Measuring straightness errors of slender shafts based on coded references and geometric constraints

Abstract

The coded references and geometric constraints based method is suggested to solve the inconsistency problem of measurement range and accuracy for slender shafts. First, a slender shaft is divided into segments. Images of each segment along with a coded and calibrated reference are taken at two object distances. The code of the reference is obtained using the template match technique. Consequently, the coordinates of the feature points of the reference are solved. Thus, the external parameters of the camera are calculated. A mathematical model of the diameter, centre coordinate and external parameters is established based on the pinhole imaging principle. The problem that only one image cannot extract the centre coordinate is solved, as is the pseudo-diameter problem. A coordinate transformation model for these feature points is established and the sectional measurement results are associated by using the model. Experiments are carried out on lead screws; the measuring uncertainty of the experimental system is 0.007 mm, which is 12.9% higher than that of a coordinate measuring machine. The systematic error of the experimental system is 0.01754 mm. It is proved that the suggested method can stably and reliably measure the straightness errors of slender shafts with high accuracy.

Keywords

• measurement errors
• calibration
• coordinate measuring machines
• shafts
• measurement uncertainty
• cameras
• mathematical analysis
• slender shaft
• pinhole imaging principle
• pseudodiameter problem
• measuring machine
• geometric constraints
• calibrated reference coding
• straightness error measurement uncertainty
• template match technique
• coordinate transformation model