Application of the finite element method in cold forging processes

The demand for more efficient manufacturing processes has been increasing in the last few years. The cold forging process is presented as a possible solution, because it allows the production of parts with a good surface finish and with good mechanical properties. Nevertheless, the cold forming sequence design is very empirical and it is based on the designer experience. The computational modeling of each forming process stage by the finite element method can make the sequence design faster and more efficient, decreasing the use of conventional "trial and error" methods. In this study, the application of a commercial general finite element software - ANSYS - has been applied to model a forming operation. Models have been developed to simulate the ring compression test and to simulate a basic forming operation (upsetting) that is applied in most of the cold forging parts sequences. The simulated upsetting operation is one stage of the automotive starter parts manufacturing process. Experiments have been done to obtain the stress-strain material curve, the material flow during the simulated stage, and the required forming force. These experiments provided results used as numerical model input data and as validation of model results. The comparison between experiments and numerical results confirms the developed methodology potential on die filling prediction.

An Hp-Adaptive Hierarchical Formulation for the Boundary Element Method Applied to Elasticity in Two Dimensions

This paper presents an HP-Adaptive Procedure with Hierarchical formulation for the Boundary Element Method in 2-D Elasticity problems. Firstly, H, P and HP formulations are defined. Then, the hierarchical concept, which allows a substantial reduction in the dimension of equation system, is introduced. The error estimator used is based on the residual computation over each node inside an element. Finally, the HP strategy is defined and applied to two examples.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Be-Fe coupled method for the analysis of 3D elastodynamic problems in the time domain

By coupling the Boundary Element Method (BEM) and the Finite Element Method (FEM) an algorithm that combines the advantages of both numerical processes is developed. The main aim of the work concerns the time domain analysis of general three-dimensional wave propagation problems in elastic media. In addition, mathematical and numerical aspects of the related BE-, FE- and BE/FE-formulations are discussed. The coupling algorithm allows investigations of elastodynamic problems with a BE- and a FE-subdomain. In order to observe the performance of the coupling algorithm two problems are solved and their results compared to other numerical solutions.

An alternative finite element formulation for determination of streamlines in two-dimensional problems

It is well known that the numerical solutions of incompressible viscous flows are of great importance in Fluid Dynamics. The graphics output capabilities of their computational codes have revolutionized the communication of ideas to the non-specialist public. In general those codes include, in their hydrodynamic features, the visualization of flow streamlines - essentially a form of contour plot showing the line patterns of the flow - and the magnitudes and orientations of their velocity vectors. However, the standard finite element formulation to compute streamlines suffers from the disadvantage of requiring the determination of boundary integrals, leading to cumbersome implementations at the construction of the finite element code. In this article, we introduce an efficient way - via an alternative variational formulation - to determine the streamlines for fluid flows, which does not need the computation of contour integrals. In order to illustrate the good performance of the alternative formulation proposed, we capture the streamlines of three viscous models: Stokes, Navier-Stokes and Viscoelastic flows.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Modelagem e simulação da desidratação osmótica em pedaços de abacaxi utilizando o método de elementos finitos

Water loss and sugar gain were modelling during the osmotic dehydration process of pieces of pineaplle. The transfer of solute to the fruit and the water to the solution was based on Fick's 2nd law. The three dimensional model was solved by the finite element method with the usage of the software COMSOL Multiphysics 3.2. The main and cross diffusion coefficients and the Biot number were determined on the simulation and the deviation between the experimental and the simulated data were 4,28% to sucrose and 1,66 to the water.

Numerical evaluation of the modulus of longitudinal elasticity in structural round timber elements of the Eucalyptus genus

Currently, the standards that deal with the determination of the properties of rigidity and strength for structural round timber elements do not take in consideration in their calculations and mathematical models the influence of the existing irregularities in the geometry of these elements. This study has as objective to determine the effective value of the modulus of longitudinal elasticity for structural round timber pieces of the Eucalyptus citriodora genus by a technique of optimization allied to the Inverse Analysis Method, to the Finite Element Method and the Least Square Method.

