Transient Finite Element Method Research Articles

Thermal and structural analysis of TCABR vacuum vessel during baking process

TCABR is a small-sized tokamak located at the University of São Paulo, in Brazil. It is planned to undergo an extensive upgrade, which includes a baking system. However, this tokamak wasn't designed considering baking as a possible wall conditioning technique. This paper analyzes whether a baking system with ohmic heating could in principle be installed on TCABR, considering the thermal stresses that it might produce on the vacuum vessel. An analytical steady-state heat transfer model was used to estimate the heat fluxes required to reach a target temperature of 200 °C. Thermal and structural transient finite element method models were developed using ANSYS Workbench®. The temperature distribution was used to calculate the thermal stresses, also considering the effects of gravity and vacuum pressure. The stresses produced in the vacuum vessel by baking were below the limit defined by the ASME stress code, but the graphite tiles’ support rails reached stress values above their material's yield strength. The resulting temperature distribution was not uniform, with some regions far from the 200 °C target. A redesign of the baking system will be required to reach a more uniform temperature field and avoid stresses above yield strength for some components.

Editors' Choice—Improving Quality of EDMed Micro-Holes on Titanium via In Situ Electrochemical Post-processing: A Transient Simulation and Experimental Study

Electrical discharge micromachining (EDM) poses challenges to the fatigue-life performance of machined surfaces due to thermal damage, including recast layers, heat-affected zones, residual stress, micro-cracks, and pores. Existing literature proposes various ex situ post-processing techniques to mitigate these effects, albeit requiring separate facilities, leading to increased time and costs. This research involves an in situ sequential electrochemical post-processing (ECPP) technique to enhance the quality of EDMed micro-holes on titanium. The study develops an understanding of the evolution of overcutting during ECPP, conducting unique experiments that involve adjusting the initial radial interelectrode gap (utilizing in situ wire-electrical discharge grinding) and applied voltage. Additionally, an experimentally validated transient finite element method (FEM) model is developed, incorporating the passive film formation phenomenon for improved accuracy. Compared to EDM alone, the sequential EDM-ECPP approach produced micro-holes with superior surface integrity and form accuracy, completely eliminating thermal damage. Notably, surface roughness (Sa) was reduced by 80% after the ECPP. Increasing the voltage from 8 to 16 V or decreasing the gap from 60 to 20 μm rendered a larger overcut. This research’s novelty lies in using a two-phase dielectric (water-air), effectively addressing dielectric and electrolyte cross-contamination issues, rendering it suitable for commercial applications.

Safety assessment of wireless chargers for electric vehicles considering thermal characteristics.

This study employs the transient finite element method and electromagnetic heat transfer theory to assess the heating generated by high-power wireless chargers during electric vehicle charging. The analysis includes simulating and analyzing the temperature distribution of two different types of shielding plates of the wireless charger and the specific absorption rate (SAR) and head temperature rise of both adults and children in close proximity to the charger. Simulation results show that the maximum temperature rise of the copper shielding plate is 16°C lower than that of the aluminum shielding plate after charging for 1h. This temperature increase does not affect the chassis' s equipment. Regarding human safety, the induced electric field strength and SAR values in the child's head tissue are higher than those in the adult, meeting the International Commission on Non-Ionizing Radiation Protection (ICNIRP) limits. When the initial temperature is set to 37°C, the temperature rise in the heads of both adults and children is approximately equal after 1h of charging, reaching a maximum temperature rise of 0.21 and 0.23°C, respectively. These values remain below the thermal limit of ICNIRP (2°C for Type 2 tissues). The findings indicate that the copper shielding plate can provide both electromagnetic shielding and heat dissipation functions, and the electromagnetic exposure absorbed by the human body and head temperature rise within safe ranges.

