Evaluate The Profile Error Of Complicated Curve

CNC gear measuring center is one kind of high accuracy and high efficiency coordinate measuring instrument. The research on the shape error measure and evaluation of the complex components with CNC gear wheel measuring center has important theory significance and economic value.The profile error is the item which applies widespread but difficult to measure and evaluate in country standard and international standard of the components shape error and position error. With the development of technology, many non-linear curve and surface have been widely used. The theory form of those curve and surface is always expressed by discrete points but not known mathematics equation. The data measured by CNC gear wheel measuring center are also discrete. It is very difficult to evaluate its profile error.The method to evaluate the profile error of complex curve and surface is always the least square method. The least square method is an approximate method, it can not fit the least zone principle. In this article, several important problems when evaluate the profile error of plane curve are discussed. The outline curve is expressed with parameters cubic spline, include actual curve and theory curve. The deviation equation between actual curve and theory curve was built,and the computational method has been analyzed. A precise mathematics model of evaluation was built and the calculate method was analyzed. An approaching method was proposed to evaluate the profile error of curve. The approaching method can adjust the coordinate difference between the measured profile and its theory profile automatically, and it can make measured profile best fitting its theory profile. The approaching method is one kind of method which can conform to the least zone principle best. While obtains the shape error, the position error between measured profile and its theory profile can obtained. The theory of equidistant curve was used to add error at theory curve. The programs of evaluate were write. The experiment proved that the approaching method can figure out the profile error of complex curve accurately.