scholarly journals Error modelling–based machining sequence optimization of a pocketed beam milling: part A, end supported beam

2021 ◽  
Author(s):  
Shaoming Yao
Keyword(s):  
Position Error ◽  
Central Plane ◽  
Induction Method ◽  
Optimal Sequence ◽  
Pocket Machining ◽  
Sequence Optimization ◽  
Representative Case ◽  
Position Errors ◽  
Fixed End ◽  
Wall Position

AbstractThis paper, on the basis of error modelling, proved the optimal pocket machining sequences of a simply end supported pocketed beam using mathematic induction method. The optimal pocket machining sequence with the minimum pocket floor height error is the machining from both ends to the middle and the optimal sequence is not unique because of the symmetric supports about the central plane; meanwhile, the optimal pocket machining sequence with the minimum wall position error is the machining from the fixed end to the free end and the optimal machining sequence is unique. A beam of Al7075 (744 mm in length, 172 mm in width, and 100 in thickness ) with 9 pockets was used to demonstrate the optimal sequences. One of the optimal sequence with minimum floor height error was used in pocketing (roughing), and the maximum distortion was 0.693 mm in the middle and the maximum floor height error appeared on both sides rather than the middle, which were 0.477 mm and 0.388 mm, and part growth produced maximum wall position error was 0.719 mm. On the same part, further demonstrated the optimal sequence with minimum wall position error in finishing (with 1 mm dimension in stock for all surfaces) and the wall position errors were fully removed. The pocketed beam machining is a typical and representative case and the results and conclusion can be extended to pocketed plate/board machining and even surfacing.

scholarly journals Consistency of the Empirical Distributions of Navigation Positioning System Errors with Theoretical Distributions—Comparative Analysis of the DGPS and EGNOS Systems in the Years 2006 and 2014

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 31
Author(s):  
Mariusz Specht
Keyword(s):  
Normal Distribution ◽  
Root Mean Square ◽  
Statistical Tests ◽  
Position Error ◽  
Positioning System ◽  
Navigation Systems ◽  
Mean Square ◽  
Positioning Systems ◽  
Position Errors ◽  
System Errors

Positioning systems are used to determine position coordinates in navigation (air, land and marine). The accuracy of an object’s position is described by the position error and a statistical analysis can determine its measures, which usually include: Root Mean Square (RMS), twice the Distance Root Mean Square (2DRMS), Circular Error Probable (CEP) and Spherical Probable Error (SEP). It is commonly assumed in navigation that position errors are random and that their distribution are consistent with the normal distribution. This assumption is based on the popularity of the Gauss distribution in science, the simplicity of calculating RMS values for 68% and 95% probabilities, as well as the intuitive perception of randomness in the statistics which this distribution reflects. It should be noted, however, that the necessary conditions for a random variable to be normally distributed include the independence of measurements and identical conditions of their realisation, which is not the case in the iterative method of determining successive positions, the filtration of coordinates or the dependence of the position error on meteorological conditions. In the preface to this publication, examples are provided which indicate that position errors in some navigation systems may not be consistent with the normal distribution. The subsequent section describes basic statistical tests for assessing the fit between the empirical and theoretical distributions (Anderson-Darling, chi-square and Kolmogorov-Smirnov). Next, statistical tests of the position error distributions of very long Differential Global Positioning System (DGPS) and European Geostationary Navigation Overlay Service (EGNOS) campaigns from different years (2006 and 2014) were performed with the number of measurements per session being 900’000 fixes. In addition, the paper discusses selected statistical distributions that fit the empirical measurement results better than the normal distribution. Research has shown that normal distribution is not the optimal statistical distribution to describe position errors of navigation systems. The distributions that describe navigation positioning system errors more accurately include: beta, gamma, logistic and lognormal distributions.

Consistency analysis of global positioning system position errors with typical statistical distributions

2021 ◽  
pp. 1-18
Author(s):  
Mariusz Specht
Keyword(s):  
Normal Distribution ◽  
Global Positioning System ◽  
Position Error ◽  
Statistical Distribution ◽  
Positioning System ◽  
Statistical Distributions ◽  
Position Errors ◽  
Global Positioning ◽  
Gps System ◽  
Best Fit

Abstract 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.

