Elementary Cube Research Articles

Predicting the Dynamic Parameters for Milling Thin-Walled Blades with a Neural Network

Accurately predicting the time-varying dynamic parameters of a workpiece during the milling of thin-walled parts is the foundation of adaptively selecting chatter-free machining parameters. Hence, a method for accurately and quickly predicting the time-varying dynamic parameters for milling thin-walled parts is proposed, which is based on the shell FEM and a three-layer neural network. The time-dependent dynamics of the workpiece can be calculated using the FEM by obtaining the geometrical parameters of the arc-faced junctions within the discrete cells of the initial and machined workpiece. It is unnecessary to re-divide the mesh cells of the thin-walled parts at each cutting position, which enhances the computational efficiency of the workpiece dynamics. Meanwhile, in comparison with the three-dimensional cube elements, the shell elements can reduce the number of degrees of freedom of the FEM model by 74%, which leads to the computation of the characteristic equation that is about nine times faster. The results of the modal test show that the maximum error of the shell FEM in predicting the natural frequency of the workpiece is about 4%. Furthermore, a three-layer neural network is constructed, and the results of the shell FEM are used as samples to train the model. The neural network model has a maximum prediction error of 0.409% when benchmarked against the results of the FEM. Furthermore, the three-layer neural network effectively enhances computational efficiency while guaranteeing accuracy.

Non-Diffraction Self-Acceleration Beams With Customized Transverse Intensity Profiles Based on 3-D-Printed Meta-Structure

In this article, two 3-D-printed all-dielectric meta-structures that can produce diffraction-free self-acceleration beams with different transverse intensity profiles are proposed in the microwave frequency band. The first single-layer meta-structure, combining the Fourier lens phase and cubic phase distributions, is engineered to generate Airy beams with highly asymmetric transverse intensity profiles. In order to flexibly customize the propagation trajectory and transverse spot shape, Bessel-like beams with symmetric transverse profiles along arbitrary trajectories are realized by the second compact meta-structure based on phase synthesis. Calculating the phase mask of the metasurface is the most critical part. In this work, phase-modulated meta-structures can map the phase information to height distribution of the cube elements that can be precisely controlled. To verify the validity, two prototypes are printed and measured. From the beam intensities at different cross sections along the propagation trajectory, the oscillating multilobe intensity pattern of the 2-D Airy beam and the symmetric non-spreading central main lobe of the Bessel-like beam can be observed in simulation and measurement. Besides that, two kinds of beams have transverse acceleration behavior and self-reconstruction property. Therefore, the proposed meta-structures have great potential in numerous challenging fields, like microwave power transmission, secure communication, imaging, and detection.

Generation of Periodic Nondiffractive Beams Along Straight and Curved Trajectories Based on 3-D-Printed Metasurface

In this paper, two kinds of periodic nondiffractive beams along arbitrary trajectories, including non-accelerating and self-acceleration types, are generated by 3D-printed all-dielectric metasurfaces. The first step is to produce continuous non-accelerating and self-acceleration beams, i.e. Bessel beam and Bessel-like beams. By an appropriate modification of the conical ray pattern of the standard Bessel beams, self-accelerating Bessel-like beams can be realized. In the second step, by removing some expanding phase equivalent circles in a periodic fashion and binary modulating of the phase masks, the central main lobe of continuous beams can be modified into pulsating ones. In the third step, we construct real physical models based on the derived theories. All phase coverage can be achieved by changing the height of the proposed cube element. Therefore, the final phase distribution can be mapped to height information of each unit cell. For demonstration, several proof-of-principle metasurfaces are printed and measured, two of which are used to generate Bessel beams along different straight directions, and two of which are used to produce Bessel-like beams along C-shaped and S-shaped trajectories. In all cases, during propagation, the intensity peak alternately switches its position between the main lobe and the outing rings. Meanwhile, the measured trajectories are highly consistent with the predefined ones. The proposed metasurfaces are expected to be utilized in numerous applications like secure communication.