Bayesian estimation and reconstruction of marine surface contaminant dispersion

Discharge of hazardous substances into the marine environment poses a substantial risk to both public health and the ecosystem. In such incidents, it is imperative to accurately estimate the release strength of the source and reconstruct the spatio-temporal dispersion of the substances based on the collected measurements. In this study, we propose an integrated estimation framework to tackle this challenge, which can be used in conjunction with a sensor network or a mobile sensor for environment monitoring. We employ the fundamental convection-diffusion partial differential equation (PDE) to represent the general dispersion of a physical quantity in a non-uniform flow field. The PDE model is spatially discretised into a linear state-space model using the dynamic transient finite-element method (FEM) so that the characterisation of time-varying dispersion can be cast into the problem of inferring the model states from sensor measurements. We also consider imperfect sensing phenomena, including miss-detection and signal quantisation, which are frequently encountered when using a sensor network. This complicated sensor process introduces nonlinearity into the Bayesian estimation process. A Rao-Blackwellised particle filter (RBPF) is designed to provide an effective solution by exploiting the linear structure of the state-space model, whereas the nonlinearity of the measurement model can be handled by Monte Carlo approximation with particles. The proposed framework is validated using a simulated oil spill incident in the Baltic sea with real ocean flow data. The results show the efficacy of the developed spatio-temporal dispersion model and estimation schemes in the presence of imperfect measurements. Moreover, the parameter selection process is discussed, along with some comparison studies to illustrate the advantages of the proposed algorithm over existing methods.

Winding Loss Suppression in Inverter-Fed Traction Motors via Hybrid Coil Materials and Configurations

In a typical inverter-fed AC drive system, the stator windings carry a current with a large harmonics content, resulting in an increased AC loss. In this paper, the additional copper losses caused by non-sinusoidal currents are investigated for different magnet wire topologies, including the flat conductor, stranded, and litz wires. Also, a two-slot simplified model is introduced for accurate prediction of the AC losses at high frequency. It is found that one of the major issues of the conventional copper coil is that the losses are not uniformly distributed across the slot, and over 70% of the losses are concentrated near the slot opening. Moreover, using the transient finite element method, different winding topologies and arrangements are simulated at the stranded level to evaluate the losses and current density for each strand under highly distorted currents. Furthermore, different coil samples are prototyped for the same slot geometries to compare their performance under the same pulse-width modulation (PWM) waveforms for a wide range of frequencies. Finally, new hybrid coil topologies are proposed, which employ different magnet wires or materials within the same slot. The results demonstrate that utilizing a mixed wire configuration can effectively mitigate the adverse effects of eddy current losses. This approach can yield up to 16–41% lower losses while also achieving a weight savings of 36–70%.

Analysis of the Magnetization-Induced Field Error in a Superconducting Bending Magnet for a Compact, Rapid-Cycling Heavy-Ion Synchrotron

An ongoing design study of a 90-degree superconducting bending magnet (SCBM) is being conducted for a compact, rapid-cycling heavy-ion synchrotron at the National Institutes for Quantum Science and Technology (QST). The SCBM is designed to generate a 3.5 T dipole field and a 1.5 T <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\cdot$</tex-math></inline-formula> m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-1}$</tex-math></inline-formula> quadrupole field for bending and horizontally defocusing heavy-ion beams. Since a heavy-ion beam is injected into the synchrotron at the field of 0.3 T, and accelerated to 3.5 T in 5 s, and then it is extracted at the field range from 1.1 T to 3.5 T, field errors derived from the magnetization at such a ramp rate will cause instability of the beam during the acceleration. In this paper, the field errors derived from both the DC and the AC effects are analyzed with numerical models in two dimensions (2D). The DC effects from the screening current in the superconducting coil and iron hysteresis behavior are estimated by the nested ellipse model and the finite element method (FEM) coupled with an inverse Jiles-Atherton model. The AC effects from the eddy current generated in the thermal shield, the beam pipe and the thermal path are estimated by a transient FEM analysis and analytical method. The change of the field error due to the magnetization is estimated to be about 1 unit at the time of beam injection.

