Error Separation Method Research Articles

An on-machine measurement technique with sub-micron accuracy on a low-precision grinding machine tool

The on-machine measurement system can effectively improve the machining efficiency and accuracy of the optics in the grinding stage, but the common grinding machine has large geometric errors and ambient temperature errors, which are the key factors restricting the accuracy of on-machine measurement. In this paper, a high-precision error separation technique including geometric error separation and temperature error separation is proposed to achieve sub-micron level measurement accuracy in the grinding stage. The on-machine measurement system is built based on the color confocal sensor. A sensitive error model is established based on Abbe's principle and multi-body dynamics, and the geometric error separation with zero Abbe's error is achieved by a high-precision reference mirror. Then the temperature error influence model is established based on the scanning path, and the temperature error separation method based on the auxiliary profile line is proposed according to the temperature error model. Finally, it is verified through experiments that after error separation, the measurement accuracy of the on-machine measurement system is improved from tens of micron to sub-micron, which exceeds the measurement accuracy of ordinary coordinate measurement machines (CMMs), and can effectively improve the machining accuracy and efficiency in the grinding stage.

An Eccentricity Error Separation Method for Rotary Table Based on Phase Feature of Moiré Signal of Single Reading Head

In view of the limitations of the existing eccentricity error separation method of the rotary table, an eccentricity error separation method based on the phase feature of the moiré signal of a single reading head is proposed herein. A grating pair transmission model is established based on the analysis of the principle of the rotary table; thereby, the influence of eccentricity error on the phase feature of the moiré signal in the rotation course of the rotary table is clarified, and the corresponding model between the phase feature spectral components and the eccentricity error is established. The verification experiments of the proposed method are carried out based on the laboratory-made circuit system. After verifying the accuracy of the data acquisition of the laboratory-made circuit board, the verification experiments of the eccentricity error separation effect of the proposed method are carried out. The experimental data are compared with those of the traditional method, and the results show that the error between the two methods is 2.34 μm, while the relative error is 2.3%.

Research on error separation method of center of gravity measurement system for large-sized solid of revolution

In order to realize mass and center of gravity measurement of large-sized rotating parts, a set of combined measurement system for center of gravity measurement was developed to adjust the distance according to the length and supporting position of the parts to adapt to different lengths of the measured parts. The study focused on the center of gravity synthesis, error factors and error separation within the system. Firstly, two sets of center of gravity measuring equipment based on multi-point weighing method were used to conduct a joint test on the large-sized measured parts, and the center of gravity measuring model was analyzed. Secondly, the measurement error and its influence on the measurement result are were analyzed when the two sets of measuring equipment were not parallel. Finally, error signals were separated using the multi-step method, Fourier transform and inverse Fourier transform. Simulation experiments show that the residual center of gravity error of Y axis and Z axis is less than 0.3 mm when the tilt angle between two sets of equipment is below 0.3°. The test results demonstrate that the center of gravity measurement error along the X axis is less than 2 mm, which indicates the measurement accuracy better than 0.02% as the length of the test object is about 10 000 mm, and the center of gravity measurement error along the Y axis and Z axis is less than 0.5 mm, which also indicates the measurement accuracy better than 0.02%. These findings indicate that the system enables high-precision measurement of the center of gravity for large-sized rotary products.

A method for separating unmodeled errors in GNSS based on the constraint of the prior variance of unit weight

In global navigation satellite system (GNSS), unmodeled errors critically affect the accuracy and reliability of positioning solutions. When the unmodeled errors are significant in the mathematical model, they are mainly processed by choosing adjustment models with additional systematic error parameters or semiparametric estimation. However, many existing methods require knowledge of prior information on unmodeled errors; otherwise, achieving better processing results is difficult. To address this problem, this study proposes a GNSS unmodeled error separation method that does not rely on prior information on unmodeled errors. This method is based on the constraint of prior variance of unit weight. First, the method effectively separates the effect of unmodeled errors in the residuals under this constraint. Second, the initial estimate of the unmodeled errors in the observation domain is used as a virtual observation. Thus, the optimal estimate and variance of the unmodeled errors are obtained. Finally, the observations are effectively corrected by combining the concepts of mean shift and variance inflation. Multiple experiments were performed in this study. The results show that the proposed method can effectively weaken the impact of unmodeled errors on the float and fixed solutions of GNSS positioning, regardless of whether unmodeled errors exist in a single observation or multiple observations.