A novel micromorphic approach captures non-locality in continuum bone remodelling

In continuum bone remodelling, bone is considered as continuous matter on the macroscale. Motivated by i) the underlying trabecular microstructure of bone resulting in size-dependence and ii) the non-local characteristics of osteocyte mechanosensing, a novel phenomenological approach based on a micromorphic formulation is proposed. Via illustrative benchmark examples, i.e. elementary unit cube, rod-shaped bone samples, and a 3D-femur sample, the novel approach is compared to the established local formulation, and the influence of the characteristic size of the microcontinuum and the coupling between macro- and microscale deformation is analysed. Taken together, the interaction between continuum points at the macroscale and their neighbourhood is effectively captured by the micromorphic formulation thus influencing the resulting distribution of nominal bone density at the macroscale.

A comprehensive study on size-effect, plastic anisotropy and microformability of aluminum with varied alloy chemistry, crystallographic texture, and microstructure

Fabrication of microparts with large aspect-ratio and complex shapes remains a huge challenge for industries and microforming is a potential solution to manufacture such microparts. However, similarity in specimen-deformation and microstructural length scales during microforming results in size effect, leading to unpredictable plastic behavior and increased process scatter. One approach to counter size effect is by engineering suitable microstructure in the material. In the present work, three grades of Al (AA1070, AA5083, AA2014) with unique alloy chemistry and microstructural profile are processed by cryorolling (CR) to 95% thickness reduction. By imparting controlled postprocess annealing on the CR materials, three distinctive microstructures – (i) ultrafine grained (UFG) with average grain size around 1 μm, (ii) fine grained (FG) with average grain size near to 5 μm, and (iii) coarse grained (CG) with approximate average grain size of 20 μm are engineered. The influence of alloy chemistry, grain boundary engineering and crystallographic texture on microformability are studied. For pure Al (AA1070), the UFG and FG microstructures show superior microformability than the CG counterparts. The equiaxed UFG grains present in these microstructures mitigate the size effect abnormalities by increasing the number of grains in the deformation volume and uniformly distributing the complex microforming strain via grain boundary mediated plasticity. Their corresponding texture containing strong Copper mixed with scattered Cube elements promotes in-plane strain condition and high resistance to localized thinning. Also, the material shows near-zero planar anisotropy that leads to a homogenous in-plane strain distribution. Unlike pure Al, the UFG and FG Al alloys suffer from increased strain localization due to presence of solute clouds and nanoprecipitates. They influence strain-aging (Portevin–Le Chatelier effect), strain gradient hardening phenomenon, and shear propensity during failure of the Al alloys. A composite texture consisting of a combination of Brass, Dillamore, S, and β-fiber elements in the Al alloys is found to be detrimental to their microformability. The Dillamore texture is contributed by formation of adiabatic shear bands during deformation of Al alloys.

Effects of Wall Topology on Statistics of Cube-Roughened Wall Turbulence

In this work, we carried out roughness-resolved direct numerical simulations of cube-roughened turbulent channel flows to investigate the effects of aligned and staggered arrangements, element spacings, and element orientations on the statistics of rough-wall turbulence. The results show that the equivalent sandgrain roughness, Reynolds stresses and dispersive stresses are affected by element spacings and arrangements in different ways depending on the cube orientations. Placing the roughness elements in a staggered way in general increases the equivalent sandgrain roughness, unless when the element–element interaction is insignificant for the cube orientation with wakes of short length. As for the Reynolds normal stresses and the streamwise component of the dispersive stresses (both are normalized by the total friction velocity), placing the cube elements in a staggered way decreases their maximal values when compared with the aligned arrangements. As for the effects of element spacing on the equivalent sandgrain roughness and the maximums of the Reynolds normal stresses, similar trends are observed for different element orientations and arrangements when increasing the element spacing l/r (where r is the cube height) from 2.0 to 2.8. When further increasing the element spacing l/r from 2.8 to 3.5, however, different trends are observed for different element orientations. As for the dispersive stresses, greater maximal values of their streamwise components are observed for larger element spacing for all the considered cube-roughened surfaces. For the turbulence statistics in the wake of the cube element, certain similarities are observed for different element spacings.

