Geometric Errors Research Articles

Uncertainty assessment of machine tool squareness error identification using on-machine measurement

Identification and compensation of geometric errors in the machine tool are widely performed to increase machining accuracy. Periodic verification of the geometric errors, as introduced in ISO 230-2, helps monitor the machine tool accuracy during continued manufacturing operation and detect accuracy degradation early on. While interferometry-based error identification techniques are commonly applied, on-machine measurement (OMM), with its increasing availability to machine tools, can be used to identify geometric errors as an alternative to traditional interferometry-based techniques. As geometric errors also contribute to OMM error, assessment of the uncertainty of error identification is essential to ensure the reliability of the identification. This work presents a method to evaluate the uncertainty in the OMM-based geometric error identification process by Monte Carlo simulation. The error ellipse model, which represents OMM errors with better accuracy, is utilized to improve the identification uncertainty. The squareness errors, as position-independent geometric errors that contribute to machining inaccuracy, are taken as an example to demonstrate the presented method. The influence of the artifact setup errors on the error identification is also investigated. A series of experiments are conducted to evaluate the uncertainty of the OMM-based identification method. The geometric error obtained with the presented method is found to deviate by less than 10% from that obtained with an interferometry-based commercial instrument. The uncertainty obtained from the proposed Monte Carlo simulation method matches well with the uncertainty results obtained by the Guide to the Expression of Uncertainty in Measurement method and repeated measurements.

Binocular vision measurement system for geometric error of 3D printers at high temperature

Binocular vision measurement system for geometric error of 3D printers at high temperature

Design and calibration of the 6-DOF motion tracking system integrated on the Stewart parallel manipulator.

Accurate pose measurement is crucial for parallel manipulators (PM). This study designs a novel integrated 6-DOF motion tracking system to achieve precise online pose measurement. However, the presence of geometric errors introduces imperfections in the accuracy of the measured pose. Based on the displacement information of six grating rulers, measurement pose is obtained through forward kinematics. By comparing the measurement results with the actual pose information captured by stereo vision, measurement errors can be obtained. A closed-loop vector-based kinematic model and an error model are established, and then the geometric errors are identified with the least-squares method. Finally, the geometric calibration experiments are conducted, and the results show that the measurement accuracy has significantly improved, with the average position error decreasing from 3.148 mm to 0.036 mm, and the average orientation error is decreased from 0.225° to 0.022°.

RELATIVE GEOMETRIC CORRECTION OF MULTIPLE SATELLITE IMAGES BY RIGOROUS BLOCK ADJUSTMENT

Abstract. With the development of satellite imaging technology, many Earth observation satellites have been launched and almost all areas of the Earth are daily covered by satellite images. It is promising to utilize such images in change detection, monitoring, semantic classification, etc. To obtain geometric information on each pixel in images, Rational Polynomial Coefficients (RPCs) of a Rational Functional Model (RFM) are provided with satellite images. However initial RPCs may include geometric errors. Therefore, errors in initial RPCs must be corrected before utilization. In this study, we attempt to perform rigorous block adjustments for refining RFMs of overlapping satellite images without ground control points. Our rigorous block adjustment method operated based on automatically extracted tie-points within overlapping areas. It estimates the optimal adjustment coefficients of RPCs and ground coordinates of tie-points. We achieved relative geometric correction of multiple satellite images by transforming the images based on the estimated adjustment coefficients. As a result, an initial RFM model with an error of around 21.73 pixels was corrected to within 1 pixel, and the reprojection error of check points decreased to 0.87 pixels. We also confirmed that our method showed more accurate results than general image registration methods, such as 2D homography transformation.

3D MODELING OF ROAD INFRASTRUCTURES ACCORDING TO CITYGML 3.0 AND ITS CITYJSON ENCODING

Abstract. This study proposes a systematic approach for standardized 3D modeling of road infrastructures based on CityGML 3.0 and its CityJSON encoding. The approach involves generating a LoD2 3D model of the road infrastructure based on a semi-automatic extraction of linear features from mobile mapping LiDAR data. This enables geometric and semantic modeling of the roads. A codification system is proposed to assign predefined codes to each linear feature, allowing each section and intersection and each road surface to be modeled separately. The resulting model is converted to a CityJSON file, stored in a document-oriented database and visualized through a web application. The proposed approach provides a cost-effective alternative to traditional manual modeling methods while maintaining a high level of accuracy and consistency. It also considers the validation of data schema and geometric primitives to ensure that any non-conformity with CityJSON schemas, and any topological and/or geometric errors can be detected and then corrected. This is important since schema changes in new versions of CityJSON can result in compatibility issues, while geometric and topological errors can affect the accuracy of 3D models and ultimately lead to inaccurate simulation outcomes or analysis results.

