scholarly journals Characterization and Correction of the Geometric Errors in Using Confocal Microscope for Extended Topography Measurement. Part I: Models, Algorithms Development and Validation

Electronics ◽  
2019 ◽  
Vol 8 (7) ◽  
pp. 733 ◽  
Author(s):  
Wang ◽  
Gómez ◽  
Yu
Keyword(s):  
Experimental Studies ◽  
Measurement Data ◽  
Confocal Microscope ◽  
Geometric Error ◽  
Linear Displacement ◽  
Geometric Errors ◽  
Scale Calibration ◽  
Squareness Errors ◽  
Kinematic Modelling ◽  
Development And Validation

This work presents a method for characterizing and correcting the geometric errors of the movement of the lateral stage of Imaging Confocal Microscope (CM) in extended topography measurement. For an extended topography measurement, a defined number of 2D images are taken and stitched by correlation methods. Inaccuracies due to linear displacement, vertical and horizontal straightness errors, angular errors, and squareness errors based on the assumption of the rigid body kinematics are described. A mathematical model for the scale calibration of the X- and Y- coordinates is derived according to the system kinematics, the axis chain vector of CM, and the geometric error functions and their approximations by Legendre polynomials. The correction coefficients of the kinematic modelling are determined by the measured and certified data of a dot grid target standard artefact. To process the measurement data, algorithms for data partitions, fittings of cylinder centers, and determinations of coefficients are developed and validated. During which methods such as form removal, K-means clustering, linear and non-linear Least Squares are implemented. Results of the correction coefficients are presented in Part II based on the experimental studies. The mean residual reduces 29.6% after the correction of the lateral stage errors.

Table-Based Volumetric Error Compensation of Large Five-Axis Machine Tools

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Jennifer Creamer ◽  
Patrick M. Sammons ◽  
Douglas A. Bristow ◽  
Robert G. Landers ◽  
Philip L. Freeman ◽  
...  
Keyword(s):  
Machine Tool ◽  
Error Compensation ◽  
Machine Tools ◽  
Data Gathering ◽  
Measurement Data ◽  
Geometric Error ◽  
Compensation Method ◽  
Geometric Errors ◽  
Simultaneous Generation ◽  
Five Axis

This paper presents a geometric error compensation method for large five-axis machine tools. Compared to smaller machine tools, the longer axis travels and bigger structures of a large machine tool make them more susceptible to complicated, position-dependent geometric errors. The compensation method presented in this paper uses tool tip measurements recorded throughout the axis space to construct an explicit model of a machine tool's geometric errors from which a corresponding set of compensation tables are constructed. The measurements are taken using a laser tracker, permitting rapid error data gathering at most locations in the axis space. Two position-dependent geometric error models are considered in this paper. The first model utilizes a six degree-of-freedom kinematic error description at each axis. The second model is motivated by the structure of table compensation solutions and describes geometric errors as small perturbations to the axis commands. The parameters of both models are identified from the measurement data using a maximum likelihood estimator. Compensation tables are generated by projecting the error model onto the compensation space created by the compensation tables available in the machine tool controller. The first model provides a more intuitive accounting of simple geometric errors than the second; however, it also increases the complexity of projecting the errors onto compensation tables. Experimental results on a commercial five-axis machine tool are presented and analyzed. Despite significant differences in the machine tool error descriptions, both methods produce similar results, within the repeatability of the machine tool. Reasons for this result are discussed. Analysis of the models and compensation tables reveals significant complicated, and unexpected kinematic behavior in the experimental machine tool. A particular strength of the proposed methodology is the simultaneous generation of a complete set of compensation tables that accurately captures complicated kinematic errors independent of whether they arise from expected and unexpected sources.

The Effect of Geometric Error on Machining Accuracy for Machining Center

2013 ◽  
Vol 690-693 ◽  
pp. 3244-3248
Author(s):  
Gui Qiang Liang ◽  
Ai Rong Zhang ◽  
Ting Ting Guo
Keyword(s):  
Great Influence ◽  
Geometric Error ◽  
Linear Displacement ◽  
Machining Accuracy ◽  
Geometric Errors ◽  
Lower Body ◽  
Body System ◽  
Research Results ◽  
Machining Center ◽  
Multi Body

In order to improve machining accuracy of machining center, the effect of geometric error on machining accuracy was researched by multi-body system theory. Taking a vertical machining center as example, topological structure of the machining center was described by lower body array. Geometric errors of the bodies in the multi-body system were expressed by homogeneous coordinate transformation. Error model for machining accuracy was deduced and geometric errors having great influence on the machining accuracy were identified. The research results show that, straightness errors and linear displacement errors in three directions have direct influence on machining accuracy, and the effect on machining accuracy caused by angle errors are related to the dimensions of the machining center and travel distance of the three axes. The research results provide guidance for analysis on sensitivity of geometric errors.

