This paper mainly focuses on the sphericity evaluation based on the minimum zone sphere (MZS) method in the Cartesian coordinate system. An asymptotic search method is proposed to search for the homocentric centre of MZS model and calculate the sphericity error. The search process of the proposed method consists two parts: geometric area search is implemented to obtain a quasi-MZS centre (close to the MZS centre) and 3+2 and 2+3 mathematical models dominating the minimum zone sphere are solved to obtain the MZS centre. The geometric area search is employed to fast convergence to the quasi-MZS centre by constructing a search sphere model. Some characteristic points distributed on the search sphere are selected to determine the search direction. A threshold is set to terminate the search process and the quasi-MZS centre is determined as a result. The quasi-MZS centre is employed as a reference centre to solve the 3+2 and 2+3 models to determine the MZS centre. According to the minimum conditions, the mathematical models are established to solve the two models. Then the judgment is implemented to ensure all the measured points are enveloped between the two homocentric spheres. As a result, the centre of two homocentric spheres is the MZS centre. The MZS sphericity error can be obtained as well. To verify the performance of the proposed method, simulation experiments and comparison experiments are implemented. The results demonstrated that the proposed method is effective, reliable and meet the requirement of sphericity evaluation.
Probe tip of the Micro-coordinate Measuring Machine (Micro-CMM) is a microsphere with diameter of several hundred microns, and its sphericity is generally controlled at tens to hundreds of nanometers. Due to the small size and high precision requirement, the measurement of the microsphere morphology is difficult. In this paper, a measurement method for probe microsphere of Micro-CMM is proposed based on two SPM (Scanning Probe Microscope) probes, and a ruby microsphere of a Renishaw commercial CMM stylus is measured by the proposed method. In the experiment, the repeatability error of a maximum section profile is test, and the repeatability error is 41 nm (peak-to-peak value). Two perpendicular maximum section profiles are measured, and the corresponding diameter and roundness are estimated by the least squares method.
The zero initial optical path difference, the integral optical path layout and the polarization interference technique are adopted to design quadruplicated polarized laser interferometer measuring system. The factors and design requirements which affect high-precision interferometer are analyzed. In order to reduce DC offset error, unequal amplitude error and non-orthogonal error, four orthogonal measuring signals are processed by a series of circuits with differential amplification and orthogonalization functions, and the two ideal orthogonal measuring signals are obtained. Beyond the VC++ environment, combined with the 200 phase subdivision, the resolution of 0.8 nm can be achieved. The measuring results are compensated and corrected according to the environmental parameters. The error sources of the measuring system are analyzed, and the quantitative values of the cosine error and abbe error are given. Compared with the British Renishaw XL-80 high-precision laser interferometer, the experimental results show that the measuring system has high stability and accuracy.