Finite Element Method Simulation Results Research Articles

Design and measurement of three-dimensional uniform-field coils based on swarm intelligence algorithms under ferromagnetic boundaries

Combination systems of high permeability magnetic shields and coils are widely used in fields such as the magnetic field standard metrology and the zero magnetic room construction. To solve the problem that the magnetic field of uniform-field coils under the ferromagnetic boundary of magnetic shields is difficult to design precisely and the uniformity is difficult to improve, three-dimensional uniform field coils are designed based on the magnetic field model of coils under the ferromagnetic boundary using the target-field method (TFM), and the weight coefficient vectors determining the coils’ structure are optimized using intelligent optimization algorithms, which improves the uniformity of the magnetic field in the target region by 2 orders of magnitude through whale optimization algorithm (WOA). Then, the radial WOA-TFMUFY coil and the axial WOA-TFMUFZ coil are designed considering sidewall optical holes, and their magnetic field distribution is analyzed and verified under different permeabilities and axial opening sizes of the shield. Compared to the traditional saddle coil and Lee-whiting coil, the maximum magnetic field non-uniformity in the target uniform field region is reduced by 82.2 % and 92.8 % for the WOA-TFMUFY coil and WOA-TFMUFZ coil. The maximum relative errors between the measured magnetic field generated by the designed coils and the finite element method (FEM) simulation results are no higher than 2.2%. This novel method can provide more precise and uniform magnetic field metrology standard elements.

Designing and experimental validation of single-layer mixed foil resonator acoustic membrane to enhance sound transmission loss (STL) within low to medium frequency range

This study presents a novel design for an acoustic membrane structure that employs a parallel-arrangement of mixed foil sound resonators to improve sound absorption and insulation capabilities in the low to medium frequency range. The structure is composed of a single layer of parallel-arranged mixed foil wedge-shaped coffers and a bottom flat panel separated by an air cavity. The mixed thickness-based foil resonators are treated as a combination of independent resonators with unique resonance frequency, resulting in improved sound insulation with broadband efficacy. A comprehensive parametric analysis was carried out using the Finite Element Method (FEM) based COMSOL Multiphysics, yielding the anticipated outcomes. The study revealed that the broadband Sound Transmission Loss (STL) can be tailored by varying the thickness of the top and side walls, the bottom plate thickness, and the depth of the rear air cavity. The findings suggest that existing acoustic membrane design can be highly efficient, achieving, and average STL of over 40 dB ∼ 45 dB across the low to medium frequency range of 500 Hz to 3000 Hz. The experimental validation was conducted in an anechoic chamber, and the results were found to be in close agreement with the FEM simulation results. In comparison to conventional uniform foil sound resonator based acoustic membrane structure, this mixed single-layer square wedge-shaped foil resonator based acoustic membrane exhibits outstanding sound insulation performances in the low to medium frequency range, owing to its lightweight structure and availability of conventional manufacturing techniques. This advanced version of the foil sound resonator based acoustic membrane holds immense promise for the use in acoustics and noise control applications across domestic, commercial, and industrial environments.

Experimental and numerical evaluation of a rubber seal in a vacuum suction pad for an automatic mooring system

The utilization of automatic mooring systems is under extensive interest with the growing technological demands for autonomous ships and smart ports. A vacuum suction pad with a rubber seal, which endures external loads to the moored ship, such as mooring forces, is a critical element in an automatic mooring system. To develop a high-performance automatic mooring system, a vacuum suction pad and a rubber seal need to be thoroughly designed, manufactured, and evaluated. This work demonstrates a protocol for evaluating the performance of a vacuum suction pad through both simulation and experimental testing. Uniaxial tensile testing was conducted to understand the mechanical behavior of a rubber seal. Stabilized stress-strain curves were utilized to find an optimal strain energy density function model and to extract material parameters for 3D finite element method (FEM) simulations. The FEM simulations were conducted to calculate strain distributions, contact status and the maximum load capacity, and along with the FEM simulation results, experimental evaluations of the vacuum suction pad were designed and conducted against static and cyclic loads. Based on the simulation and experimental results, we can conclude that the vacuum suction pad can maintain the stable suction at least up to 25 kN suitable for the use in automatic mooring systems.

