Geometric Errors Research Articles

Topology optimization of steady Navier-Stokes flow using moving morphable void method

In order to explicitly and smoothly implement fluid-based topology optimization for improving the performance and manufacturing efficiency of flow systems, the moving morphable void (MMV) method is employed to optimize the steady-state navier-stokes (NS) flow for minimizing the dissipation energy under a volume constraint. To this end, a MMV-based Brinkman term is proposed to penalize the velocity in solid area, which can expand the region controlled by the NS flow equilibrium equation from fluid to whole design domain, and can also establish the relationship between design variables and governing equations. Then, a MMV-based optimization model of NS flow is proposed and the design variables are updated by the method of moving asymptotes according to the sensitivity analysis. In benchmark examples, we can precisely track the topology boundary with detailed geometric information without the intuitive geometric judgement error. Also, by means of contrasting the results of proposed method with previous work, the effectiveness and advantages of the MMV method can be confirmed.

An ultra-broadband high-performance solar energy perfect absorber from deep ultraviolet to mid-infrared

Metamaterial absorbers possess potential applications in a large number of fields, including solar energy harvesting, photovoltaics, stealth technology and sensors, owing to their capability to achieve perfect absorption of electromagnetic waves. In this study, a solar metamaterial absorber comprising a TiN substrate, a SiO2 spacer layer and an array of patterned-layer TiN-SiO2 double circular employing the finite-difference time-domain (FDTD) method is proposed to achieve perfect absorption in ultra-broadband. Optimization results indicate that the broadband absorption spectrum of the absorber extends from deep ultraviolet to mid-infrared wavelengths with an average absorption of 98.1%. The distribution of electric and magnetic fields suggests that the absorber achieves high absorption due to the interaction between surface plasmon resonance (SPR), cavity resonance (CR) and magnetic resonance (MR). Furthermore, the proposed absorber is insensitive to large-angle incidence and polarization-independent. Moreover, the absorber can be produced at a low cost due to its tolerance of the geometrical errors. The newly proposed metamaterial absorber is expected to be applied in solar energy related fields.

Analysis of the causes determining dimensional and geometrical errors in 316L and 17-4PH stainless steel parts fabricated by metal binder jetting

This work aims at investigating the causes affecting the dimensional and geometrical accuracy of holes in metal binder jetting stainless steel parts. Parallelepiped samples with a through hole were produced using AISI 316L and 17-4PH powders, differing for diameter (3, 4, 5 mm), and position of the axes with respect to the building plane (6, 9, 12 mm distance). Dimensions and geometrical characteristics were measured at green and sintered state by a coordinate measuring machine, determining the dimensional change and the geometrical characteristics. As expected, the shrinkage of linear dimensions is anisotropic; moreover, change in volume and sintered density are significantly affected by the position in the printing chamber. Higher shrinkage was measured along building direction (Z) – 18.5 ÷ 19.5%, than in the building plane – 16.5 ÷ 17.5%, and slightly higher shrinkage – 0.5 ÷ 0.8% was measured along powder spreading direction (X) than binder injection direction (Y). A variation up to 3% in relative density of sintered parts depending on the position in the building plane was observed in 316L. The dimensional change of diameters generally confirmed the shrinkage predicted by the model previously developed—difference between real and expected dimensional changes lower than 3%, except for three geometries (4 ÷ 6%). The cylindricity form error of sintered parts was strongly underestimated by the prediction model (up to 0.15 mm), but underestimation was considerably reduced (generally lower than 0.05 mm) adding the cylindricity form error due to printing. Dimensional and geometrical accuracy of holes are strongly affected by shape distortion of the parallelepiped geometry, in turn due to layer shifting and inhomogeneous green density during printing, and to the effect of frictional forces with trays during sintering. Gravity load effect was also observed on the holes closest to the building plane. Future work will improve the reliability of the prediction model implementing the results of the present work.

