Abbe error compensation for a micro/nano CMM with a coplanar stage

Abstract

A micro/nano Coordinate Measuring Machine (CMM) with a stroke of 20 mm × 20 mm × 10 mm has been developed by our group. The “Pagoda structure” with Chinese style is adopted, which has fine mechanical stability. The base of the micro/nano CMM is made of granite to achieve high thermal stability. The stages are driven by piezoelectric motors with a resolution of 1 nm in three directions. The displacements of the stages in horizontal directions are detected by homemade Michelson interferometers. The optical axes of the two interferometers are consistent with their slide way of the coplanar stages respectively, which can reduce the Abbe errors in X and Y axes as much as possible. Semiconductor laser diodes are used as the light source of the interferometers due to low-cost and small size. A linear diffraction grating interferometer (LDGI) has also been developed to detect the displacement in Z direction. After subdivision, the measuring resolution can reach nanometer scale. The micro/nano CMM is compatible with different types of probes. A model of Abbe error and its compensation method are proposed in this paper. Experimental results show that the positioning errors were reduced from 435 nm to 91 nm and from 426 nm to 151 nm via Abbe error compensation method. The flatness of a 0-grade gauge block was tested by the micro/nano CMM, the repeatability of 44 nm (K=2) was achieved.