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.

Download Full-text

Mechanism and Compensation of Measurement Error Induced by Thermal Deformation of Digital Camera in Photo Mechanics

Applied Sciences ◽

10.3390/app10103422 ◽

2020 ◽

Vol 10 (10) ◽

pp. 3422 ◽

Cited By ~ 1

Author(s):

Shichao Zhou ◽

Haibin Zhu ◽

Qinwei Ma ◽

Shaopeng Ma

Keyword(s):

Measurement Error ◽

Thermal Deformation ◽

Environmental Temperature ◽

Digital Camera ◽

Underlying Mechanism ◽

Compensation Method ◽

Digital Cameras ◽

High Precision Measurement ◽

Compensation Methods ◽

Measurement Results

A thermal-induced measurement error induced by thermal deformation of digital camera in photo mechanics methods that has the same magnitude of the error as that in the resistance strain measurement method reduces the accuracy of high-precision measurement substantially and must, therefore, be compensated. Starting from the underlying mechanism of a thermal-induced measurement error, we investigated the image error introduced by thermal behaviours of digital cameras widely used in photo mechanics. We experimentally determined the relationships between the thermal behaviours and temperature, derived the relationship between the image error and measurement error of photo mechanics methods, and eventually established a physical model to explain the underlying relationship between the thermal-induced measurement error and temperature. Furthermore, based on the investigation of the underlying mechanism, we introduced three types of temperature compensation methods for photo mechanics, namely the model compensation method, the preheating method, and the compensation specimen method. We experimentally demonstrated the feasibility of these compensation methods. The model compensation method only needs the data regarding the environmental temperature during operation of the digital camera to implement the correction of the measurement results and enhance the measurement accuracy of photo mechanics methods. The preheating method is suitable for indoor photo mechanics measurements wherein the environmental temperature is almost constant, which ensures that the appearance of thermal balance of the digital camera after a period of self-heating. The compensation specimen method reduces the effective resolution of the images and it also requires that the image error forms in the region of tested specimen are the same as that in the region of the compensation specimen.

Download Full-text

A New Method of Angle Measurement Error Analysis of Rotary Encoders

Applied Sciences ◽

10.3390/app9163415 ◽

2019 ◽

Vol 9 (16) ◽

pp. 3415 ◽

Cited By ~ 2

Author(s):

Hua-Kun Jia ◽

Lian-Dong Yu ◽

Hui-Ning Zhao ◽

Yi-Zhou Jiang

Keyword(s):

Measurement Error ◽

Measurement Accuracy ◽

Angle Measurement ◽

Error Model ◽

Source Analysis ◽

Measuring Instruments ◽

Rotating Shaft ◽

Radial Error ◽

Precision Measuring ◽

Error Motion

In this article, a method of error source analysis and detection to improve the angle measurement accuracy of rotary encoders in precision measuring instruments is proposed. The angle measurement error caused by the installation eccentricity of the grating disk and the radial error motion of the rotating shaft is analyzed, and the error model is built. The method of measuring the radial error motion is introduced, and the visual system and image processing technology is proposed to detect the eccentricity. The verification experiment by the use of an autocollimator and a polygon is carried out. The residual error after comparison within ±6″ accounts for 9% of the angle measurement error. The proposed error model is verified, and the angle measurement error can be predicted if the installation eccentricity and radial error motion are known.

Download Full-text

A Generalized Maximum Entropy Estimator to Simple Linear Measurement Error Model with a Composite Indicator

SSRN Electronic Journal ◽

10.2139/ssrn.2257822 ◽

2013 ◽

Author(s):

Maurizio Carpita ◽

Enrico Ciavolino

Keyword(s):

Measurement Error ◽

Maximum Entropy ◽

Linear Measurement ◽

Composite Indicator ◽

Error Model ◽

Measurement Error Model ◽

Generalized Maximum Entropy ◽

Entropy Estimator

Download Full-text

A Measurement Error Model of Dichotomous Democracy Status

SSRN Electronic Journal ◽

10.2139/ssrn.2726962 ◽

2015 ◽

Cited By ~ 1

Author(s):

Sean J. Taylor ◽

Jay Ulfelder

Keyword(s):

Measurement Error ◽

Error Model ◽

Measurement Error Model

Download Full-text

An Optical Frequency Domain Angle Measurement Method Based on Second Harmonic Generation

Sensors ◽

10.3390/s21020670 ◽

2021 ◽

Vol 21 (2) ◽

pp. 670

Author(s):

Wijayanti Dwi Astuti ◽

Hiraku Matsukuma ◽

Masaru Nakao ◽

Kuangyi Li ◽

Yuki Shimizu ◽

...

Keyword(s):

Femtosecond Laser ◽

Second Harmonic Generation ◽

Frequency Domain ◽

Harmonic Generation ◽

Measurement Method ◽

Second Harmonic ◽

Angle Measurement ◽

Laser Source ◽

Optical Frequency ◽

Measurable Range

This paper proposes a new optical angle measurement method in the optical frequency domain based on second harmonic generation with a mode-locked femtosecond laser source by making use of the unique characteristic of the high peak power and wide spectral range of the femtosecond laser pulses. To get a wide measurable range of angle measurement, a theoretical calculation for several nonlinear optical crystals is performed. As a result, LiNbO3 crystal is employed in the proposed method. In the experiment, the validity of the use of a parabolic mirror is also demonstrated, where the chromatic aberration of the focusing beam caused the localization of second harmonic generation in our previous research. Moreover, an experimental demonstration is also carried out for the proposed angle measurement method. The measurable range of 10,000 arc-seconds is achieved.

Download Full-text

ON THE UNIFORM CONVERGENCE OF DECONVOLUTION ESTIMATORS FROM REPEATED MEASUREMENTS

Econometric Theory ◽

10.1017/s0266466620000572 ◽

2021 ◽

pp. 1-22

Author(s):

Daisuke Kurisu ◽

Taisuke Otsu

Keyword(s):

Multivariate Analysis ◽

Measurement Error ◽

Uniform Convergence ◽

Measurement Errors ◽

Convergence Rates ◽

Free Variable ◽

Error Model ◽

Repeated Measurements ◽

Empirical Characteristic Function ◽

Measurement Error Model

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.

Download Full-text