An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces

The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier–Stokes equations posed on a passively evolving smooth closed surface embedded in R 3 \mathbb {R}^3 . The discrete formulation employs finite difference and finite elements methods to handle evolution in time and variation in space, respectively. A complete numerical analysis of the method is presented, including stability, optimal order convergence, and quantification of the geometric errors. Results of numerical experiments are also provided.

Load Distribution Analysis and Contact Stiffness Prediction of the Dual-Drive Ball Screw Pair Considering Guide Rail Geometric Error and Slide Position

The dual-drive ball screw pair serves as a crucial element within the fixed gantry machine tool with cross-rail movement. When in service, the dual-drive ball screw pair experiences variations in axial load, impacting the contact load distribution of the ball screw pair. A calculation model for determining the axial load offset of the dual-drive ball screw pair is proposed to investigate the variation in axial load. The impact of the geometric error associated with the guide rail and the position of the slide are considered. This paper presents the contact load distribution model for the dual-drive ball screw pair. This study investigates the contact load and contact angle distribution of the dual-drive ball screw pair during the machine tool in service. Additionally, based on fractal theory, the stiffness models of individual micro-convex body and contact surfaces have been established. This study provides a comprehensive analysis of the contact stiffness of the ball screw pair, considering the influence of guide rail geometric error and slide position. In addition, the three-dimensional surface morphology of ball screw pair is obtained by experiments. This paper investigates the contact stiffness distribution of dual-drive ball screw pair during service.

Fast detection of geometric errors for three-axis machine tools with combined double-ball bars based on spatial circle detection

The geometric accuracy of the CNC machine tools determines the quality of the sculptured mechanical parts. Measuring and compensating the geometric errors of machine tools can effectively improve the machining accuracy. However, traditional measurement methods using a double-ball bar (DBB) can only detect the error along the rod length direction and thus require multiple measurements in three orthogonal planes of the machine tool. This work proposes a fast error detection method for the three-axis machine tools using combined double-ball bars (C-DBBs) based on the spatially circular detection (SCD) path. The test path of this method requires the simultaneous linkage of three linear axes of the machine tools and thus could identify 21 geometric errors of three-axis machine tool. Firstly, the measuring principle of the SCD method is introduced, and the mathematical model for detecting 21 geometric errors of the machine tool based on the SCD method is established. Then, the detection experiment based on the SCD method is carried out, and it is shown that 21 geometric errors of the three-axis machine tool are obtained. Finally, the verification experiment using a traditional DBB is conducted to validate the effectiveness of the proposed SCD method. The radial errors in three orthogonal planes measured by traditional DBB exhibit a good agreement with those predicted using 21 geometric errors obtained by the SCD method. Compared with the traditional DBB method, the proposed SCD method could detect 21 geometric errors of three-axis machine tools in a single measurement. This work provides an effective and efficient methodology for detecting all geometric errors of the three-axis machine tool.

EFFICIENT UAV FLIGHT PLANNING FOR LOD2 CITY MODEL IMPROVEMENT

Abstract. Geometric errors in LoD2 building models can be caused by the modeling algorithm but are often related to the quality of input data. One approach to tackling the modeling errors caused by the quality of input data is to collect additional data with a UAV and remodel the buildings. However, no flight planning approach exists specifically designed for efficient data recollection for model improvement. In this paper, we propose an innovative flight planning approach for this purpose. Contrary to the conventional method that recollects the data covering the entire building roof, our approach only collects the data over the erroneous region and uses it to improve the erroneous model part later. Our algorithm utilizes the existing LiDAR survey data to automatically detect model errors and design the camera networks by considering the roof geometry. We optimize the trajectory that connects the viewpoints with a genetic algorithm and develops an obstacle avoidance function with ray-casting to ensure a collision-free path. The proposed flight plan is implemented in a real-world scene. Our result shows an improved point cloud created through dense image matching with the collected UAV image data. The generated point cloud is successfully used for creating partial building models for improving the original models.

