Keith Davey

A practical method for finite element ring rolling simulation using the ALE flow formulation

Abstract Finite element ring rolling simulation by conventional Lagrangian codes carries an excessive computational cost. The main reason for this is the large number of incremental stages typically required to complete a full simulation. The nature of ring rolling however means that the amount of deformation taking place in a given increment is relatively small compared with typical metal forming processes. This paper describes measures that make the analysis of ring rolling a practicable proposition. The resulting model is based on a threefold approach, comprising the finite element flow formulation, an arbitrary Lagrangian Eulerian update strategy, and a novel iterative solution scheme called the successive preconditioned conjugate gradient method. The approach exploits the slowly evolving nature of the problem with the effect of reducing the time penalty for each deformation increment. In addition, a number of issues specific to ring rolling have been addressed including the problem of how the mandrel interface is dealt with for arbitrarily shaped rollers. The importance of addressing this particular issue is also illustrated. The method is validated by comparison with earlier experimental work and previously developed models for both pure radial, and radial–axial ring rolling.

An ALE Approach for Finite Element Ring-Rolling Simulation of Profiled Rings

Abstract The ring-rolling process involves compression of a small diameter ring-shaped workpiece between a mandrel and drive roll. This causes the ring to grow whilst allowing a profile to be developed on its surface. Compression can also take place in the axial direction between conical–axial rolls. Finite element (FE) simulation of this process is particularly difficult, suffering from excessive computational requirements and stability difficulties. Modelling using conventional Lagrangian FE codes is inefficient, involving high-density meshes. Moreover, a large number of incremental stages are typically required to complete a full simulation. This paper is concerned with a new approach founded on a split-operator arbitrary Lagrangian Eulerian (ALE) formulation, combined with a flow formulation and a novel iterative solution scheme called the successive preconditioned conjugate gradient method (SPCGM). The approach exploits the slowly evolving nature of the problem with the effect of reducing the time penalty for each deformation increment. The accuracy and stability of the method is tested against published experimental results. In addition, other modelling issues are addressed. In particular, the commonly used method of assuming zero-friction at a mandrel interface is shown to be inaccurate. This is achieved by a new approach, which properly invokes the effect of friction at the mandrel interface for arbitrarily shaped rollers.

The elastostatic three-dimensional boundary element method: analytical integration for linear isoparametric triangular elements

Abstract In this paper an analytical integration scheme is described that is designed to reduce the errors resulting from the numerical evaluation of integrals with singular integrands. The analytical scheme can be applied to linear triangular elements for use in elastostatic problems and is particularly useful for predicting distortion, to high accuracy, close to surfaces. It is demonstrated that although the analytical scheme takes longer computationally than the usual quadrature approach it is quicker when element subdivision is required to achieve reasonable accuracy. Numerical tests are performed on a simple test problem to demonstrate the advantages of the analytical approach, which is shown to be orders of magnitude more accurate than standard quadrature techniques.

The practicalities of ring rolling simulation for profiled rings

Abstract Ring rolling finite element simulation for profiled rings is currently not practicable with existing Lagrangian codes and on any realistic computational platform. The main reason for this is that a large number of incremental stages are typically required for completion of a full simulation and the computational cost per increment is high. The nature of ring rolling means that the amount of deformation that takes place in a given increment is relatively small when compared with typical metal forming processes. Small errors generated over each increment can grow to give highly inaccurate predictions after not so many ring revolutions. Inaccuracies manifest themselves in volume growth, incomplete profile filling, overall dimensional inaccuracy and inaccurate force and stress level predictions. This paper describes measures that make the analysis of profiled ring rolling a more practicable proposition. A model has been developed comprising the finite element flow formulation, an arbitrary Lagrangian–Eulerian update strategy, and a novel iterative solution scheme called the successive preconditioned conjugate gradient method. The focus of the paper is on methods developed to produce accurate predictions and that ensure numerical stability for an arbitrary high number of ring revolutions. The approach adopted includes methods for volume control, circular movement stability, circular interpolation techniques for accurate transfer of state variables, contact evolution, etc. The methods are validated by comparison with earlier experimental work and previously developed models for both pure radial, and radial–axial ring rolling. In addition, some results are presented for the analysis of commercially produced railway wheels and rings.

An efficient solution method for finite element ring-rolling simulation

Finite element ring-rolling simulation gives rise to poor conditioned non-linear equations that require repeated solution. The associated computational costs are extreme making analysis impracticable in industry. This paper is concerned with a solution strategy that addresses this problem and involves the combined use of an arbitrary Lagrangian–Eulerian (ALE) formulation and a successive preconditioned conjugate gradient method (SPCGM). This approach, coupled to a finite element flow formulation, is shown to offer considerable computational savings. Through the combined use of the ALE flow formulation and the SPCGM the stability and condition of the non-linear systems is enhanced. This purely iterative approach takes advantage of the slowly evolving velocity field and the self-preconditioning offered by the SPCGM. The performance of the solver is compared against well-known alternatives for varying problem sizes. The approach is shown to be generic but in particular makes ring-rolling simulation a more practicable proposition. Copyright

Analytical integration of linear three-dimensional triangular elements in BEM

Abstract In this paper an analytical integration scheme is described which can be applied to tringular elements for use in potential problems. It is well known that large integration errors can result when attempting to solve integral equations with singular kernels numerically. The paper shows that while the analytical scheme takes longer computationally than the usual quadrature approach, it is quicker than numerical integration if the triangle is subdivided in order to achieve a reasonable accuracy.