Toward Intelligent Online Scan Sequence Optimization for Uniform Temperature Distribution in LPBF Additive Manufacturing

2021 ◽  
Author(s):  
Keval S. Ramani ◽  
Ehsan Malekipour ◽  
Chinedum E. Okwudire
Keyword(s):  
Additive Manufacturing ◽  
Temperature Distribution ◽  
Laser Scanning ◽  
Open Architecture ◽  
Uniform Temperature ◽  
Computationally Efficient ◽  
Optimal Sequence ◽  
Sequence Optimization ◽  
Uniform Temperature Distribution ◽  
Scan Pattern

Abstract Laser powder bed fusion (LPBF) is an increasingly popular approach for additive manufacturing (AM) of metals. However, parts produced by LPBF are prone to residual stresses, deformations, and other defects linked to nonuniform temperature distribution during the process. Several works have highlighted the important role (laser) scanning strategies, including laser power, scan speed, scan pattern and scan sequence, play in achieving uniform temperature distribution in LPBF. However, scan sequence continues to be determined offline based on trial-and-error or heuristics, which are neither optimal nor generalizable. To address these weaknesses, we present a framework for intelligent online scan sequence optimization to achieve uniform temperature distribution in LPBF. The framework involves the use of physics-based models for online optimization of scan sequence, while data acquired from in-situ thermal sensors provide correction or calibration of the models. The proposed framework depends on having: (1) LPBF machines capable of adjusting scan sequence in real-time; and (2) accurate and computationally efficient models and optimization approaches that can be efficiently executed online. The first challenge is addressed via a commercially available open-architecture LPBF machine. As a preliminary step towards tackling the second challenge, an analytical model is explored for determining the optimal sequence for scanning patterns in LPBF. The model is found to be deficient but provides useful insights into future work in this direction.

scholarly journals Nonlinear Position Control Using Only Position Feedback under Position Errors and Yaw Constraints for Air Bearing Planar Motors

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1354
Author(s):  
Wonhee Kim ◽  
Donghoon Shin ◽  
Youngwoo Lee
Keyword(s):  
Position Control ◽  
Position Error ◽  
Nonlinear Observer ◽  
Closed Loop System ◽  
Tracking Errors ◽  
Position Errors ◽  
Full State ◽  
Position Feedback ◽  
Position Controller ◽  
The Stability

In this paper, we propose a nonlinear position control using only position feedback to guarantee the tolerances for position tracking errors and yaw. In the proposed method, both mechanical and electrical dynamics are considered. The proposed method consists of the nonlinear position controller and nonlinear observer. The nonlinear position controller is designed by a backstepping procedure using the barrier Lyapunov function to satisfy the constraints of position error and yaw. The nonlinear observer is developed to estimate full state using only position feedback. The stability of the closed-loop system is proven using Lyapunov and input-to-state stabilities. Consequently, the proposed method satisfies the constraints of position error and yaw using only position feedback for the planar motor.

scholarly journals Analytical study of floating effects on load sharing characteristics of planetary gearbox for off-road vehicle

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402094046
Author(s):  
Woo-Jin Chung ◽  
Joo-Seon Oh ◽  
Hyun-Woo Han ◽  
Ji-Tae Kim ◽  
Young-Jun Park
Keyword(s):  
Safety Factor ◽  
Planetary Gear ◽  
Load Sharing ◽  
Position Error ◽  
System Level ◽  
Load Factor ◽  
Road Vehicle ◽  
Design Modification ◽  
Planetary Gearbox ◽  
Position Errors

Uneven load sharing of a planetary gear set is the main cause of preventing the miniaturization and weight reduction of a planetary gearbox. Non-torque loads and carrier pinhole position errors are the main factors that worsen the load-sharing characteristics. However, their effects are seldom analyzed at a system level especially for an off-road vehicle. To make up this gap, some simulation models are proposed to investigate the effects of floating members on the load-sharing characteristics and the strength of a planetary gear set with non-torque load and carrier pinhole position error. When the error is not considered, the mesh load factor converges to unity irrespective of the type and number of floating members and the safety factors for pitting and bending are increased slightly. When the carrier pinhole position error is considered, the mesh load factor dramatically worsens. Although it is improved using the floating members, it does not converge to unity. However, the bending safety factor of the planet gear with the error is increased by 26%. This indicates that the design modification for the original planetary gearbox is needed to satisfy the safety factor requirement, but the problem is solved using only floating members.