Non-linear analysis of laminated metal matrix composites by an integrated micro/macro-mechanical model

The present paper describes an integrated micro/macro mechanical study of the elastic-viscoplastic behavior of unidirectional metal matrix composites (MMC). The micromechanical analysis of the elastic moduli is based on the Composites Cylinder Assemblage model (CCA) with comparisons also draw with a Representative Unit Cell (RUC) technique. These "homogenization" techniques are later incorporated into the Vanishing Fiber Diameter (VFD) model and a new formulation is proposed. The concept of a smeared element procedure is employed in conjunction with two different versions of the Bodner and Partom elastic-viscoplastic constitutive model for the associated macroscopic analysis. The formulations developed are also compared against experimental and analytical results available in the literature.

Object-oriented Programming Applied to the Development of Structural Analysis and Optimization Software

This paper presents the development of a two-dimensional interactive software environment for structural analysis and optimization based on object-oriented programming using the C++ language. The main feature of the software is the effective integration of several computational tools into graphical user interfaces implemented in the Windows-98 and Windows-NT operating systems. The interfaces simplify data specification in the simulation and optimization of two-dimensional linear elastic problems. NURBS have been used in the software modules to represent geometric and graphical data. Extensions to the analysis of three-dimensional problems have been implemented and are also discussed in this paper.

Numerical Simulation of the Cavitation in the Hydrodynamic Lubrication of Journal Bearings: a Parallel Algorithm

In this paper we present an algorithm for the numerical simulation of the cavitation in the hydrodynamic lubrication of journal bearings. Despite the fact that this physical process is usually modelled as a free boundary problem, we adopted the equivalent variational inequality formulation. We propose a two-level iterative algorithm, where the outer iteration is associated to the penalty method, used to transform the variational inequality into a variational equation, and the inner iteration is associated to the conjugate gradient method, used to solve the linear system generated by applying the finite element method to the variational equation. This inner part was implemented using the element by element strategy, which is easily parallelized. We analyse the behavior of two physical parameters and discuss some numerical results. Also, we analyse some results related to the performance of a parallel implementation of the algorithm.

A Design Methodology for the Compensation of Positioning Deviation in Gantry Manipulators

This work presents recent results concerning a design methodology used to estimate the positioning deviation for a gantry (Cartesian) manipulator, related mainly to structural elastic deformation of components during operational conditions. The case-study manipulator is classified as gantry type and its basic dimensions are 1,53m x 0,97m x 1,38m. The dimensions used for the calculation of effective workspace due to end-effector path displacement are: 1m x 0,5m x 0,5m. The manipulator is composed by four basic modules defined as module X, module Y, module Z and terminal arm, where is connected the end-effector. Each module controlled axis performs a linear-parabolic positioning movement. The planning path algorithm has the maximum velocity and the total distance as input parameters for a given task. The acceleration and deceleration times are the same. Denavit-Hartemberg parameterization method is used in the manipulator kinematics model. The gantry manipulator can be modeled as four rigid bodies with three degrees-of-freedom in translational movements, connected as an open kinematics chain. Dynamic analysis were performed considering inertial parameters specification such as component mass, inertia and center of gravity position of each module. These parameters are essential for a correct manipulator dynamic modelling, due to multiple possibilities of motion and manipulation of objects with different masses. The dynamic analysis consists of a mathematical modelling of the static and dynamic interactions among the modules. The computation of the structural deformations uses the finite element method (FEM).

Saline distribution during multicomponent salting in pre-cooked quail eggs

The relationship of NaCl with problems of arterial hypertension has led to a reduction in the levels of this salt in food production. KCl has been used as a partial substitute for NaCl since it cannot be completely substituted without affecting the acceptability of the end product. In this study, the diffusion that occurs during quail egg salting in static and stirred brine was simulated. The mathematical model used was based on a generalization of the Fick's 2nd law, and the COMSOL Multiphysics software was used to simulate the diffusion in the NaCl-KCl-water system. The deviations in the simulated data and experimental data were 2.50% for NaCl and 6.98% for KCl in static brine, while in the stirred brine they were 3.48% for NaCl and 4.72% for KCl. The simulation results presented good agreement with the experimental values and validated the predictive capacity of the model.