Measurement of the roller tilt angle in a double-row tapered roller bearing with strain gauges

Roller tilting can cause severe roller-edge loadings, leading to serious local heat generation or early failure of the rolling element bearing. Therefore, it is significant to obtain the roller tilt angle in real service for evaluating the bearing performance. A measurement method was proposed to determine the roller tilt angle by detecting the variation of the strain amplitude difference between two axial positions of the bearing outer surface with a notched housing. An experimental system was developed to investigate the roller tilt angles in a double-row tapered roller bearing and demonstrate the effectiveness of the proposed measurement method by conducting a comparison with the finite element method (FEM) simulation results. The experimental roller tilt angles agree well with the FEM results. Compared with other measurement methods, the proposed method offers a potential approach to achieve the in-situ and non-destructive measurement of the roller tilt angles for long-term monitoring.

Implementation of Finite Element Method Simulation in Control of Additive Manufacturing to Increase Component Strength and Productivity

Additive manufacturing (AM) technologies are becoming a global phenomenon in the manufacturing industry. The progressiveness of additive manufacturing lies in its universality. AM makes it possible to produce parts with complex shapes from different materials without any tools, using only one device. Complex and time-consuming production preparation is eliminated by using AM. It is used in a wide range of industries. Although additive manufacturing is a progressive technology, the currently applied conservative approach has significant limits. The presented work focuses on the development of a new methodology for controlling the AM process. This methodology is based on the outputs of the strength simulation of a specific component through the finite element method (FEM) and their implementation in the printing software of the production equipment. The developed algorithm for controlling the AM process consists of a sequence of successive steps. The designed CAD model of the component is subjected to FEM simulation in order to analyze the von Mises stress in the entire volume of the loaded component. Stresses are distributed asymmetrically in the volume of the component due to the shape and nature of the load. The results of the FEM analysis allow the definition of the volumes in the component with different levels of infill geometry and infill density based on different levels of stress. The FEM simulation also serves to define the effective fiber orientation. The goal of implementing FEM simulation into the building structure of the component is to achieve a symmetrical distribution of stresses in the entire volume. Through the symmetry of internal stresses, it is possible to obtain more efficient production with high productivity and component strength. The work also deals with experimental research on the effect of the building structure on flexural strength. The results of FEM simulation and experimental research are integrated into the developed slicer software to design a layering of the model and the setting of technological and material parameters of printing. This progressive approach makes it possible to generate data for 3D printing based on FEM analysis of components to obtain an optimized printed structure of components and optimized technological and material parameters with regard to maximizing the strength of components and minimizing production times and costs.

Regional evaluation method of ground stress in shale oil reservoirs-taking the Triassic Yanchang formation in northern Shaanxi area as an example

Estimating in-situ stress in shale oil reservoirs is critical for predicting hydraulic fracture height. However, the varied longitudinal lithology and transverse isotropy challenge the regional evaluation of ground stress. A new method based on the Kaiser effect method and the Sn Model was proposed to evaluate regional ground stress from point to point. Kaiser tests obtained the regional tectonic stress coefficients. Combined with the dynamic and static transformation of elastic parameters, the Sn ground stress calculation model suitable for the Northern Shaanxi Area was constructed. According to the calculation results of ground stress in the Chang 7 section of 600 wells in this region, the plane distribution maps of maximum horizontal ground stress (SH) and the difference between SH and Minimum horizontal stress (Sh) were drawn. It was found that the SH in this area was between 20 and 60 MPa, and the So was between 2.6 and 8.8 MPa. Compared with the 3D finite element method simulation results, the forward modeling results coincided well with the inversion results in this research. The causes of the plane distribution of ground stress in the Chang 7 section were explained by regional tectonic stress and paleo topography. It was found that the movement of plate and shell and deposition were critical factors of regional ground stress distribution. The research results provide a reference for further integration of geologic and engineering in evaluating shale oil reservoirs.

