A Boundary Element Method Analysis of the Thermal Aspects of Metal Cutting Processes

1991 ◽  
Vol 113 (3) ◽  
pp. 311-319 ◽  
Author(s):  
Cho Lik Chan ◽  
Abhijit Chandra
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Metal Cutting ◽  
Shear Zones ◽  
Temperature Fields ◽  
Cutting Processes ◽  
Element Method

In this paper, the boundary element method (BEM) approach is used to analyze the thermal aspects of steady state metal cutting processes. Particular attention is paid to modeling of the boundary conditions at the tool-chip and the chip-workpiece interfaces. Since the velocities in each of the regions are different, the heat transfer within the tool, the chip, and the workpiece are first calculated separately. A complete model for heat transfer during steady state turning is then obtained by matching the boundary conditions across the primary and the secondary shear zones. An exact expression for matching is developed to avoid any iterations. The temperature fields within the workpiece, the chip, and the tool for various processing conditions are obtained and presented. The numerical results obtained by the BEM are also compared to Jaeger solutions and existing FEM results reported in the literature. The BEM is found to be efficient and robust for this class of steady state conduction-convection problems.

Estimating the Position and Size of a Cavity in a Plate by Means of Boundary Element Method and Conduction Heat Transfer

2012 ◽  
Author(s):  
Sasan Sattarpanah Karganroudi ◽  
Mohammad R. Roshani ◽  
Mohammad R. Aligoodarz ◽  
Mohammad Reza Soleimani Tehrani
Keyword(s):  
Heat Transfer ◽  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
The Body ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Conduction Heat Transfer ◽  
Constant Flux ◽  
Element Method

This study proves the possibility of predicting the existence of a cavity inside a homogenous body based on the geometrical parameters and the position of cavity by means of the boundary element method. Regarding the extensive use of steel plates in heavy and huge industries, this project focuses on two-dimensional plates and studies the thermal effects of shape and position of the existing cavity by solving the two-dimensional Laplace’s equation on conduction heat transfer over the body. The thermal changes on some boundaries affected by shape and position of cavity give an appropriate estimate of cavity. Considering the bulky and big amount of calculation and iteration and also the type of boundary conditions the fast and accurate numerical method proper to the mentioned problem, Boundary Element Method, is applied to simulate the experiments. The conclusion is taken due to the results of simulation. Based on the theory of Boundary Element method, the problem is simulated as a rectangular plate with two constant temperature and two constant flux boundary conditions while the cavity is inside, so concerning the position of cavity the variation of decreasing temperature on the boundaries with constant flux rate is changing. In order to reach the idea, the proper programming code has been written in Visual Fortran programming language and the results of the program output has been compared and interpreted.

Numerical modelling of convection-diffusion problems with first-order chemical reaction using the dual reciprocity boundary element method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Salam Adel Al-Bayati ◽  
Luiz C. Wrobel
Keyword(s):  
Steady State ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Content Type ◽  
Convection Diffusion ◽  
First Order ◽  
Order Chemical Reaction ◽  
First Order Chemical Reaction ◽  
Diffusion Problems ◽  
Element Method

Purpose The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction. Design/methodology/approach The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence. Findings The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency. Originality/value Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.

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