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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。
In order to make the routed surface of the impeller as close as possible to its design surface, the theoretical model of the fixed-axis interpolation of the integral impeller is summarized as the maximum inscribed cylinder optimization problem of the channel surface. At the same time, in order to simplify the computational difficulty of this problem, the optimization problem of the maximum inscribed cylinder is transformed into the two steps of determining the straight generatrix direction and the cylinder line of the cylinder. The least square model and solution method of determining the direction of the straight bus bar of the inscribed cylinder is proposed. On this basis, the channel surface is projected along the straight generatrix of the cylinder surface. Through the cutting operation between the relevant curves, Then the line of the cylinder. Taking the line of the largest inscribed cylinder as the boundary curve during plunge milling and the straight busbar direction of the cylinder as the axial direction of the plunge cutter, the iterative algorithm for calculating the position of the cutter heart and the safety height is given. Finally, a numerical example is given to verify the correctness of the proposed method. This method will help improve the efficiency of the rough machining of the impeller, meanwhile, reserve a more uniform machining allowance for the finishing of the impeller.