Axisymmetric Finite Element Method Research Articles

Finite element modeling of material removal rate in micro-EDM process with and without ultrasonic vibration

PurposeThis research explores the finite element modeling of the crater and material removal rate (MRR) in micro-electrical discharge machining (micro-EDM) with and without vibration of the workpiece. The application of workpiece vibration in the micro-EDM process improved flushing efficiency and enhanced material removal rate (MRR).Design/methodology/approachIn this work, the two-dimensional axisymmetric finite element method (FEM) has been developed to predict the shape of the crater with and without vibration. The temperature distribution on the workpiece surface with and without vibration has been obtained in the form of the contour plot.FindingsThe MRR obtained from the numerical model revealed that there was an enhancement in MRR in micro-EDM with vibration as compared to without vibration. The effect of process parameters on MRR in micro-EDM with and without is also presented in this work.Originality/valueIn this work, the two-dimensional axisymmetric FEM model has been developed to predict the shape of the crater with and without vibration.

Three-dimensional finite element analysis of tightening and untightening process of bolt and nut connections with slight pitch difference

In industrial fields, the bolt-nut connection is widely used and unitized as an important machine component. In the previous studies, a bolt-nut connection with slight pitch difference was considered towards realizing anti-loosening performance and high fatigue strength through axisymmetric finite element method (FEM) as well as experiment. Also by applying three-dimensional FEM, the nut screwing process was analyzed to obtain the prevailing torque Tp confirming anti-loosening performance. In this study, the tightening and untightening processes after the nut touched the clamped body are analyzed through 3D FEM as well as experiment. The FEM results are in good agreement with the experimental results. The clamping force and tightening torque relationship under the pitch difference is compared to the normal nut. Then, the behaviors of the pitch difference nut in tightening and untightening process is discussed by varying the pitch difference. For the normal nut, the equation of clamping force and tightening torque relation in the untightening process is clarified by FEM. Since the nut untightening property after the nut tightening is more important to prevent the nut self-loosening, the loosening resistance torque TRu is newly defined in this process. It is found that with increasing the pitch difference the loosening resistance torque TRu increases. The large loosening resistance torque TRu suggests that the pitch difference nuts have good anti-loosening performance.

The Analytical Method to Compute the Strain on the Soft PSD in Double-Pulse SRM

In order to obtain the analytical method to compute the circumferential strain on a soft pulse separation device (PSD), deformation processes of the middle section of the soft PSD, the medicine propellant grain and the case are simplified into a two-dimensional plane strain state. It is found that the main factors affecting the circumferential strain of the soft PSD are the circumferential strain of the inner surface of the propellant grain and the gap between the soft PSD and the propellant grain. In order to study the failure mechanism of the soft PSD in the double-pulse solid rocket motor (SRM), a two-dimensional axisymmetric finite element method (FEM) model of the stress process of the soft PSD is established. The variation of the strain of the soft PSD with the internal pressure load is obtained. It is found that the excessive circumferential strain is the main reason for the failure of the soft PSD. Comparing the analytical calculations with the FEM results, it can be found that the analytical method value is slightly higher than the FEM value, so the analytical method results can be used to initially estimate the circumferential strain of the soft PSD and then predict the rationality and feasibility of the design scheme. In order to further study the failure mechanism of the soft PSD, a micro-CT test of in situ stretching of the soft PSD material is carried out and the variation of porosity and elongation of the material is studied. The test results showed that when the material elongation is large, the microinterface debonding rapidly expands into a penetrating damage, and the PSD structure fails. The conclusions obtained in this paper can provide a useful reference for the design of double-pulse SRM.

Focused Ultrasound Ablation for the Treatment of Patients With Localized Deformed Breast Cancer: Computer Simulation

Abstract This paper is carried out on the computer simulation of breast cancer treated using a high intensity focused ultrasound (HIFU). The mathematical models consist of the pressure acoustics equation, bioheat equation, heat transfer in a blood vessel, momentum equations in a blood vessel, and mechanical deformation equation. In the numerical simulation, these mathematical models are solved by using an axisymmetric finite element method (FEM) with time-dependent, thermal and acoustic properties to describe the temperature distribution and the total displacement in tissue. The comparison of the simulated results in the model with two sizes of the cancer tumor and two frequencies of ultrasound are also considered in order to approach realistic tissue modeling. The results show that the breast cancer model with deformation, which is the more accurate way to simulate the physical characteristics of therapeutic breast cancer compared to the literature results, hence leads to more useful in the medical approach and this study was conducted to prevent errors caused by inaccurate focal points.

