Parabola Error Evaluation Using Geometry Ergodic Searching Algorithm

2013 ◽  
Vol 333-335 ◽  
pp. 1465-1468
Author(s):  
Hai Yang Wang ◽  
Xian Qing Lei ◽  
Jing Wei Cui
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Geometric Features ◽  
Feature Points ◽  
Error Evaluation ◽  
Profile Error ◽  
Minimum Zone ◽  
Grid Points ◽  
Reference Feature

A method of parabola error evaluation using Geometry Ergodic Searching Algorithm (GESA) was proposed according to geometric features and fitting characteristics of parabola error. First , the feature points of least-squared parabola are set as reference feature points to layout a group of auxiliary feature grid points. After that, a series of auxiliary parabolas as assumed ideal parabolas are reversed with the auxiliary feature points.The range distance from given points to these assumptions ideal parabolas are calculated successively.The minimum one is parabola profile error.The process of GESA was detailed discribed including the algorithm formula and contrastive results in this paper.Simulation experiment results show that the geometry ergodic searching algorithm is more accurate than the least-square method. The parabola profile error can be evaluated steadily and precisely with this algorithm based on the minimum zone.

Reacher on Ellipticity Error by Use of Minimum Circumscribed Ellipse and Maximum Inscribed Ellipse Algorithm

2013 ◽  
Vol 333-335 ◽  
pp. 1461-1464
Author(s):  
Jing Wei Cui ◽  
Xian Qing Lei ◽  
Xian Ping Tu ◽  
Hai Yang Wang
Keyword(s):  
Search Algorithm ◽  
Reference Points ◽  
Least Square ◽  
Grid Search ◽  
Error Evaluation ◽  
Profile Error ◽  
Ellipse Method ◽  
Data Processing Method ◽  
Grid Points ◽  
Grid Search Algorithm

A data processing method based on a mesh search algorithm for elliptical profile error evaluation is proposed. First ellipse focuses of the least-square are set as reference points, according to a certain rules, a series of grid points are arranged and supposed as hypothetical ideal ellipse focuses respectively , then the distances of supposed ideal ellipse to the measuring points are calculated repeatedly. The minimum circumscribed ellipse and the maximum inscribed ellipse are constructed by comparison and judgment, and the corresponding value of ellipse profile error is obtained. Furthermore, the principle of the grid search algorithm and the process of ellipse profile error evaluation by using the minimum circumscribed ellipse method and the maximum inscribed ellipse method are stated . The results of examples show that the ellipse profile error can be evaluated accurately and effectively by this algorithm.

scholarly journals Cylindricity Error Measuring and Evaluating for Engine Cylinder Bore in Manufacturing Procedure

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Qiang Chen ◽  
Xueheng Tao ◽  
Jinshi Lu ◽  
Xuejun Wang
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Zone Method ◽  
Method Error ◽  
Measuring Device ◽  
Engine Cylinder ◽  
Minimum Zone ◽  
Cylinder Method ◽  
Cylinder Bore ◽  
Cylindricity Error

On-line measuring device of cylindricity error is designed based on two-point method error separation technique (EST), which can separate spindle rotation error from measuring error. According to the principle of measuring device, the mathematical model of the minimum zone method for cylindricity error evaluating is established. Optimized parameters of objective function decrease to four from six by assuming thatcis equal to zero andhis equal to one. Initial values of optimized parameters are obtained from least square method and final values are acquired by the genetic algorithm. The ideal axis of cylinder is fitted in MATLAB. Compared to the error results of the least square method, the minimum circumscribed cylinder method, and the maximum inscribed cylinder method, the error result of the minimum zone method conforms to the theory of error evaluation. The results indicate that the method can meet the requirement of engine cylinder bore cylindricity error measuring and evaluating.

Minimum Zone Evaluation of Symmetry Error for Flatness to Flatness Based on the New Generation GPS

2013 ◽  
Vol 662 ◽  
pp. 887-891
Author(s):  
Qian Qian ◽  
Mei Fa Huang ◽  
Huan Yu Li
Keyword(s):  
Least Square Method ◽  
Mathematic Model ◽  
Least Square ◽  
Adaptive Genetic Algorithm ◽  
Machining Error ◽  
Minimum Zone ◽  
New Generation ◽  
Tolerance Method ◽  
The Mathematical Model ◽  
Better Than

Least square method (LSM) is the most popular method used to evaluate machining error nowadays. However, LSM is likely to overestimate the error value, therefore its solution is only approximate and rather than minimum. In order to obtain the minimum, we study the principle of the minimum zone tolerance method (MZT), analyze the characteristics of the new generation GPS, and give the minimum zone mathematic model of the symmetry error for flatness to flatness. For the purpose of optimizing the mathematical model, this paper describes the application of adaptive genetic algorithm to achieve the best estimation. Simultaneously, the process of optimization is realized by MALTAB. Finally, the experiment shows that the evaluation results of MZT is better than evaluation results of LSM.

