A novel 3D radius compensation method of probe stylus tip in the free-form surface profile curve scanning measurement

The normal vectors of the free-form surface profile curve are generally not in the same plane, even if the profile curve is generated from the interaction between a plane and a surface. If the 2D compensation vector is adopted to reduce the cosine error, the accuracy is limited because the normal direction of the curve plane is not considered. In this paper, a novel radius compensation method adopts the 3D compensation vector instead of the 2D compensation vector like most existing works. An approximating method is proposed to estimate the 3D compensation vector, which is composed of two parts. One is the projection of the 3D vector in the curve plane that is calculated by the normal vector of the non-uniform rational Bezier spline fit curve. The other is the normal vector of the curve plane passing the measuring point. In addition, the deviation between the workpiece and CAD model may degrade the accuracy of the radius compensation. Through theoretical analysis, the influence of the deviation cannot be ignored when the deviation is larger than 0.2 mm. By setting up this threshold, under various levels of torsion angles and deviations for the free-form surface, the results show that the compensation accuracy of the proposed method has a better performance than traditional 2D compensation methods, which decreases the maximum error from 70.8 to 2.6 mu m.