scholarly journals Three dimensional mathematical model of tooth for finite element analysis

2010 ◽  
Vol 138 (1-2) ◽  
pp. 19-25 ◽  
Author(s):  
Tatjana Puskar ◽  
Darko Vasiljevic ◽  
Dubravka Markovic ◽  
Danimir Jevremovic ◽  
Dejan Pantelic ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Morphological Characteristics ◽  
Solid Modeling ◽  
3D Models ◽  
Element Analysis ◽  
Endodontically Treated Tooth ◽  
Stress And Deformation ◽  
The Mathematical Model

Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

The Finite Element Analysis and Structure Optimizing of the 42MN Flatting Mill’s Higher Beam

2010 ◽  
Vol 145 ◽  
pp. 317-320
Author(s):  
Chun Ming Zhang ◽  
Run Yuan Hao
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Structural Design ◽  
Structural Parameters ◽  
Element Model ◽  
Optimum Structure ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
The Mathematical Model

This text is on the basis of the investigation of the 42MN flatting mill’s higher beam, establishing the flatting mill’s higher beam’s finite element model and the mathematical model which has optimum structure. According to the results of their structure finite element analysis, weaved the relevant procedures and optimized them, obtained ideal structural parameters, this text provide better ideas and ways for the structural design of the flatting mill’s higher beam.

Influence of Assembly Tolerance on Dynamic Characteristics of Motor Rotation Assembly

2013 ◽  
Vol 655-657 ◽  
pp. 608-611 ◽  
Author(s):  
Wei Wen Lv ◽  
Xu Xing Jin
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Characteristics ◽  
Machine Tools ◽  
Machining Accuracy ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Assembly Tolerance ◽  
The Mathematical Model

The motor rotation assembly of machine tools is mainly composed of spindle, rotor and bearings, it is to some extent the most important component, and its dynamic characteristics directly affect the machining accuracy and efficiency. Although the finite element method is effective to solve such dynamic problem, the conventional method generally ignores the influence of assembly tolerance between the spindle and the rotor .This probably would lead to a larger error result. A new method is described to evaluate the results obtained from finite element analysis .Firstly, a finite element mathematical model of motor rotation assembly is established, and then the model is tested by means of modal experiment, finally, the mathematical model results calculated by MATLAB software is compared with that of modal experiment, the results show that this modeling method is accurate and efficient. Furthermore, rotors of different inner diameters are mounted onto the spindle of same size, and then modal experiment and a finite element analysis are applied to obtain the dynamic characteristics of the motor rotation assembly under different assembly tolerances. This research can provide some reference values for the tolerance design of the motor rotation assembly.

Modelling a Precision Positioning System

2015 ◽  
Vol 220-221 ◽  
pp. 374-379
Author(s):  
Giedrius Augustinavičius ◽  
Audrius Čereška
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Degree Of Freedom ◽  
Positioning System ◽  
Precision Positioning ◽  
Element Analysis ◽  
The Mathematical Model ◽  
Fine Adjustment

The paper presents the model and design of a flexure-based precise 4 DOF degree of freedom positioning system for micro-positioning uses. The positioning system is featured with monolithic architecture, flexure-based joints and ultra-fine adjustment screws. The mathematical model for the output displacements of the positioning system has been verified by finite element analysis (FEA).

The Research on Three-Dimensional Model of Non-Circular Gear

2012 ◽  
Vol 479-481 ◽  
pp. 953-956
Author(s):  
Guo Xing Sun ◽  
Chuan Qiong Sun ◽  
Qiang Liu
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Gear Tooth ◽  
Three Dimensional ◽  
Tooth Profile ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Element Analysis ◽  
The Mathematical Model

According to the principles of engagement and the mathematical model of non-circular gear tooth profile, the tooth profile of non-circular gear is draw. Then the three-dimensional model of the non-circular gear is created in Pro/E three-dimensional software to provide the basis for a non-circular gear motion analysis, dynamic analysis and finite element analysis.

A Mathematical Model Used in Conjunction With a Finite Element Analysis to Aid in the Design and Analysis of Bourdon Tubes

1982 ◽  
Vol 104 (3) ◽  
pp. 540-543 ◽  
Author(s):  
R. C. Weber ◽  
R. L. Davis
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Computer Program ◽  
Three Dimensional ◽  
Published Data ◽  
Element Analysis ◽  
Finite Element Program ◽  
Element Program ◽  
The Mathematical Model

A mathematical model that describes a variety of Bourdon tube geometries has been used for the three-dimensional analysis of Bourdon tubes. The variation of the stresses and tip deflections with respect to the variables used in the mathematical model are then presented as an aid in the design and analysis of the Bourdon tube. The finite element program represents a user-orientated package for calculation of tip deflections and stresses. Stresses and deflections are compared to both strain gage data and instrumented tip deflections as well as published data to establish the credibility of both the model and computer program.

