Error Separation Method Research Articles

Blind Signal Separation Method Based Machining Error Decomposition

In view of the current error separation method cannot successfully separate the dissimilar systematic error components from the whole surface machining data, a method for machining errors decomposition based on blind signal separation is proposed which can distinguish those dissimilar systematic error components. Firstly, the error transfer model to describe the errors synthesizing from the single error component caused by corresponding individual error source to the synthesis machining surface error is conducted. To determine the number of the systematic error components, the principal component analysis (PCA) method is used. Then according to the theory of blind source separation, negative entropy based fixed point algorithm is proposed to fulfill the machining error components separation, which can realize the separation of the systematic error components even in close frequency scale. Finally, a shaft surface finish turning data and a flat surface milling data are used as examples to verify the proposed method. The result shows that the proposed error separation method can effectively realize the machining error separation in close frequency scale.

Error Separation Method for Precision Measurement of the Run-Out of a Microdrill Bit by Using a Laser Scan Micrometer Measurement System

This paper describes an error separation method for a precision measurement of the run-out of a microdrill bit by using a measurement system consisting of a concentricity gauge and a laser scan micrometer (LSM). The proposed error separation method can achieve a sub-micrometric measurement accuracy of the run-out of the microdrill bit without the requirement of ultra-precision rotary drive devices. In the measurement, the spindle error motion of the concentricity gauge is firstly measured by using the LSM and a small-diameter artifact, instead of the conventionally used displacement probes and large-diameter artifact, in order to determine the fine position of the concentricity gauge when the spindle error motion is at its minimum. The microdrill bit is rotated at the fine position for the measurement of the run-out, so that the influence of the spindle error motion can thus be reduced, which could not be previously realized by commercial measurement systems. Experiments were carried out to verify the feasibility of the proposed error separation method for the measurement of the run-out of the microdrill bit. The measurement results and the measurement uncertainty confirmed that the proposed method is reliable for the run-out measurement with sub-micrometric accuracy.

Magnetic orientation system based on magnetometer, accelerometer and gyroscope

Magnetic orientation systems have widely been used by measuring the earth magnetic field and provide a pervasive source of directional information. However, to obtain the high precision, orientation systems must be compensated prior to use for the various errors of magnetometers such as the bias, misalignment and inconsistence in sensitivity, and the pitch and roll angles, especially in dynamic state. In this study, magnetic orientation system mainly consist of three single-axis magnetometers, a tri-axis accelerometer and a tri-axis gyroscope were developed. An error-separation method was introduced to calibrate magnetometers. Data from magnetometers, accelerometer and gyroscope were fused based on Kalman filtering. In addition, accelerometer and gyroscope were also calibrated before data fusion. Experimental results showed the heading error of magnetic orientation system was about 0.1° in a static state, and <3° in a dynamic state, which proved the effectivities of the calibration methods and data fusion algorithm.

A parallel error separation method for the on-line measurement and reconstruction of cylindrical profiles

An innovative parallel error separation technique for on-line measurement and reconstruction of cylindrical profile is presented. A five-probe system configured to target three adjacent cross-sections of the cylinder is proposed to simultaneously execute the three-probe roundness error separation and three-probe straightness error separation. The curved median line is determined by fitting through the least squares centers of circular cross-sectional profiles. The cylindrical profile conforming to the mathematical definition can then be reconstructed for the cylindricity error evaluation. Theoretical analysis and numerical validation have been performed. The results verify that the spindle’s radial and tilt error motions as well as the probe carriage’s straightness deviations are removed, and the least squares center of each cross-sectional profile of the cylinder is accurately extracted even if the spindle’s error motions are not repeatable in each rotation. This method has thoroughly solved the inherent problem in conventional multi-probe error separation techniques: the suppression of the first-order harmonic in separating the cross-sectional profile of the cylinder and the error motions of the spindle.