Simulation of a multi-stage railway wheel and tyre forming process

Abstract Railway wheels and tyres are manufactured at ABB Diamler-Benz Transportation (Adtranz), located in Manchester, by a multi-stage hot forming process. This process includes forging, piercing and in many cases, ring-rolling operations. This paper describes the finite element simulation of the entire process using the DEFORM™-2D metal forming program. The objective of the simulation was to determine whether alternative pre-form configurations of material and tooling could result in a final component with superior geometrical and physical properties. In addition, the sensitivity of the analysis to thermal effects was investigated by performing both isothermal and thermo-mechanical analyses of otherwise identical operations. The automatic multiple operation capability of DEFORM™ was used to allow the practical simulation of all the stages, including heat loss between forming operations in the thermo-mechanical simulation. Piercing was modelled by the fracture capability of the code, employing the Cockcroft and Latham damage criteria. Ring-rolling was included by assuming pseudo-plane strain metal flow. The exercise has demonstrated that pre-form design is a significant factor in this production process and that simulation tools can be readily employed to suggest potential improvements.

Modelling the transient thermal behavior of the pressure die-casting process with the BEM

Abstract The pressure die-casting process involves the repeated injection of a molten metal into a die cavity. The temperatures within the die exhibit a cyclic variation with a period equal to the casting cycle time. This paper is concerned with the prediction of these transient temperatures when the operating conditions have stabilized. The temperature at any point in the die can be considered to be formed from two components, one a steady-state part and the other a time-dependent perturbation. The steady- state temperatures of the die are calculated by solving the potential problem and the pertubation temperation from the parabolic heat equation. This approach enables the transient temperatures to be calculated in an efficient way, since only the cavity surfaces are considered in the pertubation analysis. The other components of the die system, that is, cooling channels and the outer surfaces of the die, are sufficiently far from the cavity to be ignored in the pertubation analysis. The boundary element method (BEM) is used to predict the cavity temperatures. In die casting, only the temperatures on the cavity surfaces are of interest, since the surface quality of a component is related significantly to the temperature distribution over the cavity. Since only thin components are considered herein, it is not necessary to model the solidification process and discretize the cast. These factors make the BEM ideally suited for the work described in this paper. To verify the results, the predicted temperatures for two components are compared with experimental values measured by using thermocouples and a thermal imaging camera. It was found that there is good agreement between the two sets of results.

Steady state thermal model for the hot chamber injection system in the pressure die casting process

Abstract This paper describes a three-dimensional numerical model that is used to predict the steady state thermal behaviour of the metal injection system of a hot chamber pressure die casting machine. The behaviour of the injection system is considered in conjunction with that of the die. The boundary element method (BEM) is employed, as surface temperatures are of primary importance. The model yields time-averaged injection system and die temperatures and the heat input from localised heating arrangements (injection system). This is valuable information that can be used in the optimisation of the process. The die model utilised is based on that presented by Davey and Hinduja (Int. J. Numer. Methods Eng. 30 (1990) 1275–1299). A number of novel techniques that improve the efficiency and performance of this model are presented. An efficient scheme is presented for modelling the flow of heat through the melt. A procedure is developed to account for the thermal effects of flow in the nozzle, gate and runner regions. An iterative procedure is developed that enables the average amount of energy supplied per cycle by the heater band, to be calculated. The coupled injection system–die model is verified using thermal data obtained from experimental work. The predicted and the measured temperatures are shown to be in good agreement. Based on the numerical predictions and the experimental data obtained, recommendations are made for improving the thermal behaviour of the existing hot chamber injection system and the die used in the experimental tests.

Efficient strategies for the simulation of railway wheel forming

Abstract Railway wheels and tyres are manufactured by a multi-stage hot-forming process. This process comprises upsetting, forging, punching, ring rolling and coining operations. The majority of these operations can readily be simulated using available commercial packages. However, the existence of the ring-rolling stage means that existing technology represents only a partial solution to this problem. The ring-rolling process carries a high run time penalty due to lack of constraint and the large number of increments required to complete a simulation. This paper considers the issues and difficulties associated with the finite element simulation of such a process. In particular, factors associated with run time and usability are addressed and the effectiveness of alternative solution methods and remeshing schemes are considered. It is seen that the poor conditioned nature of metal-forming simulation problems severely limits the usefulness of many iterative solution methods. It is found, however, that although the ring-rolling process remains a significant problem in terms of run time, the commercial viability of such activities can be enhanced by the use of solution schemes foundeds on adaptive preconditioning.