scholarly journals An Integrated Geometric and Hysteretic Error Model of a Three Axis Machine Tool and Its Identification With a 3D Telescoping Ball-Bar

2020 ◽  
Vol 4 (1) ◽  
pp. 24
Author(s):  
Sareh Esmaeili ◽  
J. R. R. Mayer
Keyword(s):  
Error Model ◽  
Test Time ◽  
Machine Error ◽  
Error Sources ◽  
Test Strategies ◽  
Hysteresis Modeling ◽  
Ball Bar ◽  
Qualitative Variables ◽  
Cubic Polynomial ◽  
Error Coefficients

The ball-bar instrument is used to estimate a maximum number of hysteretic error sources. Machine error parameters include inter- and intra-axis errors as well as hysteresis effects. An error model containing cubic polynomial functions and modified qualitative variables, for hysteresis modeling, is proposed to identify such errors of the three nominally orthogonal linear axes machine. Such model has a total of 90 coefficients, not all of which being necessary. A numerical analysis is conducted to select a minimal but complete non-confounded set of error coefficients. Four different ball-bar test strategies to estimate the model coefficients are simulated and compared. The first one consists of circular trajectories on the primary planes XY, YZ, and XZ and the others use the XY plane, as an equator, and either four, five, or nine meridians. It is concluded that the five-meridian strategy can estimate the additional eight error coefficients: ECZ1, ECZ2, ECZ3, ECZb, EZY3, EZX3, ECX3, and ECXb. The Jacobian condition number is improved by increasing the number of meridians to 5. Further increasing the number of meridians from five to nine improves neither the number of estimable coefficients nor the conditioning, and so as it increases, the test time it was dismissed.

A Complete, Continuous, and Minimal Product of Exponentials-Based Model for Five-Axis Machine Tools Calibration With a Single Laser Tracker, an R-Test, or a Double Ball-Bar

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Peng Xu ◽  
Benny C. F. Cheung ◽  
Bing Li
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Rigid Bodies ◽  
Error Model ◽  
Laser Tracker ◽  
Calibration Model ◽  
Transformation Matrices ◽  
Double Ball Bar ◽  
Ball Bar ◽  
Five Axis

Calibration is an important way to improve and guarantee the accuracy of machine tools. This paper presents a systematic approach for position independent geometric errors (PIGEs) calibration of five-axis machine tools based on the product of exponentials (POE) formula. Instead of using 4 × 4 homogeneous transformation matrices (HTMs), it establishes the error model by transforming the 6 × 1 error vectors of rigid bodies between different frames resorting to 6 × 6 adjoint transformation matrices. A stable and efficient error model for the iterative identification of PIGEs should satisfy the requirements of completeness, continuity, and minimality. Since the POE-based error models for five-axis machine tools calibration are naturally complete and continuous, the key issue is to ensure the minimality by eliminating the redundant parameters. Three kinds of redundant parameters, which are caused by joint symmetry information, tool-workpiece metrology, and incomplete measuring data, are illustrated and explained in a geometrically intuitive way. Hence, a straightforward process is presented to select the complete and minimal set of PIGEs for five-axis machine tools. Based on the established unified and compact error Jacobian matrices, observability analyses which quantitatively describe the identification efficiency are conducted and compared for different kinds of tool tip deviations obtained from several commonly used measuring devices, including the laser tracker, R-test, and double ball-bar. Simulations are conducted on a five-axis machine tool to illustrate the application of the calibration model. The effectiveness of the model is also verified by experiments on a five-axis machine tool by using a double ball-bar.

scholarly journals Study on Telescope Gain Affected by a Multilevel Hybrid Mechanism in FAST

2014 ◽  
Vol 6 ◽  
pp. 841526 ◽  
Author(s):  
Xiaoming Chai ◽  
Jin Fan ◽  
Lanchuan Zhou ◽  
Bo Peng
Keyword(s):  
Radio Telescope ◽  
Physical Meaning ◽  
Error Model ◽  
Geometric Errors ◽  
Accuracy Analysis ◽  
Positioning Error ◽  
Error Sources ◽  
Positioning Accuracy ◽  
Hybrid Mechanism ◽  
Structural Deformations

This paper focuses on the telescope gain affected by a multilevel hybrid mechanism for the feed positioning in the five-hundred-meter aperture spherical radio telescope (FAST) project, which is based on the positioning accuracy analysis of the mechanism. First, error model for the whole mechanism is established and its physical meaning is clearly explained. Then two kinds of error sources are mainly considered: geometric errors and structural deformations. The positioning error over the mechanism's workspace is described by an efficient and intuitive approach. As the feed position error will lower the telescope gain, this influence is analyzed in detail. In the end, it is concluded that the design of the mechanism can meet the requirement of the telescope performance.

