Form Error Research Articles

Turbulence model form errors in separated flows

Physics-based uncertainty quantification is applied to a boundary layer over a flat plate with a statistically stationary separation bubble to assess sources and dynamics of model error (ME) in two-equation Reynolds-Averaged Navier-Stokes turbulence models in separated flows. Two distinct ME modes are found that correspond to the qualitative behavior of ME in a turbulent wall-bounded flow (upstream of the separation bubble) and turbulent free-shear flow (within the separation bubble), with a superposition of these ME modes in intermediate regions. A complex understanding of ME results as it changes throughout the flow, but is ultimately comprised of the elements of canonical flows.

Statistical perception of the chaotic fabrication error and the self-adaptive processing decision in ultra-precision optical polishing.

Subaperture polishing is a key technique for fabricating ultra-precision optics. However, the error source complexity in the polishing process creates large fabrication errors with chaotic characteristics that are difficult to predict using physical modelling. In this study, we first proved that the chaotic error is statistically predictable and developed a statistical chaotic-error perception (SCP) model. We confirmed that the coupling between the randomness characteristics of chaotic error (expectation and variance) and the polishing results follows an approximately linear relationship. Accordingly, the convolution fabrication formula based on the Preston equation was improved, and the form error evolution in each polishing cycle for various tools was quantitatively predicted. On this basis, a self-adaptive decision model that considers the chaotic-error influence was developed using the proposed mid- and low-spatial-frequency error criteria, which realises the automatic decision of the tool and processing parameters. An ultra-precision surface with equivalent accuracy can be stably realised via proper tool influence function (TIF) selection and modification, even for low-deterministic level tools. Experimental results indicated that the average prediction error in each convergence cycle was reduced to 6.14%. Without manual participation, the root mean square(RMS) of the surface figure of a ϕ100-mm flat mirror was converged to 1.788 nm with only robotic small-tool polishing, and that of a ϕ300-mm high-gradient ellipsoid mirror was converged to 0.008 λ. Additionally, the polishing efficiency was increased by 30% compared with that of manual polishing. The proposed SCP model offers insights that will help achieve advancement in the subaperture polishing process.

A feasibility study towards traceable calibration of size and form of microspheres by stitching AFM images using ICP point-to-plane algorithm

We present a new method for traceable calibration of size and form error of microspheres, which was realised by stitching a series of atomic force microscopic (AFM) images measured at different orientations of microspheres using the metrological large range AFM of the PTB. The stitching algorithm is achieved using an iterative closest point point-to-plane algorithm. As the AFM tip geometry is one of the most significant error sources for the developed method, it was traceably calibrated to a line width standard (type IVPS100-PTB), whose feature geometry was calibrated with a traceable route to the lattice constant of crystal silicon. Measurement setup, scan strategy, and data evaluation processes have been detailed in the paper. Measurement results show high stability and robustness of the developed method. For instance, the standard deviation of four repeated measurements reaches 5 nm, indicating promising performance.

Complete topographic measurement of the monolithic multi-surface workpiece on a cylindrical cavity

Monolithic multi-surfaces workpieces (MMSWs) are widely used in aerospace, advanced optics, and other fields. The complete topographic measurement of each sub-surface in MMSWs requires high measurement flexibility and strong space constraints since each sub-surface is located in an inner cylindrical cavity. This paper proposes a complete topographic measuring method for MMSWs based on a four-axis measuring system with a rotating single-point probe. Several basic geometric parameters of the measuring system are identified in the calibration. The mapping relation between the theoretical surface equations and measuring system coordinates is established by searching for reference points. The measurement scanning paths with different orientations are designed for each sub-surface. The iterative measurement and optimization are adopted to compensate for the measurement errors from the coupling of the probe and the four-axis measuring system. A standard sphere is measured, and the deviation of the fitting radius is below 0.5 μm. Besides, a freeform four-mirror optical system is selected as the experimental study case, where the complete topographic measurement of each sub-surface is completed on an ultra-precision machine tool. The form error and the standard deviation of each sub-surface can reach the micron level.

IntelliScan: Improving the quality of x-ray computed tomography surface data through intelligent selection of projection angles.