Revolutionizing gear hobbing machine precision: Innovative thermal error compensation and intelligent error control with enhanced crystal structure algorithm and self-attention bidirectional minimal gated unit network

The thermal error stands as a pivotal determinant, significantly impacting both the precision and its stability of gear hobbing processes. Thus far, conspicuous delays in compensation and insufficiencies in precision have been duly noted. To achieve a proficient and exceedingly precise thermal error compensation, an intricate mathematical correlation is expounded, delineating the connection between the spatial pose error of the hob and the inherent thermal error in the gear hobbing machine. In addressing the thermal error linked to the B-axis, a bidirectional-minimal gated unit network is harnessed to characterize long-term memory attributes. An advanced crystal structure algorithm is introduced, encompassing components such as the population initialization mechanism, the nonlinear convergence factor, the Gaussian perturbation mechanism, and an enhanced optimization equation. The weights of the bidirectional-minimal gated unit network are judiciously assigned via the self-attention mechanism. This innovation, recognized as the improved crystal structure algorithm-self-attention-bidirectional-minimal gated unit network, is introduced for the training of the thermal error model for the B-axis. Subsequently, thermal analysis models are formulated, yielding the thermal errors of the X- and Z- axes. An error control model and an error decoupling model are established, employing the thermal errors of the B-, X-, and Z- axes as their input. Ultimately, an intelligent error control system is crafted, in which the error control model, error decoupling model, and thermal error model are seamlessly integrated. The aim is to mitigate tooth flank errors. With the integration of the intelligent error control system, the levels of precision pertaining to gear helix deviation, maximum deviation of a single pitch, and cumulative total pitch deviation are elevated by one, one, and two levels, respectively. More significantly, the geometric error reduction of the tooth flank achieved by the meticulously designed intelligent error control system surpasses that of traditional pitch compensation by a substantial margin. Furthermore, the execution efficiency of the intelligent error control system, when operating within the machine-edge-fog-cloud framework, exhibits a remarkable improvement of 24.18%, 16.20%, and 57.84% when compared to the intelligent error control system operating within the machine-edge-cloud, machine-fog-cloud, and machine-cloud frameworks, respectively.

Hierarchical Error Compensation Method for Two-Degree-of-Freedom Manipulator Positioning Error in Hybrid Robots

In this paper, taking a two-degree-of-freedom parallelogram serial manipulator of a hybrid robot as an example, a hierarchical error compensation method that combines geometric and non-geometric error compensation is proposed. First, we establish the geometric kinematic modeling and error model and use the Levenberg-Marquardt (L-M) method to identify the geometric error parameters. Then, we use the grid interpolation method to compensate for non-geometric errors, thereby improving the overall positioning accuracy of the manipulator. Finally, a simulation is presented to verify the correctness and effectiveness of the proposed method. The results show that the positioning accuracy is improved from 4.8568 mm to 0.0036 mm, and the attitude error is improved from 0.9437° to 0.0105°.

Adaptive hierarchical positioning error compensation for long-term service of industrial robots based on incremental learning with fixed-length memory window and incremental model reconstruction

Industrial robots have been extensively used in industry, however, geometric errors mainly caused by connecting rod parameter error and non-geometric errors caused by deflection and friction, etc., limit its application in high-accuracy machining. Aiming at addressing these two types of errors, parametric methods for error compensation based on the kinematic model and non-parametric methods of directly establishing the mapping relationship between the actual and target poses of the robot end-effector are investigated and proposed. Currently both types of methods are mainly offline and will be no longer applicable when the pose of the end-effector in the workspace changes dramatically or the working performance of the robot degrades. Thus, to compensate the positioning error of an industrial robot during long-term operation, this research proposes an adaptive hierarchical compensation method based on fixed-length memory window incremental learning and incremental model reconstruction. Firstly, the correlation between positioning errors and robot poses is studied, a calibration sample library is created, and thus the actively evaluating mechanism of the pose mapping model is established to overcome the problem of the robot’ workspace having a differential distribution of error levels. Then, an incremental learning algorithm with fixed-length memory window and an incremental model reconstruction algorithm are designed to optimize the pose mapping model in terms of its parameters and architecture and overcome the problem that the performance degradation of the robot exacerbates the positioning error and affects the applicability of the pose mapping model, ensuring that the pose mapping model runs stably above the target accuracy level. Finally, the proposed method is applied to the long-term compensation case of a Stäubli industrial robot and a UR robot, and compared to state-of-art methods. Verification results show the proposed method reduces the position error of the Stäubli robot from 0.85mm to 0.13mm and orientation error from 0.68° to 0.07°, as well as reduces the position error of the UR robot from 2.11mm to 0.17mm, demonstrating that the proposed method works in real world scenarios and outperforms similar methods.

