摘要
提出了一种基于最小二乘原理的平面任意位置双曲线轮廓误差评定方法。根据双曲线的几何特性和形状误差的定义,利用双曲线标准方程与平面二次曲线方程关系,得到平面任意位置双曲线的拟合方程,并通过双曲线方程及双曲线法线方程的特点,计算出各测量点到拟合出的最小二乘双曲线的法向距离从而对平面任意位置上的双曲线轮廓度进行误差评定。实例证明:该算法可以实现平面任意位置上的双曲线轮廓度误差评定,具有一定的评定精度,可适用于一些误差精度要求不高的零件或设备的轮廓度误差评定,并且不需进行坐标转换。
A method for evaluating the error of hyperbolic profile of arbitrary position on the plane based on the least square principle is presented. According to the definition of the geometric characteristics and the shape error of the hyperbolic curve, using the relationship between the hyperbolic equation and the planar quadratic curve equation, the hyperbolic fitting equation of arbitrary position on the plane is obtained. And based on the characteristics of the hyperbolic equation and the normal equation of the hyperbolic, the normal distance of the least square curve fitting is calculated to realize the error evaluation of the hyperbolic profile of arbitrary position on the plane. Example proves that this algorithm can realize the error evaluation of the hyperbolic profile of arbitrary position on the plane. It has a certain rating accuracy and can be applied to some profile error evaluation of parts or equipment which error of accuracy is not high. The coordinate transformation is not needed.
出处
《机械设计与制造》
北大核心
2016年第10期87-89,93,共4页
Machinery Design & Manufacture
基金
中国国家自然科学基金(51475145)
关键词
双曲线
任意位置
误差评定
最小二乘法
Hyperbola
Arbitrary Position
Error Evaluation
Least Square Method