X-ray computed tomography (XCT) enables the dimensional measurement and inspection of highly geometrically complex engineering components that are unmeasurable using optical and tactile instruments. Conventional XCT scans use a circular scan trajectory where X-ray projections are acquired with a uniform angular spacing; this approach treats all projections as being of equal importance, in practice, some projections contain more object information than others. In this work we capitalize on this concept by intelligently selecting projections with a view to improve the quality of surface models extracted from an XCT data-set. Our approach relies on using a priori object information to select X-ray projections in which the surfaces of the object are aligned with a ray-path, thus ensuring the surface of the object is fully sampled. Results are presented showing that the proposed method is able to reduce CAD comparison errors by 16%, reduce surface form error by 3%, and improve edge contrast by 14% for a machined aluminium component.

Study on the influence of journal form and position errors on the lubrication performance of four‐recess capillary restrictor hybrid journal bearing

AbstractIn the actual working condition, due to the manufacturing errors, improper installation, load, thermal deformation or other factors can cause the journal surface to produce the form and position errors. The mathematical models are developed that takes into account the form and position errors, the lubrication performance of four‐recess capillary restrictor hybrid journal bearings with different journal tilt angles and cylindricities is studied, and the effect of eccentricity on the oil film lubrication performance is analysed. The results show that the dimensionless oil film pressure and loading capacity increase as the journal tilt angle and eccentricity increase considering journal tilt, and the friction coefficient tends to increase and then decrease. Compared with journal alignment, the oil film thickness distorts, the oil film pressure peak shifts to the edge of bearing, and the horizontal tilt has a greater impact on bearing when the journal is tilted. The oil film pressure distribution has no significant change considering cylindricity errors, while the oil film pressure value increases, the loading capacity increases and the coefficient of friction decreases as the cylindricity and eccentricity increase. The research shows that the presence of a certain cylindricity error contributes to the lubrication performance of four‐recess capillary restrictor hybrid journal bearings.

In-Orbit Performance of the GRACE Accelerometers and Microwave Ranging Instrument

The Gravity Recovery and Climate Experiment (GRACE) satellite mission has provided global long-term observations of mass transport in the Earth system with applications in numerous geophysical fields. In this paper, we targeted the in-orbit performance of the GRACE key instruments, the ACCelerometers (ACC) and the MicroWave ranging Instrument (MWI). For the ACC data, we followed a transplant approach analyzing the residual accelerations from transplanted accelerations of one of the two satellites to the other. For the MWI data, we analyzed the post-fit residuals of the monthly GFZ GRACE RL06 solutions with a focus on stationarity. Based on the analyses for the two test years 2007 and 2014, we derived stochastic models for the two instruments and a combined ACC+MWI stochastic model. While all three ACC axes showed worse performance than their preflight specifications, in 2007, a better ACC performance than in 2014 was observed by a factor of 3.6 due to switched-off satellite thermal control. The GRACE MWI noise showed white noise behavior for frequencies above 10 mHz around the level of 1.5×10−6 m/Hz. In the combined ACC+MWI noise model, the ACC part dominated the frequencies below 10 mHz, while the MWI part dominated above 10 mHz. We applied the combined ACC+MWI stochastic models for 2007 and 2014 to the monthly GFZ GRACE RL06 processing. This improved the formal errors and resulted in a comparable noise level of the estimated gravity field parameters. Furthermore, the need for co-estimating empirical parameters was reduced.

Absolute wavelength scanning interferometry for measuring the thickness of optical elements.

A technique for measurement of the thickness of optical elements using absolute wavelength scanning interferometry is presented in this paper. To achieve high-grade optical components and systems, the thickness of both planar and non-planar optical components must be measured with an accuracy of a few micrometers. The proposed technique is based on the Fizeau interferometer and interconnects data from three different tunable laser diodes yielding a long effective wavelength range and thus low measurement uncertainty. The uncertainty of the central thickness measurement ranges from hundreds of nanometers to a few microns. The method allows to measure the thickness of both flat optical elements as well as lenses with curved surfaces. Moreover, the areal information provided by the interferometry and its high angle sensitivity help to quickly and precisely align the measured component and reduce misalignment errors. The results of thickness measurements have been validated and cross-tested with other techniques. In addition to the thickness, the technique provides some additional information (wedge, surface form error) in the case of flat samples and can be easily and quickly modified (mounting of a Fizeau transmission sphere) to measure other essential parameters of optical elements. Thus, this one approach can replace many single-purpose measuring devices while maintaining high accuracy.