Five-degrees-of-freedom error motion measurement method of precision rotary table based on BMPES

It is essential to obtain the five-degrees-of-freedom (5-DOF) error motion of a rotary table to reconstructthe real trajectory of the rotating shaft, but there are many error coupling problems when measuring the error motion of a rotary table. In order to improve the measurement accuracy of the 5-DOF error motion of the rotary table, a method of measuring the error motions based on bidirectional multi-point error separation (BMPES) is proposed. First, by analyzing the motion characteristics of the rotary table with multiple degrees of freedom error during the rotation, a detection system with a double-layer structure probe arrangement is designed. Then, the three-point method is used in the radial direction to separate the roundness error of the measuring disk, which improves the measurement accuracy of radial error. Finally, the coupling relationship between the mixing errors collected by the axial probes is researched, and a face-four-point error separation method is proposed, which can separate the flatness error of the lower surface of the measuring disk and complete the decoupling of the tilt error and the axial runout error. Simulation results show that for the measurement of radial, tilt and axial errors, the measurement errors of the BMPES method proposed in this paper are reduced by 97.89%, 68.40% and 99.99%, respectively, compared with the five-point method, and when eccentricity errors exist, the measurement errors of the radial and tilt errors are reduced by 99.06% and 85.67%, which verifies that the method can accurately obtain the 5-DOF motion of the rotary table errors.

Separation of rotary table radial error motions in gear pitch measurements using harmonic regeneration

During precision or on-machine gear pitch measurements, radial error motions of the rotary table (RT) are non-negligible factors that affect the measurement accuracy and repeatability. In this paper, an error separation method using harmonic regeneration (the ES–HR method) is presented to reduce the influence of the RT radial error motions. First, the gear pitch deviations are measured over several laps. Then, the measurement results are decomposed into different period components by a discrete Fourier transform and the integral period components are extracted to regenerate the pitch deviations. Using this method, the influence of the non-integral period RT radial error motions and most of the random errors can be eliminated. Finally, the influence of the integral period RT radial error motions, acquired synchronously or in advance, are subtracted from the regenerated pitch deviations and the actual gear pitch deviations without the influence of RT radial error motions are obtained. Experimental results showed that this proposed method can effectively eliminate the influence of the RT radial error motions and has better accuracy and less uncertainty than the pitch deviations evaluation algorithm that uses a multi-lap average. Additionally, this method does not require changes in the position of the gear relative to the RT as do existing error separation methods, and it can be easily used for measurements at production sites or on machines.

Separation and compensation of nonlinear errors in sub-nanometer grating interferometers.

In this paper, to separate and compensate the nonlinear error in the grating interferometer, we analyze the source and generation mechanism of this error, deduce the nonlinear error model of the measured signal and the calculated phase signal, and study the characteristics of the established nonlinear error model. The reason why the frequency multiples of ideal phase signals and higher-order nonlinear errors caused by ghost reflections and angular errors of the laser's z-axis are not integers is explained. Then, a nonlinear error separation and compensation method based on cross-correlation coefficient is proposed. Experiments show that the frequency multiplier relationship between the high-order nonlinear error and the ideal interference signal is close to but not equal to 3-fold. The peak-to-peak value of the compensated nonlinear error is reduced from 17.40 nm to 7.05 nm.

Radial Error Motion Measurement and Its Uncertainty Estimation of Ultra Precision Axes of Rotation with Nanometer Level Precision.

The radial error is the key performance indicator of ultra-precision axis. In order to measure and evaluate the radial error of ultra-precision axis with nanometer accuracy, a measurement system with an accuracy of nanometer based on capacitive displacement probes and standard spheres is developed. The nonlinearity error of capacitive displacement probes, misalignment error of the probes, eccentric error of standard spheres, error caused by environment temperature change, environment vibration and error separation methods are analyzed and the effects of the above factors are obtained; Multiple measurement examples carried out with the measurement system this paaper constructed indicate the repeatability of the measurement system reaches 10.5 nm and the roundness error of artifact separated is less than 4.03 nm. In order to evaluate the measurement dispersion of the ultra-precision axis radial error, the major uncertainty components and the complete process of the comprehensive evaluation of the measurement uncertainty are proposed. The combined uncertainty of radial error motion measurement of the ultra-precision axis with Donaldson reversal is 31.64 nm (k = 2).