Electroquasistatic quasi‐3D finite element simulation of a graded surge arrester

AbstractSurge arresters of station class are equipped with field grading elements that break the rotational symmetry of the arrester body. To avoid a computationally expensive full three‐dimensional (3D) simulation, a quasi‐3D simulation procedure is presented to study graded arresters. The method employs a hybrid discretization combining a two‐dimensional (2D) axisymmetric finite element (FE) method in axial and radial direction with a spectral element method in terms of trigonometric functions in azimuthal direction. Furthermore, the asymmetric boundary conditions associated with the support rods are taken into account by collocation in a saddle‐point system of equations. The method is validated and compared with a standard 3D FE simulation of a test problem. It is, subsequently, applied to study the electric field distribution of a graded station class surge arrester.

Characterization of adhesively bonded aluminum plates subjected to shock-wave loading

Adhesive joint technology is gaining acceptance since it leads to weight reduction, provides uniform stress distribution across the joints, allows the bonding of similar and dissimilar materials, and contributes to shock and vibration damping. The literature on adhesive joints subjected to static loads is extensive. However, the response of adhesive joints to high loading rates such as blast or ballistic loading has not been studied extensively. In this study, fully bonded plates composed of aluminum plates (381 mm in diameter and 1.59 mm thick) and commercial epoxy adhesive were tested under shock wave loading. Full displacement field over the test plates was obtained by digital image correlation techniques, and full-field strains of the plates were computed by classical plate theory for large deflections. An axisymmetric Finite Element Method model was used to gain more insight on the response of fully bonded plates to shock-wave loading. The material properties of the epoxy film subjected to high loading rates were estimated through an algorithm developed for an FEM-based parametric study. Finally, the influence of the adhesive thickness and Young's modulus on the behavior of the bonded adhesive under shock-wave loading were investigated using an FEM model.

Stress distributions in nanocomposite sandwich cylinders reinforced by aggregated carbon nanotube

In order to improve the static response of thick hollow cylinders, a sandwich cylinder with two carbon nanotube (CNT)‐reinforced nanocomposite face sheets are proposed in this article. Moreover, due to the use of optimum amount of high cost CNTs, the CNT distribution is suggested to be functionally graded (FG) along the thickness of cylinder. The stress and deflection profiles of the proposed sandwich cylinders subjected to internal and external pressures have been investigated using a finite element method (FEM) based on an axisymmetric model. The significant effect of formation of CNT agglomerations in the surrounded matrix is considered and the material properties of the resulted nanocomposite are estimated by Eshelby‐Mori‐Tanaka approach. Using the developed axisymmetric FEM model, the effects of CNT aggregation state, volume fraction, and distribution as well as geometrical dimension and loading condition on the stress and deflection distributions of the nanocomposite sandwich cylinders have been characterized. The extensive simulations have revealed that instead of adding higher volume fraction of CNT, the selection of suitable distribution for CNTs can lead to a nanocomposite sandwich cylinder with less deflection. POLYM. COMPOS., 40:E1918–E1927, 2019. © 2019 Society of Plastics Engineers

Primary stability of uncemented acetabular liner of a total hip prosthesis using an axisymmetric finite element method based on computed tomography

Primary stability has a great influence on behaviour during day-to-day activities and on the long-term success of uncemented acetabular components. Achieving this stability by pushing the acetabular bush (uncemented fixation) is a common practice today. In this paper, it was tried to establish a criterion for the success of fixing the acetabular cup by evaluating the short-term stability. The influence of the contact parameters established between the cup and the peripheral area of the acetabulum was investigated in this paper. These parameters depend on the intraoperative procedures: reaming and fixation. Reaming is considered without residual stress, but the acetabulum has been remodelled (a sphere has been adapted through an optimization algorithm). Uncemented fixation (press fit) involves a series of load impulses applied to the cup, simulating the impact strokes through the surgeon’s hammer. Finite Element Method (FEM) was used for this simulation along with a pelvis model based on computed tomography (CT) data. Consequently, there is a postoperative state of residual effort. Assessing this state of effort could lead to a good estimation of short-term stability.