Freeform optics characterization with surface registration and fitting algorithms for optical point-based spatial path 3D topography metrology.

Accurate characterization of the form error for freeform optics is critical for controlled manufacturing and evaluation of optical properties. To solve the difficulty of current surface registration and fitting algorithms, and improve characterization accuracy of the form error of freeform optics for optical point-based spatial path 3D topography metrology, in this paper, improved surface registration and fitting algorithms are proposed, including a B-spline surface description of freeform optics, point orthogonal projection, registration parameter optimization, and B-spline fitting. Limited by the angular characteristics of an optical point-based sensor, the slope and reference frame of freeform optics must be flexibly adjusted, and polynomial surfaces are described and fitted as B-spline surfaces based on B-spline geometric invariance. To efficiently determine corresponding points on B-spline surfaces, the point orthogonal projection algorithm without Bezier subdivision is proposed using the first-order Newton method. Then, the iteration procedure of coordinate adjustment in sphere space using Lie algebra registration parameters is proposed to solve the difficulty of the current registration parameter optimization procedure. To fit a spatial path form error, the least squares B-spline fitting method is proposed to improve the Zernike method. Through simulation experiments, the proposed registration algorithm with good convergence can improve accuracy by one to two orders of magnitude compared with current registration algorithms. Through repeated experiments of a freeform prism, the proposed method can significantly improve the peak-to-valley and RMS accuracies compared with the stylus method, and characterize the mid-high frequency form error (about 200nm) of a freeform prism.

Ultra-precision manufacturing of microlens arrays using an optimum machining process chain.

There are still significant challenges in the accurate and uniform manufacturing of microlens arrays (MLAs) with advanced ultra-precision diamond cutting technologies due to increasingly stringent requirements and shape complexity. In this paper, an optimum machining process chain is proposed based on the integration of a micro-abrasive fluid jet polishing (MAFJP) process to improve the machining quality by single point diamond turning (SPDT). The MLAs were first machined and compensated by SPDT until the maximum possible surface quality was obtained. The MAFJP was used to correct the surface form error and reduce the nonuniformity for each lens. The polishing characterization was analyzed based on the computational fluid dynamics (CFD) method to enhance the polishing efficiency. To better polish the freeform surface, two-step tool path generation using a regional adaptive path and a raster and cross path was employed. Moreover, the compensation error map was also investigated by revealing the relationship between the material removal mechanism and the surface curvature and polishing parameters. A series of experiments were conducted to prove the reliability and capability of the proposed method. The results indicate that the two integrated machining processes are capable of improving the surface form accuracy with a decrease in PV value from 1.67 µm to 0.56 µm and also elimination of the nonuniform surface error for the lenses.

Freeform based compact receiver front-end for indoor multi-cell VLC system: Fabrication, optical characterization and associated challenges

The prospect of utilizing freeform optics to develop a more compact and smaller VLC receiver front-end is explored in this study for a multi-cell indoor environment. A novel freeform surface element (FSE) has been fabricated by an ultra-precision single-point diamond turning (SPDT) machine and characterized by the mechanical and optical profiler to investigate its potential use inside a freeform diversity receiver. A 9 dB increment in average signal-to-interference-plus-noise-ratio (SINR) is observed after third iteration while the form error reduces to 1.92 µm. The communication functionality of the fabricated FSE is also validated experimentally. The average SINR over the communication floor is computed as 109.29 dB. The fabricated freeform element is further modified to a freeform Fresnel profile for more compactness. The result shows, a substantial decrease in receiver height (2.314 mm) is possible using the proposed approach. Moreover, different fabrication challenges related with freeform Fresnel have been identified and discussed to set the future research pathway.

