3D FEM Simulation Research Articles

Extending the validity of squeezed-film damper models with elongations of surface dimensions

Compact models for micromechanical squeezed-film dampers with gap sizes comparable to the surface dimensions are presented. Two different models considering both the border flow and non-uniform pressure distribution effects are first derived for small squeeze numbers. In the first ‘surface extension’ model the border effects are considered simply by calculating the damping with extended surface dimensions, and in the second ‘border flow channel’ model an additional short fictitious flow channel is placed at the damper borders. Utilizing a large amount of two-dimensional (2D) FEM simulation results by varying the damper dimensions, mainly the ratio a/h between the surface length and the air gap height, surface elongations are extracted using both elongation models. Both linear and torsional modes of motion are considered at the continuum flow regime. These results show that the ‘surface extension’ model is superior, since the extracted elongation Δa is almost constant (Δa = 1.3h), leading to a very simple model. Next, the rare gas effects are included in the ‘surface extension’ model in the slip flow regime (Knudsen number 0 < Kn < 0.13). Considering slip boundary conditions, 2D FEM simulations are repeated and the elongations, now functions of the Knudsen number, are extracted from the results. A simple fitted equation for calculating the surface extension Δa finally results. The maximum relative errors of the models are smaller than 10% for a/h > 4 in the linear motion and for a/h > 10 in the torsional motion. The model assumes incompressible flow and thus the maximum frequency where the models are valid is limited. In typical MEMS topologies where the elongations must be considered, this means that the models are valid below frequencies of 500 kHz. To also model rectangular 2D squeezed-film dampers, these elongations are applied directly in the surface length and width used in the compact models. Comparison with three-dimensional (3D) FEM simulations shows that the new model gives excellent results, and it extends the validity range of existing compact models. The maximum relative error of the models is smaller than 10% for a/h > 16 in the linear motion and for a/h > 16 in the torsional motion. The new surface extension model is useful in simulating both the circuit level and the system level behavior of gas-damped microelectromechanical devices with aspect ratios greater than 2 in the time and frequency domains.

3D nonlinear modeling of microhotplates in CMOS technology for use as metal-oxide-based gas sensors

A modeling approach has been developed to support CMOS microhotplate optimization and to allow for sensor system simulations. All steps are detailed that are necessary to arrive at a geometric hotplate representation for nonlinear 3D-FEM simulations starting from a physical microhotplate layout. A lumped-model description of the microhotplate is discussed, which forms the basis for combined simulations of sensor and circuitry. FEM simulations were performed for two different microhotplate designs. Both types of microhotplates were fabricated in a 0.8 µm industrial CMOS process by post-CMOS micromachining. The first design includes a circular microhotplate with a Si-island underneath the heated area of the microhotplate. The characteristic figures such as thermal resistance and thermal time constant were extracted from the model, which showed an agreement within 5–10% with experimental values for temperatures up to 325 °C. The second design without Si-island featured an array of temperature sensors for assessment of the temperature distribution. Experimental data from the different sensor locations were compared to simulation results, and, again, showed excellent agreement with a maximum deviation of 5%. The influence of the nanocrystalline tin oxide thick-film layer on the temperature distribution was also experimentally investigated: better temperature homogeneity in the heated area and somewhat slower temperature dynamics.

Effects of chamber shapes of porthole die on elastic deformation and extrusion process in condenser tube extrusion

Abstract This paper describes a 3D FEM simulation of porthole die extrusion process for producing condenser tubes used for a cooling system of automobiles. In general, condenser tube is mainly manufactured by the conform extrusion method, but this process is less effective as compared with the direct extrusion method in productivity per unit time and in the equipment investment. Therefore, it is essential for the conversion to the direct extrusion with porthole die that can produce condenser tube with competitiveness in costs and qualities compared with the existing conform extrusion. However, an experimental method to quantify the deformation behavior of porthole die for condenser tube extrusion has not been established yet, due to its complicated die assembly and complexity of metal flow. FEM is a good alternative to evaluate the three-dimensional deformation behavior of metals in condenser tube extrusion. Especially, an understanding of metal flow in porthole die extrusion is important, because it provides necessary information in die design for high performance extrusion. This study was designed to evaluate material flow, welding pressure, extrusion load, and the tendency of mandrel deflection that is affected by variation of chamber shape on porthole die. An estimation was carried out using FE analysis in non-steady state. Also, this study examined into the mandrel fracture behavior through investigating elastic deformation of mandrel during the extrusion.