Global Mean Square Error Separation Loss

Class imbalance problem greatly affects the accuracy of deep-learning-based object detectors. To weaken its influence, this paper proposes a global mean square error separation loss (GMSES Loss). GMSES Loss assigns a factor to each example, and then enhances the learning of hard-to-learn examples by reducing the factors of easy-to-learn examples. Meanwhile, the global mean square error separation method is introduced to enhance the learning of foreground classes. To verify the effectiveness of our algorithm, experiments are conducted with YOLOv4 and RetinaNet as the baselines, respectively. The results have shown that our loss function can improve the performance of one-stage object detectors without adding any extra hyperparameters.

Analysis and Error Separation of Capacitive Potential in the Inductosyn

High-precision rotor position information is usually needed in permanent-magnet synchronous motors, which are critical to high-performance motor control based on vector algorithm. Therefore, inductosyn is the best choice for the permanent-magnet synchronous motor position sensor. Capacitive potential is an important component of the ineffective potential in the inductosyn angle measuring system. When the effective potential of the inductosyn approaches zero, the proportion of capacitive potential in the output potential will be greatly amplified. As a result, the zero-position accuracy will be seriously affected. Error potential and effective potential always exist at the same time, so it is difficult to measure and study quantitatively. In this paper, the capacitance network model of inductosyn was established and the analytical calculation method was proposed. The factors affecting the capacitive potential and the suppression strategy were studied through the combination of theoretical analysis and the finite element method. In addition, the error separation method of capacitive potential was also proposed in this paper, which realized the accurate measurement of this part of error. The accuracy of the theoretical calculation and finite element analysis was verified by the experimental results.

Roundness error separation based on singularity detection and exact-stop of spindle in on-machine measurement of spindle rotation error

At present, non-contact sensors are being extensively used for the measurement of spindle rotation errors. However, as the measuring target of the sensors, the roundness error of the artifact inevitably mixes into the error motion of the spindle. Moreover, the challenging nature of manufacturing high-precision artifacts has resulted in the separation of the roundness error of artifacts from the spindle rotation error being considered an urgent research prospect. In this study, a roundness error separation method based on singularity detection and exact-stop of spindle was proposed to perform on-machine measurement of spindle rotation error, wherein compared to the existing methods, the proposed method implements the Donaldson reversal method. It is independent of the index signal of the spindle encoder, which is usually unavailable on actual machine tools. The singularity of measured motion was detected using the wavelet transform modulus maximum (WTMM) ridges and their Lipschitz exponents, to locate the exact-stop and rotating stages of spindle in the measured motion. Consequently, a WTMM ridge extraction method was established to extract the continuous optimal WTMM ridges of the measured motion. Further, the synchronous motion of the measured motion was used for roundness error separation to promote the separation accuracy. Finally, the effectiveness of the proposed method was verified using the measurement results of a coordinate measuring machine (CMM). Thus, the measurement error caused by the roundness error of the artifact can be reduced significantly by applying the proposed method to the on-machine measurement of the spindle error motion.

New Radius and Roundness Measurement for Microspheres Using a High-Precision Run-Out Error Separation Method

Roundness is a kind of form error in geometrical measurement in laboratory and industry and contributes significantly to the uncertainty of the measurement instruments using precision spheres, especially microspheres. A new radius and roundness measurement method for microspheres is proposed in this paper. Using this method, not only can separate different run-out errors from the measuring results, but also can obtain the true radii in different directions of the tested microsphere, which are necessary for the roundness evaluation according to ISO 1101. A new roundness measurement system has also been developed, which is mainly composed of two miniaturized Michelson interferometer (MI) systems, two elastic mechanisms, and a precision rotating stage. Repeated measurements have been performed using a ruby microsphere manufactured by Renishaw Corporation as the reference, which has a claimed diameter and roundness of 700 μm and 130 nm respectively. Experimental results show that the average radius of the tested microsphere is 349.99 μm with a maximum error of 65 nm and an expanded uncertainty of 94.0 nm (k=2). The proposed method and system can be used in the precision contact measurements of parts with micro circular characteristics such as microspheres and micro cylinders.

