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.

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.

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.

In order to improve the accuracy of ultrasonic phased array focusing time delay, analyzing the original interpolation Cascade-Integrator-Comb (CIC) filter, an 8× interpolation CIC filter parallel algorithm was proposed, so that interpolation and multichannel decomposition can simultaneously process. Moreover, we summarized the general formula of arbitrary multiple interpolation CIC filter parallel algorithm and established an ultrasonic phased array focusing time delay system based on 8× interpolation CIC filter parallel algorithm. Improving the algorithmic structure, 12.5% of addition and 29.2% of multiplication was reduced, meanwhile the speed of computation is still very fast. Considering the existing problems of the CIC filter, we compensated the CIC filter; the compensated CIC filter’s pass band is flatter, the transition band becomes steep, and the stop band attenuation increases. Finally, we verified the feasibility of this algorithm on Field Programming Gate Array (FPGA). In the case of system clock is 125 MHz, after 8× interpolation filtering and decomposition, time delay accuracy of the defect echo becomes 1 ns. Simulation and experimental results both show that the algorithm we proposed has strong feasibility. Because of the fast calculation, small computational amount and high resolution, this algorithm is especially suitable for applications with high time delay accuracy and fast detection.

A novel measuring method for virtual pitch diameter of a thread was proposed. A customized measuring tip with a perfect threaded geometry was used to represent the appropriate counter piece of a geometric-ideal thread. During the measurement process, the tip moves along a helical path relative to the work-piece and always maintains the engagement with the work-piece to be measured. According to the changes of the tip’s position and orientation, a unique imaginary and perfect thread that can just contain the actual thread in 3D space is identified finally, whose pitch diameter can be considered as virtual pitch diameter of the work-piece. Compared with existing measurement methods, the measurement result obtained in the newly established measurement process can fulfill the requirements from the definition of virtual pitch diameter given by ISO 5408: 2009. The feasibility of the proposed method was validated on a developed prototype.