Development of a 3D FEM simulator for coalbed two-phase flow with sorption/diffusion

Mobile monitoring is a strategy to characterize spatially and temporally variable air pollution in areas near sources. EPA's Geospatial Measurement of Air Pollution (GMAP) vehicle – an all-electric vehicle is outfitted with a number of measurement devices to record real-time concentrations of particulate matter and gaseous pollutants – was used to map air pollution levels near the Port of Charleston in South Carolina. High-resolution monitoring was performed along driving routes near several port terminals and rail yard facilities, recording geospatial coordinates and concentrations of pollutants including black carbon, size-resolved particle count ranging from ultrafine to coarse (6 nm–20 μm), carbon monoxide, and nitrogen dioxide. Additionally, a portable meteorological station was used to characterize local conditions. The primary objective of this work was to characterize the impact of port facilities on local scale air quality. The study determined that elevated concentration measurements of black carbon and PM correlated to periods of increased port activity and a significant elevation in concentration was observed downwind of ports. However, limitations in study design prevented a more complete analysis of the port effect.

3D FEM simulation of stationary metal forming processes with applications to slitting and rolling

A computational method is presented for the 3D FEM simulation of stationary metal forming processes. The described method has been applied to model the slitting and shape rolling processes. Some results of these simulations are given, which show that the ALE formulation used is suitable for the simulation of such processes. In the ALE formulation the grid displacement is independent of the material displacement. Therefore, the displacement of the nodes has to be defined such that the movement of the free surfaces can be followed (mesh management) and the values of the state variables have to be calculated at the new nodal positions (transfer of state variables). Both topics are addressed in this paper. Also the possibility of modelling stationary crack propagation is treated.

3D-FEM Simulation for EAC Crack Growth Evaluation and its Implication to Specimen Size Effects on Crack Growth Behavior

The primary objective of this study is to develop a quantitative model to predict the effects of materials, environment and mechanics such as loading configuration on environmentally-assisted cracking (EAC) of stainless steels in high-temperature water. It has basically been accepted that crack propagation in oxygenated high temperature water is controlled by a slip-dissolution and/or deformation-oxidation mechanism. According to this mechanism, the crack-tip strain rate is an extremely important mechanical parameter for determining the crack growth rates. Based upon a formulation obtained by combining Faraday’s equation with an elastic plastic analysis of the strain singularity at a growing crack-tip in work hardening materials, a theoretical formulation of crack-tip strain rate has been derived for plane strain and plane stress conditions. The FEM analysis for 3D crack growth can be compared to the theoretical 2D analysis. In this paper, we first make a CCP (Center Crack Plane) model, and performed a 3-dimensional Finite Element Analysis (3D-FEA) to evaluate the crack-tip stain rate paying attention to the element mesh size and to the loading history. After optimization these parameters, the calculated crack-tip strain distribution, including its logarithmic singularity, was founded to agree well with the theoretical distribution. The significance of the crack-tip strain rate upon the crack-tip strain distribution and crack growth rate was demonstrated. The specimen size effects on crack growth rates were discussed from this point of crack-tip strain distribution. Finally, we focused on the importance of crack-tip strain rate as a unique mechanical parameter that controls the crack growth rate.

Development of a 3D FEM simulator for coalbed two-phase flow with sorption/diffusion

Development of a 3D FEM simulator for coalbed two-phase flow with sorption/diffusion

Biomechanical analysis of the mechanism of elbow fracturedislocations by compression force

Fracture-dislocations of the coronoid and olecranon were produced experimentally, and their onset mechanisms were analyzed to clarify the effects of compression force on the coronoid and olecranon. The study used two-dimensional finite element method (2D-FEM) simulations and static loading experiments. The latter applied axial force distally to 40 cadaveric elbows. Posterior fracture-dislocations occurred between 15° of extension and 30° of flexion, anterior or posterior fracture-dislocations at 60°, and only anterior fracture-dislocations at 90°. Injuries were mainly to anterior or posterior support structures. The 2D-FEM simulations showed that the stress concentration areas moved from the coronoid process to the olecranon as position changed from extension to flexion. The very high frequency of concurrent fracture-dislocations of radial head or neck in the current study indicated that the radial head may also function as a stabilizer in the anterior support system.

Prediction of temperature evolution during the extrusion of 7075 aluminium alloy at various ram speeds by means of 3D FEM simulation

In the present work, an attempt was made to predict the temperature evolution during the extrusion of 7075 aluminium alloy by means of 3D FEM computer simulation. Results show that ram speed has a significant influence on the temperature distribution in the billet, which continuously changes throughout the process, as a result of complex heat generation and heat loss. The thermal effect results in characteristic variation of extrusion pressure. At a higher ram speed, the decrease of extrusion pressure is faster during the steady-state extrusion, due to more heat generation, less heat loss and thus more steeply decreased flow stress, as the process proceeds. The temperature inhomogeneity on the cross-section of the workpiece entering the die bearing is more pronounced when ram speed is higher. While going through the die, the extrudate undergoes a process of temperature redistribution and the temperature becomes more homogeneously distributed at the die exit. The present simulation does not render support to the general statement that the corner of the extrudate is hotter than the flat surfaces. Incipient melting is predicted to occur after a half of the billet is extruded at a ram speed as low as 1 mm/s corresponding to an extrusion speed of 0.48 m/min, if the billet contains the phases with low melting points. However, if the billet of the same alloy is in an improved metallurgical condition, no melting-related defects would be expected to occur to the extrudate running at a speed eight times faster. The results also confirm the linear relationship between the increase of the maximum temperature and logarithmic ram speed during the steady-state extrusion.

