Identification of position-dependent geometric errors with non-integer exponents for Linear axis using double ball bar

Geometric errors are one of the primary potential sources of error in a five-axis machine tool. There are two types of geometric errors: position-dependent geometric errors and position-independent geometric errors. A method is proposed to identify and measure the position-independent geometric errors of a five-axis machine tool with a tilting head by means of simultaneous multi-axis controlled movements using a double-ball bar (DBB). Techniques for identifying position-independent geometric errors have been proposed by other researchers. However, most of these are based on the assumption that position-dependent geometric errors (such as linear displacement, straightness, and angular errors) are eliminated by compensation, once the position-independent geometric errors have been identified. The approach suggested in this paper takes into account the effect of position-dependent geometric errors. The position-dependent geometric errors are first defined. Path generation for circle tests with two or three simultaneous control movements is then carried out to measure the position-independent geometric errors. Finally, simulations and experiments are conducted to confirm the validity of the proposed method. The simulation results show that the proposed method is sufficient to accurately identify position-independent geometric errors. The experimental results indicate that the technique can be used to identify the position-independent errors of a five-axis machine tool with a tilting head.

The simultaneous measurement and identification of position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) of dual rotary axes in five-axis machine tools remain a significant challenge in precision machining. To address this issue, this study develops a geometric error measurement system for the dual rotary axes of a five-axis machine tool by integrating a scanning probe, a block, and a calibration sphere. Unlike conventional touch-trigger probes, the scanning probe acquires continuous measurement signals along the surfaces of the block and the calibration sphere, enabling the extraction of richer geometric features and providing sufficient data for the simultaneous analysis of multiple geometric error components. The proposed measurement system is implemented on a five-axis machine tool, Uni5X-400, manufactured by FALCON Machine Tools Co., Ltd., to measure the geometric information of the calibration sphere and the block and thereby identify 20 PIGEs and PDGEs associated with the dual rotary axes. A kinematic model of the measurement system is established using homogeneous coordinate transformation matrices. By applying forward and inverse kinematics, the spatial positions of the calibration sphere and block are derived, forming an explicit relationship between volumetric errors and geometric errors. The resulting error identification equations are solved using the least squares method. Experimental results demonstrate that the proposed approach can efficiently and accurately identify the geometric errors of the dual rotary axes and maintain robust reliability under real-world operating conditions, making it suitable for practical calibration and accuracy improvement of five-axis machine tools.

This paper proposes a recognition methodology for key geometric errors using the feature extraction method and accuracy retentivity analysis and presents the approach of optimization compensation of the geometric error of a multiaxis machine tool. The universal kinematics relations of the multiaxis machine tool are first modelled mathematically based on screw theory. Then, the retentivity of geometric accuracy with respect to the geometric error is defined based on the mapping between the constitutive geometric errors and the time domain. The results show that the variation in the spatial error vector is nonlinear while considering the operation time of the machine tool and the position of the motion axes. Based on this aspect, key factors are extracted that simultaneously consider the correlation, similarity, and sensitivity of the geometric error terms, and the results reveal that the effect of the position‐independent geometric errors (PIGEs) on the error vectors of the position and orientation is greater than that of the position‐dependent geometric errors (PDGEs) of the linear and rotary axes. Then, the fruit fly optimization algorithm (FOA) is adopted to determine the compensation values through multiobjective tradeoffs between accuracy retentivity and fluctuation in the geometric errors. Finally, an experiment on a four‐axis horizontal boring machine tool is used to validate the effectiveness of the proposed approach. The experimental results show that the variations in the precision of each test piece are lower than 25.0%, and the maximum variance in the detection indexes between the finished test pieces is 0.002 mm when the optimized parameters are used for error compensation. This method not only recognizes the key geometric errors but also compensates for the geometric error of the machine tool based on the accuracy retentivity analysis results. The results show that the proposed methodology can effectively enhance the machining accuracy.

Identification and compensation of position independent geometric errors of dual rotary axes for hybrid-type five-axis machine tool based on unit dual quaternions

To meet the high-precision positioning requirements for hybrid machining units, this article presents a geometric error modeling and source error identification methodology for a serial–parallel hybrid kinematic machining unit (HKMU) with five axis. A minimal kinematic error modeling of the serial–parallel HKMU is established with screw-based method after elimination of redundant errors. A set of composite error indices is formulated to describe the terminal accuracy distribution characteristics in a quantitative manner. A modified projection method is proposed to determine the actual compensable and noncompensable source errors of the HKMU by identifying such transformable source errors. Based on this, the error compensation and comparison analysis are carried out on the exemplary HKMU to numerically verify the effectiveness of the proposed modified projection method. The geometric error evaluations reveal that the parallel module has a larger impacts on the terminal accuracy of the platform of the HKMU than the serial module. The error compensation results manifest that the modified projection method can find additional compensable source errors and significantly reduce the average and maximum values of geometric errors of the HKMU. Hence, the proposed methodology can be applied to improve the accuracy of kinematic calibration of the compensable source errors and can reduce the difficulty and workload of tolerance design for noncompensable source errors of such serial–parallel hybrid mechanism.