Machine learning-driven optimization design of hydrogel-based negative hydration expansion metamaterials

Hydrogel-based negative hydration expansion (NHE) metamaterials are composite structures composed of responsive hydrogels and polymers, and their properties depend on their unique structures. In this paper, an optimization method based on the combination of the back-propagation neural network (BPNN) and the multi-population genetic algorithm (MPGA) is developed to rapidly design isotropic and anisotropic hydrogel-based metamaterials with specific NHE effects. In this method, several dimensionless design parameters are introduced to describe the structural characteristics of the metamaterial. The initial dataset is constructed based on the finite element method simulation results, and the mapping relationship between the design parameters and the equivalent linear strain is constructed by the BPNN, and the metamaterial with specific effect is efficiently optimized by combining the MPGA. The method is proved to have high accuracy and efficiency, and is applied to design many novel 2D and 3D metamaterials. The 3D metamaterial designed by this method has an ultra-large NHE ratio about 82 %. Compared with the topology optimization method, this method can significantly reduce the amount of computation, and can effectively avoid falling into the local optimum. The results show that the optimization method based on machine learning is an efficient means to design hydrogel-based metamaterials.

Behavior of oxide regrowth during the selective Si3N4 etching process on 3D NAND structures using finite element computational simulations

Oxide regrowth should be suppressed during the etching of silicon nitride, which is used to fabricate three-dimensional Not AND (3D NAND) devices. This requires a detailed understanding on the mass-transfer characteristics of Si3N4 etching byproducts that cause oxide regrowth. Finite element method (FEM) simulations are performed to investigate the mass transfer of Si3N4 etching byproducts (EBSi3N4) and oxide regrowth during Si3N4 etching on a 3D Si3N4/SiO2 multistack. In particular, the concentration profiles of the byproducts under various etching conditions, such as different numbers of Si3N4/SiO2 multistacks, diffusion coefficients of the byproducts, etching rates of Si3N4, and initial concentrations of Si-based additives, are monitored. Furthermore, the in-situ generation of oxide regrowth under various etching conditions is evaluated. Consequently, an increase in the diffusion coefficient of the byproducts is proposed as the most promising method for suppressing oxide regrowth during Si3N4 etching on high-numbered 3D NAND stacks. The FEM simulation results are strongly supported by data from Si3N4 etching experiments on Si3N4/SiO2 multistacks.

The effect of surface roughness on the viscoelastic energy dissipation in a particle–wall collision

The particle collision on a wall with roughness is common in nature and industries, but not well understood yet. The presence of surface roughness greatly increases the complexity of local contact and makes it difficult to predict the energy dissipation by analytical models. In this work, we investigate the energy dissipation in a dynamic particle–wall collision with regular hemisphere roughness. The finite element method (FEM) with the standard linear solid model is used to solve the problem of non-ideal geometry, and extract the law of energy dissipation due to viscoelasticity. The results show that with the existence of surface roughness, the total viscoelastic dissipation is lower than that for a smooth surface, showing a higher restitution coefficient compared to the smooth surface. Based on the maximum number of asperities that particle contacts, the dynamic collisions can be categorized as the single-contact mode and multiple-contact mode. The variation of the total energy dissipation shows opposite trends with the roughness height in the two different modes. The collision time is recognized as the key to predict the total energy dissipation. Based on FEM simulation results, a piecewise correlation is established to estimate the Hertzian collision time with regular roughness. Finally, a correlation is proposed for the total energy dissipation in a viscoelastic particle–wall collision with regular roughness, which only takes the dimensionless relaxation time as the parameter. Covering different roughness heights, particle sizes, densities, relaxation times, and Young’s modulus, all the data are well correlated with the predicted curve.