Geometric Error Identification of a Three-Axis Machining Center

2013 ◽  
Vol 694-697 ◽  
pp. 1803-1807
Author(s):  
Gui Qiang Liang ◽  
Jun Xian Zhang ◽  
Fei Fei Zhao
Keyword(s):  
Working Conditions ◽  
Laser Interferometer ◽  
Great Influence ◽  
Geometric Error ◽  
Machining Accuracy ◽  
Geometric Errors ◽  
Positioning Errors ◽  
Machining Center ◽  
Influence Effect ◽  
Squareness Errors

Geometric errors of a machining center can cause great influence on machining accuracy, and these geometric errors should be identified and compensated in the actual working conditions. Taking a three-axis vertical machining center as example, 21 geometric errors of the machine tool were solved. By using the 12-line method based on a laser interferometer, identification principle of the positioning errors, straightness errors, pitch errors, yaw errors, roll errors and squareness errors are presented, and all of the 21 geometric errors of the machining center were identified. Geometric errors having great influence effect on machining accuracy can be identified. The research results provide guidance for analyze of geometric errors of machining center.

scholarly journals Characterization and Correction of the Geometric Errors using a Confocal Microscope for Extended Topography Measurement, Part II: Experimental Study and Uncertainty Evaluation

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1217 ◽  
Author(s):  
Wang ◽  
Gómez ◽  
Yu
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Confocal Microscope ◽  
Geometric Errors ◽  
Data Partition ◽  
The Monte Carlo Method ◽  
Measurement Results ◽  
The Mean ◽  
The Mathematical Model ◽  
Certified Values

This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment determines the correction coefficients of the mathematical model. The dot grid target is measured, and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analyzed. Uncertainties are evaluated using the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centers, K-means clustering, etc., are the same for the two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of the lateral stage of a confocal microscope is meaningful and practicable.

scholarly journals An Analysis of Joint Assembly Geometric Errors Affecting End-Effector for Six-Axis Robots

Robotics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 27
Author(s):  
Chana Raksiri ◽  
Krittiya Pa-im ◽  
Supasit Rodkwan
Keyword(s):  
Industrial Robot ◽  
Kinematic Model ◽  
Measurement Data ◽  
Geometric Error ◽  
Laser Tracker ◽  
Geometric Errors ◽  
Actual Measurement ◽  
End Effector ◽  
Position Errors ◽  
Joint Assembly

This paper presents an analysis of the geometric errors of joint assembly that affect the end-effector for a six-axis industrial robot. The errors were composed of 30 parameters that come from the Geometric Dimensioning and Tolerancing (GD&T) design, which is not the normal way to describe them. Three types of manufacturing tolerancing—perpendicularity, parallelism and position—were introduced and investigated. These errors were measured by the laser tracker. The measurement data were calculated with an analysis of the circle fitting method. The kinematic model and error model based on a combination of translations methods were used. The experiment was carried out in order to calculate the tolerancing of geometric error. Then, the positions of the end-effector in the actual measurement from laser tracker and exact performance were compared. The discrepancy was compensated by offline programming. As a result, the position errors were reduced by 90%.

scholarly journals Characterization and Correction of the Geometric Errors in Using Confocal Microscope for Extended Topography Measurement. Part II: Experimental Study and Uncertainty Evaluation

2019 ◽  
Author(s):  
Chen Wang ◽  
Emilio Gomez ◽  
Yingjie Yu
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Confocal Microscope ◽  
Geometric Errors ◽  
Data Partition ◽  
The Monte Carlo Method ◽  
Measurement Results ◽  
The Mean ◽  
The Mathematical Model ◽  
Certified Values

This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment aims at the determinations of the correction coefficients of the mathematical model. The dot grid target is measured and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analysed. Uncertainties are evaluated with implementation of the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centres, K-means clustering, etc., are the same for both two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of lateral stage of confocal microscope is meaningful and practicable.

Modeling and Identification of Geometric Error Based on Screw Theory

2014 ◽  
Vol 941-944 ◽  
pp. 2219-2223 ◽  
Author(s):  
Guo Juan Zhao ◽  
Lei Zhang ◽  
Shi Jun Ji ◽  
Xin Wang
Keyword(s):  
Machine Tool ◽  
Laser Interferometer ◽  
Screw Theory ◽  
Geometric Error ◽  
New Method ◽  
Geometric Errors ◽  
Volumetric Error ◽  
B Spline ◽  
The Individual

In this paper, a new method is presented for the identification of machine tool component errors. Firstly, the Non-Uniform Rational B-spline (NURBS) is established to represent the geometric component errors. The individual geometric errors of the motion parts are measured by laser interferometer. Then, the volumetric error for a machine tool with three motion parts is modeled based on the screw theory. Finally, the simulations and experiments are conducted to confirm the validity of the proposed method.

