The determination of the optimal measurement area of the articulated arm measuring machine belongs to the multi-dimensional function optimization problem under complex constraints. To realize high-precision measurement of low-precision articulated arm measuring machine, we analyze the working principle and error source of the measuring machine, and establish the optimization target model of the optimal measurement area in this paper. We propose a method for determining the optimal measurement area of an articulated arm measuring machine based on improved FOA. The basic FOA algorithm is improved, the historical optimal individual and population centroid information are added in the population iteration update process, and the fruit fly individuals in each iteration are directly used as the taste concentration judgment value, which increases cooperation and information sharing among fruit fly individuals, and improves the global optimization ability and stability of the algorithm. In the designated area of the measuring machine, we have carried out comparative experiments on the optimization results of improved FOA and basic FOA, ACO, PSO, AL-SC-FOA, LGMS-FOA, IPGS-FFO. Experimental results show that the improved FOA, ACO, PSO, and IPGS-FFO algorithms do not fall into local optimum, and the optimal measurement area determined by them is consistent with the optimization results of other algorithms, and is superior to other algorithms in convergence speed and stability, so it is more suitable for determining the optimal measurement area of articulated arm measuring machine.

To address the problems of the low accuracy of geometric error identification and incomplete identification results of the linear axis detection of computer numerical control (CNC) machine tools, a new 21-item geometric error identification method based on double ball-bar measurement was proposed. The model between the double ball-bar reading and the geometric error term in each plane was obtained according to the three-plane arc trajectory measurement. The mathematical model of geometric error components of CNC machine tools is established, and the error fitting coefficients are solved through the beetle antennae search particle swarm optimization (BAS–PSO) algorithm, in which 21 geometric errors, including roll angle errors, were identified. Experiments were performed to compare the optimization effect of the BAS–PSO and PSO and BAS and genetic particle swarm optimization (GA–PSO) algorithms. Experimental results show that the PSO algorithm is trapped in the local optimum, and the BAS–PSO is superior to the other three algorithms in terms of convergence speed and stability, has higher identification accuracy, has better optimization performance, and is suitable for identifying the geometric error coefficient of CNC machine tools. The accuracy and validity of the identification results are verified by the comparison with the results of the individual geometric errors detected through laser interferometer experiments. The identification accuracy of the double ball-bar is below 2.7 µm. The proposed identification method is inexpensive, has a short processing time, is easy to operate, and possesses a reference value for the identification and compensation of the linear axes of machine tools.

As the core component of CNC machine tools, the positioning accuracy of the XY worktable directly determines machining performance. Current research mainly focuses on single-factor error analysis, lacking comprehensive investigation on multi-factor coupling effects including cutting force, cutting point position, movement speed, and guide rail spatial position. To improve machining accuracy, this paper takes the XY worktable as the research object, reveals the multi-factor dynamic positioning error mechanism, and establishes a comprehensive error model integrating angle error, guide rail system error, and ball screw system error. Theoretical calculation, simulation, and laser interferometer experiments are conducted under different working conditions. Results show that there exists an optimal measurement speed to minimize dynamic error; the variation trends of theoretical, simulated, and experimental errors are consistent. After error compensation, the positioning error is reduced by 40.04%, which validates the effectiveness of the proposed model.

The XY worktable is a critical component of CNC machine tools and a significant source of measurement errors in on-machine measurement systems. To accurately compensate for these errors, this study proposes a compensation method based on the instantaneous rotation center of the worktable. First, the definition of the yaw, pitch, and roll instantaneous rotation centers of the machine tool XY worktable is proposed, and the determination model of the instantaneous rotation center is established. A simplified model of the XY worktable is established by using three-dimensional software. The existence of the yaw instantaneous center, pitch instantaneous center, and roll instantaneous center is verified by automatic dynamic analysis of the mechanical system’s dynamic simulation analysis method. The coordinate positions of each instantaneous center during the movement of the worktable along the X and Y directions are plotted. At the same time, the three-axis velocity sensors are used to build the experimental device for the actual experiment. According to the measured three-dimensional velocity data and the established instantaneous rotation center determination model, the actual location of the instantaneous rotation center is calculated, and the correctness of the established determination model is verified. On this basis, the influence of the yaw instantaneous center, pitch instantaneous center, and roll instantaneous center on the positioning error of the X and Y guide systems of the worktable is analyzed, and the positioning compensation model of the guide systems by using the instantaneous center is established. Meanwhile, the experimental devices for measuring the positioning error, yaw angle motion error, and pitch angle motion error of the worktable guide systems are established using a laser interferometer. The traditional positioning error compensation model and the above-mentioned positioning error compensation model of guide systems using the instantaneous center are used to compensate. From the compensation results, the positioning error compensation model based on the instantaneous center of the guide systems is better, and it can improve the measurement accuracy of the CNC machine tool on-machine measurement system more effectively.

Involute gear template is a standard measuring instrument for gear measurement. In order to ensure the high-precision calibration of gear measuring instruments, based on the structure of gear involute template processing device, the error source is analyzed in detail, and the error transmission model between each single error and the total deviation of template tooth surface is accurately established. On this basis, the simulation experiment is carried out, the primary and secondary influencing factors of the total deviation of the sample tooth surface are analyzed, and the comprehensive model of the total deviation of the sample tooth surface is established. In order to verify the correctness of the established error model, the numerical simulation experiments such as eccentricity error and guide rail error of the template are carried out by MATLAB, and the total deviation of gear involute template tooth surface is measured by inductance micrometer. The experimental results show that the eccentricity error of template installation, the deviation angle error of template, the assembly eccentricity error of double basic circular wheels, the ovality error of the working surface of basic circular wheels, and the micro-deformation error after wheel-rail contact are the main factors affecting the total deviation of template tooth surface. The precision of gear measuring instruments can be improved by accurately compensating each single error, which provides a theoretical basis for the precision improvement of gear involute template processing device.