Transverse Electrical Resistivity Evaluation of Rod Unidirectional Carbon Fiber-Reinforced Composite Using Eddy Current Method

This paper proposes a simple approach to evaluate a transverse electrical resistivity of a rod unidirectional carbon fiber-reinforced composites (UD-CFRCs). The method is based on eddy current technique. The model is associated with inverse problem method that consists of minimizing the difference between the computed and measured resistances. The ant colony algorithm which is a kind of heuristic minimizing algorithm based on population exploration is used to get transverse electrical resistivity. The findings of the work are summarized as the following. First, it was demonstrated that the induced power in the UD-CFRC and the resistance of the coil are independent of the value of longitudinal resistivity. Then, the electrical resistance is computed using direct problem which is formulated with the 2-D axisymmetric finite-element method. After that, the identified resistivity, which obtained with the inverse problem, is introduced in the direct problem to compute resistance. Finally, the confrontation between the computed resistance and the measured one shows a significant concordance between the two.

Thermo-mechanical strength analysis for energy storage improvement of horizontal storage tanks integrating evacuated tube collectors

In the present paper, a two dimensional axisymmetric Finite Element Method (FEM) is developed to carry out a thermo-mechanical analysis on a horizontal storage tank intended to storage hot water for a domestic application. The purpose of these numerical simulations is to assess the thermo-mechanical behavior of a horizontal tank with evacuated tube collectors, and consequently to suggest a new design which ensures an optimum mechanical strength according to severe applied operating conditions in terms of temperature and pressure. To achieve this goal, a thermo-mechanical 1-way sequential coupling has been used as a solving method. The physical model suggested in this study and the simulations procedure was described under detailed assumptions. In fact, the main hypotheses in the current formulation were the thermo-elastic behavior of the tank's materials and the steady state assumption analysis.This paper outlines three studies that were performed to extend the lifespan of the horizontal storage tank, through the definition of a suitable material and an optimal design. The main conclusions of the assessment are that the optimal configuration which avoid the appearance of the stress concentration zones is the configuration (c), where Ri = 11 mm and Re = 14 mm, because the stress on the tank's shell was better applied. Moreover, the effect of the material's selection was carried out, and it was found that stainless steel is the optimal material. Last but not least, a set of simulations were conducted to investigate the tank shell thickness on which the thermo-mechanical constraints were applied. The thickness t=2 mm was presenting an optimal mechanical behavior with regard to the studied operating conditions.

Levitation Force Maximization in HTS Magnetic Bearings Formulated by a Semianalytical Approach

High-speed rotatory electromechanical devices can be practically implemented using magnetic bearings that provide a contactless operation. Besides the contactless operation, high-temperature superconducting (HTS) bearings possess an exclusive feature, i.e., self-stability. This characteristic removes requiring any control schemes and consequently an easier implementation and lower costs would be expected. This paper deals with presentation of an optimal rotor configuration in radial-type HTS bearings. A semianalytical approach called Adomian decomposition method is used to efficiently solve the governing equations of HTS bearings deduced from the H-formulation combined with the E-J power law. Control variables of the optimization process include rotor dimensions as well as magnetization direction of permanent magnets. Optimization is carried out using a powerful approach called differential evolution with maximization of levitation force around the equilibrium position as its objective function. In order to verify the proposed approach, a two-dimensional axisymmetric finite element method is also implemented.

Sound radiation from impact-driven raked piles

Sound emissions from impact pile driving of raked piles present a significant azimuthal dependence in the radiated sound field due to the non-axisymmetric orientation of the pile. In this work the sound radiation from raked piles is modeled using a finite element method (FEM) model of the pile and near-field region. The near-field model of the sound field is then used as input into a normal mode model to predict the sound radiation in the far-field. The azimuthal dependence of the radiated sound field is shown to be accurately predicted using an equivalent axisymmetric FEM model of the pile configuration, thus negating the need to construct a fully three-dimensional model (3D) of the raked pile. This is achieved by matching the radiated field from the equivalent axisymmetric pile model to a vertical array of phased point sources, and then horizontally offsetting the source locations to match the incline of the raked pile. The resulting sound field closely matches the numerical predictions from a fully 3D FEM model of the raked pile. The results of numerical modeling are compared to corresponding acoustic measurements taken on the North West shelf of Western Australia.

Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking

The Greek aperitif Ouzo is not only famous for its specific anise-flavoured taste, but also for its ability to turn from a transparent miscible liquid to a milky-white coloured emulsion when water is added. Recently, it has been shown that this so-called Ouzo effect, i.e. the spontaneous emulsification of oil microdroplets, can also be triggered by the preferential evaporation of ethanol in an evaporating sessile Ouzo drop, leading to an amazingly rich drying process with multiple phase transitions (Tan et al., Proc. Natl Acad. Sci. USA, vol. 113 (31), 2016, pp. 8642–8647). Due to the enhanced evaporation near the contact line, the nucleation of oil droplets starts at the rim which results in an oil ring encircling the drop. Furthermore, the oil droplets are advected through the Ouzo drop by a fast solutal Marangoni flow. In this article, we investigate the evaporation of mixture droplets in more detail, by successively increasing the mixture complexity from pure water over a binary water–ethanol mixture to the ternary Ouzo mixture (water, ethanol and anise oil). In particular, axisymmetric and full three-dimensional finite element method simulations have been performed on these droplets to discuss thermal effects and the complicated flow in the droplet driven by an interplay of preferential evaporation, evaporative cooling and solutal and thermal Marangoni flow. By using image analysis techniques and micro-particle-image-velocimetry measurements, we are able to compare the numerically predicted volume evolutions and velocity fields with experimental data. The Ouzo droplet is furthermore investigated by confocal microscopy. It is shown that the oil ring predominantly emerges due to coalescence.

Study on the design method of equal strength rim based on stress and fatigue analysis using finite element method

Wheels are important safety components in the vehicle driving system. Automobile lightweight is the direction of the modern automobile development. In this article, steel wheel lightweight was studied. The equal strength design of rim was used to reduce the weight of the wheel. Stress analysis of the wheel was studied using UG/Nastran. A professional software WheelStrength was used to predict the radial and cornering fatigue lives of the wheel. Sheet stamping process was set up to analyze the interference fit between the disk and the rim. The assembly was simulated by axisymmetric finite element method. After calculation and analysis, the stress distributions and fatigue lives for rim under different load cases have been found. The thicknesses of wheel rim bead and the interface between rim and disk cannot be reduced. Stress and fatigue simulation results were compared using different thicknesses of the optimized region. It was found that the best thickness of the optimized region was 1.5 mm. Spinning was used to form the flared preform. The thickness of the rim after spinning and rolling forming agreed well with the simulation. The results of fatigue tests indicated that the lightweight wheel met the design requirement. The weight of the rim was reduced by about 14%.

Analytical method for levitation force calculation of radial HTS magnetic bearings

Introducing high-temperature superconductors (HTS) and their outstanding properties stimulates scientists and engineers in various fields to modernise the products with this new technology. Electric power industry also was affected by this finding in different branches including bearings. The idea of HTS bearings was rapidly developed due to its two main features, i.e. self-stability and contactless operation which leads to save remarkable amount of energy. However, a successful implementation of HTS bearing undoubtedly requires an accurate modelling in the beginning. The contribution of this study is an analytical method for simulating the electromagnetic behaviour of a radial HTS magnetic bearing. The governing non-linear system of partial differential equations in the HTS bulks deduced from the H-formulation along with the E–J power law and is efficiently solved using variational iteration method (VIM). The validity of VIM is ascertained by comparing the results with numerical two-dimensional axisymmetric finite-element method simulations.

Rapid simulation of electromagnetic telemetry using an axisymmetric semianalytical finite element method

An axisymmetric semianalytical finite element method is proposed and employed for rapid simulations of electromagnetic telemetry in layered underground formation. In this method, the layered media is decomposed into several subdomains and the interfaces between subdomains are discretized by conventional finite elements. Then a Riccati equation based high precision integration scheme is applied to exploit the homogeneity along the vertical direction in each layer. This semianalytical finite element scheme is very efficient in modeling electromagnetic telemetry in layered formation. Numerical examples as well as a field case with water based mud as drilling fluid are given to demonstrate the validity and effectiveness of this method.

