单叶双曲面螺旋弹簧参数化造型方法

Parameters Modeling Methods of Helical Spring on Hyperboloid of One Sheet

建立单叶双曲面螺旋线方程,运用平移、旋转等坐标变换法在螺旋线起点绘制基圆,使基圆面与螺旋线起点切线垂直。在AutoCAD中,利用"Extrude"命令将基圆沿螺旋线拉伸形成单叶双曲面螺旋弹簧。分析了螺旋弹簧导程与单叶双曲面参数以及基圆半径之间的关系,并构建了近似表达式。实验表明,这种近似表达法在计算机造型中应用是可行的。最后,研究了截面为非圆形单叶双曲面螺旋体的形成原理及造型方法。

The equation of the helix on hyperboloid of one sheet is given. The coordinate transformation such as rotating, moving, and so on, are used to draw a circle at the start point of the helix. The plane of the circle and the tangent of the start point of the helix are vertical. The command ＂extrude＂ in AutoCAD is used to move the circle on the spiral helix for making the helical spring on hyperboloid of one sheet. The relations about the lead of the helical spring, the parameters of the hyperboloid of one sheet and the radius of the circle are analyzed, and the approximate equation of theirs is given. It is proved that the approximate equation is a feasible method in computer modeling. Finally, the forming principle and the modeling method of which the section of the helical body on hyperboloid of one sheet is not circular are studied.