A 3D FEM simulation study on the isothermal extrusion of a 7075 aluminium billet with a predetermined non-linear temperature distribution

In this paper, computer simulations were performed on the extrusion of 7075 aluminium billets with non-uniform temperature distributions in order to inhibit excessive temperature rise that tends to occur during the conventional extrusion of a uniformly preheated billet. The simulations showed that when a linear temperature distribution was imposed on a billet with its rear end 150°C colder than its front end, the maximum temperature of the workpiece would still increase from 450°C to over 520°C at the end of an extrusion cycle, giving rise to hot shortness. Assigning a non-linear temperature distribution during preheating the billet could however significantly lessen this undesirable temperature increase, leading to isothermal extrusion. Such a non-linear temperature distribution was determined on the basis of the results obtained from the simulation of the extrusion of a billet with a linear temperature distribution. With this predetermined non-linear temperature distribution, the maximum temperature of the workpiece remained stable near the die entrance. The radial temperature variation on the cross-section of the extrudate became less significant as the material flowed through the die. In addition, the simulations showed another advantage of isothermal extrusion, i.e. an invariable die face pressure throughout an extrusion cycle. The maximum positive (tensile) principle stress was revealed at the corner of the die orifice, indicating that tearing tended to occur there.

Anomalous Surface Deformation of Sapphire Clarified by 3D-FEM Simulation of the Nanoindentation

This work clarifies the origin of anomalous surface deformation reflected by peculiar surface patterns around indentation impressions on various crystallographic planes of sapphire. The three-dimensional finite element simulation (3D-FEM) of nanoindentation in Al 2 O 3 crystal allowed the authors to localize the regions in which various kinds of twinning and slip are most prone to be activated. The work provides a novel approach to the hardness anisotropy, which was modeled so far using a modified uniaxial-stress approximation of this essentially 3D, non-isotropic contact problem. The calculated results enabled the authors to unravel the asymmetric surface deformation detected on prismatic planes by the high-resolution microscopy, which cannot be explained using simple crystallographic considerations.

A modeling methodology for finite element mesh generation of multi-region models with parametric surfaces

This paper presents a description of the reorganization of a geometric modeler, MG, designed to support new capabilities of a topological module (CGC) that allows the detection of closed-off solid regions described by surface patches in non-manifold geometric models defined by NURBS. These patches are interactively created by the user by means of the modeler's graphics interface, and may result from parametric–surface intersection in which existing surface meshes are used as a support for a discrete definition of intersection curves. The geometry of realistic engineering objects is intrinsically complex, usually composed by several materials and regions. Therefore, automatic and adaptive meshing algorithms have become quite useful to increase the reliability of the procedures of a FEM numerical analysis. The present approach is concerned with two aspects of 3D FEM simulation: geometric modeling, with automatic multi-region detection, and support to automatic finite-element mesh generation.

A 3D rigid–viscoplastic FEM simulation of the isothermal precision forging of a blade with a damper platform

A blade with a damper platform, with excellent anti-vibration characteristics and high efficiency, has become one of the most important new types of blade being developed in the aeronautical engine. However, the blade is complicated in shape, and the material used for its manufacture is difficult to deform. Therefore, it is important to undertake research on the blade-oriented precision forging process using three-dimensional finite element method (3D FEM) method numerical simulation for the practice and the development of the process. However, up to now, literature on such research has been scant. In this paper, based on the rigid–viscoplastic principle, three-dimensional finite element simulation is reported for the isothermal precision forging of the blade using the penalty function, and eight-node hexahedral isoparameteric elements for discretizing the deforming workpiece and triangular elements for discretizing the die cavity. The method of contracting from the boundary to the interior, proposed by the authors, is used for remeshing a distorted mesh system, and the method of modifying the position of nodes touching the die according to its original normal, also proposed by the authors, is used to avoid the “dead lock” problem due to the normal uncontinuity of scatted die meshes, to enable the simulation to be successful. Friction is considered for the die–workpiece interface boundary condition, and an arc is considered for the tenon–body joint, and a damper platform–body joint on the blade die cavity, respectively, which make it possible for the simulation to approach the practical forging process of a blade with a damper platform. 3D FEM simulation results have been obtained for the initial and deformed configurations, the deformed meshes of typical cross-sections, the distribution of effective strain at the final stage, load–displacement curves, in this way the deformation law of the forging of a blade with a damper platform being revealed. The achievements of this research serve as a significant guide to the optimization of design for the relevant process and dies. The method used is also of general significance to the forging processes of other type of blades and other complicated massive deformation processes.

