Optimized feed scheduling in three axes machining. Part I: Fundamentals of the optimized feed scheduling strategy

An optimized feed scheduling strategy is proposed in this paper to maximize the metal removal rate in 3-axis machining while guaranteeing the machining accuracy. The tool path is assumed defined by a cubic parametric form. In part I of this paper, the fundamentals of this strategy are presented. This strategy integrates the feed drive dynamics, described by the acceleration/deceleration (Acc/Dec) profile, with the minimum-time trajectory planning in order to achieve the desired feed rate at the appropriate position. An optimum use of the feed drive capabilities is considered to track the changes in the cutting geometry along the tool path and to ensure an acceptable contour error. Therefore, this strategy combines different constraints and various criteria in modifying the feed rate to maintain a near-constant cutting force resulting in a highly non-linear problem. The constraints include the cutting force magnitude, the feed rate boundaries, the contour error and the characteristics of the (Acc/Dec) profile of the different feed drive systems. The criteria are the maximum production rate, the machining accuracy and safety. In part II of this paper, the effectiveness of this strategy is demonstrated using ball end mill operation on a workpiece that provides variable cutting geometry along a non-linear tool path. The performance of this strategy in terms of productivity, machining safety, and machining accuracy, is compared to a feed scheduling strategy based on control points as well as to milling with constant feed rate.