scholarly journals Improved algorithm for minimum zone of roundness error evaluation using alternating exchange approach

2021 ◽  
Author(s):  
Alhadi khlil ◽  
Zhanqun Shi ◽  
Abubakar Umar ◽  
BoTong Ma
Keyword(s):  
Initial Solution ◽  
Error Evaluation ◽  
Exchange Method ◽  
Roundness Error ◽  
Error Magnitude ◽  
Comparison Results ◽  
Minimum Zone ◽  
Using Data ◽  
Optimum Solution ◽  
Improved Algorithm

Abstract Based on the computational geometry technique, an improved algorithm for minimum zone of roundness error evaluation using an alternating exchange method is presented. A minimum zone fitting function was created to enhance the roundness error evaluation. The function uses three candidate points to determine the initial solution: the expected centre, the mean circle radius, and the corresponding zone half-width. The best solution function is designed to use the initial solution as the input to determine the optimum solution for the minimum zone circle. The proposed algorithm was validated using data available in the literature. The roundness error evaluation comparison results demonstrate that the proposed method accurately detects both the centre error magnitude and minimum zone circle and overcomes the insufficiency of using selected colinear points for four selected points.

Realization Method for Detection on Arc Based on CCD

2014 ◽  
Vol 687-691 ◽  
pp. 856-860
Author(s):  
Qing Min Liu ◽  
Xue Li ◽  
L. Zhang
Keyword(s):  
Least Squares ◽  
Evaluation Methods ◽  
Detection Methods ◽  
Inspection System ◽  
Distributed Data ◽  
Error Evaluation ◽  
Roundness Error ◽  
Vision Inspection ◽  
Minimum Zone ◽  
Least Squares Algorithm

s: Arc detection is difficult for processing, assembly and testing of industrial production because of limitations of detection methods, algorithms and instruments. The least-squares algorithm is used to fit data in circle detection. The application of conventional least-squares algorithm is limited, as roundness error is bigger, precision is lower. For detecting arc with data points of non-uniform distribution, improved least-squares algorithm, developed an analysis algorithm for assessing the minimum zone roundness error. Center and radius can be solved, without iteration and truncation error. Using the discrete data instances verified different roundness error evaluation methods. Visual measurements have been carried out using the proposed methods. Calculated results using the four kinds of roundness error evaluation methods (Figure 7-10). Ball diameter errors are-0.0245mm、0.0176mm、-0.1052mm and 0.302mm, roundness errors are 0.07mm、0.063mm、0.078mm and 0.146mm. The improved least-squares algorithm and the minimum zone algorithm are suitable for distributed data of all kinds situations, particularly suitable for the realization of machine vision inspection system, fast speed, high precision, wide application.

scholarly journals Method for Roundness Error Evaluation Based on Minimum Zone Method

2020 ◽  
Vol 56 (4) ◽  
pp. 42
Author(s):  
YUE Longlong ◽  
HUANG Qiangxian ◽  
MEI Jian ◽  
CHENG Rongjun ◽  
ZHANG Liansheng ◽  
...  
Keyword(s):  
Error Evaluation ◽  
Zone Method ◽  
Roundness Error ◽  
Minimum Zone

Roundness Error Evaluation Based on Differential Evolution Algorithm

2014 ◽  
Vol 670-671 ◽  
pp. 1285-1289 ◽  
Author(s):  
Long Jin ◽  
Yue Ping Chen ◽  
Hai Yan Lu ◽  
Shu Ping Li ◽  
Yi Chen
Keyword(s):  
Differential Evolution ◽  
Differential Evolution Algorithm ◽  
Error Evaluation ◽  
New Approach ◽  
Roundness Error ◽  
De Algorithm ◽  
Implementation Techniques ◽  
Circularity Error ◽  
Minimum Zone ◽  
Evolution Algorithm

A new approach for roundness (circularity) error evaluation based on the differential evolution (DE) algorithm is proposed.The mathematical model of the roundness error under the condition of the minimum zone is derived. The background and advantages of DE are introduced, the fundamentals and implementation techniques are also given.The approach is verified by two examples.Compared with other methods, the results show that the proposed method makes the roundness error evaluation more accurate.

The minimum zone fitting and error evaluation for the logarithmic curve based on geometry optimization approximation algorithm

2019 ◽  
Vol 41 (15) ◽  
pp. 4380-4386
Author(s):  
Tu Xianping ◽  
Lei Xianqing ◽  
Ma Wensuo ◽  
Wang Xiaoyi ◽  
Hu Luqing ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Evaluation Method ◽  
Geometry Optimization ◽  
Reference Points ◽  
Approximation Technique ◽  
Error Evaluation ◽  
Iterative Approximation ◽  
Logarithmic Curve ◽  
Normal Distance ◽  
Minimum Zone

