Axial Error Research Articles

Modeling, detection, and validation for geometric errors in machine tools

Abstract This study aims to enhance the spatial precision of five-axis machining centers through a comprehensive exploration of geometric errors, encompassing modeling, efficient detection, and compensation validation. Our approach begins with the establishment of a kinematic error model covering XYZ translational axes and AC rotational axes, providing an in-depth understanding of error origins and interrelationships. Utilizing a laser tracker, we conduct direct measurements of the geometric errors associated with translational axes, and a rotational axis error detection model is developed by using a ball bar, allowing for indirect analysis of rotational axis geometric errors. The validity of both the kinematic error model and error detection is further confirmed through practical on-machine measurements.

Image Guided Interpedicular Screw Placement Simulation System for Training and Skill Evaluation. Proof of Concept

IntroductionPresent work introduces SpineST-01 system, an image guided vertebrae cannulation training system. During task execution, the computer calculates performance based metrics displaying different visual perspectives (LV, AV, APV) with the position of the instrument inside it. Finally, a report with the metrics is generated as performance feedback. MethodsA training box holds a 3D printed spine section. The computer works with two orthogonal disposed cameras, tracking passive markers placed on the instrument. Eight metrics were proposed to evaluate the surgical task’s execution performance. A preliminary study, with 25 participants divided into three groups: 12 Novices, 10 intermediates and 3 Experts, was conducted to determine the feasibility of the system to evaluate and assess the performance differences of each group using Kruskal-Wallis analysis and U Mann-Whitney. In both, Kruskal-Wallis analysis and U Mann-Whitney, a p-value ≤0.05 was considered statistically significant. ResultsWhen comparing Experts vs Novices and the three groups, the statistical analysis showed significant differences in six of the eight metrics. (Axial angle error (°), Lateral angle error (°), Average Speed (mm/s), Progress between shots (mm), Time (s), Shots) The metrics that did not show any statistically significant difference were time between shots (s), and speed between shots (mm/s). As well the average result comparison placed the Experts as the best performance group. ConclusionOn the SpineST-01 presentation, initial testing demonstrated potential for the system to practice image guided cannulation task on lumbar vertebrae. Results show objective differences between Experts, Intermediates, and Novices on the proposed metrics. Making this system a feasible option for developing basic navigation system skills, without the risk of radiation exposure and objectively evaluate task performance.

Kinematic analysis of inverted planetary roller screw considering skew error

To reveal the motion characteristics of inverted planetary roller screws under the influence of axial deviation error, the working principle of inverted planetary roller screws was elaborated, and a motion analysis model of inverted planetary roller screws based on deviation error was established. This paper analyzed the angle error, axial displacement error, and relative velocity error of the roller, and comprehensively analyzed the influence of errors and parameters on the motion state.

A new machining test to identify position-independent geometric errors of rotary axes for five-axis machine tools

A new machining test to identify position-independent geometric errors of rotary axes for five-axis machine tools

An artificial neural network based approach for predicting the proton beam spot dosimetric characteristics of a pencil beam scanning technique

Utilising Machine Learning (ML) models to predict dosimetric parameters in pencil beam scanning proton therapy presents a promising and practical approach. The study developed Artificial Neural Network (ANN) models to predict proton beam spot size and relative positional errors using 9000 proton spot data. The irradiation log files as input variables and corresponding scintillation detector measurements as the label values. The ANN models were developed to predict six variables: spot size in the x-axis, y-axis, major axis, minor axis, and relative positional errors in the x-axis and y-axis. All ANN models used a Multi-layer perception (MLP) network using one input layer, three hidden layers, and one output layer. Model performance was validated using various statistical tools. The log file recorded spot size and relative positional errors, which were compared with scintillator-measured data. The Root Mean Squared Error (RMSE) values for the x-spot and y-spot sizes were 0.356 mm and 0.362 mm, respectively. Additionally, the maximum variation for the x-spot relative positional error was 0.910 mm, while for the y-spot, it was 1.610 mm. The ANN models exhibit lower prediction errors. Specifically, the RMSE values for spot size prediction in the x, y, major, and minor axes are 0.053 mm, 0.049 mm, 0.053 mm, and 0.052 mm, respectively. Additionally, the relative spot positional error prediction model for the x and y axes yielded maximum errors of 0.160 mm and 0.170 mm, respectively. The normality of models was validated using the residual histogram and Q-Q plot. The data over fit, and bias were tested using K (k = 5) fold cross-validation, and the maximum RMSE value of the K fold cross-validation among all the six ML models was less than 0.150 mm (R-Square 0.960). All the models showed excellent prediction accuracy. Accurately predicting beam spot size and positional errors enhances efficiency in routine dosimetric checks.