Predicting the Large Deflection Path of End-Loaded Tapered Cantilever Beams

2000 ◽  
Author(s):  
Matthew B. Parkinson ◽  
Gregory M. Roach ◽  
Larry L. Howell
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Euler Equation ◽  
Large Deflection ◽  
Nonlinear Finite Element ◽  
Cantilever Beams ◽  
Element Analysis ◽  
Moments Of Inertia ◽  
Physical Testing

Abstract A simple (quadratic) mathematical model for predicting the deflection path of both non-tapered and continuously tapered cantilever beams loaded with a vertical end force is presented. It is based on the proposition that the path is a function of the ratio of the endpoints’ moments of inertia. The model is valid for both small and large (the tip makes a 70 degree angle with the horizontal) deflections. This was verified through physical testing, comparison to solution of the Bernoulli-Euler equation, and results obtained through nonlinear finite element analysis. Predicted endpoint deflections were found to be accurate within 1.8% of the actual deflection path for moment of inertia ratios varying from 1:1 to 1000:1.

Finite Element Analysis of Automobile Leaf Spring Bassed on Pro/E

2013 ◽  
Vol 753-755 ◽  
pp. 1250-1253
Author(s):  
Na Wu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Static Analysis ◽  
Solid Modeling ◽  
Leaf Spring ◽  
Assembly Process ◽  
Analysis Method ◽  
Element Analysis ◽  
Brick Element

Nunmerical analysis method was used to analyze multi-chip tapered leaf spring with the same area under vertical loads, in which the brick element of twenty nodes was used to model the spring leaves and the solid modeling using in ansys was modeled in 3D softwar. Each piece of nodes were coupled in order to simulate the leaf spring assembly process. The results of six modes analysis and static analysis could be the research basis for the further study of leaf spring.

scholarly journals MODELLING A COMPLIANT-BASED PRECISE POSITIONING STAGE / AUKŠTO TIKSLUMO POZICIONAVIMO SISTEMOS MODELIAVIMAS TAIKANT BESIDEFORMUOJANČIUS MECHANIZMUS

2013 ◽  
Vol 6 (4) ◽  
pp. 523-527 ◽  
Author(s):  
Giedrius Augustinavičius ◽  
Audrius Čereška
Keyword(s):  
Mathematical Model ◽  
Finite Element Analysis ◽  
Positioning System ◽  
Element Analysis ◽  
Precise Positioning ◽  
Positioning Systems ◽  
Positioning Stage ◽  
Amplification Mechanism ◽  
Analytical Approaches ◽  
The Mathematical Model

The paper presents modelling precise dual axis flexure-based precision positioning systems for micro-positioning applications. The positioning system is featured with monolithic architecture, flexure-based joints and piezo stacks. Its workspace has been evaluated via analytical approaches. Amplification mechanism is optimally designed. The mathematical model of the positioning system has been derived and verified by resorting to finite element analysis (FEA). The established analytical and (FEA) models are helpful for optimizing reliable architecture and improving the performance of the positioning system. Santrauka Straipsnyje pristatomas dviejų ašių didelio tikslumo pozicionavimo sistemos su paketiniais pjezovykdikliais modeliavimas, taikant besideformuojančius vientiso kūno mechanizmus. Pozicionavimo sistemą sudaro besideformuojančio vientiso kūno mechanizmas ir paketiniai pjezovykdikliai. Besideformuojantis vientiso kūno mechanizmas norimam poslinkiui pasiekti buvo optimizuotas Solidworks Simulation programiniu paketu. Platformų poslinkiams apskaičiuoti sudarytas matematinis modelis, kurio patikimumas patikrintas baigtinių elementų metodu. Sudaryto matematinio modelio ir rezultatų, gautų baigtinių elementų metodu, skirtumai yra mažesni nei 5 %, todėl pasiūlyta modeliavimo metodika gali būti taikoma kuriant pozicionavimo sistemas su besideformuojančiais elementais.

Design and Analysis of Manufacturing Component Under Sustainability Considerations: A Case Study of Electronic and Mechanical Indexing Head for Milling Operation

2018 ◽  
Author(s):  
Nand K. Jha ◽  
Mahmoud M. Amin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cost Estimation ◽  
Minimum Energy ◽  
Solid Modeling ◽  
Milling Machine ◽  
Element Analysis ◽  
Milling Operation ◽  
The Cost

An attempt has been made to design and analyze Indexing Head a very important component in milling operation under sustainability considerations. The design of each component of indexing head is presented along with solid modeling and finite element analysis. The cost estimation for indexing head for milling operation is also presented. The design and finite element analysis of indexing head should be utilized by manufacturers of this very useful device in milling operation. It is used for cutting gears, spirals, splines, etc. The cost estimated of the manufactured indexing head shows it to be within reasonable limits of market. Finite element analysis of each component is safe. An electronic indexing is suggested as an improvement over the mechanical indexing head. A schematic of electronic indexing is presented. The electronic indexing head can be used with milling machine not provided with indexing head and will be portable. The minimum energy needed to manufacture the indexing head is also estimated.

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