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.

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.

Inclination Errors Evaluation of Planar Lines with a Chaos Optimization

2010 ◽  
Vol 37-38 ◽  
pp. 525-528
Author(s):  
Ke Zhang ◽  
Xiao Ming Cao
Keyword(s):  
Optimization Algorithm ◽  
Control Experiment ◽  
Least Square ◽  
Error Evaluation ◽  
Chaos Optimization ◽  
Simplex Search ◽  
Chaos Optimization Algorithm ◽  
Continuous Problems ◽  
Minimum Zone ◽  
Optimum Model

To improve inclination error evaluation of planar lines, chaos optimization is proposed to evaluate the minimum zone error in this paper. The evolutional optimum model and the calculation process are introduced. By using the properties of ergodicity, stochastic property, and “regularity” of chaos, the efficiency of chaos optimization algorithm (COA) is much higher than some stochastic algorithms such as simulated anneal algorithm (SAA) and genetic algorithm (GA) when COA is used to a kind of continuous problems. The chaos optimization algorithm can improve the efficiency of searching in the whole field by gradually shrinking the area of optimization variable. Finally, the control experiment results evaluated by different method such as the Least Square, Simplex search, Powell optimum methods and GA, indicate that the proposed method does provide better accuracy on inclination error evaluation.

Design of Rank Accuracy Detection System for Screw

2010 ◽  
Vol 37-38 ◽  
pp. 331-334
Author(s):  
Zhao Xin Meng ◽  
Zhi Wei Li ◽  
Jun Cao
Keyword(s):  
Laser Interferometer ◽  
Detection System ◽  
Least Square Method ◽  
Solution Procedure ◽  
Least Square ◽  
Error Evaluation ◽  
Evaluation Algorithm ◽  
Low Efficiency ◽  
Frequency Laser ◽  
Static Detection

In view of defects of static detection for screw, such as low efficiency, man made errors, this paper designed a dynamic detecting system, which employs two-frequency laser interferometer as the displacement benchmark and encoder as the angle benchmark. According to the lasting standards, the solution procedure of error evaluation algorithm is optimized by least square method to reduce computation. Experiment shows this system can dynamically detected screw, of which rank accuracy is more than two.

A Skew Detection Algorithm for PDF417 Based on Feature Point

2011 ◽  
Vol 128-129 ◽  
pp. 495-499
Author(s):  
Jian Hua Li ◽  
Ping Li ◽  
Xiao Dan Li ◽  
Yi Wen Wang
Keyword(s):  
Least Square Method ◽  
Detection Algorithm ◽  
Least Square ◽  
Detection Methods ◽  
Automatic Identification ◽  
Feature Points ◽  
Skew Angle ◽  
Bar Code ◽  
Character Code ◽  
The Common

The automatic identification of 2D (two dimensional) bar code PDF417 is very sensitive to skew angle, but, the common skew angle detection methods have shortcomings such as weak performance in time complexity. In this paper, based on the properties of PDF417 character code and the extraction of feature points, we get skew angle of PDF417 bar code image using the least square method. Experiments show that this algorithm has virtue of less computation and high accuracy.

Study on the Virtual Instrument for Coaxiality Error

2012 ◽  
Vol 220-223 ◽  
pp. 45-48
Author(s):  
Li Jie Chen ◽  
Ping Zou
Keyword(s):  
High Precision ◽  
Virtual Instrument ◽  
Least Square Method ◽  
Least Square ◽  
Manufacturing Cost ◽  
Zone Method ◽  
Hardware Platform ◽  
Experimental Teaching ◽  
Data Acquisition Card ◽  
Minimum Zone

Used LabWindows/CVI as software platform, existing apparatus in laboratory and a data acquisition card as hardware platform, the virtual instrument for coaxiality error was developed. It combines the theory to measure form and position error with technology about virtual instrument. Coaxiality error by least square method and the minimum zone method is measured. The image of coaxiality error can be displayed on the screen to analyse the causes of error, so as to control the manufacturing error. The virtual instrument has the advantages of high precision, stablity, low manufacturing cost, especially the excellent function expandability. It can be used for experimental teaching and the actual production.

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