Effectiveness of repeated low-level red light in myopia prevention and myopia control

Background/aimsTo compare the effects of repeated low-level red light (RLRL) treatment on axial length growth and refractive error changes in myopic and premyopic children.MethodsSubjects were assigned randomly to four subgroups:...

Modeling and analysis of elastohydrodynamic lubrication of orthogonal face gear with installation errors

Installation error is one of the most prominent factors affecting the lubrication of face gear. To analyze the lubrication performance of the face gear with installation errors, the installation error model of the orthogonal face gear transmission system is established. Then, the contact path, equivalent curvature radius, load distribution and entrainment velocity are studied using the face gear loaded tooth contact analysis (LTCA). On this basis, the lubrication governing equations of the face gear are established according to the elastohydrodynamic lubrication (EHL) theory. In addition, the oil film thickness, oil film pressure and coefficient of friction in the process of face gear drives are calculated using the method of progressive mesh densification (PMD). Finally, the effects of axis intersection angle error, axis intersection error and axial displacement error on lubrication characteristics are analyzed. The results reveal that when the axial intersection angle error and axial displacement error are negative and the axial intersection error is positive, the minimum oil film thickness of the face gear tooth surface is less than that without error. When the error values are the same, the minimum oil film thickness and coefficient of friction have larger changes with the axial displacement error than with the axis intersection error, and the contact path has a bigger movement range.

Sub-pixel marking and depth-based correction methods for the elimination of voxel drifting in integral imaging display.

Integral imaging is a kind of true three-dimensional (3D) display technology that uses a lens array to reconstruct vivid 3D images with full parallax and true color. In order to present a high-quality 3D image, it's vital to correct the axial position error caused by the misalignment and deformation of the lens array which makes the reconstructed lights deviate from the correct directions, resulting in severe voxel drifting and image blurring. We proposed a sub-pixel marking method to measure the axial position error of the lenses with great accuracy by addressing the sub-pixels under each lens and forming a homologous sub-pixel pair. The proposed measurement method relies on the geometric center alignment of image points, which is specifically expressed as the overlap between the test 3D voxel and the reference 3D voxel. Hence, measurement accuracy could be higher. Additionally, a depth-based sub-pixel correction method was proposed to eliminate the voxel drifting. The proposed correction method takes the voxel depth into consideration in the correction coefficient, and achieves accurate error correction for 3D images with different depths. The experimental results well confirmed that the proposed measuring and correction methods can greatly suppress the voxel drifting caused by the axial position error of the lenses, and greatly improve the 3D image quality.

High-precision servo control design and optimization for dicing semiconductor wafer

The dicing of semiconductor wafers is an essential component for fabricating electronic circuits. A servo control approach with high-precision and stability was designed to enhance the positioning accuracy and stability for dicing semiconductor wafers. The principal control and dicing processes were studied. The High Definition closed-loop control algorithm was designed, and the control parameters were optimized. The control performance was enhanced using the PID + Feedforward + NOTCH filter control algorithm. The error detection of linear and rotation axes was designed to compensate servo axis errors by using the laser interferometer and control card. After error compensation, the positioning accuracy and repeatability of the Y-axis were 2.031 μm and 1.889 μm. That of the C-axis were 0.00423°, and 0.00347°. The dicing experiment revealed the maximum chipping width was <10 μm and the dicing channel width was <42 μm. The designed servo control system ensured the high-precision and stable dicing of semiconductor chips.

Equivalent Mueller matrix method for 3-D axial error analysis in 2-D SoP measurement

We explored an equivalent Mueller matrix method for analyzing 3-D axial errors in 2-D polarization state measurements for the first time, to the best of our knowledge. The method treats 2-D devices with 3-D errors as a closed system, within which the transformation of a 3-D polarization field is described using a 3×3 coherency matrix and generalized Jones matrix (GJM). The equivalent 4×4 Mueller matrix of the component is numerically evaluated from the 2-D polarization field information at the input and output ports. Furthermore, our research has identified that any 3-D axial error within the polarization state analyzer (PSA) can be classified into two categories: axial alignment error (AAE) and wave-vector alignment error (WAE). For the latter case, we have introduced a concept of equal weight variance of a wave-vector as an alternative to the spiral sampling method to estimate the upper-bound of relative state of polarization (SoP) error. A simulation result shows that for the ideal bi-plate PSA, the upper-bound remains below 3% when the deviation value is less than 17.7 deg. The equivalent Mueller matrix method can be applied to analyze the 3-D errors in an arbitrary sort of PSA, and the description of 3-D transformation in this paper is simpler than a 9×9 generalized Mueller matrix and nine-element generalized Stokes vector, which has potential value in the research of vector beam generation.