Multi-stage hysteresis modelling of magnetorheological dampers and experimental verification

An accurate theoretical model is the basis for the structural design and parameter optimisation of magnetorheological dampers (MRDs). Owing to the inability of existing models to accurately describe the motion characteristics of MRDs in the entire region, a multi-stage hysteresis (MSH) model for low-frequency conditions was proposed. The MSH model comprised a magnetic chain model and Bi-Viscous model to describe the characteristics of the pre-yield and yield flow stages, respectively. The local loss and inertia effect were considered in the MSH model. Steady-state and transient finite element methods were combined to analyse the magnetic field distribution during MRD motion, and an equivalent weighted mean magnetic field hypothesis was proposed to reduce the quantisation error and time consumption. The experimental results demonstrate the prediction effectiveness of the MSH model. Moreover, the quantitative evaluation parameters of the flow and hysteresis regions were obtained and the variation trend of the MRD main design indices with the magnetic circuit parameters was analysed. The obtained velocity distribution parameters indicate a smooth transition of the stages in the MSH model from a qualitative perspective. The mixed mode incorporates the physical properties of the shear and flow modes, but cannot simply be regarded as a linear superposition of these two modes.

Hybrid SPH-FEM solver for metal cutting simulations on the GPU including thermal contact modeling

This paper presents a hybrid Smoothed Particle Hydrodynamics (SPH) – Finite Element Method (FEM) solver for metal cutting simulations on Graphics Processing Units (GPU). For the first time in chip formation simulation, the heat transfer between an SPH model of the workpiece, and a transient FEM temperature model for the cutting tool, is established. For validation, the performance of the modeled thermal contact between two numerical domains is compared with a commercial FEM software. The sensitivity of the implemented SPH-FEM contact parameters is investigated for the first time and further insights into the thermal modeling of cutting simulations are generated. Overall, the newly developed hybrid model saves the computational time on the cutting tool side in the pure SPH method and enables more efficient high-fidelity cutting simulations. By clearly defining the thermal contact at the tool-chip interface, the simulated tool surface temperature agrees well with the experimental measurements in the literature.

Numerical modeling of phase prediction and geometry evolution of micro-drilling using single pulse laser

Due to high production capability, long laser pulses are preferred over ultrashort pulses during Laser-based machining. To reduce metallurgical defects, viz. heat-affected zone, recast layer, and micro-cracks, it is essential to analyze the causes of these defects and to derive the remedies. Generally, an extensive experimental investigation is carried out for the same. The experimental analysis is time-consuming, tedious, and requires high capital investment. Therefore, in this work, a two-dimensional axisymmetric transient finite element method (FEM) based numerical model of Laser-material interaction was developed to explore the temperature evolution, phase change, and geometry evolution with the help of coupled heat transfer and deformed mesh. The heat transfer module was implemented by considering the phase change using the apparent heat capacity method. The model was duly validated for the evolution and geometry of the Laser-drilled hole. The model was found in agreement with the experimental results, with a percentage deviation of 12% in the prediction of the responses. The numerical model will help to predict the temperate evolution and hydrodynamic behavior of the material during the laser-material interaction. This, in turn, will help to mitigate the metallurgical defects.

Eddy current loss estimation for direct drive wind turbine generators with superconducting excitation winding by numerical and analytical models

AbstractDirect drive wind turbine generators with superconducting excitation winding are studied with focus on the electromagnetic damper design. A semi‐analytical eddy current model is built for parametric design studies based on a vector potential approach. The considered generators employ open stator slots and exhibit strong saturation effects, so that an analytical expression for the source terms is not adequate. Whilst the field equations are solved analytically, an equivalent current loading, accounting for slotting effects and saturation, is obtained by magnetostatic models applying the 2D finite element method (FEM). The proposed framework for the extraction of the current loading is universal and may also be applied to other machine types (e.g., permanent magnet synchronous machines, [PMSM]). In relation to transient FEM models, a considerable time‐saving can be achieved, which is particularly beneficial in case of large models, for example, in case of fractional slot windings or intermittent feeding schemes. The eddy current loss in warm and cold rotor parts in a direct drive generator in the 7 MW power class are computed with the semi‐analytical and transient 2D FEM models under variation of the damper geometry and the stator winding configuration. Minimum damper dimensions as well as constraints regarding applicable stator windings are derived.

