Sri Hinduja

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.

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.

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.

Evaluation of existing and new feature recognition algorithms: Part 1: Theory and implementation

Abstract This is the first of two papers evaluating the performance of general-purpose feature detection techniques for geometric models. In this paper, six different methods are described to identify sets of faces that bound depression and protrusion faces. Each algorithm has been implemented and tested on eight components from the National Design Repository. The algorithms studied include previously published general-purpose feature detection algorithms such as the single-face inner-loop and concavity techniques. Others are improvements to existing algorithms such as extensions of the two-dimensional convex hull method to handle curved faces as well as protrusions. Lastly, new algorithms based on the three-dimensional convex hull, minimum concave, visible and multiple-face inner-loop face sets are described. These algorithms provide a basis for the comparative analysis that is the subject of the second paper.

Voronoi-diagram-based linking of contour-parallel tool paths for two-and-a-half-dimensional closed-pocket machining

Abstract Contour-parallel tool paths for machining milling features are formed by linking the offsets. Determination of links between offsets and the sequence in which the offsets should be traversed is a major problem. Results of efforts to link tool paths from academic researchers and developers of commercial computer-aided manufacturing (CAM) systems have shortcomings which include the fact that the linking strategies (a) are not based on clear geometric principles, (b) are not optimal, (c) do not consider technological factors such as the amount of slotting, overmilling, mode of cutting, and (d) are either not gouge-free or use tool retractions to avoid gouging. To overcome these shortcomings, this paper presents a linking algorithm which employs segments on the Voronoi diagram as links. The technological factors, hitherto ignored in previous research are considered and their optimality is ensured by employing guidelines which were mostly developed through observations of tool paths generated from a general test bed. Multiple solutions obtained after pruning out unfeasible solutions can be evaluated by users using geometrical (total tool path length) and technological (amount of overmilling, slotting, etc.) considerations or a combination of the criteria. The implementation of the algorithm is tested by generating tool paths for two two-and-a-half-dimensional (2½D) milled features. When compared with those obtained from some commercial CAM systems, they are shorter by 5 to 31 per cent.

Extendible Classification of Design and Manufacturing Features

Abstract This paper discusses three different issues in feature classification. It proposes a complete taxonomy to cater for prismatic and rotational features which can be positive or negative. It also suggests a feature definition that makes it feasible for the feature library to be extendible without additional programming effort. A unique code is given to each feature so as to avoid redundancy and ensure consistency of labelling the feature faces. This labelling is achieved by a novel formalisation method based on a newly found graph-theoretical property of a B-rep model. Results for one of the several components investigated are included.

Determination of the radial width of cut and cutting modes in milling

Abstract This paper describes a method to calculate the variation in the radial width of cut which occurs when the centre of a milling cutter follows the toolpath segments generated by a postprocessor. This variation is approximated by a stepped curve, thus enabling the toolpath segment to be divided into subsections, the radial width remaining constant over each subsection. The method also enables the cutting modes to be determined. The variation in the width of cut is obtained by performing a 2-D Boolean union between the area swept by the cutter when traversing the current segment and the area already machined. As an example, the actual widths of cut are calculated for the toolpaths for machining a pocket. The example clearly demonstrates that the actual widths of cut vary over a wide range and are very different from the value used to calculate the toolpaths. In fact, for the example considered, slotting occurs over 40% of the distance travelled, and only 10% of the actual widths of cut are approximately equal to the original value used for toolpath generation.

An Experimental and Numerical Investigation into the Thermal Behavior of the Pressure Die Casting Process

The modeling of the pressure die casting process generally requires the specification of heat transfer coefficients at the surfaces of the die. The coefficients at the cavity-casting interface and at the cooling channel surfaces are of particular importance. In order to provide estimates for these heat transfer coefficients, the behavior of a specifically designed zinc alloy casting is investigated using a three dimensional thermal model whose predictions are supported by experimentally obtained results. The numerical model uses the boundary element method for the dies, as surface temperatures are of particular importance, and the finite element method for the casting, where the nonlinear material behavior makes this technique suitable. The experimental data comprises of thermocouple measurements of both die, casting, and coolant temperatures for three sets of operating conditions. These measurements are complemented by qualitative data of casting defects caused by incomplete solidification and thermal imaging temperature measurements. An experimental technique for obtaining average heat transfer coefficients for the casting-die interface is presented. Although the technique circumvents the need to place thermocouples in the casting and provides average heat transfer coefficients of sufficient accuracy for modeling purposes, it is not sufficiently responsive to provide accurate transient information. The presence of coolant boiling is detected by its effect on the rates of heat extraction. Heat transfer coefficients are determined for the cooling channels using a boiling model. Comparison between predicted and experimental rates of heat transfer to the coolant support the need for a boiling model. Good agreement is obtained between experimental and numerical predictions.

Determination of Heat Transfer Coefficients Using a 1-D Flow Model Applied to Irregular Shaped Cooling Channels in Pressure Diecasting

A mesh partitioning strategy is presented which facilitates the application of boundary conditions to irregular shaped cooling channels in the pressure diecasting process. The strategy is used to partition a boundary element mesh, but can also be applied to the surface of a cooling channel bounded by a finite element mesh. The partitioning of the mesh into a series of element packs enables a one-dimensional flow model to be applied to the coolant. The flow model is used in conjunction with a steady-state thermal model which initially assumes that no boiling is taking place on the die/coolant interface, Values of bulk temperature, pressure, and velocity in the coolant are thus ascertained. This information, together with die temperatures, is then used in empirical relationships which model the various heat transfer mechanisms, including nucleate and transitional film boiling, between die and coolant. Effective heat transfer coefficients are calculated and applied at the die/coolant interface. The steady-state thermal code and the empirical boiling model are then used iteratively until stable values for the effective heat transfer coefficients are obtained. The models are tested by casting a small thin component using a die with conventional cooling channels and also using a novel die with irregular shaped cooling channels running on a hot chamber proprietary die casting machine. Simulation results are shown and experimental results using the hot chamber pressure die casting machine are reported.

Modelling the pressure die casting process with the boundary element method: Die deformation model for flash prevention

Abstract In pressure die casting, the thermal loads, injection pressure and clamping forces cause the individual blocks of a die to deform. This deformation results in gaps between the interface surfaces which, if big enough and in the vicinity of the cavity, permit material to seep into the gaps, causing flash. This paper describes a thermoelastic model to predict the deformation of the die so that it can be machined to prevent flash. The model is based on the boundary element method and allows the use of linear isoparametric or quadratic subparametric elements. Each die block is analysed as a separate problem. To avoid the occurrence of flash, the model suggests the amounts that should be machined from each die block. The predicted deformation has been experimentally verified by measuring the profile of a test die using displacement transducers and die impressions. It is shown that there is good agreement between the predicted and experimental results for different operating conditions. By machining the amounts suggested by the model, the test die was run without flash at operating conditions that had previously resulted in flash.