Research on Rotor Axis Orbit Measurement of High Speed Precision Spindle Under Unbalance Fault

Rotor axis orbit measurement can reflect a lot of running characteristics of the rotor, however, it’s hard to acquire the rotor axis orbit accurately for precision spindle, in particular the rotor of the high speed spindle is working under fault conditions. The most common fault of the high speed spindle is unbalance fault, which is must exist with the rotating machinery, also the unbalanced fault has a direct influence on the working precision of spindle. At the same time, the rotor axis orbit measurement result has often been influenced by the surface roundness error of the measurement object. In order to solve this problem, the error separation method is using for extracting the accurately rotor axis orbit, also the surface roundness error of the measurement object has been acquired. Compared with the rotor axis orbit measurement result under unbalance fault and balance state, though the measurement experiment, the rotor axis orbit measurement results are different and the surface roundness error separation results are almost the same. The experiment result prove that the unbalance fault could influence the result of the rotor axis orbit, but the surface roundness will not be influenced by the unbalance fault and it’s intrinsic attributes of the measurement object, in addition that the results verify the accuracy of the error separation algorithm.

Precision measurement of Z-slide vertical error motion of an ultra-precision lathe by using three-probe method

This paper presents a precision measurement of the Z-slide vertical error motion of an ultra-precision lathe based on a three-probe measurement method. The vertical error motion of the Z-slide, which is composed of the vertical parallelism error motion and the vertical straightness error motion, is measured by utilizing three displacement measuring probes to scan a self-cut roll workpiece and an accurate straightedge, respectively. A series of factors which could influence the measurement of the vertical error motion, including the error motion of the spindle, the surface form error of the reference object and the horizontal error motion of the Z-slide, are all successfully removed by using the proposed three-probe measurement system with an error separation method. The influence of the gravity induced deflection of the roll workpiece on the measurement of the Z-slide vertical parallelism error motion is also discussed. Experiments were carried out to verify the feasibility of the proposed methods on a three-axis ultra-precision lathe. The vertical straightness error motion was evaluated to be 133 nm with a measurement repeatability of 21 nm and the vertical parallelism error motion was evaluated to be 12.1 μm with a measurement repeatability of 38 nm.

Radial Error Motion Measurement of Ultraprecision Axes of Rotation With Nanometer Level Precision

Error motion of an ultraprecision axis of rotation has great influences on form error of machined parts. This paper gives a complete error analysis for the measurement procedure including nonlinearity error of capacitive displacement probes, misalignment error of the probes, eccentric error of artifact balls, environmental error, and error caused by different error separation methods. Nonlinearity of the capacitive displacement probe targeting a spherical surface is investigated through experiments. It is found that the additional probe output caused by lateral offset of the probe relative to the artifact ball greatly affects the measurement accuracy. Furthermore, it is shown that error motions in radial and axial directions together with eccentric rotation of the artifact lead to lateral offset. A novel measurement setup which integrates an encoder and an adjustable artifact is designed to ensure measurement repeatability by a zero index signal from the encoder. Moreover, based on the measurement setup, once roundness of the artifact is calibrated, roundness of the artifact can be accurately compensated when radial error motion is measured, and this method improves measurement efficiency while approaches accuracy comparable to that of error separation methods implemented alone. Donaldson reversal and three-probe error separation methods were implemented, and the maximum difference of the results of the two methods is below 14 nm. Procedure of uncertainty estimation of radial error motion is given in detail by analytical analysis and Monte Carlo simulation. The combined uncertainty of radial error motion measurement of an aerostatic spindle with Donaldson reversal and three-probe methods is 14.8 nm and 13.9 nm (coverage k = 2), respectively.

Easy measuring instrument for analyzing the radial and tilt error motions of a rotating shaft

In this study, a real-time measurement system to easily apply multi-probe error separation method for error motion measurement of a shaft was designed and developed. An arrangement condition of sensing probes for accurate multi-probe error separation method was examined and verified by a simulation test. By following the examined arrangement condition for multi-probe method, a measurement system to measure radial and tilt error motions of a shaft was designed and developed. The efficiency of the multi-probe method with the examined arrangement condition was checked by comparing the error motion results for a rotary stage with the error motions in the specifications of the guarantee. It is expected to apply this system to a real-time monitoring system of failure diagnosis for rotating shafts in ships and plants.

