基于近似测地线的分层次自动铺带轨迹规划方法

自动铺带技术是一种增量制造技术，适用于制造翼面、壁板等大尺寸、小曲率复合材料构件，具有加工成本低、效率高等特点。轨迹规划是自动铺带技术的关键环节，它直接关系到复合材料构件的成型精度与质量。现有的自动铺带轨迹规划方法难以便捷兼顾调控铺放间隙与防止铺放褶皱，保证铺带产品的最终质量。有鉴于此，提出了一种基于近似测地线的分层次铺放轨迹规划方法。主要目标是合理利用预浸带允许变形能力，在防止铺放褶皱产生的前提下，保证相邻带料不产生覆盖，且间隙不超过2.5 mm。首先，研究了铺放间隙的产生与演化规律，给出了几种典型曲面上初始铺放间隙的优化方法。接下来，提出了近似测地线的数学模型与求解格式。然后，基于铺放褶皱的产生机制与铺放间隙的演化规律，确定了近似测地线的测地曲率大小与符号。最后，在双曲面模具以及自由曲面模具上验证了所提出方法的有效性。

A Multi-level Trajectory Planning Method Based on Quasi-geodesic for Automated Tape Placement

Automated tape placement (ATP) is one kind of additive manufacturing technology, and suitable for manufacturing composite components with large size and small curvature, such as airfoil and panel. This technology has the advantage of low cost and high efficiency. Trajectory planning is the key link of ATP, which directly affects the precision and efficiency of the lay-up process, and the quality of final product. Existing trajectory planning methods for ATP generally show difficulties in adjusting lay-up gaps and conveniently suppressing the appearance of wrinkles at the same time. For this reason, a multi-level trajectory planning method based on quasi-geodesic is presented. The proposed approach takes advantage of the deformability of prepreg to prevent overlaps and gaps which are greater than 2.5 mm between adjacent tapes. Firstly, the evolution law of lay-up gaps on non-developable surfaces is deduced. At the same time, an optimization strategy for initial lay-up gaps on several typical surfaces is introduced. Then, a mathematical model for quasi-geodesic is established on the basis of differential geometry. Next, the magnitude and sign of the geodesic curvature on the quasi-geodesic is specified based on the forming mechanism of wrinkles and the evolution law of lay-up gaps. Lastly, the proposed methodology is validated on a hyperboloid surface and a freeform surface.