中文摘要：

针对由三坐标测量获得并经预处理的数据,提出通过NURBS法进行模型重构并通过两步匹配法实现对非圆锥齿轮复杂曲面的误差评定。首先,利用NURBS插值法对变速比非圆锥齿轮的齿面进行曲线及曲面重构,并用最小二乘法进行逼近,获得重构曲面模型。然后,综合应用ICP算法和BFGS算法,建立齿面误差评定模型,将测量数据与设计模型进行初始匹配和精确匹配,并通过MATLAB编程求解,得到欧氏变换矩阵,最终求得齿面误差为0.053 22 mm,满足齿轮设计要求。结果表明,该方法具有较高的重构精度和运算效率,并能较好地解决复杂曲面的误差评定问题。

英文摘要：

Based on the data obtained from the three -coordinate measuring and pre -processing, a NURBS method to reconstruct the complex surface of non - circular bevel gear and a two - step matching method to implement the complex surface error evaluation is proposed. The curve and surface reconstruction of the teeth surface is carried out by NURBS interpolation, and the least square approximation is adopted to gain the model of the reconstruction surface. Integrating ICP and BFGS algorithm, an error evaluation model is built, and the measuring data is initially matched and precisely matched to the design model. The model is solved by MATLAB programming, the Euclid transformation matrix is gotten and then the surface profile error of the gear can be achieved. Finally, the obtained error is 0. 053 22 mm, which meets the requirements of gear design. The calcu- lating results show that this method has high accuracy and speed to reconstruct the surface and can solve the error evaluation problem for the complicated surface.