A comprehensive error evaluation method for non-rigid body gantry machine tools considering quasi-static crosstalk based on optimized multilateration measurement

For large-scale machine tools, the impact of non-rigid body behavior on volumetric error accuracy cannot be ignored, which hasn't been considered in general volumetric error model. This paper presents a comprehensive error evaluation method for large-scale gantry machine tools considering non-rigid body effect, aiming to provide guidance for volumetric error calibration process. An extended kinematic model is established based on the analysis of crosstalk influence on geometric error motions. An optimized multilateration measurement with improved accuracy and robustness is carried out for volumetric error identification, verified by Monte Carlo simulations. The main novelty of the optimization is to introduce a space uniformity index to generate specialized calibration point sets for any measurement points. A new volumetric error prediction method based on classified descriptions of geometric error motions is proposed, according to their relationship with crosstalk. Experimental results show that the proposed method achieves higher prediction accuracy in crosstalk-sensitive directions.

Error Analysis of an Economical On-Site Calibration System for Linear Optical Encoders

A calibration system was designed to evaluate the accuracy of linear optical encoders at the micron level in a fast and economical manner. The system uses a commercial interferometer and motor stage as the calibrator and moving platform. Error analysis is necessary to prove the effectiveness and identify areas for optimization. A fixture was designed for the scale and interferometer target to meet the Abbe principle. A five-degree-of-freedom manual stage was utilized to adjust the reading head in optimal or suboptimal working conditions, such as working distance, offset, and angular misalignment. The results indicate that the calibration system has an accuracy of ±2.2 μm. The geometric errors of the calibration system, including mounting errors and non-ideal motions, are analyzed in detail. The system could be an inexpensive solution for encoder manufacturers and customers to calibrate a linear optical encoder or test its performance.

An experimental investigation into the influence of water column height in submerged mode of abrasive waterjet trepanning on the hole quality

Abrasive waterjet (AWJ) trepanning/drilling exhibits immense potential to realize holes of various shapes and sizes in a diverse range of materials, ranging from soft-and-ductile to hard-and-brittle, making it highly valuable for various industries. AWJ trepanning offers the advantage of not requiring tool changes to accommodate different hole shapes and sizes; adjusting the jet path can produce the desired hole geometry, proving exceptionally advantageous for mass production. However, the stochastic nature of the jet results in geometrical errors (diametric deviation, taper angle (α)), form errors (circularity error (Ce), cylindricity error (Cy)) and quality issues (damage region, edge radius (R), surface roughness (Ra), and waviness (Wa)). To address these issues, trepanning in submerged mode can be adopted as it attenuates the mist region and aggressiveness of the jet. This study analyzes the influence of the submerged mode of trepanning on the geometry, form, and quality of trepanned holes relative to the in-air mode. The study found that submerged trepanning produces a more consistent hole diametrical profile along the depth and minimizes the average Ce and α by 23.18 % and 29.20 %, respectively. The maximum Cy in in-air trepanning was reduced in submerged mode by 36.76 %. The average damage region and R reduced by 50.80 % and 35.49 %, respectively. The qualitative and quantitative analysis of the trepanned surface morphology is presented in-air and submerged mode: the results show that the Ra and Wa decrease at the hole entry and middle zone and increase at the exit zone. Finally, the process parameters level settings for achieving near-optimal trepanning responses (α, Cy, Ce, damage region, R, Ra, and Wa) suggested with the help of mean response- and parallel coordinate- plots. Micrographs of submerged trepanned surfaces show that the material removal mechanism (MRM) governs by shallower craters and grooves at the entry and middle zone of the hole, and at the exit zone, the MRM is random, in comparison to the in-air mode.

Research on geometric error compensation of ultra-precision turning-milling machine tool based on macro–micro composite technology

Research on geometric error compensation of ultra-precision turning-milling machine tool based on macro–micro composite technology

A vector error gradient compensation method for geometric error of boring deep holes on thin-walled boxes

A vector error gradient compensation method for geometric error of boring deep holes on thin-walled boxes

A Transit Tilt and Offset Errors Calibration Method for Improving Laser Tracker Measurement Accuracy Based on the Telecentric Measurement System