Order, disorder, and monopole confinement in the spin- 12 XXZ model on a pyrochlore tube

We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction $J_z$ and a transverse exchange interaction $J_{x}$, on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the system. When $J_z$ is antiferromagnetic ($J_{z}>0$) and $J_x$ is ferromagnetic ($J_{x}<0$), we find a transition from a spin liquid to an XY ferromagnet, which has power-law correlations at $T=0$. For $J_{z}<0$ and $J_{x}>0$, spin-two excitations are found to have lower energy than spin-one at the transition away from the fully polarized state, showing evidence for incipient spin-nematic order. When both interactions are antiferromagnetic, we find a non-degenerate ground state with no broken symmetries and a robust energy gap. The low energy spectra evolve smoothly from predominantly Ising to predominantly XY interactions. In the spin-liquid regime of small $|J_{x}|$, we study the confinement of monopole-anti-monopole pairs and find that the confinement length scale is larger for $J_x<0$ than for $J_{x}>0$, although both length scales are very short. These results are consistent with a local spin-liquid phase for the Heisenberg antiferromagnet with no broken symmetries.

Parametric sub-structuring models of large space truss structures for structure/control co-design

Modern and future high precision pointing space missions face increasingly high challenges related to the widespread use of large flexible structures. The development of new modeling tools which are able to account for the multidisciplinary nature of this problem becomes extremely relevant in order to meet both structure and control performance criteria. This paper proposes a novel methodology to analytically model large truss structures in a sub-structuring framework. A three dimensional unit cube element has been designed and validated with a Finite Element commercial software. This model is composed by multiple two-dimensional sub-mechanisms assembled using block-diagram models. This constitutes the building block for constructing complex truss structures by repetitions of the element. The accurate vibration description of the system and its minimal representation, as well as the possibility of accounting for parametric uncertainties in its mechanical parameters, make it an appropriate tool to perform robust Structure/Control co-design. In order to demonstrate the strengths of the proposed approach, a structure/control co-design study case is proposed and solved using structured robust H∞-synthesis. The objective is to optimize the pointing performances of an antenna, minimizing the perturbations coming from the Solar Array Driving Mechanisms (SADM) of two solar panels, performing active control by means of multiple Proof Mass Actuators (PMA), and simultaneously reduce the mass of the truss-structure which connects the antenna to the main spacecraft body.

Hybrid Modeling of Position-Dependent Dynamics of Thin-Walled Parts Using Shell Elements for Milling Simulation

Abstract This article presents a hybrid model to update the position-dependent structural dynamic parameters of thin-walled workpieces as the metal is removed during machining. The initial workpiece is modeled by shell elements, and its full stiffness and mass matrices are used to solve the eigenvalues and mode shapes to predict the frequency response function (FRF) at a fixed location. The model is calibrated using the experimentally measured FRF, which reduces the errors contributed by the uncertainties in the material properties and damping values. The optimized finite element (FE) model is then perturbed at discrete cutting locations to obtain the updated natural frequencies and mode shapes of the part without solving the computationally prohibitive eigenvalue problem. The accuracy of the model is further improved by using either full FE solutions or experimental measurements of FRFs at a few intermediate steps which reduce the accumulated perturbation errors along the tool path. The proposed method is verified in five-axis milling of a thin-walled twisted fan blade. It is shown that using shell elements reduces the computation effort by ∼20 times compared to the conventional three-dimensional (3D) cube elements. The experimental calibration of the numerical model at a few discrete locations reduces the prediction error of natural frequencies by about 50%.

