Linear Displacement Error Research Articles

A Range-Extension Method for an Indoor Standard Device for Large-Scale Length Measurement

The Laser interferometer plays an important role in the field of geometrics for large-size measuring applications. Its linear displacement error can be traced from indoor large-scale standard devices. However, the measuring range of the indoor large-scale standard device is too limited to meet the full range measurement of the laser interferometer. So, the lack of accuracy of the results is one of the key issues of laser interferometers. To solve this problem, the corner reflector is used to extend the range of indoor large-scale standard devices, which meet the indication errors in the effective measuring range of the laser interferometer. The range-extension method not only doubles the effective measuring range, but also provides a way to trace the source of other large-size measuring instruments. This work proposes a significant solution to the field of length measurement.

Calibration method for structure parameters of a binocular stereo vision system equipped with polarizers.

For structure parameter calibration of a binocular stereo vision system equipped with polarizers, the optimal calibration polarization angle needs to be determined. There are no corresponding solutions for the determination of the optimal polarization angle of structure parameter calibration. Furthermore, existing research considers the polarization angle that causes the image to possess the lowest brightness (gray value) as the optimal polarization angle. This reduces image contrast, and eventually the texture information of the image is lost, which also affects the accuracy of feature extraction. In this paper, we propose a new calibration method for the structure parameters of a binocular stereo vision system equipped with polarizers. We calculated the pose of the target relative to each camera for different polarization angles. The sum of the object-space errors corresponding to each polarization angle was considered as the evaluation criterion to determine the optimal calibration polarization angle. The calibration of structure parameters was finished using images captured on the premise of the optimal calibration polarization angle. This angle can also be considered as the reference of the polarization angle for measurement. Experiment results show that using the calibration results of our method, the reconstructed length error of a 275×200mm target was less than ±0.052mm, the reconstructed linear displacement error was less than ±0.048mm for the range of 0-30 mm, and the reconstructed rotary angle error was less than ±0.048∘ for the range of-30∘-30∘.

The Method of Geometric Error Measurement of NC Machine Tool Based on the Principle of Space Vector’s Direction Measurement

To achieve the quick and accurate calibration of the geometric errors of NC machine tool, a new method with laser tracker on the basis of space vector’s direction measurement principle is proposed in the paper. A series of measuring points are mounted on the moving part of the machine tool, and then adjacent measuring points are connected to form a space vector respectively. Due to the motion error of the machine tool, the direction of the vectors composed will be changed. Meanwhile, the deviation of vector’s direction only relates to angular displacement error rather than linear displacement error. Based on the characteristic, the change of vectors’ direction is measured by laser tracker based on the multi-station and time-sharing measurement during the motion of machine tool, and then the angular displacement errors and linear displacement errors of each axis can be accurately identified successively, which reduces the complexity of error identification. By establishing the mathematical model of geometric error measurement of machine tool based on the principle of space vector’s direction measurement, the base station calibration algorithm by measuring the motion of the designed precise turntable, the measuring point determination algorithm and geometric error separation algorithm are derived respectively, and the accuracy of these algorithms are verified by simulations. In addition, the results of the experiments show the feasibility of the proposed method.

Experimental sampling of the Z-axis error and laser positioning error of an EOSINT M280 DMLS machine

The Z axis table motion errors and laser positioning errors an EOSINT M280 were evaluated using a set of standard metrology techniques and instrumentation. While the linear displacement error of the table is quite low (4.5 μm), straightness, yaw and pitch errors on the other hand were significantly higher and may contribute from 20 to 30 microns of form and orientation tolerances over a large size build.The performance of the laser positioning system was much worse. The system consistently positioned the beam short by a significant amount at the edges of the workspace. A designed artifact was produced, and used to evaluate the laser performance against a set of tolerance controls extracted from the ASME Y14.5-2009 Standard. The largest scatter of values was observed on the position of small circular features located over the working area. The largest tolerance magnitude (239 μm) was calculated as the combined effect of location, orientation, size and form errors in the trace of a large quadrifolium etched over the working area of the laser. The errors measured in this research are substantial.