The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.

To address the problems of the low accuracy of geometric error identification and incomplete identification results of the linear axis detection of computer numerical control (CNC) machine tools, a new 21-item geometric error identification method based on double ball-bar measurement was proposed. The model between the double ball-bar reading and the geometric error term in each plane was obtained according to the three-plane arc trajectory measurement. The mathematical model of geometric error components of CNC machine tools is established, and the error fitting coefficients are solved through the beetle antennae search particle swarm optimization (BAS–PSO) algorithm, in which 21 geometric errors, including roll angle errors, were identified. Experiments were performed to compare the optimization effect of the BAS–PSO and PSO and BAS and genetic particle swarm optimization (GA–PSO) algorithms. Experimental results show that the PSO algorithm is trapped in the local optimum, and the BAS–PSO is superior to the other three algorithms in terms of convergence speed and stability, has higher identification accuracy, has better optimization performance, and is suitable for identifying the geometric error coefficient of CNC machine tools. The accuracy and validity of the identification results are verified by the comparison with the results of the individual geometric errors detected through laser interferometer experiments. The identification accuracy of the double ball-bar is below 2.7 µm. The proposed identification method is inexpensive, has a short processing time, is easy to operate, and possesses a reference value for the identification and compensation of the linear axes of machine tools.

The geometric accuracy of linear axes lays a foundation for the machining accuracy of 5-axis machine tools. Although some geometric error identification and compensation approaches were developed for linear axes, the implementation efficiency and cost remain to be improved. In this paper, a novel 13-line identification method by using a laser interferometer is proposed, and the linear axes are compensated through the modification of compensation parameters in the NC system. The verification experiments are conducted through the tri-axial movement accuracy measurement and manufactured National Aerospace Standard test piece inspection, in which three circumstances, i.e., without compensation, with lead screw error compensation, and with error compensation based on the 13-line method, are compared. By using the 13-line method, the average accuracy of the tri-axial movement and test pieces are improved by 82.2 and 41.9 %, respectively, whereas the accuracy stability are improved by 77 and 46 %, respectively. Results show that the proposed identification and compensation method is effective and efficient.

The double ballbar (DBB) test, which captures actual data from multiple error origins of axes interaction, was defined as sinusoid error map model plus noise. When the number of sinusoids is the same as the number of individual errors of moving axis in the test map, we can extract a single source geometric error value from the DBB error map by modeling the well-known geometric error of linear axis. We considered the “noise” as mixed errors from other sources than geometric errors. This method is applicable to both a full circle and a truncated DBB test path.

To study the residual settlement of goaf’s law and prediction model, we investigated the Mentougou mining area in Beijing as an example. Using MATLAB software, the wavelet threshold denoising method was used to optimize measured data, and the grey model (GM) and feed forward back propagation neural network model (FFBPNN) were combined. A grey feed forward back propagation neural network (GM-FFBPNN) model based on wavelet denoising was proposed, the prediction accuracy of different models was calculated, and the prediction results were compared with original data. The results showed that the prediction accuracy of the GM-FFBPNN was higher than that of the individual GM and FFBPNN models. The mean absolute percentage error (MAPE) of the combined model was 7.39%, the root mean square error (RMSE) was 49.01 mm, the scatter index (SI) was 0.06%, and the BIAS was 2.42%. The original monitoring data were applied to the combination model after wavelet denoising, and MAPE and RMSE were only 1.78% and 16.05 mm, respectively. Compared with the combined model before denoising, the prediction error was reduced by 5.61% and 32.96 mm. Thus, the combination model optimized by wavelet analysis had a high prediction accuracy, strong stability, and accorded with the law of change of measured data. The results of this study will contribute to the construction of future surface engineering in goafs and provide a new theoretical basis for similar settlement prediction engineering, which has strong popularization and application value.