Sensitivity Analysis of Rotor Parameters in Axially Magnetized Radial HTS Magnetic Bearings Using an Analytical Method

Nowadays, high-temperature superconducting (HTS) bearings are well known in various fields requiring contactless operation, which results in decreasing loss and saving a great deal of energy. Self-stability serves as another advantage of HTS bearings, which emerges due to the flux pinning phenomenon. Consequently, the need for control equipment and excess costs disappears. One of the most important applicable characteristics to design HTS bearings is referred to as levitation force. In this paper, sensitivity analysis of rotor parameters in order to enhance levitation force is performed. For this purpose, an analytical method called the variational iteration method is applied to efficiently solve the governing nonlinear system of partial differential equations in the HTS bulks deduced from the H-formulation along with the E-J power law. A numerical two-dimensional axisymmetric finite-element method is also invoked to verify results obtained by the analytical method.

Shape optimization of a metallic flywheel using an evolutive system method: Design of an asymmetrical shape for mechanical interface

In this work, a novel optimization approach is used to define the shape of a flywheel for energy storage. The procedure acts on a two-dimensional axisymmetric finite element method model, in which many parameters are used to describe the geometry. The optimization is performed by an evolutive system method, whereby the population’s genome is described with statistical quantities. An accurate definition of the fitness function allows for a broad spectrum of objectives. The evolution of the fitness value during population generation is discussed. The procedure does not benefit from parallelization: an alternative way of parallelizing the optimization process is presented, where the population is equally divided among the cores and calculated independently, allowing for an approximately linear performance scaling with the number of cores. The method is applied to the minimization of the mass in a flywheel for energy storage application, displaying great flexibility to the variation of the parameters describing the rotational speed, geometry constraints, and material properties. The true potential of the evolutive method is then demonstrated by optimizing an asymmetrical flywheel, where a mechanical interface lies on one side only. Usually additional parts are added manually on the optimized shape, increasing the thickness where necessary; this method permits to directly optimize to the final shape. The script used in this work is available upon request. Matlab and Ansys APDL software are needed.

Numerical Modeling of Radiated Sound for Impact Pile Driving in Offshore Environments

In this paper, a coupled near-to-far-field numerical model for predicting the acoustic emissions from impact pile driving in offshore environments is presented. The near-field region of the pile is modeled via an axisymmetric finite element method (FEM) model which is solved in the frequency domain. The calculated radiated field at a chosen radial distance in the FEM model is then expanded into a series of local normal modes (NMs) which are propagated into the far field, to predict the piling sound characteristics, such as the peak pressure and sound exposure levels, at large ranges. Numerical examples are presented for the same pile configuration adopted for the COMPILE 2014 benchmark workshop on predicting offshore pile-driving noise, and these results are compared in both the near and far fields to those of several other research groups who presented results at the workshop. Results from the present FEM-NM near-to-far-field model are shown to be generally in good agreement with those results from the other research groups. In the near field, similar signal waveforms are predicted by the various models which employ the same pile wall boundary conditions. In the far field, the selected models showed a variation of $\pm$ 1 dB at 1.5 km, and $\pm$ 4 dB at 50 km for the predicted peak pressure levels, and a variation of $\pm$ 1.5 dB over the 50-km range for the predicted sound exposure levels.

Analysis and optimisation of an axial flux permanent magnet coreless motor based on the field model using the superposition principle and genetic algorithm

Abstract In the paper, methodologies for the magnetic field simulation in an axial flux permanent magnet coreless (AFPMC) motor have been proposed and discussed. Two approaches have been considered and investigated, both based on representing the 3D field distribution by superimposing axisymmetric 2D patterns. The first of studied approaches applies directly to the Biot-Savart law while the second uses a 2D axisymmetric finite element method. The selected results of magnetic field distributions and electromagnetic torque characteristics for the considered AFPMC motor have been presented and compared with results obtained using the commercial FEM package ‘Maxwell’. The elaborated algorithms have been incorporated into the design routines allowing multi-parameter optimisation of the considered motor construction.