一種螺槳葉片幾何外形建構方法

A Method for Constructing the Geometry of Propeller Blades

本文嘗試推導了一套關於螺槳葉片幾何外形的建構方法，其處理之方式有別於傳統之方法，於此方法中，三維螺槳實體模型之葉片於某一半徑處之剖面曲線（即實際葉片曲面與等於該半徑之圓柱曲面之交線）是建構在圓柱面所展開之平面上，展開之方式係依螺槳於該半徑之螺距所形成之螺線剪開並攤平成一平行四邊形之平面，此一平面以參數式平面LP(u, v)表示，將給定之某一剖面曲線之一組座標點轉換至此一平面上對應之位置，可得其（ u , v）座標值（u1, v1）、（u2, v2）、…、（un, vn），再藉由參數u與v之對應關係利用曲線適合（fitting）方法，即可完成整條剖面曲線在平行四邊形上之定義，將平行四邊形平面捲回成圓柱面，完成之剖面曲線即完全落在圓柱面上，滿足以二維翼理論定義個別剖面曲線之想法，將此一過程應用於所有不同半徑之剖面曲線，再引用曲面架築（surface lofting）之方法，可得一通過所有剖面曲線之葉片曲面。最後，將建立完成之方法應用於數個螺槳幾何外形的建構，包括了一般商船用之傳統螺槳、穿水式螺槳，以及藉由調整後傾角以抵銷歪斜誘導後傾的翹曲螺槳。 In this paper, a new geometry modeling method for propeller blades is proposed. In the method, the cross-sectional curve at a radius of a three-dimensional propeller blade (intersection between an actual propeller blade and a cylindrical surface with that radius) is constructed on the expanded plane surface from the cylindrical surface. Thereby, the cylindrical surface is cut along a helix curve with a corresponding pitch and then expanded to a parallelogram, which is defined by a parametric formulation ( ) v u p , r . A set of points on a given cross-sectional curve are transformed to corresponding positions on this parallelogram. Their (u,v) coordinates are denoted by (u1,v1), (u2,v2), …, (un,vn). Based on the relationship between the parameters u and v, a complete curve on the parallelogram can be constructed by a curve-fitting method. Rolling the parallelogram back to the cylindrical surface, a curve “crawling” on the cylindrical surface can be obtained, which is satisfied with the idea of designing each cross-sectional curve by 2D foil theory. After the transforming procedure mentioned above has been applied to all cross-sectional curves, a complete blade surface can be lofted through these spatial cross-sectional curves. This method is applied to generate the geometries of several practical propellers, including propellers for commercial ships, a surface-piercing propeller, and a warp propeller which adjusts the rake to nullify the skew induced rake.