通道曲面的柱面逼近方法及其在叶轮插铣中的应用

为了使叶轮粗加工后的通道表面与其设计曲面尽可能接近，将整体叶轮的定轴插铣理论模型概括为通道曲面的最大内接柱面优化问题。同时，为简化该问题的计算难度，将最大内接柱面的优化问题转化为柱面直母线方向和柱面准线的确定两个步骤。提出了确定内接柱面直母线方向的最小二乘模型与解算方法，在此基础上，将通道曲面沿柱面的直母线方向进行投影，通过相关曲线间的裁剪操作，获得了最大内接柱面的准线。以最大内接柱面的准线作为插铣加工时的边界曲线，以柱面直母线方向作为插铣加工时平头刀的轴线方向，给出了计算刀心位置和安全高度的迭代算法。最后通过数值算例验证了所提方法的正确性。该方法将有助于叶轮粗加工效率的提高，同时为叶轮的精加工预留较均匀的加工余量。

Approximation Method of Tunnel Surfaces with General Cylindrical Surfaces and Its Application in Plunge Milling of Impellers

In order to make the machined tunnel surface of an impeller as close as possible to its designed surface, the theoretical model of the plunge milling of an impeller with fixed rotating axis is summarized as an optimization problem of finding the maximum inscribed general cylindrical surface of the impeller's tunnel surface. This optimal problem is then divided into two processes to reduce the computational difficulties, i.e., the determination of the direction of the ruled line and the determination of the directrix of the general cylindrical surface. A least square model and its corresponding solving methods for the determination of the direction of the ruled line of the general cylindrical surface are presented. Based on these, the tunnel surface is projected on a plane in the direction of the ruled line, and the directrix of the general cylindrical surface is resolved based on the intersecting operations between the related curves. For the plunge milling of the impeller's tunnel surface, the acquired directrix is used as the boundary curve of the machining area, and the axis of the flat end mill is set to be parallel to the direction of the ruled line. An iterative algorithm for determining the cutter center and the safe height of the flat end mill is given. Finally, the effectiveness of the proposed methods is verified by a numerical example. The proposed method will be helpful for the enhancement of the rough milling efficiency and the evenness of the remained finish machining allowance of the impeller.