Optimized Mass and Stiffness Matrices for Accurate and Efficient 3D Acoustic Wave Modeling

AbstractNumerical modeling of the 3D acoustic wave equation regularly faces a trade‐off between accuracy and efficiency. Usually, an improved computational efficiency leads to a compromised numerical accuracy, in which the numerical dispersion error increases. Such a trade‐off is commonly reported for the finite difference methods, and the consistent, lumped, eclectic finite element matrices, and the high‐order spectral element methods. Therefore, we present a methodology that simultaneously optimizes both the accuracy and the computational efficiency of the finite element method for modeling the 3D acoustic wave equation in the frequency domain. The numerical dispersion objective function is derived and minimized for a tri‐linear interpolation function of a cube element in terms of the mass and the stiffness matrices. With four grid points per wavelength sampling, for less than 0.5% error in velocities, the optimized modeled solutions outperform the results from extant approaches. Numerical experiments with the homogeneous, 3D unbounded 2‐layer and the 3D Society of Exploration Geophysicists salt velocity models reveal that the optimized accuracy is persistent across all source‐receiver offsets, a performance observably absent from other finite element matrices. The optimized matrices are not only useful for numerical modeling, but are also readily available for accurate computation of the sensitivity matrices of the density and the bulk modulus parameters for the multi‐parameterization inversion.

The Construction of the Origami Level-n Menger Sponge Complement by the PJS Technique

In 2015, the author developed a new origami technique, called PJS technique (where PJS stands for “pleat and join strips”), by which we can construct polycubes, that are polyhedrons composed of elementary cubes, called units, connected face to face. Each strip, pleated in squares, has to cover four faces of a tower of stacked units, called a segment, having as length the number of units that form the tower. Each unit is composed by weaving together three paper strips in the three spatial directions and the length of each strip depends on the length of the segment in each respective direction. The PJS technique allowed the author to build, at the end of 2016, the first specimen of a level-4 origami Menger sponge and three yeas later, the first level-3 complement model. In this paper, we give a formula to compute the number of segments that make up a level-n Menger sponge complement in all directions and consequently, the number of modules needed for each length to build this polycube with the PJS technique.

The magical number four in children’s mental rotation of cube aggregates.

We investigated mental rotation in children by systematically varying the adult cube aggregate's set size, rotation angle, and picture/depth plane rotations in a new test. Eighty 4- to 11-year-old mainly middle-class children (British Indian and British African majority and white minority; 40 girls and 40 boys) were assessed using the new matching-to-sample Colored Mental Rotation Test (CMRT) and, for comparison, the Raven Colored Progressive Matrices Test (RCPM). A high Cronbach's alpha of .94 and the Rasch model demonstrated item homogeneity of the CMRT. As expected, there were main effects of age showing increases in accuracy and of sex as boys outperformed girls. A main effect of set size showed that from age four until age 10 as four-cube aggregates proved to be the most economical three-dimensional (3D) object for mental rotation. Several higher-order interactions all involved four-cube aggregates, for example, 3D cube element protrusions had the largest effect in the four-cube-aggregate. We thus suggest that the magical number four (Cowan, 2001) as an attentional limit may also be valid in mental rotation and linked to the 'Good Gestalt' design of the four-cube aggregate. The cross-validation of CMRT with the RCPM showed high correlations increasing from .69 in 4- to 5-year-olds to .77 in 10- to 11-year-olds. Interestingly, 4- to 5-year-olds girls scored higher in the Raven test of nonverbal reasoning than in the CRMT scores with 3D cube aggregates demonstrating the particular complexity of 3D pictorial space. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Analysis of molecular bonds by the spectrum of nitrogen atoms in order to optimize the synthesis of mineral fertilizers

The model of the structure of the crystal cubic lattice proposed by the authors takes into account the presence of short and long diagonal bonds passing along the faces and through the center of the elementary cube. The mechanism of energy distribution between two and three valence electrons of the N atom in the ground and excited states is described. It is shown that the optical spectrum of the N atom is mirrored on the set of energies of the 2p2 term, called the spectral memory of the nitrogen atom by the authors. The mechanism of “trigger of excitation” of N atoms is described for the first time. The optical spectrum of N atoms determines the energies of the FCC → HCP phase transitions; solid → liquid phase of the hcp; boiling and melting points. The error in calculating the temperatures of phase transitions is ± 3.3%, and the density at the boiling and melting points is not more than 1%.

