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A method to identify the position error of direct drive numerical control turntable by measuring current and eccentric load is proposed, and the position error model of direct drive numerical control turntable based on whale Optimized BP (WOABP) neural network is established. The test-bed is built to measure the current, eccentric load and position error. The measured current and eccentric load are trained by WOABP neural network, and the position error of direct drive numerical control turntable is obtained. By comparing the original error, the error obtained by BP neural network and the error obtained by WOABP neural network, the effectiveness of WOABP neural network model is verified. The position error of direct drive numerical control turntable is compensated by the error obtained by the model.

The contour following task of a multi-axis servo system is one of the most important applications of modern computer numerical control (CNC) machining. Reducing the contour error is an important content in the multi-axis contour following task. A common method to solve this problem is the cross-coupling control (CCC). Since the traditional CCC method cannot meet the requirements of tracking accuracy and contour control accuracy at large curvature positions in free-form curve machining, the main contribution of this paper is to propose a novel integrated control strategy based on arc length parameters for contour error compensation, which consists of a double-circle weighted approximation contour error estimation model based on arc length parameters module, an improved cross-coupling position command shaping controller (CPCSC) module, and an improved position error compensator (PEC) module. To improve the accuracy of contour error estimation for large free-form curvature trajectories, a double-circle weighted approximation contour error estimation model based on arc length parameters is proposed. The method first finds the nearest interpolation point by backtracking method and calculates the backward reference points by using the method based on arc length parameters. Then, the obtained backward reference points are used as the expected instruction points by the double-circle weighted approximation method, and the estimated value of contour error is calculated. Moreover, an improved structure of CPCSC is proposed. Compared with the traditional biaxial CCC structure, the advantage of this new structure is that the compensator design and stability analysis in its CCC are relatively simple, and it can be easily implemented on most current systems by reprogramming the reference position command subroutine. In addition, an improved PEC method is further proposed to reduce contour error. The main advantage of this module is that it can simultaneously improve tracking and contouring performances by compensating position errors in advance. The feasibility of the proposed integrated control strategy is verified by serval non-uniform rational B-spline (NURBS) parametric curve contour following experiments. Moreover, the results of comparative experiments indicate that the proposed integrated control strategy can significantly improve the tracking and contour control accuracy of biaxial contour following tasks compared with none-CCC method and CCC method, and has better contour control performance in large curvature positions.

The feed axis system of computer numerical control (CNC) machine tool is affected by temperature changes and axial loads during the machining process, which reduces the position accuracy of CNC machine tools. Due to the complexity of processing conditions and the difficulty in error detection, the formation mechanism of position error in actual working conditions is still vague. The purpose of this paper is to investigate the evolution of position error under thermal–mechanical coupling loads and identify, evaluate, and predict the position error. First, the formation mechanism and influencing factors of position error are clarified through theoretical analysis. Secondly, based on cluster analysis, the distribution of temperature measurement points is optimized to select the thermal key points which best reflect the impact between temperatures and errors. Finally, experimental data are used to decompose and evaluate the evolution process of the position error curve and the motion state of the feed axis, radial basis function neural network (RBFNN) is employed to model and predict the position error under thermal–mechanical coupling loads. The findings of this paper can help trace the source of position error and accurately assess the operating status of the machine tool.

Ball screws are subjected to complex loads during machining processes, which affects the position accuracy of the feed shaft of machine tools. The lack of a reliable model for analyzing the deformation of the ball screw, coupled with the unclear relationship between the deformation of the ball screw and the position error of the feed shaft, makes it challenging to accurately predict and compensate for the position error. The objective of the present research is to investigate the correlation between the deformation of the ball screw and the position error of the feed shaft to improve the accuracy of the machine tool. First, this paper establishes a FEM model to explore the loading and deformation of the ball screw. Secondly, a method for predicting position errors based on the deformation of the ball screw is proposed. Finally, the ball screw-loading test device is used for the position error compensation experiment to verify the reliability of the prediction method. This paper serves as a reference for understanding the generation mechanism of position errors in machine tool feed systems.