A framework for post‐processing bird tracks from automated tracking radar systems

Abstract Radar is an effective tool for continuous monitoring and quantification of aerial bird movement and used to study migration and local flight behaviour. However, systems with automated tracking algorithms do not provide the level of processing sufficient to guarantee reliable data. Therefore, post‐processing such radar data is required but often non‐trivial, especially in challenging environments such as open sea. We present a post‐processing framework that implements knowledge of the radar system and bird biology to filter the data and retrieve reliable, high‐quality tracking data. The framework is split into three modules, each with a specific aim: (I) sub‐setting based on prior knowledge of the radar system and bird flight, (II) improving bird track quality and (III) detecting and removing spatio‐temporal sections of data that have a clear bias for false observations. The effectiveness of the framework is demonstrated with a case study comparing track densities inside and outside an offshore wind farm, and by applying the workflow to a dataset of visually validated radar tracks. Application of Module I resulted in a dataset of 520.894 bird tracks (19.5% of total data) within a 10.4 km2 area. Additionally, 18.734 tracks were corrected for geometric errors in Module II, and Module III identified 236 of 719 observation hours and an area of 1.55 km2 as unreliable for spatio‐temporal analysis. No difference in track densities was found between the area inside and outside the wind farm when using the post‐processed data, whereas using the unprocessed bird tracks, lower track densities were observed outside the wind farm. Of the visually validated radar tracks, the framework removed 85% of false positive bird tracks, while retaining 80% of true positive bird tracks. The framework provides a logical workflow to increase the reliability and quality of a bird radar dataset while being adaptable to the radar system and its surroundings. This is a first step towards standardising the post‐processing methodology for automated bird radar systems, which can facilitate comparative analyses of bird movement in space and time and improve the quality of ecological impact assessments.

Geometric error modeling and compensation for high precision composite optical measurement systems

Composite optical measurement systems are widely used in the field of precision measurement due to their combination of inspection with high accuracy, speed, wide range, real-time, and other advantages. Whereas errors are prevalent in measurements, in order to improve detection accuracy, the systems must be compensated for geometric errors in three-dimensional space. Aiming at the complex situation of multi-probes and multi-zooms in the composite optical measurement system, the current error modelling methods are difficult to be directly applied, so this paper establishes a unified three-dimensional volumetric error model based on the theory of multi-body system and combined with the principle of geometric optics, performs the error verification through the direct measurement method, and finally realises the compensation of geometric error in the continuous space of the whole measurement range. Eventually, the accuracy of the proposed error model and the effectiveness of the error compensation method were verified by a laser interferometer and standard objects to be measured, and the integrated geometric error of the system was decreased by 76.55%, which effectively improved the accuracy of the system. The error modelling and compensation method proposed in this paper provides a new idea for the error compensation of the zoom measurement system, and at the same time, it is universal for the measurement systems of different structures and motion forms, which can be widely used in the field of precision measurement.

Estimation of Shape Error with Monitoring Signals

Recently, extensive research has actively been conducted in relation to intelligent manufacturing systems. During the machining process, various factors, such as geometric errors, vibrations, and cutting force fluctuations, lead to shape errors. When a shape error exceeds the tolerance, it results in improper assembly or functionality issues in the assembled part. Predicting shape errors before or during the machining process helps increase production efficiency. In this paper, we propose a methodology that uses monitoring signals and on-machine measurement (OMM) results to predict machining quality in real time. We investigate the correlation between monitoring signals and OMM results and then construct a machine learning model for shape error estimation. The developed model implements a tool offset compensation strategy. The performance of the proposed method is evaluated under various sliding window sizes and the compensation weights. The experimental results confirmed that the proposed algorithm is effective for obtaining a uniform machining quality.

R-test-based identification method for geometric errors of rotary axes in a five-axis machine tool with a rotary table and tilting head

This paper uses an R-test method to identify the 20 geometric errors of the two rotary axes in a five-axis machine tool with a tilting head and a rotary table. The Position-Independent Geometric Errors (PIGEs) result in deviations of the actual axis from the ideal axis, leading to the overall deviation of the set points on the circular trajectory. Therefore, the actual circular trajectory can be fitted by measuring the actual coordinates of the set points, and the actual axis can be further solved to establish the solution equation of PIGEs. Further, the volumetric error model for the set points is constructed, and the unknown motion matrices associated with the linear axes in the volumetric error model are adjusted, allowing for the determination of Position-Dependent Geometric Errors (PDGEs). This method can identify geometric errors of the two rotary axes by measuring six sets of circular trajectories under three setups.

