Minimax Optimization Strategy for Process Parameters Planning: Toward Interference-Free Between Tool and Flexible Workpiece in Milling Process

In milling of flexible workpieces, like axial-flow compressor impellers with thin-wall blades and deep channels, interference occurrence between workpiece and tool shaft is a great adverse issue. Even though interference avoidance plays a mandatory role in tool path generation stage, the generated tool path remains just a nominally interference-free one. This challenge is attributed to the fact that workpiece flexibility and dynamic response cannot be considered in tool path generation stage. This paper presents a strategy in process parameters planning stage, aiming to avoid the interference between tool shaft and flexible workpiece with dynamic response in milling process. The interference problem is formulated as that to evaluate the approaching extent of two surfaces, i.e., the vibrating workpiece and the swept envelope surface generated by the tool undergoing spatial motions. A metric is defined to evaluate quantitatively the approaching extent. Then, a minimax optimization model is developed, in which the optimization objective is to maximize the metric, so as the interference-free can be guaranteed while constraints require the milling process to be stable and process parameters to fall into preferred intervals in which material removal rate is satisfactory. Finish milling of impeller using a conical cutter governed by a nominally interference-free tool path is numerically simulated to illustrate the dynamics responses of the spatially distributed nodal points on the thin-wall blade and approaching extent of the time-varying vibrating blades to the tool swept envelope surface. Furthermore, the present model results suggest to use an optimal process parameters set in finish milling, as a result improving machining efficiency in addition to ensuring the interference-free requirement. The model results are verified against milling experiments.