How to implement user-defined fiber-reinforced hyperelastic materials in finite element software

Finite element modeling is often used in biomechanical engineering to evaluate medical devices, treatments and diagnostic tools. Using an adequate material model that describes the mechanical behavior of biological tissues is essential for a reliable outcome of the simulation. Pre-programmed material models for biological tissues are available in many finite element software packages. However, since these pre-programmed models are presented to the user as a black box, without the possibility to modify the material description, many researchers turn to implementing their own material formulations. This is a complex undertaking, requiring extensive knowledge while documentation is limited.This paper provides a detailed description, at the level of the biomedical engineer, of the implementation of a nonlinear hyperelastic material model using user subroutines in Abaqus®, in casuUANISOHYPER_INV and UMAT. The Gasser-Ogden-Holzapfel material model is used as an example, resulting in four implementation variations: the built-in implementation, a UANISOHYPER_INV formulation, a UMAT with analytical tangent stiffness formulation and a UMAT with numerical tangent stiffness formulation. In addition, three different element formulations are used: a continuum compressible, a continuum incompressible and a plane stress incompressible. All cases are thoroughly verified by applying a series of deformations on a single cube element and by simulating an extension-inflation experiment with non-homogeneous deformations and multiple elements. In these test cases, stresses, displacements, reaction forces, the required number of iterations and the total CPU time were compared.The results show that the four implementation variations are very similar, with total relative errors between 10−3 and 10−15, number of iterations that varied by maximum one iteration, and a comparable CPU time. In addition to this detailed overview, the user subroutines are added as supplementary material to this tutorial, which can be used as the ideal starting point for biomechanical engineers to implement their own material models at different levels of complexity.

Strong cube texture of super-high tungsten Ni–W alloy substrates used in REBCO coated conductors

Biaxially textured super-high tungsten Ni–W alloy substrates have been fabricated through the composite substrate method in view of coated conductor applications. The tungsten content exceeds 10% in the obtained substrates. The excellent super-high tungsten substrate (Ni10W) had a strong cube texture consistent with commercial Ni5W and better than Ni8W or Ni9W substrate. Furthermore, yield strength ∼310 MPa (twice of Ni5W) and saturation magnetization of only 4% to that of Ni5W at the temperature of 77 K was calculated for Ni10W substrate. The novel Ni10W substrate with strong cube texture and negligible magnetization is best suited to be utilized for 2nd generation coated conductor REBCO. It can significantly improve the progress of using the RABiTS route in the fabrication of REBCO tapes. Meantime, the mechanisms of the cube evolution and elements diffusion in super high tungsten substrate are also studied.

Effect of potassium for cesium replacement in atomic level structure of potassium cobalt hexacyanoferrate(II)

Abstract Potassium cobalt hexacyanoferrate(II) [K2CoFe(CN)6] is an extremely selective ion exchanger for cesium ions. To examine the atomic level background for the selectivity a computational structural study using DFT modelling was carried out for K2CoFe(CN)6 and for products where Cs has replaced K in the elemental cube cages closest to the surface. In the K-form compound the potassium ions are not in the center of the Co–Fe–CN elementary cube cages closest to the surface but locate about 140 pm from the cube center towards the surface. When cesium ions are exchanged to these potassium ions they locate much deeper from the surface, being only about 70 pm upwards from the cube center. This apparently leads to much stronger bonding of cesium compared to potassium. Once taken up into the outermost cube cages on the surface of the crystallites cesium ions are not able to penetrate further since they are much larger than the electron window between the cubes. Furthermore, they are not able to return to the solution phase either leading to a practically irreversible sorption.