Calibration of link errors in rotary axes of five-axis machine tools using a six-dimensional motion measuring device

In this study, the position-independent geometric errors (PIGEs) of five-axis machine tools are identified and calibrated using a Stewart–Gough platform (SGP) based Motion Measuring Device (MMD). As the MMD of micrometer-level accuracy is cable of six-dimensional pose measurements, a closed kinematic chain is established by installing the upper and lower plate of the MMD to the spindle and rotary worktable of the machine tool, respectively. Particularly, the sensor-mounting misalignments, which are inevitable but mostly ignored in the previous PIGE identification methods, are formulated and identified together with the PIGEs. Thus, the sensor-mounting misalignments will not affect the accuracy of PIGE calibration. The proposed method is verified by simulation and experimental results. The synchronous motion test (SMT) demonstrates that the five-axis machine tool owns a high accuracy of 5 micrometers in the tested motion range after PIGE calibration.

Fast and precise DEM parameter calibration for Cucurbita ficifolia seeds

The lack of discrete element method (DEM) models and calibration parameters for Cucurbita ficifolia seeds, as well as low accuracy and efficiency of common parameters calibration methods, hinder the application of DEM for computer simulation in air-suction directional seeding equipment. In this study, the DEM parameters of the seeds were calibrated. The angle of repose (AOR), intrinsic parameters, and partial contact parameters of the seeds were experimentally measured. The seed 3D models were reconstructed based on the three-view profile information. The parameters and their value ranges were filtered through the Plackett–Burman design and steepest ascent test. The response surface method (RSM) and machine learning were utilised for optimisation inversion of the parameters. The experiments showed that the geometric relative error of the seed model was 0.69–6.54%, which meets the modelling requirements for DEM. The seed–seed static friction coefficient, the seed–seed and the seed–PVC rolling friction coefficient were 0.341, 0.026, and 0.059, respectively, which were obtained by inverting the GA-BP regression model via the Genetic Algorithm. The simulated AOR was 26.64°, with a relative error compared to the actual AOR of 1.64%, which was better than the simulated AOR obtained by RSM optimisation. The greater the smoothing value setting in EDEM software, the less the particle filling, resulting in improved simulation efficiency but reduced model accuracy. The CPU + GPU(CUDA) solver showed high DEM solution efficiency. The results reveal that the method can be used to quickly and accurately construct a 3D model of the seed, and the parameter optimisation accuracy of GA-BP-GA is better than that of RSM.

Gear involute artifacts with sub-micron profile form deviations: manufacture and new design

Gear involute artifact (GIA) is a kind of calibration standard used for traceability of involute metrology. To machine GIAs with sub-micron profile form deviations, the effect on the involute profile deviations caused by the geometric deviations and 6-DoF errors of the machining tool based on the double roller-guide involute rolling generation mechanismwas analysed.At the same time, a double roller-guide involute lapping instrument and a lapping method for GIAs was proposed for lapping and in-situ measuring the gear involute artifacts. Moreover, a new GIA with three design base radii (50 mm, 100 mm, and 131 mm) was proposed for more efficient calibration and was machined with profile form deviations of 0.3 μm (within evaluation length of 38 mm, 68 mm, 80 mm, respectively, measured by the Chinese National Institute of Metrology), and the surface roughness Ra of the involute flanks was less than 0.05 μm. The research supports small-batch manufacturing for high-precision GIAs.

ESTIMATION OF MACHINE TOOL ACCURACY BASED ON MONTE CARLO SIMULATION USING MOVEMENT AXES GEOMETRIC ERRORS MODEL

Accuracy is one of the most important feature of a machine tool. Being able to estimate the overall accuracy of a machine tool represented by the total volumetric error can be a huge advantage in the design process. This paper provides overview of methods used for geometric error transfer modeling and volumetric error modeling. An error transfer rigid body model is derived and after that, a random linear guideway straightness error profile generator is proposed. This allows to simulate a movement axis with random straightness errors of rails and computed geometric errors of an assembled axis. Volumetric error of a 3-axis machine tool is then modeled using its kinematic scheme and homogenous transformation matrices with 21 kinematic errors. Using simulated axes as input to the volumetric model, an entire machine tool can be simulated. From that, the total volumetric error can be obtained and a Monte Carlo simulation carried out. This allows to analyze statistics of the total volumetric error and with slight input changes (rail straightness tolerance), a sensitivity analysis can be performed to determine the most influential errors in the machine tool.