Laser trackers are instruments used to measure the three-dimensional coordinates of objects with high precision. It is necessary to study calibration methods to identify geometric errors of laser trackers so as to compensate for errors and improve measurement accuracy. Among the offsets, tilts, and eccentricity errors in the system, the transit tilt and offset errors play important roles and have an essential effect on the measurement accuracy, which need to be calibrated and compensated for. Current methods for detecting geometric errors between the transit and standing axes are complex and time-consuming. In this paper, a fast and novel calibration method is proposed, which can be easily operated with high precision. Two test rods are coaxially mounted on the ends of the transit axis to extend the hidden transit axis. Then, a telecentric measurement system is used to record the projection images of the test rods and identify the position of the transit axis. The transit offset and tilt errors were thus obtained by comparing the central axis positions of the two test rods before and after the standing axis rotated 180 degrees. Moreover, a numerical analysis method was proposed based on the least square circle fitting method to calibrate the installation eccentricity errors of the test rods. Experimental results verify that the measurement accuracy of the laser tracker can be improved after error compensation using the calibrated transit offset and tilt errors. The measurement error of the laser tracker can be reduced from 161 µm to about 73 µm after compensation at a distance of 5 m, while the error can be decreased from 143 µm to about 108 µm at a distance of 10 m.

Optimal design method for geometric errors of horizontal machining center based on Sobol method and IPSO

Optimal design method for geometric errors of horizontal machining center based on Sobol method and IPSO

Micro/nanopositioning coplanar stage with real-time compensation of volumetric error

A micro/nanopositioning coplanar stage is designed with real-time compensation of volumetric error. According to the topological structure of the stage, it has 13 geometric error components. Furthermore, there are positional shifts of a functional point from the displacement feedback point and the measurement point of geometric errors. To improve the positional accuracy, it is crucial to real-time measure, model, and compensate for the volumetric error at the functional point. Therefore, a volumetric error measuring unit (VEMU) is designed to simultaneously real-time measure 13 geometric error components. A volumetric error model is established using the Abbe and Bryan principles. A control unit with two backpropagation neural networks-based PID controllers combines with the VEMU and volumetric error model to realize the real-time compensation of the volumetric error. The positional error of the micro/nanopositioning coplanar stage is reduced approximately 97.6 %, from which the effectiveness and applicability of the proposed methods are verified.

Marching Windows: Scalable Mesh Generation for Volumetric Data With Multiple Materials.

Volumetric data abounds in medical imaging and other fields. With the improved imaging quality and the increased resolution, volumetric datasets are getting so large that the existing tools have become inadequate for processing and analyzing the data. Here we consider the problem of computing tetrahedral meshes to represent large volumetric datasets with labeled multiple materials, which are often encountered in medical imaging or microscopy optical slice tomography. Such tetrahedral meshes are a more compact and expressive geometric representation so are in demand for efficient visualization and simulation of the data, which are impossible if the original large volumetric data are used directly due to the large memory requirement. Existing methods for meshing volumetric data are not scalable for handling large datasets due to their sheer demand on excessively large run-time memory or failure to produce a tet-mesh that preserves the multi-material structure of the original volumetric data. In this article we propose a novel approach, called Marching Windows, that uses a moving window and a disk-swap strategy to reduce the run-time memory footprint, devise a new scheme that guarantees to preserve the topological structure of the original dataset, and adopt an error-guided optimization technique to improve both geometric approximation error and mesh quality. Extensive experiments show that our method is capable of processing very large volumetric datasets beyond the capability of the existing methods and producing tetrahedral meshes of high quality.

A second-order-accuracy finite difference scheme for numerical computation on two-dimensional three-neighboring-node unstructured grids

The computation of the finite difference method in curvilinear coordinates usually necessitates coordinate transformation. Eliminating geometric errors induced by coordinate transformation can be achieved with geometric conservation law. However, no research has been conducted to implement a difference scheme on two-dimensional three-neighboring-node unstructured meshes and achieve a second-order accuracy. In this paper, a new finite difference method is proposed for a numerical simulation on these meshes, and it can achieve a second-order accuracy with the use of the gradient interpolation and the discrete criterion, freezing the metrics and Jacobian at local nodes. The results of several numerical tests demonstrate that the method achieved reliable performance and robustness on unique and randomized unstructured grids for a complex flow with discontinuity, subsonic inflow, and diffraction. The method had comparable accuracy to the second-order difference scheme on structured grids.

