Sphericity measurement based on telecentric imaging mechanism with image distortion correction and eccentricity error compensation

Abstract Sphericity is an essential geometric parameter for determining the processing manufacturing quality of spherical components. This study presents a sphericity measurement method based on telecentric imaging mechanism with image distortion correction and eccentricity error compensation. A sphericity measurement system is designed, and the projection images of the cross-section on the equatorial plane of the measured sphere are acquired using a line scan camera with bilateral telecentric lenses. An analytical camera model for this sphericity measurement system is established by considering major sources of image distortion. The subpixel edge points of the projection images are extracted and converted to cross-sectional profiles on the equatorial plane according to the camera model. An eccentricity error compensation strategy for contour matching of the obtained cross-sectional profile on the equatorial plane is also developed to obtain the three-dimensional contour point coordinates of the sphere. Sphericity is then calculated according to the least square criterion. The effectiveness of the proposed method is verified by measuring two steel balls with diameter in 20 mm and 30 mm. The sphericity measurement error is reduced by 0.3383 mm and 0.4653 mm respectively after image distortion correction and is reduced by 0.2268 mm and 0.0795 mm respectively after eccentricity error compensation. The proposed method can be extended to form error measurements for opaque components with rotary structure on the outer contour.