In-wheel, outer rotor, permanent magnet synchronous motor design with improved torque density for electric vehicle applications

In electric vehicle applications, the torque density of electric motor plays an important role in improving the performance of the vehicle. The main objective of this paper is to investigate a possible method for improving the torque density of a permanent magnet synchronous motor used in electric vehicles. At the same time, other machine specifications were taken into account and kept within the acceptable level. This was achieved by incorporating performance enhancement strategies such as investigating ofhigh-efficient winding topology for the motor’s stator to give the highest winding factor and optimizing the machine dimensions to achieve the best performance. MagNet 7.4.1 software package with static and transient finite element method solver was used for implementing the proposed design. The results showed a significant improvement in the torque density with keeping the overall machine performance.

Optimal design of a short primary double‐sided linear induction motor based on derived Quasi‐3D equivalent circuit model using an improved differential evolution

Due to its simple construction, the linear induction motor (LIM) provides a linear driving force without any intermediate motion translation system. LIMs are widely used in various industrial applications, including maglev rail transit and the national defense industry. However, LIMs are affected by the end effect and suffer from problems such as low efficiencies and low power factors. To make improvements, in this paper, an ensemble multi-objective optimal design method for a short primary double-sided linear induction motor (SP-DLIM) is proposed. First, a simplified Quasi-3D equivalent circuit model (ECM) for an SP-DLIM applicable to the model in this paper is derived. The 3-D transient finite element method and an experimental prototype are utilised to prove that the derived ECM is accurate enough to solve the SP-DLIM optimisation problem. Second, an ensemble multi-objective optimal design method of SP-DLIM is presented, with proposed design constraints and four different optimisation problems. Then, an improved differential evolutionary (IDE) algorithm is proposed to optimise the efficiency, power factor, and tooth weight of the motor. The three-dimensional time-stepping finite element method is utilised to verify the validity of the optimisation method. Further, a comparison of the results suggests that the IDE yields the best performance to those of other advanced heuristic algorithms.

Design and Optimization of Interface Morphology of Thermal Barrier Coatings Based on Regulation of Residual Stress: A Finite Element Simulation Study

Laser surface texture (LST) technology can be used to increase the adherence of thermal barrier coating (TBC). The primary research method is to conduct a large number of laser experiments to determine the optimal texture parameters. To minimize costs and enhance efficiency, in the current work, five types of circular pit textures were summarized; the plane strain model was established using the transient thermomechanical coupling finite element method; the residual stress field after spraying was used as the prestress field; the influence of different textures on the distribution of the residual stress field after a thermal cycling was analyzed; and the propagation law of cracks in the coating was predicted. The current work focuses on: (1) The two-dimensional cross-sectional morphology of texture; (2) the principal stress s22 perpendicular to the interface (resulting in mode I interface crack) and the shear stress s12 parallel to the interface (resulting in mode II interface crack); (3) texture variables—diameter, depth, and spacing. The results revealed that after thermal cycling, the texture in the ceramic top coat (TC) bore tensile stress of around 350 MPa. Both sides of the pit in the metallic bond coat (BC) bore tensile stress, while the bottom bore compressive stress. Among them, the positive tensile stress of the texture with a sinusoidal section was the greatest, whereas the shear stress was the least. The maximum stress in texture increased as the diameter and depth increased, while the minimum principal stress was obtained by adjusting the spacing among the adjacent textures. The stress level in the coating was reduced by selecting the appropriate texture morphology, and the crack propagation was more complex, that is, it took a longer time before reaching failure, which is expected to improve the life.

Improving the performance of helical motion resolver based on accurate modelling of longitudinal end effect

Using multiple position sensors in the control system of Two-Degrees of Freedom (2-DOF) motors causes it more complicated than that of conventional 1-DOF ones. However, employing a 2-DOF position sensor in comparison with two independent sensors, reduces the complexity, mass and volume of the system. The common 2-DOF sensors are able to determine the position in linear, rotational, and helical motion. Yet, they suffer from accuracy reduction due to the longitudinal end effect. Therefore, analytical modelling and the relevant compensation methods are discussed. The accuracy of the model is approved by comparing its results with those of 3D time transient finite element method. Afterwards, the model is used for compensating the end effects. Finally, the optimised 2-DOF resolver is prototyped and tested. The result of experimental test shows the proposed resolver's success.