An Efficient Kinematic Calibration Method for Parallel Robots With Compact Multi-Degrees-of-Freedom Joint Models

Abstract Forward kinematics-based modeling approaches are capable of constructing complete kinematic error models for parallel robots in a general way. The existing forward kinematics-based modeling methods replace multi-degrees-of-freedom (multi-DOF) joints with several 1DOF joints, allowing each limb of the parallel robot to be modeled like a serial robot. Nonetheless, this substitution complicates the kinematic model and results in additional computation. To overcome this limitation, an efficient kinematic calibration method adopting compact multi-DOF joint models is proposed. First, compact kinematic models for multi-DOF joints are established with the product of exponentials formula and adopted in the forward kinematic formulation of limbs. Error models of limbs are derived by simplifying the forward kinematic formulas' differentials, and the geometric error model for parallel robots is established by further concatenating and reformulating the limb error models. Next, the kinematic model is iteratively updated with the geometric parameter errors identified by the Levenberg–Marquardt algorithm. Error compensation is achieved through the inverse kinematics of the calibrated kinematic model. Finally, simulations and an experiment are implemented for validation. Compared with the existing forward kinematics-based modeling approaches, the error modeling procedures are simplified as the equivalent substitution of multi-DOF joints is avoided. The proposed approach also enhances the error compensation efficiency while maintaining high accuracy improvement.

Projections of Drug-Drug Interactions Caused by Time-Dependent Inhibitors of Cytochrome P450 1A2, 2B6, 2C8, 2C9, 2C19, and 2D6 Using In Vitro Data in Static and Dynamic Models.

In vitro time-dependent inhibition (TDI) kinetic parameters for cytochrome P450 (CYP) 1A2, 2B6, 2C8, 2C9, 2C19, and 2D6, were determined in pooled human liver microsomes for 19 drugs (and 2 metabolites) for which clinical drug-drug interactions (DDI) are known. In vitro TDI data were incorporated into the projection of the magnitude of DDIs using mechanistic static models and Simcyp®. Results suggest that for the mechanistic static model, use of estimated average unbound exit concentration of the inhibitor from the liver resulted in a successful prediction of observed magnitude of clinical DDIs and was similar to Simcyp®. Overall, predictions of DDI magnitude (i.e., fold increase in AUC of a CYP-specific marker substrate) were within 2-fold of actual values. Geometric mean-fold errors were 1.7 and 1.6 for static and dynamic models, respectively. Projections of DDI from both models were also highly correlated to each other (r2 = 0.92). This investigation demonstrates that DDI can be reliably predicted from in vitro TDI data generated in HLM for several CYP enzymes. Simple mechanistic static model equations as well as more complex dynamic PBPK models can be employed in this process. Significance Statement Cytochrome P450 time-dependent inhibitors (TDI) can cause drug-drug interactions (DDI). An ability to reliably assess the potential for a new drug candidate to cause DDI is essential during drug development. In this report, TDI data for 19 drugs (and 2 metabolites) were measured and used in static and dynamic models to reliably project the magnitude of DDI resulting from inhibition of CYP1A2, 2B6, 2C8, 2C9, 2C19, and 2D6.

Swin-transformer-enhanced detector z-axis virtual alignment method for cone-beam CT system

ABSTRACT X-ray cone beam computed tomography (CBCT) is a common imaging tool in medical and industrial fields due to its non-invasive and efficient approach to 3D internal imaging. However, obtaining clear cross-section image with CBCT requires precise geometry alignment. Previous alignment methods have mostly relied on specially designed phantoms and/or the iterative optimisation of reconstructed images, both of which are costly and inefficient. This paper presented a Swin-Transformer-enhanced detector z-axis virtual geometry alignment method, which considered the tilt angle (around the central column of the detector) and the horizontal deviation of the centre of projection. The method took advantage of both cross-section and projection domains to virtually restore the geometric misalignments with the help of mathematical models. The maximum prediction error of the tilt angle was 0.0696°, and the single prediction time was about 0.0395 s. To the best of our knowledge, this work was the first study to detect the multiple geometric errors from the slice using deep learning method. It provided a new geometric alignment method for the CBCT system.