Modeling and prediction of full-term thermal error in linear axis of machine tools based on MSTGCN-A

Modeling and prediction of full-term thermal error in linear axis of machine tools based on MSTGCN-A

Correction of axial length measurement error by IOLMaster 700 could improve refractive prediction accuracy in silicone oil-filled eyes.

To determine whether correcting the axial length (AL) measurement error of the IOLMaster 700 could improve the refractive prediction accuracy in silicone oil-filled eyes. This study included 265 cataract patients (265 eyes) with silicone oil tamponade who were scheduled for phacoemulsification with intraocular lens (IOL) implantation. The performances of various formulas, including Barrett Universal II, Emmetropia Verifying Optical, Hoffer-QST, Kane, Ladas Super Formula, Pearl-DGS, Radial Basis Function and traditional formulas (Haigis, Hoffer Q, Holladay 1 and SRK/T), were evaluated. The refractive prediction errors (PE) calculated with measured AL (ALmeas) and corrected AL with silicone oil adjustment (SOAL) were compared. Subgroup analysis was performed based on the ALmeas (<23 mm; 23-26 mm; ≥26 mm). Using SOAL significantly reduced the hyperopic PE of formulas when compared to ALmeas (-0.05 to 0.17 D vs 0.15 to 0.38 D, p < 0.001). After applying AL correction, all formulas showed a lower mean absolute PE (0.47-0.57 D vs 0.50-0.69 D). The percentage of eyes within ±1.0 D of PE increased from 84.91%-88.68% to 89.81%-91.32% for new formulas and from 78.11%-83.40% to 85.66%-88.68% for traditional formulas, with the use of SOAL. Subgroup analysis showed that the majority of formulas with SOAL in prediction accuracy for eyes with an AL ≥26 mm (p < 0.05). The refractive prediction accuracy in silicone oil-filled eyes was improved by correcting the AL measurement error of the IOLMaster 700, especially for long eyes.

Clinical and Genetic Landscape of Ectopia Lentis Based on a Cohort of Patients From 156 Families.

To extend the mutation spectrum and explore the characteristics of genotypes and ocular phenotypes in ectopia lentis (EL). Variants in all 14 reported EL-associated genes were selected from in-house data sets as well as literature review, and available clinical data were analyzed. Likely pathogenic variants in three genes were identified in 156 unrelated families with EL from the in-house cohort, of which 97.4% resulted from variants in FBN1, whereas the remaining were caused by variants in ADAMTSL4 (1.3%) and LTBP2 (1.3%). A comparative analysis of the in-house data and literature review suggested several characteristics: (1) a higher proportion of cysteine involvement variants in FBN1, either variants introducing or eliminating cysteine, and an earlier diagnosis age were presented in our cohort than in published literature; (2) the axial length (AL) and refractive error increased more rapidly with age in preschool EL children than normal children, and the increased rate of AL was slower in patients with surgery than those without surgery; (3) aberrant astigmatism was common in EL; and (4) worse vision and earlier onset age were observed in patients with non-FBN1 variants (all P < 0.05). Variants in FBN1 are the predominant cause of EL, with the most common cysteine involvement variants. Early-stage EL manifests refractive error but gradually converts to axial myopia through defocus introduced by lens dislocation. Aberrant astigmatism is a suggestive sign of EL. Non-FBN1 variants cause early-onset and severe phenotypes. These results provide evidence for early diagnosis as well as timely treatment for EL.

