Error compensation technology offers a significant means for improving the geometric accuracy of CNC machine tools (MTs) as well as extending their service life. Measurement and identification are important prerequisites for error compensation. In this study, a measurement system, mainly composed of a self-developed micro-angle sensor and an L-shape standard piece, is proposed. Meanwhile, a stepwise identification method, based on an integrated error model, is established. In one measurement, four degrees-of-freedom errors, including two-dimensional displacement and two-dimensional angle of a linear guideway, can be obtained. Furthermore, in accordance with the stepwise identification method, the L-shape standard piece is placed in three different planes, so that the measurement and identification of all 21 geometric errors can be implemented. An experiment is carried out on a coordinate measuring machine (CMM) to verify the system. The residual error of the angle error, translation error and squareness error are 1.5″, 2 μm and 3.37″, respectively, and these are compared to the values detected by a Renishaw laser interferometer.

The micro-displacement measurement system with 2D/3D has become increasingly important in the field of scientific research and technology application. In order to explore the application of an optical surface in micro-displacement measurement, a novel and simple 2D micro-displacement measurement method based on the elliptical paraboloid was designed and subjected to experiment. The measurement system takes advantage of the elliptical paraboloid instead of a plane mirror in the optical structure of an autocollimator which has been ameliorated to adapt to curved surface measurement. Through the displacement of the light spot on the CCD (Charge Coupled Device) detector, the displacement of the target could be measured with a linear correlation coefficient of 0.9999. The accuracy of the system is about ± 0.3 µm in a wide range in two dimensions. The results were in good agreement with the theoretical analysis and indicated the potential applicability of the proposed system in the detection of geometric errors of CNC (Computerized Numerical Control) machine tools.

In order to improve the accuracy of the linear motion of computer numerical control (CNC) machine tools, a novel method based on a new type of 1-D (1-dimensional) artifact is proposed to measure the geometric errors. Based on the properties of the displacement measurement of a revolutionary paraboloid and the angle measurement of plane mirrors, the 1-D artifact can be applied to identify position errors and angle errors. Meanwhile, the concrete 6 degrees-of-freedom error identification method is described in this paper in sufficient detail. Through measuring the 1-D artifact horizontally and vertically using the machine tool, the geometric errors can be obtained by calculating the deviation between the characteristic parameter of the 1-D artifact measured by the machine tool and that measured by a more precise method, for example, laser interferometry. Experiments were carried out on a coordinate measuring machine, and the validity and accuracy of the method were discussed by comparing the result with the identification error measured by a laser interferometer.

Using an optical freeform surface to realize the precision measurement of displacement has become a research focus in the present day. However, the measurement range of this method is limited by the size of the freeform surface processed. In order to overcome this difficulty, this paper presents a two-dimensional displacement measurement system with a large range, which is composed of a slope sensor and a rotating paraboloid array. The slope sensor utilizes the optical structure of an autocollimator with minor optimization, and the rotating paraboloid array expands the measurement range of the system in a discrete manner. The experimental results showed that the optimized optical system enhanced the measurement accuracy to ±0.4 μm within the range of 1500 μm and the overall measurement error was approximately ±2 μm when measured within the range of 450 mm. The developed measurement system has potential applicability for detection of errors, such as the position error and straightness error of multi-axis systems.

The elliptical paraboloid array plays an important role in precision measurement, astronomical telescopes, and communication systems. The calibration of the vertex distance of elliptical paraboloids is of great significance to precise 2D displacement measurement. However, there are some difficulties in determining the vertex position with contact measurement. In this study, an elliptical paraboloid array and an optical slope sensor for displacement measurement were designed and analyzed. Meanwhile, considering the geometrical relationship and relative angle between elliptical paraboloids, a non-contact self-calibration method for the vertex distance of the elliptical paraboloid array was proposed. The proposed self-calibration method was verified by a series of experiments with a high repeatability, within 3   μ m in the X direction and within 1   μ m in the Y direction. Through calibration, the displacement measurement system error was reduced from 100   μ m to 3   μ m . The self-calibration method of the elliptical paraboloid array has great potential in the displacement measurement field, with a simple principle and high precision.