The study on rapid identification of the key error sources of multi axis motion system based on quasi-rigid body error model

2016 ◽  
Vol 12 (2) ◽  
pp. 181
Author(s):  
Yangpeng Liu ◽  
Jianjun Ding ◽  
Fengdong Wang ◽  
Xingyuan Long ◽  
Zhuangde Jiang
Keyword(s):  
Rigid Body ◽  
Rapid Identification ◽  
Error Model ◽  
Error Sources ◽  
Motion System

Mathematical Model for the Effect of Dynamic Parameter Posed on Free Floating Space Manipulator’s Kinematic Accuracy

2011 ◽  
Vol 216 ◽  
pp. 254-260 ◽  
Author(s):  
Yue Sheng Tan
Keyword(s):  
Screw Theory ◽  
Error Model ◽  
Space Robot ◽  
Structural Parameter ◽  
Kinematic Error ◽  
Space Manipulator ◽  
Error Sources ◽  
Kinematic Accuracy ◽  
Mass Error ◽  
Kinematic Error Model

Aiming at kinematic accuracy and its’ error sources of a free floating space robot, a mathematical kinematic error model based on the concept of virtual manipulator and screw theory is proposed in this paper for a free-floating space robot. Based on screw theory, structural parameters in the form of motion screw and their error expressions derived from various error sources are deduced. The effect of mass error, CM (Center of Mass) error and structural parameter error on the kinematic accuracy of the free-floating space manipulator is analyzed. A simulation is demonstrated for verifying the correctness of the kinematic error model and the effect of various error sources on the free-floating space robot. The error model and the result deriving from analyzing are vital for studying the kinematic accuracy of the space manipulator when it is under a free-floating mode, and for controlling and assigning various errors when a space robot is developed.

scholarly journals Impact of Model Complexity in the Monitoring of Machine Tools Condition Using Volumetric Errors

2020 ◽  
Vol 14 (3) ◽  
pp. 369-379
Author(s):  
Kanglin Xing ◽  
◽  
J. R. R. Mayer ◽  
Sofiane Achiche
Keyword(s):  
Machine Tool ◽  
Recognition Rate ◽  
Error Model ◽  
Model Complexity ◽  
Model Parameters ◽  
Machine Error ◽  
Error Models ◽  
Tool Condition ◽  
Volumetric Errors ◽  
Five Axis

The scale and master ball artefact (SAMBA) method allows estimating the inter- and intra-axis error parameters as well as volumetric errors (VEs) of a five-axis machine tool by using simple ball artefacts and the machine tool’s own touch-trigger probe. The SAMBA method can use two different machine error models named after the number of model parameters, i.e., the “13” and “84” machine error models, to estimate the VEs. In this study, we compare these two machine error models when using VE vector directions and values for monitoring the machine tool condition for three cases of machine malfunctions: 1) a C-axis encoder fault, 2) an induced X-axis linear positioning error, and 3) an induced straightness error simulated fault. The results show that the “13” machine error model produces more focused concentrated VE directions but smaller VE values when compared with the “84” machine error model; furthermore, although both models can recognize the three faults and are effective in monitoring the machine tool condition, the “13” machine error model achieves a better recognition rate of the machine condition. This paper provides guidelines for selecting machine error models for the SAMBA method when using VEs to monitor the machine tool condition.

Improved Position Error Model for Airborne Hyperspectral Imaging Systems

2019 ◽  
Vol 33 (05) ◽  
pp. 1954017
Author(s):  
Yu Jiang ◽  
Na Li ◽  
Xuemei Gong ◽  
Guorui Jia ◽  
Huijie Zhao
Keyword(s):  
Hyperspectral Imaging ◽  
Ground Truth ◽  
Error Model ◽  
Position Error ◽  
Imaging Systems ◽  
Error Sources ◽  
Position Errors ◽  
Propagation Law ◽  
Setting Error ◽  
Camera Position

An improved position error model for airborne hyperspectral imaging systems is proposed to quantify the position errors caused by the deficiencies of instruments and the manual installation of integrated systems. The model is based on a thorough analysis of position error sources, which include uncertainties caused by camera position and altitude, interior camera parameters, gyro stabilized mount, position setting error of the global positioning system antenna, and boresight angle error. An improved position error model that describes these error sources is established based on collinear equations. This model is then expanded into the first-order Taylor series. Finally, the error propagation law is applied to estimate the position errors. The performance of the proposed method is evaluated based on real hyperspectral images of Hymap. Results show that the mean square error of the position error is better than 2.1 pixels, which is almost the same as that of ground truth.