Extended Principal Component Analysis for Spatiotemporal Filtering of Incomplete Heterogeneous GNSS Position Time Series

When ordinary principal component analysis (PCA) is employed to analyze the position time series of a regional GNSS station network, the GNSS time series are assumed to be homogeneous, and the missing data in the time series must be restored beforehand. To directly process incomplete and heterogeneous GNSS position time series, we develop the extended PCA (EPCA) and weighted EPCA approaches to solving for the missing values based on the best low-rank approximation in the spatiotemporal domain. The proposed approaches are used to process the real GNSS position time series of 24 stations in North China spanning 2011 to 2019 and successfully extract the common mode errors (CMEs). The proposed approaches are compared with modified PCA (MPCA) and weighted MPCA, in which an additional optimization criterion needs to be introduced in the frequency domain. The results show that EPCA can extract more CMEs than MPCA for both the unweighted and weighted cases. Consequently, EPCA outperforms MPCA in reducing noise and improving the accuracy of site velocity estimates. Repeated simulation experiments show that the CMEs extracted by EPCA are closer to the simulated true values than those extracted by MPCA. When the formal errors of the time series are considered, both weighted EPCA and weighted MPCA outperform their unweighted counterparts, and the former outperforms the latter. In addition, EPCA is computationally more efficient than MPCA since fewer unknowns need to be estimated.

Application of the p-version of FEM to hierarchic rod models with reference to mechanical contact problems

The formulation of a system of hierarchic models for the simulation of the mechanical response of slender elastic bodies, such as elastic rods, is considered. The present work is concerned with aspects of implementation and numerical examples. We use a finite element formulation based on the principle of minimum potential energy. The displacement fields are represented by the product of one-dimensional field functions and two-dimensional director functions. The field functions are approximated by the p-version of the finite element method. Our objective is to control both the model form errors and the errors of discretization with a view toward the development of advanced engineering applications equipped with autonomous error control procedures. We present numerical examples that illustrate the performance characteristics of the algorithm.

Peer Assessment in German Writing Essay for 11th Graders of Language Class SMA Islam Kepanjen Malang

This study aims to describe the students' writing errors that often appear in writing essays and to describe results of the peer assessments. This research was conducted offline to 13 students of class XI Language of SMA Islam Kepanjen Malang. To collect data, a test technique was used using instrument, namely the Family theme writing test. Then, the essays were assessed by peers based on completeness of content, communicative form, and grammar. To answer the purpose of describing students' writing errors, the study shows grammatical errors often appear. In the aspect of completeness of content, most of content related to 'hobby' were not written by students. Communicative form errors are made, because they often do not use connecting words between sentences. Related to the second purpose, in peer assessment students are fully involved in identifying errors, correcting, and providing feedback. Grammatical errors also occupy the highest number of errors.

Spiral tool path optimization method for fast/slow tool servo-assisted diamond turning of freeform surfaces with highly form accuracy

Spiral tool path generation methods for ultra-precision diamond turning of freeform surfaces can significantly affect form accuracy and machining efficiency. However, there is no previous research treating the tool path generation as a multi-objective optimization problem. In this study, a multi-objective optimization method for tool path generation based on a novel surface analysis model was proposed for the first time. In this method, spiral tool path generation methods were uniformly described on the basis of the newly established surface analysis model. The relation between cutting point sampling details and the resulting form error of freeform surfaces was analyzed and simulated. Then, corresponding fitness function and constraint function models were established, and the non-dominated sorting genetic algorithm (NSGA-II) was used to solve the path optimization problem to obtain the pareto optimal solution of the cutting point sampling parameters. Next, based on the optimization results of tool path, machining simulations with experimental parameters were performed to evaluate the quality of optimized tool path. To demonstrate the effectiveness of the proposed method, turning tests of near-rotational freeform surfaces were attempted on single-crystal germanium using the optimization method and the measurement results demonstrated that the optimized tool path can achieve sub-micron form accuracy, which further verified the effectiveness of the proposed optimization method. The proposed optimization method has been further applied in the machining of larger diameter freeform optics.

A theoretical and experimental investigation into tool setting induced form error in diamond turning of micro-lens array

Micro-lens array (MLA) has been widely used for 3D imaging, etc., due to its excellent functional performances. Ultra-precision diamond turning (UPDT) offers a satisfying solution to the high-quality fabrication of MLA with sub-micrometric form accuracy and nanometric surface roughness. However, in UPDT tool setting, errors would deteriorate form accuracy as a crucial factor. This study focuses on discussing the tool setting effect on form error of MLA and proposes a new two-step tool setting method for UPDT. Firstly, a theoretical model was established for form error of MLA under tool setting errors. Moreover, a new two-step tool setting method was developed with high accuracy to control the tool setting errors. Finally, a series of experiments were carried out with different tool setting errors for the MLA fabrication, and its form error would be measured. The theoretical and experimental results are found that the proposed tool setting method is effective with a high-precision accuracy and the tool setting errors would crucially induce periodical form error at the MLA of UPDT. Significantly, the study draws up a comprehensive understanding of the tool setting effect on form accuracy of MLA in UPDT with the further improvement.

