A Model for Bending, Torsional, and Axial Vibrations of Micro- and Macro-Drills Including Actual Drill Geometry—Part I: Model Development and Numerical Solution

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Sinan Filiz ◽  
O. Burak Ozdoganlar
Keyword(s):  
Cross Section ◽  
Model Development ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Three Dimensional Model ◽  
Axial Thrust ◽  
One Dimensional ◽  
Three Dimensional Models ◽  
The Individual ◽  
Actual Geometry

Part I of this work presents a combined one-dimensional/three-dimensional approach for obtaining a unified model for the dynamics of micro- and macro-drills. To increase the numerical efficiency of the model, portions of the drill with circular cross-section (shank, extension, and tapered sections) are modeled using one-dimensional beam models without compromising model accuracy. A three-dimensional model is used for an accurate representation of the fluted section, considering the actual geometry with the pretwisted shape and axially varying (nonaxisymmetric) cross-section. The actual cross-section of the drills is incorporated to the model through a polynomial mapping while the pretwist effect is captured by defining a rotating reference frame. The boundary-value problem for both one- and three-dimensional models are derived using a variational approach, based on the extended Hamilton’s principle, and are subsequently solved by applying the spectral-Tchebychev technique. A component-mode synthesis is used for connecting the individual sections to obtain the dynamic model for the entire drill. Convergence of the model is studied by varying the number of polynomials for each section. The experimental validation of the model is included in Part II for both macro- and micro-drills. Also included in Part II is an analysis of drill dynamics for varying drill-geometry parameters and axial (thrust) force.

Axially Symmetric Waves in Elastic Rods

1960 ◽  
Vol 27 (1) ◽  
pp. 145-151 ◽  
Author(s):  
R. D. Mindlin ◽  
H. D. McNiven
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Elastic Rod ◽  
One Dimensional ◽  
Axial Shear ◽  
Wave Numbers ◽  
Complex Wave

A system of approximate, one-dimensional equations is derived for axially symmetric motions of an elastic rod of circular cross section. The equations take into account the coupling between longitudinal, axial shear, and radial modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite rod is explored in detail and compared with the analogous solution of the three-dimensional equations.

On the Critical Plunger Speed and Three-Dimensional Effects in High-Pressure Die Casting Injection Chambers

2003 ◽  
Vol 125 (3) ◽  
pp. 529-537 ◽  
Author(s):  
J. Lo´pez ◽  
F. Faura ◽  
J. Herna´ndez ◽  
P. Go´mez
Keyword(s):  
Molten Metal ◽  
Cross Section ◽  
Die Casting ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
One Dimensional ◽  
Pressure Die Casting

During the initial slow stage of the injection process in high-pressure die casting machines with horizontal cold chamber, a plunger pushes the molten metal which partially fills the injection chamber, causing the formation of a gravity wave. The evolution of the wave surface profile, which depends on the plunger acceleration law, may trap air in the molten metal, causing porosity when the metal solidifies. In this work, a one-dimensional shallow-water model, which is solved numerically using the method of characteristics, and a three-dimensional numerical model, based on a finite element formulation and the volume of fluid (VOF) method for treating the free surface, are used to analyze the flow of molten metal in an injection chamber of circular cross section. The results for the evolution of the free surface obtained from both models for different plunger motion laws and initial filling fractions of the injection chamber were in good agreement for broad ranges of operating conditions. The existence of a critical plunger speed, above which the reflection of the wave of molten metal against the chamber ceiling might appreciably increase air entrapment effects, is investigated. The results for the wave profiles in chambers of circular cross section are compared with those obtained in an equivalent two-dimensional configuration of the injection chamber, for which the shallow-water model is solved analytically. It is shown how the results obtained by applying the one-dimensional model to a two-dimensional chamber configuration can be used to reproduce, with an acceptable degree of accuracy, the salient characteristics of the flow of molten metal in a real injection chamber of circular cross section.

A Three-Dimensional Model for Strength Assessment of Type-C Independent Cargo Tank Structures

2020 ◽  
Vol 36 (04) ◽  
pp. 271-279
Author(s):  
Ming Song ◽  
Bin Qin ◽  
Li Zhou ◽  
Zhengru Ren
Keyword(s):  
Three Dimensional ◽  
Liquefied Petroleum Gas ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Strength Assessment ◽  
One Dimensional ◽  
Proposed Model ◽  
Linear Spring ◽  
Type C ◽  
Three Dimensional Models

For the analysis of the arrangement and strength of Type-C independent cargo tank structures, the linear spring or rod elements are usually used to model supporting woods, in which one-dimensional and linear contact behaviors are assumed. This study aimed at developing a three-dimensional model for achieving more accurate strength assessment. In the model, solid elements are modeled to simulate the supporting woods. The nonlinear contact between the cargo tanks and the supporting woods is taken into account through LS-DYNA software. Numerical simulations of a 22,000-m3 liquefied petroleum gas carrier are carried out using both one-dimensional and three-dimensional models. Three load cases including one static and two dynamic cases are considered to assess the strength of the tank structures and supporting woods. The results obtained by the proposed model are compared with the results on the basis of spring elements. It is found that this new model can provide more reasonable strength predictions of the tank structures and the supporting woods. The method based on spring elements underestimates the wood stress, which indicates that it may be not conservative. Some discussions and suggestions are presented.

