Study of Analysis Method for Hertz Contact Problem in Friction Drive

2014 ◽  
Vol 900 ◽  
pp. 798-802
Author(s):  
Ling Ling ◽  
Ju Qun Yi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problem ◽  
Elliptic Integral ◽  
Computational Cost ◽  
Point Contact ◽  
Computation Method ◽  
Hertz Contact ◽  
Hertz Contact Problem ◽  
Element Method

In order to deal with Hertz contact problem of friction drive in continuously variable transmission (CVT), two methods were proposed in this paper. One is a numerical computation method by MATLAB to solve the elliptic integral equations of Hertz contact, while the other is a finite element method (FEM) which uses the ANSYS Workbench to calculate the point contact between two elastic bodies. The computation results of Hertz contact problem of friction drive in a new CVT proposed by our research group show that, compared with a look-up table method, the numerical solution of MATLAB has many advantages such as high precision and less computational cost, while the finite element method has more simplicity and better visibility. The present methods can provide a reference for the solution of Hertz contact problem of common friction drive.

Element Selection and Meshing in Finite Element Contact Analysis

2010 ◽  
Vol 152-153 ◽  
pp. 279-283
Author(s):  
Run Bo Bai ◽  
Fu Sheng Liu ◽  
Zong Mei Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problem ◽  
Nonlinear Problem ◽  
Mechanical Engineering ◽  
Contact Analysis ◽  
The Finite Element Method ◽  
Different Types ◽  
Set Up ◽  
Element Method

Contact problem, which exists widely in mechanical engineering, civil engineering, manufacturing engineering, etc., is an extremely complicated nonlinear problem. It is usually solved by the finite element method. Unlike with the traditional finite element method, it is necessary to set up contact elements for the contact analysis. In the different types of contact elements, the Goodman joint elements, which cover the surface of contacted bodies with zero thickness, are widely used. However, there are some debates on the characteristics of the attached elements of the Goodman joint elements. For that this paper studies the type, matching, and meshing of the attached elements. The results from this paper would be helpful for the finite element contact analysis.

Semi-Implicit Coupling of CS-FEM and FEM for the Interaction Between a Geometrically Nonlinear Solid and an Incompressible Fluid

2015 ◽  
Vol 12 (05) ◽  
pp. 1550025 ◽  
Author(s):  
Tao He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Incompressible Fluid ◽  
Computational Cost ◽  
Geometrically Nonlinear ◽  
Arbitrary Lagrangian Eulerian ◽  
Coupling Strategy ◽  
Smoothed Finite Element Method ◽  
Characteristic Based Split ◽  
Element Method

A semi-implicit coupling strategy under the arbitrary Lagrangian–Eulerian description is presented for the incompressible fluid flow past a geometrically nonlinear solid in this paper. The incompressible fluid is solved by means of the characteristic-based split (CBS) finite element method while the cell-based smoothed finite element method is employed to settle the governing equation of the geometrically nonlinear solid. Because of the CBS fluid solver, the present coupling strategy is performed in a semi-implicit fashion. In particular, the first step of the CBS scheme is explicitly treated whereas the others are implicitly coupled with the structural motion. The computational cost is hence reduced because no subiterations are included in the explicit coupling step and the fluid mesh is frozen in the implicit coupling step. A classic cantilever problem is dealt with to validate the structural solver, and then flow-induced vibrations of a restrictor flap in a uniform channel flow is analyzed in detail. The obtained results agree well with the existing data.

A solution of transient rolling contact with velocity dependent friction by the explicit finite element method

2016 ◽  
Vol 33 (4) ◽  
pp. 1033-1050 ◽  
Author(s):  
Xin Zhao ◽  
Zili Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problem ◽  
Rolling Contact ◽  
Explicit Finite Element Method ◽  
Content Type ◽  
Explicit Finite Element ◽  
Friction Law ◽  
Transient Rolling ◽  
Element Method

Purpose – The purpose of this paper is to develop a numerical approach to solve the transient rolling contact problem with the consideration of velocity dependent friction. Design/methodology/approach – A three dimensional (3D) transient FE model is developed in elasticity by the explicit finite element method. Contact solutions with a velocity dependent friction law are compared in detail to those with the Coulomb’s friction law (i.e. a constant coefficient of friction). Findings – The FE solutions confirm the negligible influence of the dependence on the normal contact. Hence, analysis is focussed on the tangential solutions under different friction exploitation levels. In the trailing part of the contact patch where micro-slip occurs, very high-frequency oscillations are excited in the tangential plane by the velocity dependent friction. This is similar to the non-uniform sliding or tangential oscillations observed in sliding contact. Consequently, the micro-slip distribution varies greatly with time. However, the surface shear stress distribution is quite stable at different instants, even though it significantly changes with the employed friction model. Originality/value – This paper proposes an approach to solve the transient rolling contact problem with the consideration of velocity dependent friction. Such a problem was usually solved in the literature by the simplified contact algorithms, with which detailed contact solutions could not be obtained, or with the assumption of steady rolling.

scholarly journals Applications of A Hyper–Graph Grammar System in Adaptive Finite–Element Computations

