Strategy to Decrease the Angle Measurement Error Introduced by the Use of Circular Grating in Dynamic Torque Calibration

A circular grating angle encoder is a key component in the dynamic torque calibration system. To improve the accuracy of an angle measurement, in this paper, the source of the angle measurement error of the circular grating is analyzed; an eccentricity error model and an inclination error model are proposed, respectively; further, these two models are combined to establish a total error model. Through the simulation study with the models, the conditions, in which the eccentricity error or inclination error can be ignored, are discussed. The calibration and compensation methods of the angle measurement error are given, and a progressive error compensation function which integrates the first harmonic fitting and the second harmonic fitting is obtained. An experiment is performed to verify the proposed calibration and compensation methods. The peak-to-peak value of the compensated angle measurement error of the single reading head can be reduced by about 93.76%, which approximates to the error of the mean value of the double reading heads. The experimental results show that the error calibration and compensation method based on the proposed error model can effectively compensate the angle measurement error of the circular grating with a single reading head, and obtain a high-precision measurement angle.

Correcting the Eccentricity Error of Projected Spherical Objects in Perspective Cameras

Projective transformation of spheres onto images produce ellipses, whose centers do not coincide with the projected center of the sphere. This results in an eccentricity error, which must be treated in high precision metrology. This article provides closed formulations for modeling this error in images to enable 3-dimensional (3D) reconstruction of the center of spherical objects. The article also provides a new direct robust method for detecting spherical pattern in point clouds. It was shown that the eccentricity error in an image has only one component in the direction of the major axis of the ellipse. It was also revealed that the eccentricity is zero if and only if the center of the projected sphere lies on the camera’s perspective center. The effectiveness of the robust sphere detection and the eccentricity error modeling method was evaluated on simulated point clouds of spheres and real-world images, respectively. It was observed that the proposed robust sphere fitting method outperformed the popular M-estimator sample consensus in terms of radius and center estimation accuracy by a factor of 13, and 14 on average, respectively. Using the proposed eccentricity adjustment, the estimated 3D center of the sphere using modeled eccentricity was superior to the unmodeled case. It was also observed that the accuracy of the estimated 3D center using modeled eccentricity continuously improved as the number of images increased, whereas the unmodeled eccentricity did not show improvements after eight image views. The results of the investigation show that: (i) the proposed method effectively modeled the eccentricity error, and (ii) the effects of eliminating the eccentricity error in the 3D reconstruction become even more pronounced in a larger number of image views.

Research on Eccentricity Performance of Capacitance Rod Position Measurement Sensor for Measuring Non-Metallic Rod

Rod position measurement sensor is the key equipment of control rod hydraulic drive line, the measurement accuracy of the sensor is directly related to the safety and reliability of the reactor. Capacitance rod position measurement sensor is generally composed of excitation and detection electrodes, ceramic tube, outer shielding layer and measuring rod. For the double helix capacitance rod position measurement sensor with non-metallic measuring rod, the static characteristic experiment of the sensor was completed, the finite element method was used to establish the calculation model and the model was verified by the experimental results. By the calculation model, the influence of electrode angle, pitch, thickness and relative permittivity of ceramic tube on the eccentricity error of the sensor was systematically analyzed, the optimal combination of design parameters were obtained by orthogonal test method. The results show that the calculation results are in good agreement with the experimental results, the eccentricity error can be reduced by reducing the electrode angle, increasing the electrode pitch, increasing the thickness and reducing the relative permittivity of the ceramic tube. The design scheme of the sensor obtained by the orthogonal test can greatly reduce the eccentricity error and realize the requirement of rod position measurement without losing step. The research results provide guidance for the design and optimization of capacitance rod position measurement sensor.

Investigation of the Transmission Accuracy of Ball Screw Considering Errors and Preloading Level

Transmission accuracy is one of the most important parameters in ball screw mechanism (BSM), however, very few researches can be found on the transmission accuracy modelling for BSM. Therefore, this paper proposes a novel model to predicate the transmission accuracy of BSM considering the manufacturing errors, installation errors, as well as the errors due to the contact deformation under different loading status. Meanwhile, the transmission accuracy of a typical BSM under five different preloading levels is measured on the basis of a transmission accuracy measuring system. The experimental results show that the difference is 21.6% under no preload condition, and is less than 11% under different preload conditions, largely owing to the uneven distribution of clearance can increase the travel deviation. Further analysis shows that the eccentricity error, which belongs to the installation error, is the most important factor, mainly generating the periodic fluctuation and amplitude of the transmission error. More importantly, the travel deviation increases with the increase of the preload, which indicates that the transmission accuracy of the BSM deteriorates when the load is increased.

A Novel Concentric Circular Coded Target, and Its Positioning and Identifying Method for Vision Measurement under Challenging Conditions

Coded targets have been demarcated as control points in various vision measurement tasks such as camera calibration, 3D reconstruction, pose estimation, etc. By employing coded targets, matching corresponding image points in multi images can be automatically realized which greatly improves the efficiency and accuracy of the measurement. Although the coded targets are well applied, particularly in the industrial vision system, the design of coded targets and its detection algorithms have encountered difficulties, especially under the conditions of poor illumination and flat viewing angle. This paper presents a novel concentric circular coded target (CCCT), and its positioning and identifying algorithms. The eccentricity error has been corrected based on a practical error-compensation model. Adaptive brightness adjustment has been employed to address the problems of poor illumination such as overexposure and underexposure. The robust recognition is realized by perspective correction based on four vertices of the background area in the CCCT local image. The simulation results indicate that the eccentricity errors of the larger and smaller circles at a large viewing angle of 70° are reduced by 95% and 77% after correction by the proposed method. The result of the wing deformation experiment demonstrates that the error of the vision method based on the corrected center is reduced by up to 18.54% compared with the vision method based on only the ellipse center when the wing is loaded with a weight of 6 kg. The proposed design is highly applicable, and its detection algorithms can achieve accurate positioning and robust identification even in challenging environments.

Analysis on Meshing Characteristics and Transmission Error of Elliptic Gears

As an important parameter to distinguish noncircular gear from cylindrical gear, eccentricity is very important for the meshing characteristics and transmission error of noncircular gear. In order to study the transmission characteristics of the elliptic gear, a pair of elliptic gear in the reversing device of a new type of drum pumping was taken as the research object. Based on the analysis of the transmission pressure angle and instantaneous contact ratio of the elliptic gear, the eccentricity error was introduced into the analysis model of transmission error. The influences of the eccentricity on the transmission pressure angle, instantaneous contact ratio, and transmission error were analyzed, and the analysis accuracy is verified by the finite element method. The results show that the eccentricity has a great influence on the transmission pressure angle, instantaneous contact ratio, and transmission error of the elliptic gear, and the eccentricity error has a significant influence on the transmission error. In order to ensure the normal meshing condition of the elliptic gear, the eccentricity should be less than 0.7071, and the maximum instantaneous contact ratio is 1.809. The research results can provide some guidance for the following noncircular spur gear transmission test and transmission error research.