Simple implementation of aperture modulation quantitative differential phase contrast imaging

As one of the quantitative phase imaging methods, aperture modulation quantitative differential phase contrast (amqDPC) imaging has isotropic lateral resolution, being widely used in many fields such as biological cell morphology detection. However, the devices required to implement it are poorly controlled and very expensive. In addition, due to the weak phase approximation, there is a large axial phase error, and the full spectrum center pass during aperture modulation will cause distortion. Therefore, a method that enables simple and low-cost implementation of amqDPC, high axial phase accuracy, and isotopic lateral resolution is reported. Through simulations and experimental verifications, axial accuracy is greatly improved in the phase range of [0, π], and an isotropic lateral resolution of 870 nm can be achieved. In addition, experiments on transparent glass circular step sample and mouse kidney tissue slice also prove the practicability of this method. According to this study, researchers can accurately and simply measure the axial height of a slightly thick sample, which is achieved by capturing two intensity images to reconstruct a quantitative phase.

Patient Cranial Angle and Intrafractional Stability in CyberKnife Robotic Radiosurgery: A Retrospective Analysis.

Purpose: The aim of this study was to investigate whether variations in cranial angles and treatment accuracy during CyberKnife robotic radiosurgery necessitate adjustment of the margins of the planning target volume. Patients and Methods: Data from 66 patients receiving CyberKnife treatment for brain tumors were retrospectively analyzed. Patients were immobilized using a thermoplastic mask and headrest. The cranial angle was measured on planning CT and patients were divided into 2 groups: ≤10° (Group A) and >10° (Group B). Intrafractional motion was recorded using the CyberKnife tracking system over 50 min. Translational and rotational errors were compared between groups, and planning target volume margins were calculated. Results: In Group A, significant translational error differences were found along with the X-axis over time (P < .02). In Group B, significant differences occurred along with the Z-axis (P < .03). No significant rotational or 3-dimensional vector differences were found in either group. Group A had significantly lower Y-axis (P < .045) and roll axis (P < .005) errors compared to Group B. Estimated planning target volume margins in Group A were 0.56 mm (X), 0.46 mm (Y), and 0.47 mm (Z). In Group B, margins were 0.62 mm (X), 0.48 mm (Y), and 0.46 mm (Z). Margins covering 95% of intrafraction motion were 0.49 to 0.50 mm (X, Y, Z) and 0.69 mm (3-dimensional vector) for Group A, and 0.48 to 0.60 mm and 0.79 mm for Group B. With a 1-mm margin, complete coverage was achieved in Group A while 2.1% of vectors in Group B exceeded 1 mm. Conclusion: Adjusting cranial angle to ≤10° during thermoplastic mask molding provided better or similar intrafractional stability compared to >10°.

Axis alignment and error analysis of a novel rotating laser-scanning system

Axis alignment and error analysis of a novel rotating laser-scanning system

The physiological, in-vitro simulation of daily activities in the intervertebral disc using a load Informed kinematic evaluation (LIKE) protocol

Current spinal testing protocols generally adopt pure moments combined with axial compression. However, daily activities involve multi-axis loads, and multi-axis loading has been shown to impact intervertebral disc (IVD) cell viability. Therefore, integrating in-vivo load data with spine simulators is critical to understand how loading affects the IVD, but doing so is challenging due to load coupling and variable load rates. This study addresses these challenges through the Load Informed Kinematic Evaluation (LIKE) protocol, which was evaluated using the root mean squared error (RMSE) between desired and actual loads in each axis. Stage 1 involves obtaining the kinematics from six-axis load control tests replicating 20 Orthoload activities at a reduced test speed. Stage 2 applies these kinematics in five axes, with axial compression applied in load control, at the reduced speed and at the physiological test rate. Stage 3 enables long-term tests through six-axis kinematic control combined with diurnal height correction to account for the natural height fluctuations of the IVD. Stage 1 yielded RMSEs within twice the load cell noise floor. Low RMSEs were maintained during stage 2 at reduced speed (Tx:0.80 ± 0.30 N; Ty:0.77 ± 0.29 N; Tz:1.79 ± 0.50 N; Rx:0.02 ± 0.01Nm; Ry:0.02 ± 0.01Nm; and Rz:0.02 ± 0.01Nm) and at the physiological test rate (Tx:3.45 ± 1.81 N; Ty:3.82 ± 1.99 N; Tz:11.32 ± 8.69 N; Rx:0.13 ± 0.07Nm; Ry:0.16 ± 0.11Nm; and Rz:0.07 ± 0.04Nm). To address unwanted oscillations observed in longer tests (>2h), Stage 3 was introduced to enable the stable and consistent replication of activities at a physiological test rate. Despite higher RMSEs the axial error was 85.5 ± 24.27 N (equivalent to ∼ 0.16 MPa), with shear RMSEs similar to other testing systems conducting pure moment tests at slower rates. The LIKE protocol enables the replication of physiological loads, providing opportunities for enhanced investigations of IVD mechanobiology, and the pre-clinical evaluation of IVD devices and therapies.

