Uncertainty Estimation due to Geometrical Imperfection and Wringing in Calibration of End Standards

Uncertainty in gauge block measurement depends on three major areas, thermal effects, dimension metrology system that includes measurement strategy, and end standard surface perfection grades. In this paper, we focus precisely on estimating the uncertainty due to the geometrical imperfection of measuring surfaces and wringing gab in calibration of end standards grade 0. Optomechanical system equipped with Zygo measurement interferometer (ZMI-1000A) and AFM technique have been employed. A novel protocol of measurement covering the geometric form of end standard surfaces and wrung base platen was experimentally applied. Surface imperfection characteristics of commonly used 6.5？mm GB have been achieved by AFM in 2D and 3D to be applied in three sets of experiments. The results show that there are obvious mapping relations between the geometrical imperfection and wringing thickness of the end standards calibration. Moreover, the predicted uncertainties are clearly estimated within an acceptable range from 0.132？μm, 0.164？μm and 0.202？μm, respectively. Experimental and analytical results are also presented. 1. Introduction In nonmetrology, estimation of uncertainty in dimension measurements is a vital part in calibration processes. The uncertainty estimation is always influenced by the procedures and the conditions of length measurement. End-to-end effects in calibration of end standards are constantly a necessary part in length metrology. From the calibration of primary length standards (a stabilized laser wavelength) to the calibration of secondary end standards (gauge blocks, GBs), it was important to accurately identify the major impacts on the uncertainty estimation. There are many grades of gauge blocks (00, , 0, and industrial grade) that are commonly working as end standards in different accurate industrial applications, especially in automotive and airspace industries. One must know the requirements of gauge blocks: the surfaces must have a smooth finish, the surfaces must be flat, the double faces must be parallel, and the actual size must be known as a natural expression of the nominal size [1, 2]. Materials of GBs are made including specific conditions such as hardness, temperature stability, corrosion resistance, and high-quality finish. Figure 1 emphasizes the truth of the metrologists saying “No surface is perfectly smooth.” The surface of GB is rarely so flat or smooth, but most commonly it is a combination between the tolerances limits and due to the surface finish quality. In dimensional metrology, such calibration should be performed to