Modeling and experiments of the thermal degradation behavior of PMMA during laser transmission welding process

Reducing thermal degradation of plastics during laser transmission welding (LTW) process is the key to obtain high-quality weld seam. In this study, a thermal degradation prediction model is proposed. First, using polymethyl methacrylate (PMMA) as an exemplary material, the weld seams are prepared at different process parameters, including the laser power, welding velocity and carbon black (CB) content. Full characterization of the prepared weld seams was performed through shear tests, scanning electronic images, and ultra-depth-of-field microscope. The results reveal that thermal degradation occurs with bubbles at the interface and decreases the shear strength of the weld seam. Second, the thermal history model during LTW is simulated through a 3-D transient heat transfer finite element method (FEM), where the highest temperature is extracted to aid in comprehension of thermal degradation mechanism. Third, a thermal degradation prediction model is proposed based on the thermal history model and thermal degradation kinetic model which is solved by the thermogravimetric analysis (TGA). The results from the proposed prediction model is consistent with the occurrence of the initial thermal degradation and the trend of shear strength of the weld seam. Therefore, this study might present a potential way to optimize the processing window by effectively suppressing the appearance of thermal degradation.

Continuum Damage Dynamic Model Combined with Transient Elastic Equation and Heat Conduction Equation to Solve RPV Stress

The development of the world cannot be separated from energy: the energy crisis has become a major challenge in this era, and nuclear energy has been applied to many fields. This paper mainly studies the stress change of reaction pressure vessels (RPV). We established several different physical models to solve the same mechanical problem. Numerical methods range from 1D to 3D; the 1D model is mainly based on the mechanical equilibrium equations established by the internal pressure of RPV, the hoop stress, and the axial stress. We found that the hoop stress is twice the axial stress; this model is a rough estimate. For 2D RPV mechanical simulation, we proposed a new method, which combined the continuum damage dynamic model with the transient cross-section finite element method (CDDM-TCFEM). The advantage is that the temperature and shear strain can be linked by the damage factor effect on the elastic model and Poission ratio. The results show that with the increase of temperature (damage factor μ^,d^), the Young’s modulus decreases point by point, and the Poisson’s ratio increases with the increase of temperature (damage factor μ^,Et). The advantage of the CDDM-TCFEM is that the calculation efficiency is high. However, it is unable to obtain the overall mechanical cloud map. In order to solve this problem, we established the axisymmetric finite element model, and the results show that the stress value at both ends of RPV is significantly greater than that in the middle of the container. Meanwhile, the shape changes of 2D and 3D RPV are calculated and visualized. Finally, a 3D thermal–mechanical coupling model is established, and the cloud map of strain and displacement are also visualized. We found that the stress of the vessel wall near the nozzle decreases gradually from the inside surface to the outside, and the hoop stress is slightly larger than the axial stress. The main contribution of this paper is to establish a CDDM-TCFEM model considering the influence of temperature on elastic modulus and Poission ratio. It can dynamically describe the stress change of RPV; we have given the fitting formula of the internal temperature and pressure of RPV changing with time. We also establish a 3D coupling model and use the adaptive mesh to discretize the pipe. The numerical discrete theory of FDM-FEM is given, and the numerical results are visualized well. In addition, we have given error estimation for h-type and p-type adaptive meshes. So, our research can provide mechanical theoretical support for nuclear energy safety applications and RPV design.

Determining alloyed layer thickness in electric discharge alloying by inverse estimation of energy distribution

Electric discharge alloying (EDA) is an important surface modification process, however, accurate determination of alloyed layer thickness is essential for effective utilization of this process in the industry. The spark energy distribution among the tool and workpiece controls alloyed layer thickness. In this work, a novel method is developed for accurate and quick determination of alloyed layer thickness through inverse estimation of energy distribution factor. A nonlinear transient finite element method based direct numerical model is developed for the analysis of EDA. The inverse estimation of the energy distribution factor is carried out by reducing the difference between actual and direct model computed data. For this purpose, an integrated finite element method–artificial neural network based method is developed. Physical experiments at the shop floor were also performed, which suggested that the inversely obtained energy distribution factor is sufficiently accurate in estimating the alloyed layer thickness at changed operating conditions.

