Geometric Errors Research Articles

Sensitivity analysis and compensation for tooth surface deviation of spiral bevel gear machine tool

To analyze the quantitative mapping relationship between the geometric errors of the five-axis CNC machine tool and the tooth surface deviation of spiral bevel gears, and identify the key geometric errors that affect the machining deviation of the spiral bevel gear tooth surface, a sensitivity analysis method for tooth surface machining deviation of spiral bevel gear based on screw theory and EFAST method is proposed. Firstly, the machining model of the spiral bevel gear tooth surface based on the five-axis CNC machine tool is established. Then, the geometric error transfer model of the machine tool is established based on the screw theory. Combined with the EFAST global sensitivity analysis method, the key geometric errors that affect tooth surface deviation are identified. Finally, the reliability and effectiveness tests are performed by comparing the results to the local sensitivity analysis method and simulating compensation for the key geometric errors. The result of compensation shows that the tooth surface deviation is reduced significantly according to global sensitivity analysis. The feasibility of applying sensitivity analysis to control the tooth surface deviation of spiral bevel gears has been demonstrated.

A deep learning approach for pose error prediction in parallel robots

Parallel robots are increasingly favored in industrial automation due to their high precision, stability, and rigidity in high-speed and heavy-load tasks. However, factors such as manufacturing tolerances, assembly deviations, loads, and environmental conditions can lead to pose inaccuracies, manifesting as both geometric and non-geometric errors. Traditional model-driven approaches effectively predict geometric errors but often neglect non-geometric factors, potentially impacting the overall accuracy. This paper presents a deep learning-based method for comprehensive pose error prediction in parallel robots, addressing both geometric and non-geometric errors. The proposed approach employs an encoder-decoder network that takes target pose inputs and outputs predicted pose errors. The encoder integrates multi-layer convolutional sparse coding (CSC) blocks and efficient channel attention (ECA) modules to extract features from the network inputs. Monte Carlo dropout is utilized to estimate prediction uncertainties, enhancing the reliability of the network predictions. Experimental validation on a Stewart platform demonstrates the high accuracy and robustness of the method under various loading conditions. Comparative analyses with several typical models affirm the superior performance of the proposed network, indicating its potential to improve the operational accuracy and reliability of parallel robots in high-precision applications.

Assessment of Femoral Head Sphericity Using Coordinate Data through Modified Differential Evolution Approach

Coordinate measuring machines (CMMs) are utilized to acquire coordinate data from manufactured surfaces for inspection reasons. These data are employed to gauge the geometric form errors associated with the surface. An optimization procedure of fitting a substitute surface to the measured points is applied to assess the form error. Since the traditional least-squares approach is susceptible to overestimation, it leads to unreasonable rejections. This paper implements a modified differential evolution (DE) algorithm to estimate the minimum zone femoral head sphericity. In this algorithm, opposition-based learning is considered for population initialization, and an adaptive scheme is enacted for scaling factor and crossover probability. The coefficients of the correlation factor and the uncertainty propagation are also measured so that the result’s uncertainty can be determined. Undoubtedly, the credibility and plausibility of inspection outcomes are strengthened by evaluating measurement uncertainty. Several data sets are used to corroborate the outcome of the DE algorithm. CMM validation shows that the modified DE algorithm can measure sphericity with high precision and consistency. This algorithm allows for an adequate initial solution and adaptability to address a wide range of industrial problems. It ensures a proper balance between exploitation and exploration capabilities. Thus, the suggested methodology, based on the computational results, is feasible for the online deployment of the sphericity evaluation. The adopted DE strategy is simple to use, has few controlling variables, and is computationally less expensive. It guarantees a robust solution and can be used to compute different form errors.

Dynamic phase measurement based on two-step phase-shifting interferometry with geometric phase grating

Abstract This paper proposes a novel dynamic 2-step phase-shifting interferometry method with a geometric phase grating and direct aberration-free object phase recovery algorithm. By exploring the amplitude-phase modulation property of the geometric phase grating, two-step phase-shifting interferograms with π / 2 phase shift can be obtained in a single shot through two kinds of spatial-multiplexing arrangements. Then the restriction on the background uniformity of the 2-step phase-shifting algorithms and the system aberration can be avoided simultaneously, based on the presented direct and fast object phase demodulation strategy with an object-free state recorded in advance, so an accurate object measurement result can be guaranteed. Accordingly, a detailed analysis of the theoretical model of error sources is conducted by taking the depolarization error of geometric phase grating and phase measurement model error into consideration, with a Least Squares Iteration optimization strategy established to further improve the measurement accuracy. Experiments on various types of phase objects, such as a photo-etched quartz substrate, the spatial light modulator, and a silicon chip, validate the effectiveness and accuracy of our method when compared with the reference phase obtained from 4-step temporal phase-shifting method. The dynamic phase measurement capability is demonstrated by exhibiting the evaporation process of alcohol droplet.