The minimum zone fitting and error evaluation for the logarithmic curve has important applications. Based on geometry optimization approximation algorithm whilst considering geometric characteristics of logarithmic curves, a new fitting and error evaluation method for the logarithmic curve is presented. To this end, two feature points, to serve as reference, are chosen either from those located on the least squares logarithmic curve or from amongst measurement points. Four auxiliary points surrounding each of the two reference points are then arranged to resemble vertices of a square. Subsequently, based on these auxiliary points, a series of auxiliary logarithmic curves (16 curves) are constructed, and the normal distance and corresponding range of values between each measurement point and all auxiliary logarithmic curves are calculated. Finally, by means of an iterative approximation technique consisting of comparing, evaluating, and changing reference points; determining new auxiliary points; and constructing corresponding auxiliary logarithmic curves, minimum zone fitting and evaluation of logarithmic curve profile errors are implemented. The example results show that the logarithmic curve can be fitted, and its profile error can be evaluated effectively and precisely using the presented method.

The shape error evaluation methods of the foils for a multi-leaf foil bearing

2018 ◽  
Vol 233 (2) ◽  
pp. 504-513 ◽  
Author(s):  
Yuan Yu ◽  
Cheng Ren ◽  
Yanhua Sun
Keyword(s):  
Evaluation Method ◽  
Least Square ◽  
Shape Error ◽  
Pressing Pressure ◽  
Error Evaluation ◽  
Profile Error ◽  
Roundness Error ◽  
Manufacturing Method ◽  
Foil Bearing ◽  
Curve Profile

The geometric parameters of the elastic foil bearing are important basis for designing the foil bearing. Whether the main shape indices of the pressed foils meet the design requirements is the key to evaluate a manufacturing method. The inconsistent curvature radii of the top foils, the inconsistent bump heights of the bumps on the bump foil, the roundness error of the top foil, and the curve profile error of the bump foil may cause the pre-tightening assembly difference and different bearing capacity of each bearing shell. Aiming at the shape error evaluations of the foils for a multi-leaf foil bearing, first, the algorithm of geometric area optimization for circle roundness error is introduced and an evaluation method of arc roundness error is put forward according to the minimum zone principle in this paper. This method can be used to calculate the roundness error of the top foil for a multi-leaf foil bearing. The results show that the corresponding roundness error of the top foil decreases with the increasing of the pressing pressure. The relative roundness error is small (less than 7%), which changes a little with different pressing pressures. For the measurement of a bottom bump foil, the method of matching feature points is used in pre-location and then fine-positioning for the measured curve is implemented based on the least square method in order to eliminate the position error between the measured curve and the design curve. Thus, the curve profile error evaluation of the bottom bump foil for a multi-leaf foil bearing is implemented and the profile error of each bump can be obtained. According to the shape error evaluation values of the top foil and the bump foil, the quality control strategy and the error compensation by improving the mold structure can be further researched.

Circularity Error Evaluation Based on Differential Evolution Algorithm

2011 ◽  
Vol 143-144 ◽  
pp. 416-421
Author(s):  
Dong Xia Wang ◽  
Ai Guo Song ◽  
Xiu Lan Wen ◽  
Feng Lin Wang
Keyword(s):  
Global Convergence ◽  
Differential Evolution ◽  
Evolutionary Algorithm ◽  
Differential Evolution Algorithm ◽  
Suggested Method ◽  
Error Evaluation ◽  
Circularity Error ◽  
Minimum Zone ◽  
Evolution Algorithm ◽  
Adaptive Ability

An algorithm based on the differential evolutionary (DE) computation is proposed to evaluate circularity error. It is a heuristic evolutionary algorithm based on population optimization .In the meantime, the suggested method is used to solve the minimum zone circularity error. Compared with other methods, the results show the presented method has very strong self-adaptive ability to environment and better global convergence. Examples proves that the proposed method is effective, convergence and robustness in the process of optimization. And this method makes the circularity error evaluation more accurate.

Form Error Evaluation: An Iterative Reweighted Least Squares Algorithm*

2004 ◽  
Vol 126 (3) ◽  
pp. 535-541 ◽  
Author(s):  
Xiangyang Zhu ◽  
Han Ding ◽  
Michael Y. Wang
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Chebyshev Approximation ◽  
Approximation Problem ◽  
General Purpose ◽  
Geometric Features ◽  
Error Evaluation ◽  
Form Error ◽  
Minimum Zone ◽  
Effectiveness And Efficiency

This paper establishes the equivalence between the solution to a linear Chebyshev approximation problem and that of a weighted least squares (WLS) problem with the weighting parameters being appropriately defined. On this basis, we present an algorithm for form error evaluation of geometric features. The algorithm is implemented as an iterative procedure. At each iteration, a WLS problem is solved and the weighting parameters are updated. The proposed algorithm is of general-purpose, it can be used to evaluate the exact minimum zone error of various geometric features including flatness, circularity, sphericity, cylindericity and spatial straightness. Numerical examples are presented to show the effectiveness and efficiency of the algorithm.

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