Kinematic and dynamic errors during the measurement of linear displacements using the angle transducers

Dependence of linear displacement error, while measuring with angle transducers, on angle measurement system errors, kinematic and geometric errors of mechanism of linear motion transformation to rotation is shown. Dynamic processes, acting in an elastic element, connecting a movable compound, which linear displacement is measured, with the shaft of the angle measurement transducer, are modeled. Vibration modes, influencing the uncertainty of linear displacement measurement by an angle transducer, are defined. Results of numerical study by using FEM are verified and complemented by experimental research. Research stands and equipment are described.DOI: http://dx.doi.org/10.5755/j01.mech.22.3.14180

Total measurement of geometric errors of a three-axis machine tool by developing a hybrid technique

A hybrid measurement technique using a five-DOF measuring system and laser interferometer is suggested for all geometric errors of a three-axis machine tool. All geometric errors are defined in a single coordinate system, by eliminating the effect of Abbe’s offsets, for accurate measurement. The five-DOF measurement comprises five capacitive sensors and an L-type reference mirror. The system measures three PIGEs (position independent geometric errors) and five PDGEs (position dependent geometric errors) for each axis. The 18 geometric errors of the machine tool are measured using the results from two experiments (XY and YZ-planes), and the homogeneous transform is used to identify the geometric errors in a single coordinate system, eliminating the effects of installation errors such as mirror misalignment. A laser interferometer is used to measure three PDGEs (one linear displacement error and two straightness errors) for each axis. The two straightness errors are used to estimate the optimal Abbe’s offsets (for the X, Y and Zaxes) between the two measuring coordinate systems, and the linear displacement of each axis is calculated, minimizing the effect of Abbe’s offsets. Through this analytical approach, all geometric errors are expressed for a single coordinate system. The suggested measurement technique can therefore be used to investigate all geometric errors of a three-axis machining tool.

Multi-DOF Incremental Optical Encoder with Laser Wavelength Compensation

This study used a reflective diffraction grating as the medium to develop a multi-DOF incremental optical encoder for motion stage. The optical encoder can measure three angular displacements, roll, yaw and pitch of the motion stage simultaneously, as well as the horizontal straightness and linear displacement, summed to five DOF errors of motion stage by only using the positive and negative first-order diffracted light. The grating diffraction theory, Doppler effect, and optical interference technique were used. Two quadrant photodetectors were used to measure the changes in three-dimensional space of diffraction direction of diffracted light, in order to construct a multi-DOF incremental optical encoder. Considering the working stability of a laser diode and preventing the influence of the zeroth-order diffracted light returning to the laser diode, an additional optical isolation system was designed and a wavelength variation monitoring module was created. The compensation for the light source wavelength variation could be 0.001 nm. The multi-DOF verification results showed that the roll error is ±0.7/60 arcsec, the standard deviation is 0.025 arcsec; the yaw error is ±0.7/30 arcsec, the standard deviation is 0.05 arcsec; the pitch error is ±0.8/90 arcsec, the standard deviation is 0.18 arcsec, the horizontal straightness error is ±0.5/250 μm, the standard deviation is 0.05 μm and the linear displacement error is ±1/20000 μm, the standard deviation is 12 nm.

초정밀 직선 스테이지에서 5 자유도 운동의 정적 및 동적 성능 평가

In this study, the five-DOF motion at ultra-precision linear stage under static and dynamic conditions are evaluated through the extending application of ISO 230-2. As the performance factors, the bi-directional accuracy and repeatability of the five-DOF motion are quantitatively evaluated with the measurement uncertainties which are determined using the standard uncertainty of equipment used in experiment. The motion under static condition are analyzed using geometric errors. The five geometric errors except the linear displacement error are measured using optimal measurement system which is designed to enhance the standard uncertainty of geometric errors. In addition, the motion under dynamic conditions are analyzed with respect to the conditions with different feed rate of the stage. The experimental results shows that the feed rate of stage has a significant effect on straightness motions.

Performance evaluation of five-DOF motion in ultra-precision linear stage

In this study, the performance of five-DOF motion in ultra-precision linear stage is evaluated accurately by extending the application of the ISO 230-2 International Standard, which is focused only on the linear displacement motion of a linear stage. The bidirectional accuracy and bidirectional repeatability of positioning in five-DOF motion are calculated by measured geometric errors. Five geometric errors except for the linear displacement error of a linear stage are measured simultaneously using the optimal measurement system, which is designed to enhance the standard uncertainty of the estimated geometric errors. The geometric errors are in good agreement with those from the laser interferometer. In addition, the confidence intervals of the performances are determined by the uncertainties of the equipment used in the experiment.

