Obtaining reliable and stable winding paths for complex shapes with current filament winding technologies is still a challenge. Aiming at a practical design of the filament winding process, a novel discrete non-iterative semi-geodesic (NIS) algorithm is proposed, in which a first-order ordinary different equation (ODE) of the tangent vector is directly solved over triangle meshes and then the tangent vector is parallel transported along a geodesic path. Compared to the existing discrete iterative semi-geodesic algorithm, the NIS algorithm does not require trial-and-error to determine the next path point and the time complexity of the NIS algorithm to generate a semi-geodesic path is O(n). The relative error of the NIS algorithm compared with analytical method is less than 1% in terms of mandrel’s rotation angle and winding angle. Then, a complete discrete winding path planning method based on the NIS algorithm is presented, including constant-wall-thickness winding paths at regular winding region, semi-geodesic winding paths at return regions and certain winding pattern construction. This winding path planning method does not require knowledge of the parametric equations of mandrel and is particularly useful for designing winding path for all applicable mandrels, such as vessel, rocket motor and so on.

使用当前的灯丝缠绕技术为复杂形状获得可靠稳定的缠绕路径仍然是一个挑战。针对灯丝缠绕过程的实际设计，提出了一种新的离散非迭代半测地线 (NIS) 算法，其中切向量的一阶常微分方程 (ODE) 在三角形网格上直接求解，然后切向量沿测地线路径平行传输。与现有的离散迭代半测地线算法相比，NIS算法不需要反复试验来确定下一个路径点，NIS算法生成半测地线路径的时间复杂度为O(n)。NIS算法与解析法相比，芯轴旋转角度和缠绕角度的相对误差小于1%。然后，提出了一种基于NIS算法的完整的离散绕组路径规划方法，包括规则绕组区域的等壁厚绕组路径、返回区域的半测地线绕组路径和一定的绕组模式构造。这种曲折路径规划方法不需要心轴参数方程的知识，特别适用于为所有适用的心轴设计曲折路径，例如船舶、火箭发动机等。