Review of self-referenced measurement algorithms: Bridging lateral shearing interferometry and multi-probe error separation

With the development of new materials and ultra-precision processing technology, the sizes of measured objects increase, and the requirements for machining accuracy and surface quality become more exacting. The traditional measurement method based on reference datum is inadequate for measuring a high-precision object when the quality of the reference datum is approximately within the same order as that of the object. Self-referenced measurement techniques provide an effective means when the direct reference-based method cannot satisfy the required measurement or calibration accuracy. This paper discusses the reconstruction algorithms for self-referenced measurement and connects lateral shearing interferometry and multi-probe error separation. In lateral shearing interferometry, the reconstruction algorithms are generally categorized into modal or zonal methods. The multi-probe error separation techniques for straightness measurement are broadly divided into two-point and three-point methods. The common features of the lateral shearing interferometry method and the multi-probe error separation method are identified. We conclude that the reconstruction principle in lateral shearing interferometry is similar to the two-point method in error separation on the condition that no yaw error exists. This similarity may provide a basis or inspiration for the development of both classes of methods.

Error-separation method for the calibration of magnetic compass

Magnetic compass is widely used in the navigation system by measuring the orientation of the earth’s magnetic field and must be calibrated before used to eliminate the errors caused by the bias, misalignment, inconsistence in sensitivity, etc. In this paper, the fully digital magnetic compass was developed by using magnetic-induced magnetometers and MEMS accelerometers and the error-separation method based on a non-magnetic three-axis rotation platform was presented to calibrate the magnetic compass. The parameters about misalignment and non-orthogonality of the sensor axes and the response curve of the sensor’s output signals to earth magnetic fields were obtained. Furtherly, the sensitivity of magnetometers and the bias from the offset and hard-magnetic interference were estimated according to the response curve. The independent effect of non-orthogonality and misalignment, bias and inconsistence in sensitivity on the heading error can be evaluated with the error-separation method, respectively. After calibration, the maximum heading error of magnetic compass was about 0.4° when both pitch angle and roll angle were in the range from −60° to 60°, indicating the error-separation method is effective and efficient to calibrate magnetic compasses.

Improved PPP ambiguity resolution by COES FCB estimation

Precise point positioning (PPP) integer ambiguity resolution is able to significantly improve the positioning accuracy with the correction of fractional cycle biases (FCBs) by shortening the time to first fix (TTFF) of ambiguities. When satellite orbit products are adopted to estimate the satellite FCB corrections, the narrow-lane (NL) FCB corrections will be contaminated by the orbit’s line-of-sight (LOS) errors which subsequently affect ambiguity resolution (AR) performance, as well as positioning accuracy. To effectively separate orbit errors from satellite FCBs, we propose a cascaded orbit error separation (COES) method for the PPP implementation. Instead of using only one direction-independent component in previous studies, the satellite NL improved FCB corrections are modeled by one direction-independent component and three directional-dependent components per satellite in this study. More specifically, the direction-independent component assimilates actual FCBs, whereas the directional-dependent components are used to assimilate the orbit errors. To evaluate the performance of the proposed method, GPS measurements from a regional and a global network are processed with the IGSReal-time service (RTS), IGS rapid (IGR) products and predicted orbits with $$>$$ 10 cm 3D root mean square (RMS) error. The improvements by the proposed FCB estimation method are validated in terms of ambiguity fractions after applying FCB corrections and positioning accuracy. The numerical results confirm that the obtained FCBs using the proposed method outperform those by conventional method. The RMS of ambiguity fractions after applying FCB corrections is reduced by 13.2 %. The position RMSs in north, east and up directions are reduced by 30.0, 32.0 and 22.0 % on average.

