基于能量法的B样条农机工作部件曲线光顺研究

在农机工作部件曲面设计中关键曲线的好坏直接影响整个曲面的质量，因此对关键曲线的光顺成为其曲面造型的重点。基于能量的曲线光顺以应变能最小为光顺准则对数据点进行光顺，而当数据点较多时，传统能量法的存储量较大，计算速度较慢。该文对基于B样条的农机工作部件曲面关键曲线的光顺处理的传统能量法进行了改进，利用B样条曲线的性质直接对目标函数的线性方程组进行求解，大大地减少了数据的存储量，提高了计算速度。其基本原理是：用光顺后的农机工作部件曲面的特殊曲线，对整张曲面进行反求，得到新的曲面控制顶点，并依据新的控制顶点得到新的曲面，以达到对农机工作部件曲面光顺的目的。文中以农机工作部件中的犁体曲面为对象进行了算例研究，研究结果表明，利用该文的方法可以使光顺前后犁体曲面的等高斯曲率线图的平滑状况明显好转，新曲面的光顺状况比旧曲面得到改善。

Curve fairing for parts of agricultural machinery using B-spline based on the energy methodology

The special curve affects the quality of parts of agricultural machinery, so it is important how to fair the special curves of parts of agricultural machinery. The criterion is minimum strain energy on fairing curves and surface. For many data points, the traditional energy method has too much storage space and computing speed is too slow. This paper presents a practical methodology of fairing for B spline curves based on the energy methodology. The method directly solves the equation by the B-spline properties. The improved method needs much less storage space and computing speed is much faster. The principle of fairing surface is: fairing the special curve of parts of agricultural machinery, then attaining the control point of the new suface. In this paper, plow surface is regarded as a sample. At last, the iso-curvature curve of parts of agriculture machinery surface before and after fairing was attained. The research result shows that the surface fairing was improved.