【摘要】 针对当前测量领域内球度差的超精密测量和评定这一薄弱环节 ,采用“经线法”球度误差测量技术 ,通过超精型圆度仪和相应的支承装置实现对外球面轮廓的测量 .建立了采样数据的维数转换数学模型和球度误差最小二乘法评定数学模型 ,在最小区域法、最小外接球法、最大内接球法评定球度时 ,充分利用了最优化理论的单纯型法 .为了验证该理论及软件的精度 ,作了大量仿真试验 ,并利用不同半径的球体、椭球、以及带有一定规律误差的球进行验证 ,通过分析可证明“经线法”理论是正确的 ,该系统的设计方案是切实可行的 ,并且该算法精度较高 ,可达到 0 .0 1μm .更多还原

【Abstract】 Aiming at the difficult problem of measurement land evaluation of sphericity error in the field of measurement, a further research on this problem is done based on the theory of "Longitude Method" for sphericity error measurement, and the outer sphere profile is measured by the ultra precision roundness measuring machine and its support. The least squares criterion is used and the key problem of transforming two dimension data sampled from the roundness measuring machine to three dimension data is solved. Simplex method of optimization theory is adopted in spherecity evaluation using the methods of minim circumsphere (MCS), Maxim inscribed sphere (MIS) and minim zone sphere (MZS). Simulation experiments for sphericity error measurement, and calibration and evalutation are made on the computer on the base of above work. The profiles of different radius sphere, elliptical sphere and sphere with error are given. By analyzing the experiment results and the experiment system, the validity of "Longitude Method" sphericity error measurment theory and the feasibility of above measuring methods and material measures are verified, and 0.01μm precision is obtained.更多还原