scholarly journals Ball Bar Measurement on Machine Tools with Rotary Axes

2012 ◽  
Vol 6 (2) ◽  
pp. 180-187 ◽  
Author(s):  
Yukitoshi Ihara ◽  
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Industrial Robots ◽  
Error Sources ◽  
Rotary Axes ◽  
Rotary Axis ◽  
Test Conditions ◽  
Ball Bar ◽  
Articulated Robots ◽  
Five Axis

A ball bar is a very convenient device for measuring the motion accuracy of machine tools. Some trials have also been done for measuring motion accuracy of industrial robots. Nowadays, multi-axis machines such as five-axis machining centers are very popular, and therefore, there is increased demand for checking their accuracy. This paper introduces an idea for checking the motion accuracy of five-axis machining centers and diagnosing error sources by reviewing trial measurements on articulated industrial robots. There are two problems. The first problem is that the ball bar can measure only distances, and the second problem is that the ball bar is a linear device and therefore not suitable for the rotary axis motion of 5-axis machines and articulated robots. Finally, the test conditions for the measurement of the motion accuracy of a machine tool showing conical motion, by using the ball bar and ISO/DIS 10791-6 (which is currently being edited) are reviewed and verified.

scholarly journals Identification of Motion Error Sources on Five-axis Machine Tools by Ball-bar Measurements (1st Report)

2010 ◽  
Vol 76 (3) ◽  
pp. 333-337 ◽  
Author(s):  
Soichi IBARAKI ◽  
Yoshiaki KAKINO ◽  
Takayuki AKAI ◽  
Naoshi TAKAYAMA ◽  
Iwao YAMAJI ◽  
...  
Keyword(s):  
Machine Tools ◽  
Error Sources ◽  
Motion Error ◽  
Ball Bar ◽  
Five Axis

Measurement-While-Drilling MWD Error Model Validation – Does the Model Reflect Reality?

2021 ◽  
Author(s):  
David Gutierrez ◽  
Chad Hanak
Keyword(s):  
Real Time ◽  
Service Providers ◽  
Error Model ◽  
Error Sources ◽  
Error Models ◽  
Sensor Error ◽  
Magnetic Model ◽  
Measurement While Drilling ◽  
Standard Deviations ◽  
Directional Sensor

Abstract It has been well documented that magnetic models and Measurement-while-Drilling (MWD) directional sensors are not free from error. It is for this reason that directional surveys are accompanied by an error model that is used to generate an ellipse of uncertainty (EOU). The directional surveys represent the highest probable position of the wellbore and the EOU is meant to encompass all of the possible wellbore positions to a defined uncertainty level. The wellbore position along with the individual errors are typically presumed to follow a Normal (Gaussian) Distribution. In order for this assumption to be accurate, 68.3% of magnetic model and directional sensor error should fall within plus or minus one standard deviation (1σ), 95.5% within two standard deviations (2σ), and 99.7% within three standard deviations (3σ) of the limits defined in the error model. It is the purpose of this study to evaluate the validity of these assumptions. The Industry Steering Committee on Wellbore Survey Accuracy (ISCWSA) provides a set of MWD error models that are widely accepted as the industry standard for use in wellbore surveying. The error models are comprised of the known magnetic model and MWD directional sensor error sources and associated limits. It is the purpose of this paper to determine whether the limits defined in the ISCWSA MWD error models are representative of the magnitude of errors observed in practice. In addition to the ISCWSA defined error model terms, this research also includes an analysis of the sensor twist error term and the associated limits defined in the Fault Detection, Isolation, and Recovery (FDIR) error model. This study is comprised of 138 MWD runs that were selected based on the criteria that they were processed using FDIR with overlapping gyro surveying to ensure highly accurate and consistent estimated values. The error magnitudes and uncertainties estimated by FDIR were compiled and analyzed in comparison to the expected limits outlined in the error models. The results conclude that the limits defined in the ISCWSA error models are not always representative of what is observed in practice. For instance, in U.S. land the assumed magnitudes of several of the error sources are overly optimistic compared to the values observed in this study. This means that EOUs with which wells are planned may not be large enough in some scenarios which could cause the operator to assume unanticipated additional risk. The final portion of this analysis was undertaken to test the hypothesis that preventative measures such as additional non-magnetic spacing are generally being taken by operators and directional service providers to minimize additional injected error when survey corrections are not being implemented while drilling the well. This hypothesis was tested by dividing the 138 MWD runs into Historical (survey corrections were not utilized in real-time) and Real-Time (survey corrections were utilized in real-time) categories. The results indicate that there are no significant differences in the error estimates between the Historical and Real-Time categories. This result in combination with the determination that the majority of the error model error terms should be categorized as fat-tail distributed indicate that proper well spacing and economics calculated using separation factor alone are insufficient without the use of survey corrections in Real-Time.

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