The Effect of Geometric Error on Machining Accuracy for Machining Center

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.

Multi-DOF Incremental Optical Encoder with Laser Wavelength Compensation

This study used a reflective diffraction grating as the medium to develop a multi-DOF incremental optical encoder for motion stage. The optical encoder can measure three angular displacements, roll, yaw and pitch of the motion stage simultaneously, as well as the horizontal straightness and linear displacement, summed to five DOF errors of motion stage by only using the positive and negative first-order diffracted light. The grating diffraction theory, Doppler effect, and optical interference technique were used. Two quadrant photodetectors were used to measure the changes in three-dimensional space of diffraction direction of diffracted light, in order to construct a multi-DOF incremental optical encoder. Considering the working stability of a laser diode and preventing the influence of the zeroth-order diffracted light returning to the laser diode, an additional optical isolation system was designed and a wavelength variation monitoring module was created. The compensation for the light source wavelength variation could be 0.001 nm. The multi-DOF verification results showed that the roll error is ±0.7/60 arcsec, the standard deviation is 0.025 arcsec; the yaw error is ±0.7/30 arcsec, the standard deviation is 0.05 arcsec; the pitch error is ±0.8/90 arcsec, the standard deviation is 0.18 arcsec, the horizontal straightness error is ±0.5/250 μm, the standard deviation is 0.05 μm and the linear displacement error is ±1/20000 μm, the standard deviation is 12 nm.

3613 レーザステップ対角線測定を用いた工作機械の三次元空間精度の測定法(S64 工作機械,S64 工作機械)

The laser step diagonal measurement is a method for the identification of all the volumetric error components, including linear displacement errors, straightness and squareness errors by using only a laser interferometer and a flat mirror. This research first discusses inherent and critical issues with the conventional formulation of the laser step diagonal measurement. Then, we propose a new formulation of the laser step diagonal measurement to accurately estimate the machine's volumetric errors even under the existence of setup errors.

Accuracy enhancement of a horizontal machining center by real-time error compensation

A real-time error compensation system was developed to improve the geometric-thermal volumetric accuracy of a T-10 machining center by using sensing, metrology, modeling, and computer control techniques. Including thermal errors, 32 error components are formulated as a four-dimensional error field in the time-space domain. Fifteen thermal sensors are used to characterize the temperature field of the machine. A compensation controller based on the IBM/PC has been linked with an Acramatic-950 CNC controller to compensate for machine errors in real time. The maximum linear displacement error in four body diagonals was reduced from 140 μm to 34.5 μm with this compensation system, and the spindle thermal drift in space was reduced from 147.3 μm to 16.8 μm.

Development of computer integrated system for error diagnosis of a CMM using calibrated mechanical artefacts

Error calibration and frequent reverification of coordinate measuring machines (CMMs) and machine tools are currently acknowledged as essential processes in order to maintain high performance of the machines and high quality of products. This paper shows a micro-computer integrated error calibration system, which is a fast and efficient error calibration system: a micro-computer stores calibration data of mechanical artefacts, such as ring and step gauges that have been calibrated with respect to more precise equipment, then the machine probes the gauges. The gauge probing data are compared with the gauge calibration data. The micro-computer plans measurement paths thus generating CNC codes for measurement of the mechanical artefacts located in a working volume of a commercial CMM. Then measurement operations are performed according to the planned paths for practical measurement of the gauges. For ring gauge measurement, the lobing error of the probe stylus has been efficiently measured then used for the probe compensation. The circular errors are successfully calculated from the comparison between the ring gauge geometry and the ring gauge probing data after the probe stylus compensation in terms of software. Then from the error pattern of circular error, machine errors such as scale errors and orthogonality error are successfully calculated, showing good approximation to the evaluated circular error. In the case of the step gauge measurement, the gauge probing data are compared with those of calibration data; thus complete linear displacement error analysis is successfully evaluated along any direction in a working volume. The error evaluations are then processes in real time, and presented in computer graphic environments. Practical application to a commercial CMM of CNC-type shows the validity and efficiency of the developed system. Thus a rigorous computer integrated error calibration system is proposed with the full potential of practical application to most commercial CMMs and machine tools of a CNC-type.