2018 ◽  
Vol 28 (3) ◽  
pp. 569-582 ◽  
Author(s):  
Piotr Gurgul ◽  
Konrad Jopek ◽  
Keshav Pingali ◽  
Anna Paszyńska
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Cost ◽  
Three Dimensional ◽  
Parallel Execution ◽  
Graph Grammar ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Grammar System ◽  
Element Method

Abstract This paper describes application of a hyper-graph grammar system for modeling a three-dimensional adaptive finite element method. The hyper-graph grammar approach allows obtaining a linear computational cost of adaptive mesh transformations and computations performed over refined meshes. The computations are done by a hyper-graph grammar driven algorithm applicable to three-dimensional problems. For the case of typical refinements performed towards a point or an edge, the algorithm yields linear computational cost with respect to the mesh nodes for its sequential execution and logarithmic cost for its parallel execution. Such hyper-graph grammar productions are the mathematical formalism used to describe the computational algorithm implementing the finite element method. Each production indicates the smallest atomic task that can be executed concurrently. The mesh transformations and computations by using the hyper-graph grammar-based approach have been tested in the GALOIS environment. We conclude the paper with some numerical results performed on a shared-memory Linux cluster node, for the case of three-dimensional computational meshes refined towards a point, an edge and a face.

scholarly journals A Numerical Simulator Based on Finite Element Method for Diffusion-Advection-Reaction Equation in High Contrast Domains

2021 ◽  
Author(s):  
Hani Akbari
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Cost ◽  
Nonlinear Parabolic Equations ◽  
High Contrast ◽  
Nonlinear Parabolic ◽  
2D And 3D ◽  
Reaction Problem ◽  
Numerical Simulator ◽  
Element Method

Implementation of finite element method (FEM) needs special cares, particularly for essential boundary conditions that have an important effect on symmetry and number of unknowns in the linear systems. Moreover, avoiding numerical integration and using (off-line) calculated element integrals decrease the computational cost significantly. In this chapter we briefly present theoretical topics of FEM. Instead we focus on what is important (and how) to carefully implement FEM for equations that can be the core of a numerical simulator for a diffusion–advection-reaction problem. We consider general 2D and 3D domains, high contrast and heterogeneous diffusion coefficients and generalize the method to nonlinear parabolic equations. Although we use Matlab codes to simplify the explanation of the proposed method, we have implemented it in C++ to reveal the efficiency and examples are presented to admit it.

A Novel Compact Method for Thermal Modeling of On-Chip Interconnects Based on the Finite Element Method

2003 ◽  
Author(s):  
Siva P. Gurrum ◽  
Yogendra K. Joshi ◽  
William P. King ◽  
Koneru Ramakrishna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thermal Modeling ◽  
Computational Cost ◽  
Compact Model ◽  
Maximum Temperature ◽  
The Finite Element Method ◽  
Detailed Model ◽  
Modeling Methodology ◽  
Element Method

Prediction of the temperature field generated with Joule heating in multilayer interconnect stacks is of critical importance for the design and reliability of future microelectronics. Interconnect failure due to electromigration is strongly dependent on its temperature. Simple models fail to capture thermal interaction between layers and within the layer. Detailed simulations on the other hand, take tremendous time and require large storage. This paper describes a threedimensional compact thermal modeling methodology that captures thermal interactions at a lower computational cost and storage requirements. The method is applicable for arbitrary geometries of interconnects due to the use of the finite element method. Case studies with three interconnects placed on a single level at a pitch of 1.0 μm generating different heat rates are reported. The compact model predicts a temperature rise of 4.11 °C at a current density of 10 MA/cm2 for 6.0 μm long interconnects of 0.18 μm width and an aspect ratio of 2. The error in maximum temperature is about 5% when compared with detailed simulations. The compact model for the current cases consists of 219 nodes whereas the detailed model has 99,000 nodes where temperature is computed.

scholarly journals Frictionless Contact Problem for a Functionally Graded Layer Loaded Through Two Rigid Punches Using Finite Element Method

2019 ◽  
Vol 35 (5) ◽  
pp. 591-600 ◽  
Author(s):  
A. Polat ◽  
Y. Kaya ◽  
K. Bendine ◽  
T.Ş. Özşahin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problem ◽  
Functionally Graded ◽  
Homogeneous Layer ◽  
Elastic Plane ◽  
Infinite Plane ◽  
The Finite Element Method ◽  
Initial Separation ◽  
Element Method

ABSTRACTIn this study, continuous contact problem in the functionally graded (FG) layer loaded with two rigid flat blocks resting on the elastic semi-infinite plane was analyzed by the finite element method. The two-dimensional numerical model of the FG layer was made with the software added to the ANSYS program. This software can be adapted to all contact problem types by making minor changes. The accuracy check of the program was performed by comparing with the analytical solution of the problem by homogeneous layer and its solution by the finite element method. So, fast and practical solutions can be obtained by the developed finite element method on many applications such as; automotive, aviation and space industry applications. The comparisons made showed that the proposed solution gave good results at acceptable levels. In the problem, it was thought that all surfaces were frictionless. The external loads P and Q were transmitted to the FG layer via two flat rigid blocks. Normal stresses between the FG layer and the elastic plane, initial separation loads, initial separation distances and contact stresses under the blocks were investigated for various dimensionless quantities.

Sign in / Sign up

Export Citation Format

Share Document