Predicting the dynamics of thin-walled parts with curved surfaces in milling based on FEM and Taylor series

The effect of material removal on workpiece dynamics has a great influence on suppressing resonance and regenerative vibrations in milling of thin-walled structures. Although some works have been done to obtain the varying dynamics of the workpiece, many researchers take plate structures as research objects. In this paper, a method based on FEM and Taylor series is proposed to predict the time-varying dynamics of thin-walled blade structures in milling. The input data in the method is the mass and stiffness matrices of the initial workpiece and the change of the matrices caused by material removal. The initial matrices can be obtained through the FEM model established by the mechanical analysis of the eight-node shell element, and the change of the matrices can be obtained by a third-order Taylor series. In comparison with three-dimensional cube elements, the shell elements can reduce the number of degrees of freedom of the FEM model by 74%, which leads to about 9 times faster computation of the characteristic equation. Meanwhile, the proposed method eliminates the necessities of re-building and re-meshing the FEM model at each cutting position, then the computational efficiency of workpiece dynamics is improved. Finally, the result of experiments shows that the maximum prediction error of the proposed method is about 4%.

The method of strengthening the church building in terms of the planned mining exploitation

This article describes the method of strengthening a church building in Ruda Śląska against predicted effects of mining exploitation. The building had been already exposed to effects of 22 mining incidents which significantly damaged walls and vaults. Therefore, it was decided to strengthen the building before new exploitation works. Strengthening works included longitudinal walls support with the tendon system built over the vault support. Additionally, ribs were strengthened by suspending them to new reinforced concrete ribs placed over the existing ones. And precast concrete cube elements were used in new ribs.

Optimisation of the scintillation light collection and uniformity for the SoLid experiment

This paper presents a comprehensive optimisation study to maximise the light collection efficiency of scintillating cube elements used in the SoLid detector. Very short baseline reactor experiments, like SoLid, look for active to sterile neutrino oscillation signatures in the anti-neutrino energy spectrum as a function of the distance to the core and energy. Performing a precise search requires high light yield of the scintillating elements and uniformity of the response in the detector volume. The SoLid experiment uses an innovative hybrid technology with two different scintillators: polyvinyltoluene scintillator cubes and 6LiF:ZnS(Ag) screens. A precision test bench based on a 207Bi calibration source has been developed to study improvements on the energy resolution and uniformity of the prompt scintillation signal of antineutrino interactions. A trigger system selecting the 1 MeV conversion electrons provides a Gaussian energy peak and allows for precise comparisons of the different detector configurations that were considered to improve the SoLid detector light collection. The light collection efficiency is influenced by the choice of wrapping material, the position of the 6LiF:ZnS(Ag) screen, the type of fibre, the number of optical fibres and the type of mirror at the end of the fibre. This study shows that large gains in light collection efficiency are possible compared to the SoLid SM1 prototype. The light yield for the SoLid detector is expected to be at least 52±2 photo-avalanches per MeV per cube, with a relative non-uniformity of 6 %, demonstrating that the required energy resolution of at least 14 % at 1 MeV can be achieved.

Effect of curing temperature on the behaviour of UHPFRC at elevated temperatures

Ultra-high performance fibre reinforced concrete is one of the construction materials that is still in need of more research to evaluate its performance under fire, particularly regarding explosive spalling. In this study, the effect of curing temperature on the fire resilience of ultra-high performance fibre reinforced concrete (UHPFRC) has been tested. In particular, the influence of cold (20 °C) and hot (90 °C) water curing temperatures on the performance of UHPFRC exposed to elevated temperatures has been investigated. Beams, cured in cold water and in hot water were tested under the standard ISO 834 heating regime. The test results showed that the beam cured in hot water spalled significantly more than the beam cured in cold water. The study further investigated the influence of curing temperature on the residual strength of UHPFRC (containing both steel and polypropylene fibres). The cube elements were heated at eight selected temperatures between 200 °C and 900 °C. The cold-cured concrete exhibited higher relative residual strength at all temperatures. The results further showed that UHPFRC have high strength retention up to 600 °C. The residual peak strength for both the cold and the hot-cured occurred at 400 °C.