Improving electrocardiographic imaging solutions: A comprehensive study on regularization parameter selection in L-curve optimization in the Atria

BackgroundIn electrocardiographic imaging (ECGI), selecting an optimal regularization parameter (λ) is crucial for obtaining accurate inverse electrograms. The effects of signal and geometry uncertainties on the inverse problem regularization have not been thoroughly quantified, and there is no established methodology to identify when λ is sub-optimal due to these uncertainties. This study introduces a novel approach to λ selection using Tikhonov regularization and L-curve optimization, specifically addressing the impact of electrical noise in body surface potential map (BSPM) signals and geometrical inaccuracies in the cardiac mesh. MethodsNineteen atrial simulations (5 of regular rhythms and 14 of atrial fibrillation) ensuring variability in substrate complexity and activation patterns were used for computing the ECGI with added white Gaussian noise from 40 dB to -3dB. Cardiac mesh displacements (1–3 cm) were applied to simulate the uncertainty of atrial positioning and study its impact on the L-curve shape. The regularization parameter, the maximum curvature, and the most horizontal angle of the L-curve (β) were quantified. In addition, BSPM signals from real patients were used to validate our findings. ResultsThe maximum curvature of the L-curve was found to be inversely related to signal-to-noise ratio and atrial positioning errors. In contrast, the β angle is directly related to electrical noise and remains unaffected by geometrical errors. Our proposed adjustment of λ, based on the β angle, provides a more reliable ECGI solution than traditional corner-based methods. Our findings have been validated with simulations and real patient data, demonstrating practical applicability. ConclusionAdjusting λ based on the amount of noise in the data (or on the β angle) allows finding optimal ECGI solutions than a λ purely found at the corner of the L-curve. It was observed that the relevant information in ECGI activation maps is preserved even under the presence of uncertainties when the regularization parameter is correctly selected. The proposed criteria for regularization parameter selection have the potential to enhance the accuracy and reliability of ECGI solutions.

Equivalent Error Based Modelling for Prediction and Analysis of Measuring Accuracy in 3-Axis FXYZ Coordinate Measuring Machines from Position, Repeatability and Reversibility Errors

AbstractThe measuring accuracy of coordinate measuring machines (CMMs) will be affected by the different geometrical and dynamic errors, including the deviations associated to the axis displacement, the working table and the part to be measured. This work is focused on the analysis of the influence of the position errors, repeatability errors and reversibility errors in 3-axis FXYZ coordinate measuring machines, and it will be developed by a numerical model that is known as EE-based stochastic model. This model implements a new error index that is named equivalent error (EE), which will integrate the totality of machine errors of the CMMs and will allow a global description of all these error sources by means of a unique error parameter. The results obtained by this numerical model have been compared with the application of a traditional method, and it was probed that the EE-based model makes possible an increase of a 13.29% in the linear modelling of the performance of CMMs from the machine errors considered in this work, which implies a relevant improvement for the analysis and description of the effect of the distinct error sources on the achievable measuring accuracy of CMMs. For this reason, the EE-based model will be of special interest for industrial applications such as the quality control to be applied inside the production systems dedicated to manufacture mechanical components of high dimensional accuracy.