Modeling and compensation of enhanced volumetric error of machine tools containing crosstalk errors

The error compensation method is an economical and effective method to improve the machining accuracy of machine tools. Conventional volumetric error modeling of machine tools is based on the rigid body kinematics model using 21 terms of geometric errors and assumes the geometric error of one axis is independent of other axes. However, if the error motion does not satisfy this assumption in serial machine tools, it may significantly influence the overall machine tool accuracy. This paper reveals the existence of mutual crosstalk of angular errors in coupling axes by experiments with equipping the five-degree-of-freedom (5-DOF) embedded sensor module in each axis. A new on-machine measurement method is proposed for detecting crosstalk errors of the coupling axes covering the whole coupling area. It is confirmed that the position-dependent geometric errors (PDGEs) of each axis should be modified by two-dimensional dependence. Therefore, extended from the normal volumetric error model (NVEM) that is commonly used nowadays, a novel enhanced volumetric error model (EVEM) that contains crosstalk's PDGEs is proposed. The real-time error compensation controller (RECC) embedded in CNC system kernel has been developed in collaboration with the vender by writing in the application function. The effectiveness and feasibility of the EVEM and RECC are verified by non-cutting and cutting experiments. Through comparison tests with laser interferometer on body diagonals, the accuracy improving rate of EVEM is about 10 % higher than NVEM. The real-cutting tests on the ISO10791 sample are verified by a CMM and the results show the accuracy improvement of EVEM is better than NVEM by about 20 %.

A Novel Combined Method for Measuring the Three-Dimensional Rotational Angle of a Spherical Joint.

To improve the measurement accuracy of the three-dimensional rotation angle of a spherical joint, a novel approach is proposed in this study, which combines magnetic detection by a Hall sensor and surface feature identification by an eddy current sensor. Firstly, a permanent magnet is embedded in the ball head of a spherical joint, and Hall sensors are set and distributed in the ball socket to measure the variation in the magnetic flux density when the spherical joint rotates, which are related to the 3D rotation angle. In order to further improve the measurement accuracy and robustness, we also set grooves on the ball head and use eddy current sensors to synchronously identify the rotation angle of the ball head. After the combination of two signals is performed, a measurement model is established using the RBF neural network by training, and the real-time measurement of the 3D rotation angle of the spherical joint is realized. The feasibility and superiority of this method are validated through experiments. The experimental results indicate that the measurement accuracy is substantially promoted compared to the preliminary measurement scheme based on spherical coding; the average measurement error of the single axis is reduced by 9'9″. The root mean square errors for the measurements of the 3D rotation angles in this proposed method are as follows: pitch angle α has an error of 1'8″, yaw angle β has an error of 2'15″, and roll angle γ has an error of 29'6″.

Thermal analytical modeling of machine tool structural components via dual-layer equivalence

Precision machine tools are sensitive to thermal effects. Thermal deformation of machine tool structural components can lead to changes in the relative pose between the spindle tool and the workpiece, causing thermally induced machining errors. Gaining insight into the mechanistic correlation between critical thermal condition parameters of heat sources and thermal errors in machine tools is essential to elevate the design of machine tool thermal attributes. To address this issue, this paper proposes a dual-layer equivalent analytical modeling method for characterizing the thermal properties of structural components. The construction of the temperature field analytical model for the dual-layer equivalent structure is achieved by setting and handling different interlayer heat flows and temperature boundary conditions. The dual-layer equivalent approach simplifies complex structural components into top and bottom layers, providing a more flexible and accurate capability for characterizing the thermal properties of structural components. This modeling method enables rapid prediction and evaluation of machine tool thermal characteristics. Furthermore, based on this analytical approach, the calculation method of sensitivity coefficient of thermal power to thermal error is proposed to elucidate the mapping relationship between different thermal condition parameters and thermal errors. This method facilitates the fast and accurate prediction of six thermally induced errors under various thermal conditions. Experimental results demonstrate that the key point temperature deviation predicted using the dual-layer analytical modeling method is less than 0.8 °C, and the thermally induced axial linear error deviation is less than 1.8 μm. The dual-layer analytical modeling approach introduced in this study presents a versatile technique applicable to enhancing the design and control of machine tool thermal characteristics, holding significant potential for advancing the stability of machine tools thermal accuracy.