Sensitivity Analysis of Geometric Errors for Five-Axis CNC Machine Tool Based on Multi-Body System Theory

2012 ◽  
Vol 271-272 ◽  
pp. 493-497
Author(s):  
Wei Qing Wang ◽  
Huan Qin Wu
Keyword(s):  
System Theory ◽  
Sensitivity Analysis ◽  
Machine Tool ◽  
Geometric Error ◽  
Machining Accuracy ◽  
Geometric Errors ◽  
Body System ◽  
Cnc Machine ◽  
Multi Body ◽  
Five Axis

Abstract: In order to determine that the effect of geometric error to the machining accuracy is an important premise for the error compensation, a sensitivity analysis method of geometric error is presented based on multi-body system theory in this paper. An accuracy model of five-axis machine tool is established based on multi-body system theory, and with 37 geometric errors obtained through experimental verification, key error sources affecting the machining accuracy are finally identified by sensitivity analysis. The analysis result shows that the presented method can identify the important geometric errors having large influence on volumetric error of machine tool and is of help to improve the accuracy of machine tool economically.

Specific features of estimating calculated rainfall rates with account of extreme rain showers

2021 ◽  
pp. 50-55
Author(s):  
С.Н. Волков ◽  
А.И. Житенев ◽  
О.Н. Рублевская ◽  
Ю.А. Курганов ◽  
И.Г. Костенко ◽  
...  
Keyword(s):  
Rainfall Intensity ◽  
Experimental Studies ◽  
Measurement Data ◽  
Extreme Rainfall ◽  
Experimental Information ◽  
Wastewater Disposal ◽  
Rain Gauges ◽  
Experimental Base ◽  
Extreme Rain ◽  
Official Data

Анализ официальных источников информации показывает, что распределение экстремальных дождей по территории происходит с учетом микроклиматических особенностей ее местности. Для оценки степени достоверности таких закономерностей в пределах мегаполисов проведены экспериментальные исследования, в которых в качестве экспериментальной базы принята система водоотведения Санкт-Петербурга, в качестве средств измерения – сеть из 34 автоматических осадкомеров, осуществляющих записи с интервалом 5 минут, в качестве экспериментальной информации – база данных результатов измерений в течение шести лет. В результате исследований установлено, что в городской среде формируется микроклимат, отличающийся от климата за ее пределами. Кроме того, в масштабах мегаполисов имеются микроклиматические зоны, в которых зависимости интенсивностей осадков от их повторяемости могут существенно отличаться. При этом отличия начинают проявляться при периодах р однократного превышения расчетной интенсивности дождей от 1,5–2 лет, а при их меньших значениях отличия не выявлены. Полученный результат согласуется с данными исследований других авторов, экспериментально установивших, что количество экстремальных дождей увеличивается в тех районах мегаполисов, как правило, исторических,в которых меньше зеленых насаждений и, соответственно, более высокая степень перегрева поверхности в летнее время. The analysis of official data resources shows that the distribution of extreme rainfall over the territory is carried out with account of the microclimatic features of the area. To estimate the degree of reliability of such patterns within megalopolises, experimental studies were carried out, where the wastewater disposal system of St. Petersburg was assumed as an experimental base; a network of 34 automatic rain gauges recording with an interval of 5 minutes was assumed as a measuring instrument, and a base was used as experimental information, i. e., a measurement data base for six years. As a result of the research, it has been established that a microclimate is formed in the urban environment that differs from the climate outside it. Besides, on a megacity scale, there are microclimatic zones where the dependences of precipitation intensities on their frequency can differ significantly. In this case, the differences begin to manifest at periods p of one-time excess of the calculated rainfall intensity from 1.5–2 years, whereas at lower values, no differences have been found. The result obtained is consistent with the research data obtained by other authors, who experimentally established that the amount of extreme rainfall increased in those areas of megacities, as a rule, historical ones, where fewer green spaces are located, and, accordingly, a higher degree of surface overheating in summer is recorded.

A New Method for On-line Measurement of the Straightness Error of Machine Tools Using an Acceleration Sensor

2021 ◽  
Author(s):  
Kuo Liu ◽  
Yiming Cui ◽  
Zhisong Liu ◽  
Jiakun Wu ◽  
Yongqing Wang
Keyword(s):  
Machine Tools ◽  
Signal To Noise Ratio ◽  
Measurement Data ◽  
Geometric Error ◽  
Ar Model ◽  
High Signal ◽  
Line Measurement ◽  
On Line ◽  
Straightness Error ◽  
Zero Phase

Abstract In order to improve the poor efficiency in the measurement of the geometric error of machine tools’ linear axes, this paper has presented a method to measure and restructure the geometric error of linear axes that is based on accelerometers. This method takes advantage of the phenomenon that when acceleration is measured under different measuring speeds, different frequencies and amplitudes are produced. The measurement data of the high signal-to-noise ratio for various velocities was fused together and the straightness error of the measured axis was obtained by integrating the acceleration twice. In order to remove the trend terms error in the integration, a zero phase IIR Butterworth filter was designed, which guarantees the signal’s phase invariance after filtering. The data was continued with the AR model to eliminate the endpoints’ effect in the filtering. The proposed method was verified by numerical values and experiments. The results showed that the proposed method has better robustness, a wider bandwidth and a higher efficiency than the methods of measuring by laser interferometer. It is also able to measure the geometric error of linear axes with an accuracy that reaches the micron scale.

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