Filling the gaps: missing taxon names at the ranks of class, order and family.

The International Code of Nomenclature of Prokaryotes (ICNP) recently underwent some major modifications regarding the higher taxonomic ranks. On the one hand, the phylum category was introduced into the ICNP, which rapidly led to the valid publication of more than forty names of phyla. On the other hand, a decision on the retroactivity of Rule 8 regarding the names of classes was made, which removed most of the nomenclatural uncertainty that had affected those names during the last decade. However, it turned out that a number of names at the ranks of class, order and family are either not validly published or are validly published but illegitimate, although these names occur in the literature and are based on the type genus of a phylum with a validly published name. A closer examination of the literature for these and similar cases indicates that the names are unavailable under the ICNP either because of minor formal errors in the original descriptions, because another name should have been adopted for the taxon when the name was proposed, because of taxonomic uncertainties that were settled in the meantime, or because the names were placed on the list of rejected names. The purpose of this article is to fill the gaps by providing the missing formal descriptions and to ensure that the resulting taxon names are attributed to the original authors who did the taxonomic work.

Study on the tool setting for microlens array machining via swing cutting

Ultra-precision cutting is widely applied in the fabrication of micro-spherical lens arrays (MSLAs). However, due to the geometric limitations of the cutting tool and the degrees of freedom of the machine tool, the traditional cutting strategy cannot be employed to fabricate high-quality microscale lenses with high efficiency. In this paper, the novel tool swing cutting (TSC) method is presented to efficiently fabricate MSLAs, and its tool setting technique is introduced. First, the principle of TSC is analyzed, and the relationships between the tool parameters and machining structure are determined. In the proposed method, the tool is precisely located in the rotating center of the B-axis via charge-coupled device (CCD) camera tool setting and trial cutting. Finally, an MSLA is experimentally machined based on the proposed TSC method, and the results reveal the achievement of good machining quality with a form error of <354 nm and a surface roughness of <3.74 nm.

ANALISIS KESALAHAN LINGUITIK HASIL TERJEMAHAN GOOGLE TRANSLATE DARI TEKS BAHASA INGGRIS KE DALAM BAHASA INDONESIA

Currently, various ICT-based automatic translation machines are available to help translate foreign language texts, especially for those who are less proficient in foreign languages, one of which is Google's Google Translate. A student, especially one who is not from a non-English study program, in doing translation tends to use machine translation; “Google Translate” and take advantage of its linguistic competence. The translation is done with or without the machine, will cause errors in a certain form. The ability to translate is one of the language competencies needed by academics. This study aims to analyze linguistic errors resulting from the translation of the Google Translate machine from English into Indonesian texts for students of the Indonesian Language and Literature Study Program STKIP YPM Bangko on the syntactic and semantic aspects. This study uses the Mix Method method which combines quantitative and qualitative research methods. The results showed that most of the students were wrong in translating the given text. Most of the translation errors are in the form of syntax errors with an average percentage of 73% while semantic errors are 27%.

A comprehensive parametric study on abrasive waterjet trepanning of Al-6061 alloy

ABSTRACT Abrasive waterjet (AWJ) can be used to realize holes of any size and shape in difficult-to-machine ductile materials with negligible heat-affected zone by simply changing the jet path. In this study, the influence of various process parameters, such as waterjet pressure (P), jet traverse speed (), abrasive mass flow rate (m a ) on the AWJ-trepanned hole’s geometrical features (diameter, taper angle, profile), form characteristics (circularity error, cylindricity error), quality measures (damage region, edge radius, burr formation, uncut material, surface morphology), and material removal mechanism in Al-6061 alloy is studied. The results show that higher P and m a at lower are desirable for achieving nominal geometrical features, minimal form error, burr length, and uncut material. Damage region reduces with the decrease in P and m a at higher . Edge radius reduces with the increase in P at lower and m a . The micrographs showed that the initial damage region is uniform at higher P and lower . Better surface quality is obtained at higher P and m a as lip formation and material pile-up are minimum. Material fracture and cracks in the vicinity of the burr are observed. Based on the mean response analysis, near-optimal parameters are suggested for efficient trepanning.