studied the influence of tool path strategy [1, 2], spindle speed [3, 4] and feed rate [5] on the machining process and proposed many machining technologies with variable machining parameters. Among them, the feed rate variation strategy is one of the most direct and efficient methods to improve machining efficiency. However, the selection of excessive feed rate will markedly aggravate the cutting force, tool deflections and increase the risk of tool wear, chipping and surface quality losses of theworkpiece. Therefore, the proper selection of planning technology and control parameter are two key factors in the design of a feed rate variation strategy. According to much research in recent years, three kinds of feed rate optimization methods have been proposed and reviewed by [PERSON] et al. [6]. The first is a traditional feed rate scheduling strategy based on the material removal rate (MRR) model, in which the feed rate is expected to be proportional to either average or instantaneous material removal rate [7]. In the optimization of the 5-axis milling cutting parameters, [PERSON] et al. [8] used the MRR assumption to adjust the feed rate iteratively. The optimized results were validated to be accurate experimentally, but the iteration process was found to be time-consuming. The MRR model is more suitable for the roughing process, and much commercial software has embedded the optimization module based on it, but the optimal feed rate can hardly be obtained due to the complexity of real machining force prediction. Consequently, the second method uses a mechanistic model as a basis. In this method, the cutting force is the most important control parameter because in addition to the tool deflections, the feed rate variation will affect the machining force directly, leading to surface form errors and tool wear. The more accurate the force calculation approach is, the better the feed rate strategy can be, but it is still difficult to integrate into the workshop. A user-defined threshold to keep the resultant cutting force constant has been used in the research of [PERSON] et al. [9] and [PERSON] et al. [10]. Their strategies are quick but lack precision. As for end-milling on a 5-axis machining center, more complex features like concave corners, upward and downward cutting must be considered. [PERSON] et al. [11] proposed two methods of offline feed rate scheduling according to multiple feed-dependent constraints for 5-axis flank milling with serrated, tapered, helical, ball-end milling cutters with variable-pitch flutes. Nearly half of the cycle time could be saved in their experiment; the performance was discussed in detail. [PERSON] et al. [12] compared the MRR based and force-based feed rate scheduling strategies theoretically and experimentally for 3-axis ball-end milling of freeform surfaces. It was shown that MRR based feed rate strategy outputs higher feed rate values compared with a force-based feed rate strategy, and the high feed rate values of the MRR strategy increased the cutting forces extensively, which can damage the tool and violate the part's dimensional accuracy. The last kind of optimization method is based on artificial intelligence techniques, including the artificial neural network [13] and the genetic-simulated annealing algorithm [14]. [PERSON] et al.