Influence of stator segmentation on iron losses in PMSMs for traction applications

PurposeThis paper presents a comparative study of different stator-segmentation topologies of a permanent magnet synchronous machine (PMSM) used in traction drives and their effect on iron losses. Using stator segmentation allows one to achieve more significant copper fill factors, resulting in increased power densities and efficiencies. The segmentation of the stators creates additional air gaps and changes the soft magnetic material’s material properties due to the cut edge effect. The aim of this paper is to present an in-depth analysis of the influence of stator segmentation on iron losses. The main goal was to compare various segmentation methods under equal excitation conditions in terms of their influence on iron loss.Design/methodology/approachA transient finite element method analysis combined with an extended iron-loss model was used to evaluate discussed effects on the stator’s iron losses. The workflow to obtain a homogenized airgap length accounting for cut edge effects was established.FindingsThe paper concludes that the segmentation in most cases slightly decreases the iron losses in the stator because of the overall reduced magnetic flux density B due to the additional air gaps in the magnetic circuit. An increase of the individual components, as well as total power loss, was observed in the Pole Chain segmentation design. In general, segmentation did not change the total iron losses significantly. However, different segmentation methods resulted in the different distortion of the magnetic field and, consequently, in different iron loss compositions. The analysed segmentation methods exhibited different iron loss behaviour with respect to the operation points of the machine. The final finding is that analysed stator segmentations had a negligible influence on the total iron loss. Therefore, applying segmentation is an adequate measure to improve PMSMs as it enables, e.g. increase of the winding fill factor or simplifying the assembly processes, etc.Originality/valueThe influence of stator segmentation on iron losses was analysed. An in-depth evaluation was performed to determine how the discussed changes influence the individual iron loss components. A workflow was developed to achieve a computationally cheap homogenized model.

Optimal Design of a Short Primary Double-Sided Linear Induction Motor for Urban Rail Transit

Linear induction motors (LIMs) have been widely used in rail transit. However, Due to the breaking of the primary core and the large air gap, the efficiency and power factor of LIMs are seriously damaged, causing a large amount of energy waste. To improve the efficiency and power factor of LIMs for urban rail transit, we present a new optimization method for the design of a short primary double-sided linear induction motor (SP-DLIM) with a rated speed of 45 km/h and small thrust. The method is based on a steady state equivalent circuit model and the differential evolutionary algorithm (DEA). Moreover, the design constraints and the objective functions are proposed for the optimization problem. Finally, the optimized SP-DLIM is simulated by 2D transient finite element method (FEM). The 2-D transient FEM results verify the accuracy of the optimization method proposed in this paper.

Numerical calculation of transient electric field considering space charge in oil-paper insulation of converter transformers

PurposeThe purpose of this paper is to develop a numerical simulation method based on the transient upstream finite element method (FEM) and Schottky emission theory to reveal the distribution characteristics of space charge in oil-paper insulation.Design/methodology/approachThe main insulation medium of the converter transformer in high voltage direct current transmission is oil-paper insulation. However, the influence of space charge is difficult to be fully considered in the insulation design and simulation of converter transformers. To reveal the influence characteristics of the space charge, this paper proposes a numerical simulation method based on Schottky emission theory and the transient upstream FEM. This method considers the influence of factors, such as carrier mobility, carrier recombination coefficient, trap capture coefficient and diffusion coefficient on the basis of multi-physics field coupling calculation of the electric field and fluid field.FindingsA numerical simulation method considering multiple charge states is proposed for the space charge problem in oil-paper insulation. Meanwhile, a space charge measurement platform based on the electrostatic capacitance probe method for oil-paper insulation structure is built, and the effectiveness and accuracy of the numerical simulation method is verified.Originality/valueA variety of models are calculated and analyzed by the numerical simulation method in this paper, and the distribution characteristics of the space charge and total electric field in oil-paper insulation medium with single-layer, polarity reversal of plate voltage and double-layer are obtained. The research results of this paper have the guiding significance for the engineering application of oil-paper insulation and the optimal design of converter transformer insulation.