Implementation of straightness measurements at the Nanometer Comparator

We report on results of high precision straightness measurements of a graduated scale and a comparison of two different error separation methods. One approach is based on the Traceable Multi-Sensor method. For this purpose, a sensor element consisting of three heterodyne interferometers was integrated at PTB's length reference comparator to measure the straightness deviation of structures on scales. For a scale with a grating of 322 mm length a standard uncertainty below 1.5nm was achieved using this method. A comparison with another method based on reversal technique was realized and revealed a difference below 2.5nm (PV) between both results.

Geometric Error Modeling, Separation, and Compensation of Tilted Toric Wheel in Fewer-Axis Grinding for Large Complex Optical Mirrors

In ultraprecision grinding, especially for large complex optical mirrors, the geometric accuracy of grinding wheel plays a vital role and almost dominates the success of the entire grinding process. In this paper, a complete set of geometric error modeling, separation, and compensation methods of tilted toric wheel is established for fewer-axis grinding of large complex optical mirrors. Based on the kinematic equations with the assumptions of virtual axes for toric wheel, a mirror surface error model including all wheel error components is established, providing an error prediction for mirror surface. By linearizing the mirror surface error model and using the error information of mirror surface, solving and separating wheel error components are achieved. Then, the mirror surface with highly improved accuracy is obtained after the compensation of wheel trajectories with calculated wheel error components. Finally, the above method is well verified by the simulation.

Traceability analysis and coupling compensation for guideway-induced errors in large CNC gantry guideway grinder

Guideway-induced errors are the main factors affecting the machining accuracy in computer numerical control (CNC) machine tools. In this paper, the guideway-induced errors of a large CNC gantry guideway grinder are analyzed and measured to realize the traceability analysis and coupling compensation. To establish the error model, an automatic error modeling application is developed based on the least-square fitting of orthogonal polynomial method and visual basic. The comprehensive error model of the grinder is established using the homogenous transformation matrix to realize the error distribution analysis in a three-dimensional workspace. The error separation method is used to achieve the traceability analysis of the guideway-induced errors. To realize the coupling compensation for guideway-induced errors, an external mechanical origin offset (EMOO) and Ethernet-based error compensation method are proposed in this research. Experimental results showed that the maximum error was compensated by 91.2 % compared with no compensation.

Research on the rotational accuracy measurement of an aerostatic spindle in a rolling bearing performance analysis instrument

An ultra-precision instrument is developed to measure the rotational accuracy of a rolling bearing under working conditions. This instrument uses a high-precision aerostatic spindle, which has high-stiffness to support a test bearing under large axial loading. This work demonstrates the capabilities of the double-probe error separation method for the measurement of aerostatic spindle error motion at various axial forces and rotational speeds. The rotational performance of an aerostatic spindle is discussed. The results indicate that the error motion and the form of the error of the measurement surface are reliably separated at various axial forces and rotational speeds. In addition, the error motion of the aerostatic spindle is very stable, increasing slightly and smoothly as the rotational speed increases. The error motion is less than 0.18 um when the speed reaches 1920 rpm. In the future, it will be possible to separate the error motion of an aerostatic spindle from the measurement results of a test bearing.

Precision evaluation of surface form error of a large-scale roll workpiece on a drum roll lathe

This paper presents on-machine evaluation of surface form error components of a large-scale roll workpiece, including the out-of-roundness, the out-of-straightness, the taper angle and the diameter deviation, on a drum roll lathe. A pair of capacitive-type displacement probes is mounted on the carriage slide to target the two sides of the roll workpiece mounted on the spindle, which has a length of 2000mm, a diameter of 320mm and a mass of 350kg. The outputs of the probes are employed to accurately evaluate the surface form error components through separating the influences of the motion errors of the spindle and the carriage slide of the lathe. It has been difficult to apply the reversal error-separation method for measurement of the out-of-roundness component of such a large workpiece because it is difficult to reverse the workpiece with respect to the spindle on the lathe due to its large size and heavy mass. An improved reversal operation technique, in which the spindle is rotated with respect to the stationary roll workpiece being held by a crane, is therefore proposed to solve this problem. Measurement uncertainty analysis is carried out to verify the reliability of the new technique for on-machine evaluation of the out-of-roundness component. The out-of-straightness component and the taper angle component of the roll workpiece are then evaluated by using a previously developed method. A simple and effective algorithm for evaluation of the diameter deviation component is also presented.