A piezoelectric–electromagnetic hybrid energy harvester inspired by flapping motion of the Diptera insect

Low-frequency vibration is widespread in nature. Vibration energy harvesting is considered to be a reliable and sustainable method to achieve continuous power supply. It is a feasible method to design an energy harvesting system of the bio-inspired mechanical structure to improve the efficiency of energy harvesting. A hybrid energy harvester piezoelectric–electromagnetic that mimics the flapping wing motion of the Diptera insect. The biomimetic energy harvesting device consists of two piezoelectric cantilever beams structure with the mass block installed, which mimics the flapping movement mechanism of the Diptera insect. The intermediate part of this harvester inspired by the insect skeleton and muscle structure of the Diptera insect is composed of magnetic levitation coupled repulsion structure, which is easily affected by vibration and changes greatly, to realize electromagnetic energy harvesting. The ‘click’ mechanism of the Diptera insect is constructed by storing energy in springs to improve the performance of energy harvesting devices. The hybrid energy harvesting device realizes piezoelectric–electromagnetic energy harvesting with multiple energy outputs at one excitation input. A dynamic model of the proposed energy harvester is constructed based on the electromechanical coupling characteristics. The modal analysis and structure optimization of this device is realized by the finite element method (FEM). The FEM simulation and experimental results can verify that under the low-frequency excitation of 3 Hz, the maximum output power of the designed harvester reaches 12.33 mW in the low-frequency environment.

Analysis of BLDC Electric Motor Shaft Treatment Model Using Numerical Method

This research studies the shaft strength of a BLDC electric motor. A Shaft is one of the components in a rotary engine and functions to transmit power. The design calculation is needed to determine the effect of the strength of the material being treated. The strength analysis of the shaft used FEM (Finite Element Method). The shaft is modeled on the manufacturing design and tested by numerical simulation with Ansys Mechanical 14.5-BRIN commercial license software. The static simulation used a structural statics module with static and dynamic load input. The research method comparing the results of FEM simulations with two different types of materials is determined. Based on the simulation parameters, the selected material types are JIS S45C tempered and AISI 1045 cold-drawn. The simulation results represent the maximum stress (von Mises) and total deformation. The deformation value of S45C tempered material is slightly higher than that of AISI 1045 cold drawn. However, both materials have the same maximum von Mises stress.

Numerical Simulation of Crack Condition in Forging Products of M50 Bearing Steel Based on Processing Map Theory

The microstructure of forged products significantly impacts their properties, and defects or carbide distribution are not visible to the naked eye. Isothermal compression tests on M50 steel with a Gleeble 3500 tester were conducted to study microstructure behavior during forging. Tests examined the hot deformation behavior within a temperature range of 900–1200 °C and a strain rate range of 0.01–10 s−1. Power dissipation efficiency (η) and flow instability (ξ), which are crucial processing map parameters, were employed to analyze the high-temperature deformation behavior of M50 steel. The 3D processing map determined the optimum forging conditions, indicating that hot working should start at an initial temperature of 1050 °C or higher and a strain rate of 1 s−1, decreasing the strain rate and temperature as the strain increases. The 3D power dissipation efficiency map displayed an average value of 0.43 or higher at a strain rate of 0.1 s−1 and a temperature of 1150 °C before reaching a strain rate of 0.8. The Finite Element Method (FEM) simulated results, revealing ξ and η distributions, and confirmed that microstructure observation during deformation matched the hot forging parameters. This approach can effectively predict microstructure changes during hot forging.

Structural Mechanical Properties of 3D Printing Biomimetic Bone Replacement Materials

One of the primary challenges in developing bone substitutes is to create scaffolds with mechanical properties that closely mimic those of regenerated tissue. Scaffolds that mimic the structure of natural cancellous bone are believed to have better environmental adaptability. In this study, we used the porosity and thickness of pig cancellous bone as biomimetic design parameters, and porosity and structural shape as differential indicators, to design a biomimetic bone beam scaffold. The mechanical properties of the designed bone beam model were tested using the finite element method (FEM). PCL/β-TCP porous scaffolds were prepared using the FDM method, and their mechanical properties were tested. The FEM simulation results were compared and validated, and the effects of porosity and pore shape on the mechanical properties were analyzed. The results of this study indicate that the PCL/β-TCP scaffold, prepared using FDM 3D printing technology for cancellous bone tissue engineering, has excellent integrity and stability. Predicting the structural stability using FEM is effective. The triangle pore structure has the most stability in both simulations and tests, followed by the rectangle and honeycomb shapes, and the diamond structure has the worst stability. Therefore, adjusting the porosity and pore shape can change the mechanical properties of the composite scaffold to meet the mechanical requirements of customized tissue engineering.