Geometric error compensation method using the Laser R-test

Traditional methods for measuring geometric errors in machine tools, including interferometry and Double Ball Bar (DBB), are known to be expensive and time-intensive. Consequently, a non-contact calibration system called the “Laser R-test” has been developed. This innovative system is designed to measure both position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) efficiently. Since its development in 2000, this tool has been instrumental in analyzing eccentricity errors, angular position errors, and simultaneous trajectory errors. Through extensive research, it has been determined that the total error in a five-axis machine tool can be controlled to below 40 µm after compensating for eccentricity parameters and angular position errors. However, reducing this error to below ± 10 µm is challenging, primarily due to wobble errors in the orientation of the rotary axis without compensating. In this study, a new methodology based on Laser R-test and Rodrigues’ rotation formula has been developed to establish a PIGE model of rotary axis. Based on the methodology, the 8 PIGEs can be analyzed by measuring 5 coordinate positions. The compensation of 8 PIGEs in the rotary axis is completed within 30 min using the inspection path. Compatibility with ISO-10791–6 standards for BK1, BK2, and BK4 path tests is confirmed, validating the compensation effects. A precision of below ± 10 µm is achieved, with inspection time reduced by over 50%. This system can complete multiple errors by simply using the different paths. This greatly reduces the setup time for future users, enhancing its commercial applicability.

High-precision robotic kinematic parameter identification and positioning error compensation method for industrial robot

Abstract A method based on laser tracing multi-station measurement technology is proposed in this paper. The method identifies the robotic kinematic parameters and compensates for the absolute positioning errors of industrial robots to improve the absolute positioning accuracy further. The position coordinates of industrial robots are typically measured using laser tracking devices. In this study, the measurement accuracy of an industrial robot is further enhanced using laser tracer multi-station measurement technology. Additionally, the least absolute shrinkage and selection operator (LASSO) algorithm was used to identify the robotic kinematic parameters. Compared with the commonly used least squares algorithm, the LASSO algorithm improved the parameter identification accuracy and the compensation effect on absolute positioning errors. A position error model was established based on the parameters of the modified Denavit–Hartenberg model of an industrial robot. Using the LASSO algorithm, the robotic kinematic parameters were accurately identified, and the original data in the controller were replaced to compensate for the geometric errors of the industrial robot. In the compensation experiments, after implementing the geometric error compensation, the average absolute positioning error of the industrial robot decreased by 41.15%, demonstrating a significant improvement in the absolute positioning accuracy.

Adaptive Identification of the Position-independent Geometric Errors for the Rotary Axis of Five-axis Machine Tools to Directly Improve Workpiece Geometric Errors

Adaptive Identification of the Position-independent Geometric Errors for the Rotary Axis of Five-axis Machine Tools to Directly Improve Workpiece Geometric Errors

Quantification of geometrical errors and thermal effects during wire EDM of thin wall structures—A numerical study

Machining thin-walled structures with a high aspect ratio using Wire EDM can lead to geometrical errors, primarily of two types; overcut error due to kerf formation and thermal deformation of the entire wall section. To understand the driving mechanisms behind these errors three distinct numerical models were developed. Initially, a model based on a moving heat source was created, employing the apparent heat capacity approach to predict kerf width and the associated overcut error. These insights were then utilized to formulate a transient temperature distribution model with a redesigned geometry, considering time-dependent evolution of the kerf and corresponding changes in the material properties of the sub-domains. Finally, a thermo-mechanical coupled model was developed to predict geometrical errors caused by the deflection of the wall, considering the varying stiffness of the part. A series of experiments were conducted to gain insight into the effect of the designed wall thickness on wall deflection. For the selected design profile and machine parameters, the model predicts a 62.4% reduction in thickness and a corresponding over-cut error of 188μm. Similarly, the model predicts wall deformation in the range of 6μm to 312μm for various wall thickness levels and these findings were validated with experimental observations.