Analysis of models of measurement and correction of volumetric error of three-axis metal-cutting machine tool

The paper considers the improvement of the quality of products of machined production in connection with the quality of machining of various products and, accordingly, with the accuracy of the equipment used. It is noted that geometrical errors, which account for up to 40 % of the total error of a multi-axis, especially three-axis, metal-cutting machine tool, have the greatest influence on the accuracy of product machining. In order to improve the quality of product machining, it is necessary to correct its parameters according to the measurement information received during machine tool operation, for which the methods of mathematical modelling are used. Models of the volumetric error of a three-coordinate metal-cutting machine tool are developed, taking into account the summands of the first (linear) and second (quadratic) order of smallness. A comparative analysis of the developed models is carried out. The results of experiments on measurement of volumetric errors of the STAN S500 complex and their correction on the basis of the nonlinear theoretical model are given. It is found that in the range of angular errors 0–2.5′ the consideration of quadratic terms of the model in addition to linear ones does not lead to a significant reduction of the volumetric error. It is shown that when processing measurement information of multi-axis metal-cutting machines it is sufficient to limit the consideration of components of the volumetric error not higher than the first order of smallness. The research results are useful for the acceptance and periodic control of the volumetric error of metal-cutting machines, as well as for the programme reduction of the volumetric error.

Research on positioning accuracy of the swivel head of milling and turning complex machining center

Abstract This article focuses on the swivel head of a milling-turning complex machining center and establishes a geometric error model between the rotary axes based on the multi-body system theory and the homogeneous coordinate transformation method. The double ball bar (DBB) is used to identify the geometric errors of the machine tool swivel head position-independent by measuring circular trajectories. The impact of PIGEs on the measurement trajectory is simulated. The swivel head is rotated at four angles (B0°, B45°, B90°, B-15°), and the laser tracker is used to analyze and study the linear axis straightness, perpendicularity, and the center coordinates and plane errors of the swivel head movement along the XZ plane. A swivel head rotation accuracy test fixture is designed to correct the positioning accuracy of a swivel head with a 45° inclination of the rotation axis. The research results show that the fluctuation of the center plane degree of freedom of the swivel head moving along the XZ plane is small, and the maximum value is 0.0086mm. Under the 45° angle posture of the swivel head, both the center coordinate error value and the plane error value are the largest. The simulation results of the swivel head position error are fairly consistent with the center coordinate error of the swivel head plane movement. A backward tilt displacement of 0.01mm~0.015mm of the machine column during assembly can reduce the influence of the weight of the swivel head on the perpendicularity and straightness of the vertical reciprocating motion, and adding auxiliary support near the base of the swivel head zero position can reduce machine straightness error.

Systematic analysis of geometric inaccuracy and its contributing factors in roboforming

Incremental sheet metal forming is a highly versatile die-less forming process for manufacturing complex sheet metal components. Robot-assisted incremental sheet forming, or roboforming, allows a wider range of tool motion, providing the capability to shape intricate components. This makes roboforming the most flexible variant of the incremental forming method. However, the serial arrangement of links and joints in a robotic manipulator results in low positional accuracy under forming loads due to insufficient structural stiffness. The stiffness of the machine frame and tool directly impacts the accuracy of the final formed profile. The impact of machine compliance on component shape in incremental sheet forming is substantial in roboforming. This work presents a methodology for systematic analysis of the factors contributing to the errors in the geometric shape of robot-based forming. Experimental and numerical methods are used to estimate the material springback, tool/tool holder deflections, and errors due to machine compliance. The CNC machine frame is relatively stiffer than the industrial robots, such that material springback is estimated based on the experimental trials on CNC for cone and variable wall angle cone profiles. Tool and tool holder deflections are estimated using finite element simulations. The analytical method using the Virtual Joint Model is used to model the joint stiffness, and consequently, the robot Cartesian stiffness is estimated to predict path deviation contributing to geometric shape errors. The proportional contribution of each factor in the overall deviation in the Roboforming is also quantified.

Noise-Robust 3D Pose Estimation Using Appearance Similarity Based on the Distributed Multiple Views.

In this paper, we present a noise-robust approach for the 3D pose estimation of multiple people using appearance similarity. The common methods identify the cross-view correspondences between the detected keypoints and determine their association with a specific person by measuring the distances between the epipolar lines and the joint locations of the 2D keypoints across all the views. Although existing methods achieve remarkable accuracy, they are still sensitive to camera calibration, making them unsuitable for noisy environments where any of the cameras slightly change angle or position. To address these limitations and fix camera calibration error in real-time, we propose a framework for 3D pose estimation which uses appearance similarity. In the proposed framework, we detect the 2D keypoints and extract the appearance feature and transfer it to the central server. The central server uses geometrical affinity and appearance similarity to match the detected 2D human poses to each person. Then, it compares these two groups to identify calibration errors. If a camera with the wrong calibration is identified, the central server fixes the calibration error, ensuring accuracy in the 3D reconstruction of skeletons. In the experimental environment, we verified that the proposed algorithm is robust against false geometrical errors. It achieves around 11.5% and 8% improvement in the accuracy of 3D pose estimation on the Campus and Shelf datasets, respectively.