An advanced Fourier-based separation method for spindle error motion identification

Classical error separation methods (Donaldson reversal, multistep, and multiprobe methods) were developed by separating both the spindle synchronous radial error motions of precision measurement instruments and the roundness deviations of cylindrical or spherical material standards. The application of such methods improves the measurement uncertainty, even though some methods are time-consuming (multistep) or require a more complex set-up (e.g., the Donaldson reversal and multiprobe methods). In this study, an advanced Fourier-based method for error separation in roundness measurements is developed and implemented. It can be considered a fully stable method, achievable through a reduced number (two or three) of angular shifts, and uses at least one fixed probing system. The proposed Fourier-based method is optimised, tested, and validated on simulated datasets and scenarios combining synchronous and asynchronous spindle error motions and roundness deviations. The given results are accurate at the sub-nanometre level (<0.5 nm) and the effectiveness of the Fourier-based method for ultra-high accuracy applications is proven. Further, Monte Carlo simulations, performed to investigate the influence of artefact indexing errors on measurement uncertainties, confirmed the numerical investigation. Finally, an experiment was conducted on spherical material standards made of ceramic using a high-precision roundness measurement machine. The given results are more accurate (at nanometre level) than those of the ‘classical’ multistep methods.

Implementation and verification of a dual-probe measurement system for geometric form evaluation of a ring-type cylinder

This paper presents the implementation and verification of a dual-probe measurement system with a novel method and easily integrated chromatic confocal probes, for synchronous evaluation of not only the inner and outer cylindricity but also the thickness distribution of a ring-type cylinder. A pair of measuring probes mounted on a four-axis scanning stage, which is composed of XYZ-slides and a spindle, is utilized to target the two sides of the ring-type cylinder. In the developed system, to reduce the influence of the positioning errors and tilt misalignments of the confocal probes and the cylinder, alignment methods are developed. The outputs of the measuring probes are employed to accurately evaluate the geometric errors of the ring-type cylinder through performing spiral scanning while separating the Z-slide and spindle motion errors of the scanning stage based on a reversal error separation method. To verify the performance of the proposed system and method, the geometric errors of a thin-walled cylinder which has a nominal outer diameter of 50 mm, an inner diameter of 40 mm, and a length of 100 mm are evaluated in experiments. The experimental results are further compared with those by a coordinate measuring machine (CMM), and the high correspondence of the comparison results well confirm the feasibility of the implemented measurement system. Finally, measurement uncertainty analysis is conducted to demonstrate the reliability of the proposed method for the evaluation of the geometric errors of ring-type cylinders. The measurement accuracy is comparable to that of a CMM.

Estimation Algorithm of Ionospheric Delay Correction Parameters Based on Neural Network

Aiming at the difficulty of separating the ionospheric delay error in the user pseudoring observations of a single-frequency receiver, this paper proposes an error separation method based on BP neural network. The receiver’s observation data for a continuous week is used as a training sample, and the time in the sample is the satellite altitude, azimuth and pseudoring observations are used as the input unit of the BP neural network. The high-precision GIM provided by CODE is used to calculate the corresponding ionospheric delay error, and it is used as the output unit to train the BP neural network. At the end of the thesis, the single-frequency PPP model that uses parameter estimation in the ionosphere is discussed. Finally, the positioning accuracy that this model can achieve is verified through actual calculation examples.

Validation and uncertainty analysis of a reduced self-calibrating method for pitch measurements of cylindrical gears

The three-rosette method is a well-established self-calibrating error-separation method used for highly accurate pitch calibrations of cylindrical gears on coordinate measuring machines or gear measuring machines. It is based on the principle of circle closure and uses multiple measurements in different relative positions of the gear with respect to the measuring device. However, since its measurement effort is proportional to the square of the number of teeth, the method is of limited usability for gears with a large number of teeth. In this paper, a reduced method which requires much fewer measurements is described. This method is based on the same error model and is still self-calibrating. The measurement uncertainties for this method are only slightly higher than for the complete method. After an introduction to the three-rosette method, this paper describes the impact of the number and choice of the measured relative positions on the measurement uncertainty. Moreover, the problem of an erroneously determined gear axis is addressed. Finally, the effectiveness of the reduced three-rosette method is shown in intercomparison measurements with four participants. The obtained E n scores show that the reduced three-rosette method allows pitch calibrations with nearly the same accuracy as can be achieved with the complete method. The reduced three-rosette method is part of the TraCIM online service (https://tracim.ptb.de) of the Physikalisch-Technische Bundesanstalt (PTB) allowing software manufacturers or calibration laboratories to obtain a certificate for their algorithms of the reduced three-rosette method after a successfully performed software test. Moreover, calibration laboratories can receive accreditation by the German national accreditation body (DAkkS) for pitch calibrations performed by using the reduced three-rosette method.