Steering wheel angle is an important and essential parameter of the navigation control of autonomous wheeled vehicles. At present, the combination of rotary angle sensors and four-link mechanisms is the main sensing approach for steering wheel angle with high measurement accuracy, which is widely adopted in autonomous agriculture vehicles. However, in a complex and challenging farmland environment, there are a series of prominent problems such as complicated installation and debugging, spattered mud blocking the parallel four-bar mechanism, breakage of the sensor wire during operation, and separate calibrations for different vehicles. To avoid the above problems, a novel dynamic measurement method for steering wheel angle is presented based on vehicle attitude information and a non-contact attitude sensor. First, the working principle of the proposed measurement method and the effect of zero position error on measurement accuracy and path tracking are analyzed. Then, an optimization algorithm for zero position error of steering wheel angle is proposed. The experimental platform is assembled based on a 2ZG-6DM rice transplanter by software design and hardware modification. Finally, comparative tests are conducted to demonstrate the effectiveness and priority of the proposed dynamic sensing method. Experimental results show that the average absolute error of the straight path is 0.057° and the corresponding standard deviation of the error is 0.483°. The average absolute error of the turning path is 0.686° and the standard deviation of the error is 0.931°. This implies the proposed dynamic sensing method can accurately realize the collection of the steering wheel angle. Compared to the traditional measurement method, the proposed dynamic sensing method greatly improves the measurement reliability of the steering wheel angle and avoids complicated installation and debugging of different vehicles. The separate calibrations for different vehicles are not needed since the proposed measurement method is not dependent on the kinematic models of the vehicles. Given that the attitude sensor can be installed at a higher position on the wheel, sensor damage from mud blocking and the sensor wire breaking is also avoided.

Hemispherical resonance gyroscope originated in the 1960s. With its outstanding advantages of high precision, simple structure and long service life, it is increasingly widely used in aerospace, tactical weapons and other fields. The hemispherical resonator, the core part of the gyroscope, is a thin-walled part with high steepness curved surface and hard and brittle material. Limited by the current processing level, it is difficult to obtain good shape and position accuracy, resulting in uneven mass distribution and frequency cracking, which affects the accuracy of the gyroscope. Based on the precision machining of hemispherical resonator, this paper carries out the research on the measurement method of shape and position error, focuses on the measurement method of the roundness and end face of the resonator, uses the cylindricity meter to complete the measurement of the roundness error of the inner and outer hemispherical shell of the resonator, and uses the white light interferometer and the subaperture stitching technology to realize the measurement of the full aperture surface of the end face of the hemispherical shell. This work provides theoretical guidance for subsequent processing and is of great significance to improve the quality of harmonic oscillator.

Research into statistical distributions of φ, λ and two-dimensional (2D) position errors of the global positioning system (GPS) enables the evaluation of its accuracy. Based on this, the navigation applications in which the positioning system can be used are determined. However, studies of GPS accuracy indicate that the empirical φ and λ errors deviate from the typical normal distribution, significantly affecting the statistical distribution of 2D position errors. Therefore, determining the actual statistical distributions of position errors (1D and 2D) is decisive for the precision of calculating the actual accuracy of the GPS system. In this paper, based on two measurement sessions (900,000 and 237,000 fixes), the distributions of GPS position error statistics in both 1D and 2D space are analysed. Statistical distribution measures are determined using statistical tests, the hypothesis on the normal distribution of φ and λ errors is verified, and the consistency of GPS position errors with commonly used statistical distributions is assessed together with finding the best fit. Research has shown that φ and λ errors for the GPS system are normally distributed. It is proven that φ and λ errors are more concentrated around the central value than in a typical normal distribution (positive kurtosis) with a low value of asymmetry. Moreover, φ errors are clearly more concentrated than λ errors. This results in larger standard deviation values for φ errors than λ errors. The differences in both values were 25–39%. Regarding the 2D position error, it should be noted that the value of twice the distance root mean square (2DRMS) is about 10–14% greater than the value of R95. In addition, studies show that statistical distributions such as beta, gamma, lognormal and Weibull are the best fit for 2D position errors in the GPS system.