A unified geometric error model applicable to all configurations of three-axis machine tools

A unified geometric error model applicable to all configurations of three-axis machine tools

Robotic MR-guided high dose rate brachytherapy needle implantation in the prostate (ROBiNSon)—a proof-of-concept study

Objective. A robotic needle implant device for MR-guided high-dose-rate (HDR) prostate brachytherapy was developed. This study aimed to assess the feasibility and spatial accuracy of HDR brachytherapy using the robotic device, for a single intraprostatic target point. Approach. Five patients were treated from November 2019–June 2022 with the robot. The robot fits a 1.5 T MR scanner and the needle can be shifted and angulated. An intraprocedural MR scan was fused with the diagnostic MR and one preplanned needle position was selected for robotic insertion. The needle entry point and angles were set for a needle tip target point within the intraprostatic target volume. The needle was tapped stepwise towards the target point pneumatically. Final needle position was verified with MR, followed by plan optimization and dose delivery. Any remaining planned needles were inserted manually. Needle tip to geometrical target error (NTG-error) was defined as the deviation of the actual tip position relative to the predefined geometric target point, using MR-coordinates. Needle tip to treatment target error (NTT-error) was defined as the deviation of the actual tip position relative to the treatment target point, using fused MR-images pre- and post-needle implantation taking into account prostate deformation. Difference between NTT-error and NTG-error and fiducial marker shifts indicated prostate movement. For determining prostate deformation, the Jaccard index and prostate volumes were assessed. Main results. The robotic device was able to tap the needle to the planned depth for all patients. Mean robotic procedure duration was 142 min. NTG-error was 3.2 (range 1.1–6.7) mm and NTT-error 4.5 (range 2.6–9.6) mm. Marker displacements were smaller than 3 mm. No treatment-related acute toxicity was reported. Feasibility of needle placement within the prostate was considered adequate. Significance. MR-guided robotic needle insertion is feasible with a mean geometric accuracy of 3.2 mm and <3 mm prostate movement.

Joint sensitivity analysis method of impeller aerodynamic performance to key geometric errors of five-axis machine tool

As a high-performance workpiece, an impeller must ensure both dimensional accuracy and aerodynamic performance. A five-axis machine tool has various geometric errors, which seriously influence the impeller processing quality, hence it is crucial to identify the key error items and compensate them. In this study a joint sensitivity analysis method for the key geometric errors of a five-axis machine tool is proposed that focuses on the aerodynamic performance of an impeller. First, a volumetric error model and an aerodynamic performance model were built, representing the relationships between the tool center point volumetric errors and each of the geometric errors and the impeller aerodynamic performance. Then, the improved Sobol method was implemented to compute the total sensitivity index of each variable in the two models, from which two sensitivity distribution matrices were obtained. Finally, a joint sensitivity analysis was performed on these two matrices to identify the key geometric errors. Experiments were executed to ascertain the impact of compensation strategies on the impeller aerodynamic performance. The results showed that after compensating for the key errors, the total pressure ratio and isentropic efficiency loss rate of the impeller are reduced by 72.2% and 55.8% under the design parameters. The significant improvement in the aerodynamic performance of the impeller demonstrates the accuracy of key geometric error identification.

Active prediction compensation strategy: A new positioning compensation technique for improving the accuracy of the dual ball screw feed mechanism under load

The dual ball screw feed mechanism (DBSFM) is commonly employed in high-end machining applications. However, its accuracy is challenging to enhance due to variations in the axial stiffness of the dual actuators under load, making geometric error compensation (GEC) difficult. To address this, our research establishes a comprehensive error model that integrates geometric error and load-induced error (LIE) to improve feeding accuracy. The axial stiffness matrix of the DBSFM is identified using motor current information, and an active prediction error matrix is defined based on the geometric error model, milling force model, and axial stiffness matrix. We propose and analyze the active prediction compensation (APC) strategy as a new method to enhance accuracy under load. Experimental validation using a gantry-type machine tool demonstrates that the APC strategy can reduce the positioning error of the DBSFM to ±2 μm under load, representing significant improvements over the established GEC method. Specifically, the APC strategy achieves a 53.07% and 57.04% enhancement in accuracy along the two axes. This work illustrates the effectiveness of the APC strategy in reducing positioning errors and improving feeding accuracy in DBSFM machining processes.