Generalized actual inverse kinematic model for compensating geometric errors in five-axis machine tools

It is extremely important to explore the heavy metal content and spatial distribution in different cultivated soils. In our study, cokriging (COK) method was used to investigate the relationship between heavy metals and land use types. A total of six heavy metals including Zn, Fe, Cu, Mn, B, S were selected to forecast the heavy metals in cultivated soils. Five types of cultivated land were considered in the study area, including vegetable land, irrigated land, irrigated paddy field, dry land, orchard. Test of normality was firstly carried out to assure that higher prediction accuracy can be obtained, and then correlation analysis and analysis of variance (ANOVA) were performed to find out the most sensitive heavy metals for spatial interpolation. The analysis results showed that Zn, Cu and Fe were the primary heavy metals in soil of the study area. It was obvious that the effect of Mn and Fe were much greater caused by land use types, while they were smaller for B and S. Three errors of mean standard (MS), root mean square error (RMSE), and root mean square standardized error (RMSSE) were derived to assess the prediction accuracy. In comparison with ordinary kriging (OK), the MS of COK approached to 1, the RMSE was much smaller and the RMSSE also approached to 1, which showed that COK can make better predictions than OK.

The aim of the present research is to calculate the Relative Accuracy (R.A) and Root Mean Square Error (RMSE) for the location of Technical Institute, Mosul in Nineveh Governorate, Iraq. at the northern part of Mosul city by using surveying Instruments (GPS 1230 , Total Station 06 & Level NAK2), to calculate the coordinates and elevations of (16) Ground Control Points which covered the study area. The field data, remote sensing techniques and GIS software (Arc Map GIS10.3) are used to check the digital map of study area that helped the administrator to take the correct decision, determining positions of the future expansionist for buildings, roads, measuring lengths, areas and there coordinates, directions as well as the total costs estimation needed for any development from the final map. The gradient percentage between the highest and lowest points is calculated to be (9.954%). Relative accuracy for the based measured points (R.A) = 1:60000), and Root Mean Square error in Easting coordinates (RMSE) = ± 0.102m, in Northing coordinates (RMSN) = ± 0.096m, the Root Mean Square for the resultant (RMSR) = ± 0.099m, and Root Mean Square for Elevations ( RMSRL)= ± 0.005m. We Matched and correlated (10) measured points from study area with their graphic data positions on the aerial photo, determining the offsets for position and elevations as follows: (RMSE = ± 0.076m), (RMSN = ± 0.125m), (RMSR = ± 0.088m), and (Root Mean Square for Elevations = RMSRL= ± 0.045m). This research enable us after checking the results to produce new maps from Aerial photograph or Digital Image to use it for land uses and future extensions in whole study area.

BackgroundThe multileaf collimator (MLC) is a critical component to accurate intensity-modulated radiotherapy (IMRT) delivery. This study examined MLC positional accuracy via MLC logs from Varian machines from six institutions and three delivery techniques to evaluate typical positional accuracy and treatment and mechanical parameters that affect accuracy. Typical accuracy achieved was compared against TG-142 recommendations for MLC performance; more appropriate recommendations are suggested.MethodsOver 85,000 Varian MLC treatment logs were collected from six institutions and analyzed with FractionCHECK. Data were binned according to institution and treatment type to determine overall root mean square (RMS) and 95th percentile error values, and then to look for correlations between those errors and with mechanical and treatment parameters including mean and maximum leaf speed, gantry angle, beam-on time, mean leaf error, and number of segments.ResultsResults of treatment logs found that leaf RMS error and 95th percentile leaf error were consistent between institutions, but varied by treatment type. The step and shoot technique had very small errors: the mean RMS leaf error was 0.008 mm. For dynamic treatments the mean RMS leaf error was 0.32 mm, while volumetric-modulated arc treatment (VMAT) showed an RMS leaf error of 0.46 mm. Most MLC leaf errors were found to be well below TG-142 recommended tolerances. For the dynamic and VMAT techniques, the mean and maximum leaf speeds were significantly linked to the leaf RMS error. Additionally, for dynamic delivery, the mean leaf error was correlated with RMS error, whereas for VMAT the average gantry speed was correlated. For all treatments, the RMS error and the 95th percentile leaf error were correlated.ConclusionsRestricting the maximum leaf speed can help improve MLC performance for dynamic and VMAT deliveries. Furthermore, the tolerances of leaf RMS and error counts for all treatment types should be tightened from the TG-142 values to make them more appropriate for clinical performance. Values of 1 mm for the 95th percentile of leaf RMS error and 1.5 mm for the 95th percentile leaf error are suggested as action levels for all treatment types.

OPINION article Front. Physiol., 22 January 2014Sec. Integrative Physiology Volume 4 - 2013 | https://doi.org/10.3389/fphys.2013.00403