249 高周波焼入れ過程の温度・応力解析

A 3D-FEM simulation program for induction hardening of S35C steel was made up. An electromagnetic field analysis, a heat conduction analysis and an elastic-plastic stress analysis during the induction hardening process of S35C steel gear were carried out by using this program, considering changes of the magnetic permeability, the resistivity, the thermal expansion coefficient and the yield stress with the temperature, and then residual stresses and hardened layers were obtained. Calculated temperatures during induction heating process and hardened layer were compared with measured temperatures and hardened layer. On the basis of these results, the validity of this computation program was confirmed.

627 すべり酸化モデルに基づく環境助長割れの 3 次元有限要素解析

627 すべり酸化モデルに基づく環境助長割れの 3 次元有限要素解析

2308 高周波焼入れ焼結金属歯車の残留応力・硬化層と曲げ疲労強度

A 3D-FEM simulation program for induction hardening of sintered metal gears was made up. An electromagnetic field analysis, a heat conduction analysis and an elastic-plastic stress analysis during the induction hardening process of sintered metal gears were carried out by using this program, considering changes of the magnetic permeability, the resistivity, the thermal expansion coefficient and the yield stress with the temperature. The measurement of hardness distribution and the bending fatigue test of induction hardened sintered metal gears were performed. Effects of the heating time on residual stress, hardened layer and bending fatigue strength of induction hardened sintered metal gears were examined, and compared with those of induction hardened wrought steel (S35C) gears.

135 Anomalous surface deformation of sapphire clarified by 3D-FEM simulation of the nanoindentation

135 Anomalous surface deformation of sapphire clarified by 3D-FEM simulation of the nanoindentation

A 3D rigid–viscoplastic FEM simulation of compressor blade isothermal forging

Based on the rigid–viscoplastic principle, three-dimensional finite element simulation using the penalty function was performed for the isothermal forging of a compressor blade. The key technologies of 3D rigid–viscoplastic FEM simulation are introduced. The workpiece was discretized into eight-node hexahedral isoparameteric elements and the die cavity was discretized into triangular elements. The methods proposed by the authors to remesh the distorted mesh system and to modify a node touching the die have been used. By means of 3D FEM simulation of the compressor blade, the initial and deformed configurations, the deformed meshes of typical cross-sections, the contours of effective strain at the final stage, the vertical load–displacement curve for the upper die, and the horizontal load–displacement curves for the upper and lower dies have been obtained, and so the deformation law of compressor blade forging has been obtained. The research results show that the 3D rigid–viscoplastic FEM simulation system developed in this paper is practical and reliable. In the present simulation, the tenon and the body on the blade die cavity are joined by an arc which coordinates the deformation between the tenon and the body, and friction is considered along the interface between the die and the workpiece. Thus, this simulation approaches practical compressor blade forging. The computational results can also be applied effectively to other types of blade forging processes.

Mechanical Properties of Hardened AISI 52100 Steel in Hard Machining Processes

This paper provides an approach using tensile tests at elevated temperatures to estimate mechanical properties of the work material for both elastic and plastic deformations in a broad range of strain, strain rate, and temperature in machining. The proposed method has been applied to estimate mechanical properties of hardened AISI 52100 steel in hard machining. Tensile testing is shown capable of estimating the mechanical properties of both elastic and plastic regions with large strains at elevated temperatures. Flow stresses at high strain rates in machining can be obtained by extrapolating the data from tensile tests by using the velocity-modified temperature. Flow stress data from tensile and cutting tests is consistent with regard to the velocity-modified temperature. Temperature is the dominant factor of mechanical properties of this material, while the effect of strain rate is secondary. Cutting forces and chip geometry predicted by the 3D FEM simulation of hard turning using the material property data obtained from the developed method agree well with the experimental data.

Flow Stress, Yield Criterion and Constitutive Equation of Mushy/Semi -Solid Alloys

New mathematical models of yield criterion and constitutive equations of mushy/semi -solid alloys (hereinafter described as semi -solid alloys) are proposed in order to investigate their flow features and deformation characteristics in various forming and shaping processes. First, a large number of uniaxial compression tests of semi -solid alloys are carried out and their stress -strain curves are measured. Through the tests, the remarkable drop of their flow stress is observed when their solid fraction decreases from 100%. The second, a new formula of yield criterion of semi -solid alloys is proposed. It can express the drop of their flow stress in semi -solid state. In addition, so -called constitutive equations, which describe flow and deformation of such alloys in forming and shaping processes, are derived from the formulated yield criterion. At the last stage, the obtained constitutive equations are introduced to 3D FEM simulation of upsetting of billets.