Research on impact of geometric errors of heavy CNC machine tools on machining errors of wind turbine bearing raceways

Research on impact of geometric errors of heavy CNC machine tools on machining errors of wind turbine bearing raceways

Geometry accuracy control in abrasive water jet taper hole machining of ultra‐thick carbon fiber‐reinforced polymer (CFRP) laminates

AbstractThe primary factors affecting the geometric accuracy of abrasive water jet (AWJ) machining of ultra‐thick carbon fiber‐reinforced polymer (CFRP) laminates are the cutting front drag and kerf width deviation caused by energy dissipation. Firstly, this study comprehensively analyzes the influence of the coupling relationship between cutting front drag and kerf width deviation on the geometric accuracy of hole machining. Secondly, a gradient distribution theory for jet traverse speed with cutting depth is proposed for taper hole machining characteristics. Finally, a general geometric error model applicable to both straight and taper hole machining of ultra‐thick CFRP laminates using AWJ is established, along with a geometric error compensation method. A series of experiments validate the accuracy of the proposed geometric error model and compensation method. The novelty of this research lies in unifying the geometric error models for straight and taper hole machining of ultra‐thick CFRP laminates by considering the gradient distribution of jet traverse speed. The proposed error compensation method reduces the high degree of freedom required for machine tools. This study provides a general geometric error model and compensation strategy for AWJ hole machining of ultra‐thick CFRP laminates, which has significant engineering value for achieving 3D controllable AWJ machining of complex ultra‐thick CFRP components.Highlights The high geometric precision taper holes machining technique is a necessary prerequisite for achieving precise machining of complex trajectories in ultra‐thick CFRP with abrasive water jet. The influence of the coupling relationship between cutting front drag and kerf taper on the geometric accuracy of hole processing is comprehensively analyzed. A model considering the gradient distribution of traverse speed during taper holes machining was established, and a geometric error model considering this gradient distribution of traverse speed was developed. A taper holes machining geometric error compensation method with high engineering applicability was proposed. Geometric error prediction experiments and error compensation experiments were conducted, and the results proved the accuracy of the geometric error model and error compensation method.

Stochastic vibration analysis for linear rolling guide with considering geometric errors

Stochastic vibration analysis for linear rolling guide with considering geometric errors

Particle swarm algorithm-based identification method of optimal measurement area of coordinate measuring machine.

A particle swarm algorithm-based identification method for the optimal measurement area of large coordinate measuring machines (CMMs) is proposed in this study to realize the intelligent identification of measurement objects and optimize the measurement position and measurement space using laser tracer multi-station technology. The volumetric error distribution of the planned measurement points in the CMM measurement space is obtained using laser tracer multi-station measurement technology. The volumetric error of the specified step distance measurement points is obtained using the inverse distance weighting (IDW) interpolation algorithm. The quasi-rigid body model of the CMM is solved using the LASSO algorithm to obtain the geometric error of the measurement points in a specified step. A model of individual geometric errors is fitted with least squares. An error optimization model for the measurement points in the CMM space is established. The particle swarm optimization algorithm is employed to optimize the model, and the optimal measurement area of the CMM airspace is determined. The experimental results indicate that, when the measurement space is optimized based on the volume of the object being measured, with dimensions of (35 × 35 × 35) mm3, the optimal measurement area for the CMM, as identified by the particle swarm algorithm, lies within the range of 150mm < X < 500mm, 350mm < Y < 700mm, and -430mm < Z < -220mm. In particular, the optimal measurement area is defined as 280mm < X < 315mm, 540mm < Y < 575mm, and -400mm < Z < -365mm. Comparative experiments utilizing a high-precision standard sphere with a diameter of 19.0049mm and a sphericity of 50nm demonstrate that the identified optimal measurement area is consistent with the results obtained through the particle swarm algorithm, thereby validating the correctness of the method proposed in this study.

Geometric error compensation method of five-axis CNC machine tool based on improved genetic algorithm

Geometric error compensation method of five-axis CNC machine tool based on improved genetic algorithm

A Newton method with characteristic value correction for geometric error calibration of parallel mechanism

A Newton method with characteristic value correction for geometric error calibration of parallel mechanism