FEM-SPH adaptive method for analysis protection mechanism of B4C ceramics

To simulate the collision of a tungsten heavy alloy projectile with different velocities on the B4C ceramic target, an adaptive conversion model from Lagrangian elements to SPH particles is developed due to the limitations of the traditional finite element method (FEM) with the element erosion technique. By comparing the simulation results with experimental data and FEM simulation results, the accuracy and effectiveness of the model were validated. According to the damage morphological characteristics, the target damage was classified into the central crush area, cone cracks area, radial/circular area, and fragment falling area by analyzing the damage nephogram, and the formation causes of each area were discussed in detail. According to the simulation results, the impact process between the projectile and target is split into three stages: initial impact stage, erosion stage, and crack propagation stage, and the energy dissipation in each phase was computed and examined. Finally, the protection mechanism is summarized in detail. This study contributes to improve the protection mechanism system of B4C ceramic target.

Acoustic Performance of Stress Gradient-Induced Deflection of Triangular Unimorphic/Bimorphic Cantilevers for MEMS Applications

This paper reports two piezoelectric materials of lead zirconium titanate (PZT) and aluminum nitride (AlN) used to simulate microelectromechanical system (MEMS) speakers, which inevitably suffered deflections as induced via the stress gradient during the fabrication processes. The main issue is the vibrated deflection from the diaphragm that influences the sound pressure level (SPL) of MEMS speakers. To comprehend the correlation between the geometry of the diaphragm and vibration deflection in cantilevers with the same condition of activated voltage and frequency, we compared four types of geometries of cantilevers including square, hexagon, octagon, and decagon in triangular membranes with unimorphic and bimorphic composition by utilizing finite element method (FEM) for physical and structural analyses. The size of different geometric speakers did not exceed 10.39 mm2; the simulation results reveal that under the same condition of activated voltage, the associated acoustic performance, such as SPL for AlN, is in good comparison with the simulation results of the published literature. These FEM simulation results of different types of cantilever geometries provide a methodology design toward practical applications of piezoelectric MEMS speakers in the acoustic performance of stress gradient-induced deflection in triangular bimorphic membranes.

A Data-Fusion Method for Uncertainty Quantification of Mechanical Property of Bi-Modulus Materials: An Example of Graphite

AbstractThe different elastic properties of tension and compression are obvious in many engineering materials, especially new materials. Materials with this characteristic, such as graphite, ceramics, and composite materials, are called bi-modulus materials. Their mechanical properties such as Young’s modulus have randomness in tension and compression due to different porosity, microstructure, etc. To calibrate the mechanical properties of bi-modulus materials by bridging finite element method (FEM) simulation results and scarce experimental data, the paper presents a data-fusion computational method. The FEM simulation is implemented based on parametric variational principle (PVP), while the experimental result is obtained by digital image correlation (DIC) technology. To deal with scarce experimental data, maximum entropy principle (MEP) is employed for the uncertainty quantification (UQ) and calibration of material parameters and responses, which can retain the original probabilistic property of a priori data. The non-parametric p-box is used as a constraint for data fusion. The method presented in this paper can quantify the mechanical properties of materials with high uncertainty, which is verified by a typical example of bi-modulus graphite. It is possible to find applications in the real-time estimation of structural reliability by combining with digital twin technology in the future.

Effects of Strain Rate on Stress-Strain Curves in 2024 Aluminum Alloy After Solution Heat Treatment

Strain rate sensitivity of effective stress and fracture strain of aluminum alloy 2024 were examined considering the period from solution heat treatment. Notched round bar tensile test specimens were employed for obtaining stress-strain curves. Because the necking area of tensile tests is under multiaxial stress, effective stresses of aluminum alloy 2024 were corrected by an optimization method using experimental and simulation results. In the optimization, the experimental and finite element method simulation results of tensile force–true strain of the notched area in the tensile direction were compared. After stress correction, the effective stresses at a true strain of 0.002 were almost the same or showed a small strain rate sensitivity. The effective stresses at a true strain of 0.15 and 0.20 clearly decreased with increasing strain rate and clearly increased at a high strain rate. Fracture strain also decreased clearly with increasing strain rate and clearly increased at a high strain rate.

