风机叶片的Riemann几何研究

A Study of Air-blower Vanes by Using Riemannian Geometry

用 Riemann几何方法研究了风机叶片的设计问题 .得到了螺旋线切曲面的 Riemann曲率张量 Rlkij=0 ,从而指出了切曲面为可展曲面 ,并给出了设计单片式连续曲面结构叶片的有关参数 .

The problem of designing air-blower vanes is studied by using Riemannian geometry. It is shown that the Riemannian curvature tensor is zero R lkij =0 for the Tangent Surface of a spiral. Hence it is unfoldable. The relation between the diameters of the unfolded annulus and the Spiral pitch and axis diameter is given.