Evaluation Modeling and Optimal Adjustment of Position Error Based on Localization Sensitivity Analysis

2011 ◽  
Vol 697-698 ◽  
pp. 258-261
Author(s):  
G.Y. He ◽  
C.X. Hu ◽  
X. Liu
Keyword(s):  
Sensitivity Analysis ◽  
Evaluation Model ◽  
Geometric Error ◽  
Position Error ◽  
Position Errors ◽  
Surface Deviation ◽  
Optimal Adjustment ◽  
Fixture System ◽  
System Errors ◽  
The Relationship

Sensitivity analysis is to evaluate how sensitive the surface deviation of a workpiece is to a geometric error of locator. With this thinking, the relationship between geometric error of locators and the position error of holes group is presented. The fixture system errors model and evaluation model of position errors are established. Furthermore with both models, a method of optimizing the position errors by adjusting the locators’ position is presented, which can get to accuracy localization. At last, a simulation study is used to verify the method.

Efficient Spot Welding Sequence Optimization in a Geometry Assurance Digital Twin

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Roham Sadeghi Tabar ◽  
Kristina Wärmefjord ◽  
Rikard Söderberg ◽  
Lars Lindkvist
Keyword(s):  
Spot Welding ◽  
Welding Process ◽  
Combinatorial Problems ◽  
Optimal Sequence ◽  
Sequence Optimization ◽  
Digital Twin ◽  
Final Assembly ◽  
Geometrical Quality ◽  
Welding Sequence ◽  
The Individual

Abstract A digital twin for geometry assurance contains a set of analyses that are performed to steer the real production for securing the geometry of the final assembly. In sheet metal assemblies, spot welding is performed to join the parts together. The sequence of the welding has a considerable influence on the geometrical outcome of the final assembly. In industry, the sequence of welding to secure the geometry is mainly derived by tacit manufacturing knowledge. Including such knowledge to mimic the production process requires extensive knowledge management, and the result might be just a good enough solution. Theoretically, spot welding sequence optimization for the optimal geometrical quality is among NP-hard combinatorial problems. In a geometry assurance digital twin, where assembly parameters are selected for the individual assemblies, time constraints define the quality of the optimal sequence. In this paper, an efficient method for spot welding sequence optimization with regards to the geometrical quality is introduced. The results indicate that the proposed method reduces 60–80% of the time for the sequencing of the spot welding process to achieve the optimal geometrical quality.

scholarly journals GNSS/INS/LiDAR-SLAM Integrated Navigation System Based on Graph Optimization

2019 ◽  
Vol 11 (9) ◽  
pp. 1009 ◽  
Author(s):  
Le Chang ◽  
Xiaoji Niu ◽  
Tianyi Liu ◽  
Jian Tang ◽  
Chuang Qian
Keyword(s):  
Navigation System ◽  
Vertical Direction ◽  
Position Error ◽  
Measurement Unit ◽  
Integrated Navigation ◽  
Integrated Navigation System ◽  
Position Errors ◽  
The North ◽  
Window Method ◽  
Graph Optimization

A Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS)/Light Detection and Ranging (LiDAR)-Simultaneous Localization and Mapping (SLAM) integrated navigation system based on graph optimization is proposed and implemented in this paper. The navigation results are obtained by the information fusion of the GNSS position, Inertial Measurement Unit (IMU) preintegration result and the relative pose from the 3D probability map matching with graph optimizing. The sliding window method was adopted to ensure that the computational load of the graph optimization does not increase with time. Land vehicle tests were conducted, and the results show that the proposed GNSS/INS/LiDAR-SLAM integrated navigation system can effectively improve the navigation positioning accuracy compared to GNSS/INS and other current GNSS/INS/LiDAR methods. During the simulation of one-minute periods of GNSS outages, compared to the GNSS/INS integrated navigation system, the root mean square (RMS) of the position errors in the North and East directions of the proposed navigation system are reduced by approximately 82.2% and 79.6%, respectively, and the position error in the vertical direction and attitude errors are equivalent. Compared to the benchmark method of GNSS/INS/LiDAR-Google Cartographer, the RMS of the position errors in the North, East and vertical directions decrease by approximately 66.2%, 63.1% and 75.1%, respectively, and the RMS of the roll, pitch and yaw errors are reduced by approximately 89.5%, 92.9% and 88.5%, respectively. Furthermore, the relative position error during the GNSS outage periods is reduced to 0.26% of the travel distance for the proposed method. Therefore, the GNSS/INS/LiDAR-SLAM integrated navigation system proposed in this paper can effectively fuse the information of GNSS, IMU and LiDAR and can significantly mitigate the navigation error, especially for cases of GNSS signal attenuation or interruption.

