Geometric Approximation Technique for Minimum Zone Sphericity Error

The mathematical modeling for evaluation of the sphericity error is proposed with minimum radial separation center. To obtain the minimum sphericity error from the form data, a geometric approximation technique was devised. The technique regarded the least square sphere center as the initial center of the concentric spheres containing all measurement points, and then the center was moved gradually to reduce the radial separation till the minimum radial separation center was got where the constructed concentric spheres conformed to the minimum zone condition. The method was modeled firstly, then the geometric approximation process was analyzed, and finally,the software for data processing was programmed. As evaluation example, five steel balls were measured and the measurement data were processed with the developed program. The average iteration times of the approximation technique is 4.2, and on average the obtained sphericity error is 0. 529μm smaller than the least square solution,with accuracy increased by 7. 696%.

ALGORITHM FOR SPHERICITY ERROR AND THE NUMBER OF MEASURED POINTS

The data processing technique and the method determining the optimal number of measured points are studied aiming at the sphericity error measured on a coordinate measurement machine （CMM）. The consummate criterion for the minimum zone of spherical surface is analyzed first, and then an approximation technique searching for the minimum sphericity error from the form data is studied. In order to obtain the minimum zone of spherical surface, the radial separation is reduced gradually by moving the center of the concentric spheres along certain directions with certain steps. Therefore the algorithm is precise and efficient. After the appropriate mathematical model for the approximation technique is created, a data processing program is developed accordingly. By processing the metrical data with the developed program, the spherical errors are evaluated when different numbers of measured points are taken from the same sample, and then the corresponding scatter diagram and fit curve for the sample are graphically represented. The optimal number of measured points is determined through regression analysis. Experiment shows that both the data processing technique and the method for determining the optimal number of measured points are effective. On average, the obtained sphericity error is 5.78 μm smaller than the least square solution, whose accuracy is increased by 8.63%; The obtained optimal number of measured points is half of the number usually measured.