Research of Special-Shaped Membrane Electrode Assembly for Direct Methanol Fuel Cell

2011 ◽  
Vol 464 ◽  
pp. 409-413 ◽  
Author(s):  
Xing Xing Wang ◽  
Hong Jun Ni ◽  
Yu Zhu ◽  
Ming Yu Huang ◽  
Ping Liao
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Catalyst Layer ◽  
Membrane Electrode Assembly ◽  
Gas Diffusion ◽  
Cathode Layer ◽  
Membrane Electrode ◽  
Titanium Mesh ◽  
Three Dimensional Model

In order to reduce the costs, improve the performances and promote the industry process, basing on calculus and finite element thinking, conceptual design of special-shaped membrane electrode assembly (S-MEA) was proposed, including six shapes. S-MEA size was determined by calculating, admeasuring and devising elaborately, whose basic parameter was gained from experiment datum. S-MEA was made up of titanium mesh anode layer, anode catalyst layer, Nafion membrane layer, cathode catalyst layer, gas diffusion layer and titanium mesh cathode layer in turn, which was different from MEA of the fluid field bipolar plates in the macro-structure but had the same micro-mechanism. Three-dimensional model was devised through Pro/E, planar diagrammatic drawing was created by the software also, and detail drawing was designed further with CAD. The process of preparing S-MEA was researched basing on the design. Then three typical S-MEA prototypes were made by bend-hot-pressing with home-made molds and precision hydraulic machine, including open triangular cross-section MEA, circular cross-section MEA and square cross-section MEA.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

Phonetic iconicity in the evaluative morphology of a sample of Indo-European, Niger-Congo and Austronesian languages

2010 ◽  
Vol 3 (2) ◽  
pp. 156-180 ◽  
Author(s):  
Renáta Gregová ◽  
Lívia Körtvélyessy ◽  
Július Zimmermann
Keyword(s):  
Three Dimensional ◽  
Sound Symbolism ◽  
Three Dimensional Model ◽  
Austronesian Languages ◽  
Place Of Articulation ◽  
European Languages ◽  
Phonetic Symbolism ◽  
The Individual ◽  
Core Vocabulary

Universals Archive (Universal #1926) indicates a universal tendency for sound symbolism in reference to the expression of diminutives and augmentatives. The research ( Štekauer et al. 2009 ) carried out on European languages has not proved the tendency at all. Therefore, our research was extended to cover three language families – Indo-European, Niger-Congo and Austronesian. A three-step analysis examining different aspects of phonetic symbolism was carried out on a core vocabulary of 35 lexical items. A research sample was selected out of 60 languages. The evaluative markers were analyzed according to both phonetic classification of vowels and consonants and Ultan's and Niewenhuis' conclusions on the dominance of palatal and post-alveolar consonants in diminutive markers. Finally, the data obtained in our sample languages was evaluated by means of a three-dimensional model illustrating the place of articulation of the individual segments.

On the Flexural-Torsional Behavior of a Straight Elastic Beam Subject to Terminal Moments

1993 ◽  
Vol 60 (2) ◽  
pp. 498-505 ◽  
Author(s):  
Z. Tan ◽  
J. A. Witz
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Beam ◽  
Cartesian Coordinate System ◽  
Kinematic Constraints ◽  
Torsional Behavior ◽  
Cartesian Coordinate

This paper discusses the large-displacement flexural-torsional behavior of a straight elastic beam with uniform circular cross-section subject to arbitrary terminal bending and twisting moments. The beam is assumed to be free from any kinematic constraints at both ends. The equilibrium equation is solved analytically with the full expression for curvature to obtain the deformed configuration in a three-dimensional Cartesian coordinate system. The results show the influence of the terminal moments on the beam’s deflected configuration.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

scholarly journals Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

2013 ◽  
Vol 05 (01) ◽  
pp. 1350002 ◽  
Author(s):  
I. Benedetti ◽  
F. Barbe
Keyword(s):  
Three Dimensional ◽  
Constitutive Modelling ◽  
Polycrystalline Materials ◽  
High Fidelity ◽  
Computational Capability ◽  
Mechanical Models ◽  
Three Dimensional Models ◽  
The Individual ◽  
Individual Grains ◽  
Micro Structures

A survey of recent contributions on three-dimensional grain-scale mechanical modelling of polycrystalline materials is given in this work. The analysis of material micro-structures requires the generation of reliable micro-morphologies and affordable computational meshes as well as the description of the mechanical behavior of the elementary constituents and their interactions. The polycrystalline microstructure is characterized by the topology, morphology and crystallographic orientations of the individual grains and by the grain interfaces and microstructural defects, within the bulk grains and at the inter-granular interfaces. Their analysis has been until recently restricted to two-dimensional cases, due to high computational requirements. In the last decade, however, the wider affordability of increased computational capability has promoted the development of fully three-dimensional models. In this work, different aspects involved in the grain-scale analysis of polycrystalline materials are considered. Different techniques for generating artificial micro-structures, ranging from highly idealized to experimentally based high-fidelity representations, are briefly reviewed. Structured and unstructured meshes are discussed. The main strategies for constitutive modelling of individual bulk grains and inter-granular interfaces are introduced. Some attention has also been devoted to three-dimensional multiscale approaches and some established and emerging applications have been discussed.

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