圆锥面等测地曲率曲线的轨迹规划方法

为解决复合材料锥壳铺放过程中的纤维残余应变过大的问题,提出了等测地曲率曲线的轨迹规划方法。通过分析发现轨迹的测地曲率决定了纤维的残余应变,于是通过计算圆锥上任意曲线的测地曲率推导出了等测地曲率曲线的表达式,并证明在圆锥展开面上等测地曲率曲线是圆弧。最后,通过计算等测地曲率轨迹的残余应变及其与圆锥母线的夹角分析该轨迹铺放工艺性。结果表明:等测地曲率轨迹相较于固定角轨迹与测地线轨迹具有良好的可设计性和铺放工艺性。

Trajectory planning method for constant geodesic curvature curve of cone

To solve the problem of excessive residual strain of fiber in conical shell laying process,a trajectory planning method with constant geodesic curvature is proposed.Analysis shows that the geometric curvature of the trajectory determines the residual strain of the fiber.The expression for the constant curvature curve is then derived by calculating the geometrical curvature of the arbitrary curve on the cone,and the constant geodesic curvature curve is proved to be a circular arc on the conical surface.The trajectory laying process is analyzed by calculating the residual strain of the constant geodesic curvature trajectory and its angle with the conical busbar.The results show that the constant geodesic curvature trajectory is better designability and laying processability than the fixed angle trajectory and the geodesic trajectory.