Optimization method for systematically improving non-contact R test accuracy

Abstract

Non-contact R-test is an instrument to measure the synchronous errors of five-axis machine tools. However, there are still some deficiencies in its researches, such as the difficult and laborious calibrations. How to systematically improve the measurement accuracy with a good balance to minimum cost is a real problem in guiding practice. This paper proposes a new systematic optimization method to solve this problem based on comprehensive understanding of the non-contact R-test in terms of structure parameters and relations. Firstly, the algorithm for sphere center coordinates is established based on the self-adaptive differential evolution algorithm to obtain the definite computational accuracy and efficiency. Secondly, the parameters of the fixture structure are optimized to maximize the measurement stability, measuring space and noninterference space. Thirdly, the on-machine calibration is performed to replace pre-calibration and re-calibration, and to establish the positional relationships between sensors, the fixture and the machine tool simultaneously. It can reduce the difficulties of manufacture, maintenance and application. Fourthly, the measurement accuracy can be evaluated to determine whether the iterative optimization achieves the goal. The proposed method has been verified with case studies to support optimized non-contact R-test setting up, leading to cost-effective and accuracy test on five-axis machine tools.

Research on the Novel Hardware Configuration Methods of the Contact R-test Based on the Constraint Models

“…However, it can be known from the structural characteristics of the R-test that the position coordinates of the sensors are directly affected by the installation errors of the sensors, which include the installation angle deviation Δαi between the sensor axis and the Z-axis of the CSYSM, and the angle deviation Δβi projected on the reference plane of the three sensor axes. In general, the sensor installation error can be eliminated during the instrument calibration process, and the most common calibration methods mainly include two methods: preliminary calibration and on-machine calibration [16] . Moving the feed axis of the calibration equipment accurately in the CSYSM, the sphere center is located at 6 arbitrary calibration points Pj (xj, yj, zj), j=1,2,...,6 within the measuring range of the sensor.…”

“…when there is a small amount of position change at the sphere center. The relational expression is , 1, 2,3 (9) where ΔP = (Δx, Δy, Δz), and the Jacobian matrix J represents the mapping relationship between ΔP and Δli , which is only related to the installation angle of the sensor [16] . The smaller amplitude of Δli, the better measuring stability.…”

“…Based on the Eqs. ( 10), the installation angle requirement for maximum stability can be obtained by solving the second-order condition number of the matrix formed by the partial derivative of the sphere center coordinates relative to the sensor reading [16] , and the detailed solution process will not be repeated here. (2) The constraint model of measuring space As for the measuring space, when the sensor installation angles are certain, it is simultaneously affected by the sensor range, the sensor detection plane radius and the ball radius.…”

“…It can be known from the optimization method in the literature [16] and Eqs. ( 10) that the measuring stability of the R-test is only related to the sensor elevation angle α, and is not affected by the sensor range l0 and the ball radius R. Therefore, the maximum measuring stability can be ensured by determining the parameter of the sensor elevation angle α, and the maximum measuring stability can be obtained when α is 35.3°.…”

“…Li et al derived the transformation model between the sensor reading and the three-direction displacement of the measuring sphere, and determined the main error factors affecting the error measurement device and analyzed the overall uncertainty of the device based on the model [15] . Jiang et al improved the calculation accuracy and efficiency of the spherical center coordinates using the adaptive differential evolution algorithm, optimized the structural parameters based on the measurement performance indicators, and finally formed system optimization methods to balance the measurement accuracy and cost [16] .…”