This review presents the main results of the author’s study, obtained as part of the post-doctoral (habilitation) dissertation entitled “Research on Statistical Distributions of Navigation Positioning System Errors”, which constitutes a series of five thematically linked scientific publications. The main scientific aim of this series is to answer the question of what statistical distributions follow the position errors of navigation systems, such as Differential Global Positioning System (DGPS), European Geostationary Navigation Overlay Service (EGNOS), Global Positioning System (GPS), and others. All of the positioning systems under study (Decca Navigator, DGPS, EGNOS, and GPS) are characterised by the Position Random Walk (PRW), which means that latitude and longitude errors do not appear randomly, being a feature of the normal distribution. The research showed that the Gaussian distribution is not an optimal distribution for the modelling of navigation positioning system errors. A higher fit to the 1D and 2D position errors was exhibited by such distributions as beta, gamma, and lognormal. Moreover, it was proven that the Twice the Distance Root Mean Square (2DRMS(2D)) measure, which assumes a priori normal distribution of position errors in relation to latitude and latitude, was smaller by 10–14% than the position error value from which 95% fixes were smaller (it is known as the R95(2D) measure).

The performance of the National Centre for Medium Range Weather Forecasting-UK Met office (NCUM) global model in prediction of tropical cyclones (TCs) over the North Indian Ocean (NIO) at 25-km resolution is evaluated on the basis of 43 forecasts for 11 TCs. For this purpose, the analyses are carried out based on (1) basins of formation, (2) straight-moving and recurving/looping TCs, and (3) TC intensity at model initialization. The overall performance of NCUM global model has been found reasonably well in predicting TCs over NIO basin as it demonstrates a good skill irrespective of the region of formation, nature of movement, and intensity. The model has reasonably well predicted the tracks of the TCs in maximum number of the IC runs at different stages of the storms. The mean Direct Position Errors (DPEs) (skill with reference to CLIPER model) over the NIO vary from 97 to 248 km (5–57%) for 12–72-h forecast lengths. The NCUM model is found to be more skillful for track prediction of TCs when initialized at the Severe Cyclone Stage rather than at the Cyclonic Stage or lower. Therefore, the DPEs are lesser with higher model ICs run in each TC case. The model is more capable to predict the landfall location than the landfall time of the storms. The results also show that, on average, forecast tracks as predicted by NCUM lie to the right (i.e., model shows eastward bias of the best-track position) in all simulations for all the basins. The analysis of Along-Track errors reveals that the model forecast positions are biased to the south of (behind) the observed positions. It is evident that the NCUM forecasts are slower relative to the actual translation speed of the system for all forecast lengths, and the NCUM model predicts a delayed landfall. It is observed that the NCUM model has less predictability of intensity prediction of intense storms.

2D position error in the Global Positioning System (GPS) depends on the Horizontal Dilution of Precision (HDOP) and User Equivalent Range Error UERE. The non-dimensional HDOP coefficient, determining the influence of satellite distribution on the positioning accuracy, can be calculated exactly for a given moment in time. However, the UERE value is a magnitude variable in time, especially due to errors in radio propagation (ionosphere and troposphere effects) and it cannot be precisely predicted. The variability of the UERE causes the actual measurements (despite an exact theoretical mathematical correlation between the HDOP value and the position error) to indicate that position errors differ for the same HDOP value. The aim of this article is to determine the relation between the GPS position error and the HDOP value. It is possible only statistically, based on an analysis of an exceptionally large measurement sample. To this end, measurement results of a 10-day GPS measurement campaign (900,000 fixes) have been used. For HDOP values (in the range of 0.6–1.8), position errors were recorded and analysed to determine the statistical distribution of GPS position errors corresponding to various HDOP values. The experimental study and statistical analyses showed that the most common HDOP values in the GPS system are magnitudes of: 0.7 ( = 0•353) and 0.8 ( = 0•432). Only 2.77% of fixes indicated an HDOP value larger than 1. Moreover, 95% of measurements featured a geometric coefficient of 0.973 – this is why it can be assumed that in optimal conditions (without local terrain obstacles), the GPS system is capable of providing values of HDOP ≤ 1, with a probability greater than 95% (2 ). Obtaining a low HDOP value, which results in a low GPS position error value, calls for providing a high mean number of satellites (12 or more) and low variability in their number.