Prestack seismic facies analysis via waveform sparse representations

Seismic facies analysis based on prestack data is becoming popular. Vertical elastic transitions produce the spatial structure variation of prestack waveforms, whereas lateral elastic transitions produce the amplitude intensity variation. In stratigraphic seismic facies analysis, more attention should be paid to waveform spatial structure than amplitude intensity. Conventional classification methods based on distance metrics are difficult to adapt to stratigraphic seismic facies analysis because a distance metric is a comprehensive measure of waveform structure and amplitude intensity. We have developed a dictionary learning (DL) method for prestack seismic facies analysis. The method first learns several dictionaries from labeled prestack waveform data, and these dictionaries consist of several normalization vector bases. The prestack waveform spatial structure is, therefore, embedded in these learned dictionaries, and the amplitude intensity is eliminated by the normalization process. Afterward, these dictionaries are used to sparsely represent prestack seismic data. Seismic facies are classified and determined according to representation error. A source error separation method is used to improve the antinoise performance of DL by iteratively segmenting the noise out in the training data. The results on synthetic and field seismic data show that the proposed method has a stronger tolerance to noise than K singular value decomposition, and the obtained seismic facies boundary is more accurate and clearer than the support vector machine and k-nearest neighbors algorithm. This demonstrates that the proposed method is an effective seismic facies analysis technique.

정밀 원통 부품의 4-프로브법을 이용한 온-머신 측정 기술

In this research, an on-machine measurement system is developed, in which the multiprobe error separation (MPES) method is applied to give feedback on errors from the machining tools. To measure the roundness of the cross-sectional form-component (roundness and diameter) of the workpiece, the principle of the Fourier model-based MPES method was analyzed to solve the major problem of harmonic distortion in this technique. Using this process, the on-machine measurement system was created for machining equipment, and its performance was evaluated. The comparison between the proposed system and the general one-probe-based measuring system showed that performance of the former was 25 times better than that of the latter. This indicates the possibility of effective compensation of the motion error of rotors.

Single probe shear scanning method for on-machine measurement of an optical profile.

This study presents a new (to the best of our knowledge) error separation method with a single displacement probe, named as single probe shear scanning (SPSS) method, for the on-machine optical profile measurement to overcome the problems of the existing multiprobe method like the large deviation of probe spacing and the probes' performance difference. The confocal sensor with superior dynamic range, high lateral resolution, and large measurement angle to surface is applied in this study to fulfill the measurement of the optical aspheric surface. The single probe measurement system, in which the probe fixed on a flexure hinge is driven straight within a millimeter-level travel range, is established to realize the function of the multiprobe. For the established system, a new exact profile reconstruction algorithm is built to eliminate the influences of straightness errors of the scanning stage and the systemic errors of shear stage, and to reduce the effect of the sensor drift. The reconstruction algorithms by difference measurement with two shears are studied to build the bidirectional segment stitching reconstruction method, which reduces the error accumulation and improves the reconstruction accuracy under the condition of measuring errors. A profile reconstruction method with three shears measurement is proposed to make a further improvement on the reconstruction accuracy. The proposed reconstruction method with three shears measurement is successfully employed for the on-machine measurement of an aspheric surface profile, and the evaluation results agree well with those from the Taylor profiler.

A cylindricity evaluation approach with multi-systematic error for large rotating components

For reduction of the cylindricity evaluation uncertainty for large rotating components with large radius and height, the cylindrical profile measurement model is designed with multi-systematic error considering eccentricity, probe offset, probe radius, geometric axis tilt, support rod tilt, and guide rail tilt. In addition, an error separation method is proposed based on the multi-systematic error measurement model. The combined influence of multi-systematic error on the measurement results is analyzed, and cylindricity results are evaluated based on the proposed method. It is verified that, compared with other measurement models, the cylindrical profile measurement model with six systematic errors is the most accurate and stable in the standard cylindrical component measurements using a large high-precision cylindricity measuring instrument. In this experiment, compared with the cylindrical profile measurement model with two systematic errors, the cylindricity evaluation uncertainty obtained by the proposed method reduces from 55.2 µm to 21.0 µm with increasing radius and height of the standard cylindrical component. The proposed method is especially suitable for the cylindrical component measurements with large radius and height. The paper provides an accurate measurement model for high-precision error separation, tolerance allocation and cylindricity comparison for accredited laboratories, national metrology institutes etc.