scholarly journals Climbing fibers predict movement kinematics and performance errors

2017 ◽  
Vol 118 (3) ◽  
pp. 1888-1902 ◽  
Author(s):  
Martha L. Streng ◽  
Laurentiu S. Popa ◽  
Timothy J. Ebner
Keyword(s):  
Motor Control ◽  
Purkinje Cells ◽  
Linear Regression Analysis ◽  
Linear Representation ◽  
Complete Characterization ◽  
Position Error ◽  
Climbing Fibers ◽  
Data Set ◽  
Complex Spike ◽  
Position Errors

Requisite for understanding cerebellar function is a complete characterization of the signals provided by complex spike (CS) discharge of Purkinje cells, the output neurons of the cerebellar cortex. Numerous studies have provided insights into CS function, with the most predominant view being that they are evoked by error events. However, several reports suggest that CSs encode other aspects of movements and do not always respond to errors or unexpected perturbations. Here, we evaluated CS firing during a pseudo-random manual tracking task in the monkey ( Macaca mulatta). This task provides extensive coverage of the work space and relative independence of movement parameters, delivering a robust data set to assess the signals that activate climbing fibers. Using reverse correlation, we determined feedforward and feedback CSs firing probability maps with position, velocity, and acceleration, as well as position error, a measure of tracking performance. The direction and magnitude of the CS modulation were quantified using linear regression analysis. The major findings are that CSs significantly encode all three kinematic parameters and position error, with acceleration modulation particularly common. The modulation is not related to “events,” either for position error or kinematics. Instead, CSs are spatially tuned and provide a linear representation of each parameter evaluated. The CS modulation is largely predictive. Similar analyses show that the simple spike firing is modulated by the same parameters as the CSs. Therefore, CSs carry a broader array of signals than previously described and argue for climbing fiber input having a prominent role in online motor control. NEW & NOTEWORTHY This article demonstrates that complex spike (CS) discharge of cerebellar Purkinje cells encodes multiple parameters of movement, including motor errors and kinematics. The CS firing is not driven by error or kinematic events; instead it provides a linear representation of each parameter. In contrast with the view that CSs carry feedback signals, the CSs are predominantly predictive of upcoming position errors and kinematics. Therefore, climbing fibers carry multiple and predictive signals for online motor control.

scholarly journals Correlation Between Average Segment Width and Gamma Passing Rate as a Function of MLC Position Error in Volumetric Modulated Arc Therapy

2021 ◽  
Vol 20 ◽  
pp. 153303382110599
Author(s):  
Young Min Moon ◽  
Sang Il Bae ◽  
Moo Jae Han ◽  
Wan Jeon ◽  
Tosol Yu ◽  
...  
Keyword(s):  
Least Squares Method ◽  
Linear Regression Analysis ◽  
Volumetric Modulated Arc Therapy ◽  
Position Error ◽  
Coefficient Of Determination ◽  
Position Errors ◽  
Visual Basic For Applications ◽  
Passing Rate ◽  
Arc Therapy ◽  
Gamma Passing Rate

Objective: This study analyzed the correlation between the average segment width (ASW) and gamma passing rate according to the multi-leaf collimator (MLC) position error. Method: To evaluate the changes in the gamma passing rate according to the MLC position error, 21 volumetric modulated arc therapy (VMAT) plans were generated using pelvic lymph node metastatic prostate cancer patient's data which is sensitive to MLC position errors as they involve several long, narrow, irregular fields. The ASW for each VMAT plan was calculated using our own code developed using Visual Basic for Applications (VBA). The gamma passing rate of the VMAT plan according to the MLC position error was evaluated using ArcCHECK (Sun Nuclear, Melbourne, FL, USA) while inducing symmetric MLC position errors in 0.25 mm intervals from −1 mm to +1 mm in the infinity medical linear accelerator (Elekta AB, Stockholm, Sweden). Finally, we examined the correlation between the change in the passing rate ([Formula: see text]) due to the MLC position error and the ASW in VMAT through linear regression analysis using the least squares method. Results: The ASW and [Formula: see text] were found to have a linear correlation according to the MLC position error, and the coefficient of determination was 0.88. For a 1 mm position error of MLC in VMAT, the gamma passing rate improved by approximately 11.9% as the ASW increased by 10 mm. Conclusion: These results are expected to be employed as guidelines to minimize the dose uncertainty due to MLC position error in VMAT.

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