Error Separation and Dynamic Compensation Method in Coplanar Planar Grating Displacement Measurement System

To improve the measurement accuracy of two-dimensional (2D) precision working stages in the semiconductor manufacturing industry, an error separation and dynamic compensation method based on a planar grating is proposed for a 2D coplanar displacement measurement system. In the system, a planar grating of HEIDENHAIN PP281R is fixed in the center of precision working stage to build coplanar structure and reduce Abbe errors. And the system errors including grating period carved error, temperature effect, vibration effect and mount effect are modeled, calculated and separated. Then the separated errors are dynamically compensated from the corresponding displacement measurement results through data-processing software. Analysis results show that the proposed error separation and dynamic compensation method based on planar grating can improve the measurement accuracy of the coplanar displacement measurement system effectively.

Nano-level instrumentation for analyzing the dynamic accuracy of a rolling element bearing

The rotational performance of high-precision rolling bearings is fundamental to the overall accuracy of complex mechanical systems. A nano-level instrument to analyze rotational accuracy of high-precision bearings of machine tools under working conditions was developed. In this instrument, a high-precision (error motion < 0.15 μm) and high-stiffness (2600 N axial loading capacity) aerostatic spindle was applied to spin the test bearing. Operating conditions could be simulated effectively because of the large axial loading capacity. An air-cylinder, controlled by a proportional pressure regulator, was applied to drive an air-bearing subjected to non-contact and precise loaded axial forces. The measurement results on axial loading and rotation constraint with five remaining degrees of freedom were completely unconstrained and uninfluenced by the instrument's structure. Dual capacity displacement sensors with 10 nm resolution were applied to measure the error motion of the spindle using a double-probe error separation method. This enabled the separation of the spindle's error motion from the measurement results of the test bearing which were measured using two orthogonal laser displacement sensors with 5 nm resolution. Finally, a Lissajous figure was used to evaluate the non-repetitive run-out (NRRO) of the bearing at different axial forces and speeds. The measurement results at various axial loadings and speeds showed the standard deviations of the measurements' repeatability and accuracy were less than 1% and 2%. Future studies will analyze the relationship between geometrical errors and NRRO, such as the ball diameter differences of and the geometrical errors in the grooves of rings.

Effect of step number on roundness determination using multi-step method

Error separation technique is the one of the best ways for accurate and precise determination of roundness form. The multi-step technique is an important method of roundness error separation. Many national metrology institutes (NMIs), industrial calibration laboratories and research institutes have been using the multi-step method for high precision and high accuracy in roundness measurement. Number of step used by various institutes is different. In this paper, effect of number of step employed for the error separation was investigated. The results of these experiments successfully indicate that number of step used in multi-step method plays an important role to the accuracy level of the roundness measurement result. In order to achieve accuracy at the ultra-high level, at least 10 steps should be employed using multi-step method to satisfy the geometrical form of roundness measurement.

An experimental investigation of spindle rotary error on high-speed machining center

A method is described in this paper for measuring the spindle rotation error and a technique for separating the eccentric error caused by setup error of the master cylinder. The system consists of two non-contact capacitance sensors used to measure the radial displacement of the rotating master cylinder and an LMS Test.Lab used to collect the measurement data. LMS Test.Lab offers a complete engineering solution for rotating machinery. Based on our experimental research, it indicates that this system can be used to measuring the spindle rotary error at different speeds. It is also verified the feasibility of the error separation methods developed in this paper.