Numerical Simulation and Equivalent Circuit Model of Multi-Band Terahertz Absorber Composed of Double-Sided Graphene Comb Resonator Array

Multi-band terahertz (THz) absorber based on a non-symmetric double-sided graphene comb resonator array is designed and simulated by the finite element method (FEM) in CST Software. Then, an equivalent circuit model (ECM) based on admittance with a fast MATLAB code is proposed to analyze the absorber in the THz region. The admittance-based ECM approach could be used for any metamaterial absorber containing one layer of resonators sandwiched between two dielectric slabs and backed by a metal layer consisting of a layer of resonators with a thickness much smaller than the minimum wavelength in the considered wavelength range. The proposed absorber is dynamically tunable with a one-layered resonator array. It has strong linear dichroism (LD) response of 98% and the frequency range of 0.7-5 THz with absorption > 96%: two absorption bands for TE mode and three for TM mode. The proposed absorber can be used in polarization-sensitive devices and systems in the THz region. The ECM model of the metastructure was derived to provide an efficient approach to analyzing the performance of the absorber. The FEM simulation results are in good agreement with the ECM ones.

Finite element analysis of zero magnetic field shielding for polarized neutron scattering

Polarized neutron scattering, as one of the experimental techniques of neutron scattering, is a powerful tool for exploring the microstructure of matter. In polarized neutron scattering experiments, magnetic field maintains and guide the neutron polarization, as well as define the sample magnetic environment. For complex magnetic sample, it is often necessary to apply zero-field environment at the sample position, so that general polarization analysis becomes available. To achieve effective zero-field environment for polarized neutron experiment, carefully designed magnetic field shielding and constrain is required. In this paper, we demonstrate a zero-field sample chamber designed for polarized neutron experiment utilizing both Permalloy material and high-T<sub>C</sub> superconducting films. This design adopts a simple and low-maintenance 'deep-well' shape to achieve effective shielding. The study uses finite element simulation methods to analyze the effect of different dimensions on the magnetic field shielding performance of the device of the model, including height, arm length, opening radius, and superconductor distance. At optimal dimensions, the designed zero field chamber achieves an internal magnetic field integral of 0.67 G٠cm along the neutron path under the geomagnetic field conditions. The maximum polarization deflection for 4 Å neutrons is 0.76%, which reaches the advanced level. The finite element method simulation results are verified by neutron Bloch Equation dynamics simulations and by the actual measurement. Based on the established effective zero-field shielding design we further discuss the dependence of magnetic field shielding and the dimensions of the device. The prospective application of the device to spectrometers and the future improvements of the device structure are also discussed.

High-power test of an interdigital H -mode drift tube linac for the J-PARC muon g−2 and electric dipole moment experiment

We conducted a high-power test of a prototype cavity of a 324-MHz interdigital H-mode drift tube linac (IH-DTL) for the precise measurement of the muon anomalous magnetic moment ($g\ensuremath{-}2$) and electric dipole moment (EDM). This prototype cavity (short IH) was developed to verify the fabrication methodology for the IH-DTL cavity with a monolithic drift tube structure. The electromagnetic field distribution was measured and compared with the finite element method simulation results, and the fabrication accuracy of the monolithic drift tube was confirmed to satisfy the requirements. After 40 h of conditioning, the short IH was stably operated with an rf power of 88 kW, which corresponds to a 10% higher accelerating field than the design field (${E}_{0}$) of $3.0\text{ }\text{ }\mathrm{MV}/\mathrm{m}$. In addition, the thermal characteristics and frequency response were measured, verifying that the experimental data were consistent with the three-dimensional model. In this paper, the design, fabrication, and low-power and high-power tests of this IH-DTL for muon acceleration are described.