Application of bending under tension test to determine the effect of tool radius and the contact pressure on the coefficient of friction in sheet metal forming

To quantify the frictional behaviour in sheet forming operations, several laboratory experiments which simulate the real forming conditions are performed. The Bending Under Tension Test is one such experiment which is often used to represent the frictional flow of sheet material around a die or a punch radius. Different mathematical representations are used to determine the coefficient of friction in the Bending Under Tension Test. In general the change in the strip thickness in passing over the die radius is neglected and the radius of curvature to thickness ratio is assumed to be constant in these equations. However, the effect of roller radius, sheet thickness and the surface pressure are also omitted in some of these equations. This work quantitatively determined the effect of roller radius and the tooling pressure on the coefficient of friction. The Bending Under Tension Test was performed using rollers with different radii and also lubricants with different properties. The tool radii were found to have a direct influence in the contact pressure. The effect of roller radius on friction was considerable and it was observed that there is a clear relationship between the contact pressure and the coefficient of friction.

Elastic bending of steel-polymer-steel (SPS) laminates to a constant curvature

The shear strain of the interlayer in the elastic regime for a Steel-Polymer-Steel (SPS) laminate material has been studied during bending to a constant curvature. An analytical model is developed and the influence of process parameters are analyzed. The tension in the cover sheets is also determined and, finally, a moment diagram is calculated. The results show that the moment in the SPS laminate is nonuniform along the bent strip even though the curvature is constant because of the tension and compression forces introduced in the cover sheets by the shear reaction force of the interlayer material.

Facets of the polytope of the asymmetric travelling salesman problem with replenishment arcs

The Asymmetric Travelling Salesman Problem with Replenishment Arcs (RATSP) is a new class of problems arising from work related to aircraft routing. Given a digraph with cost on the arcs, a solution of the RATSP, like that of the Asymmetric Travelling Salesman Problem, induces a directed tour in the graph which minimises total cost. However the tour must satisfy additional constraints: the arc set is partitioned into replenishment arcs and ordinary arcs, each node has a non-negative weight associated with it, and the tour cannot accumulate more than some weight limit before a replenishment arc must be used. To enforce this requirement, constraints are needed. We refer to these as replenishment constraints.

In this paper, we review previous polyhedral results for the RATSP and related problems, then prove that two classes of constraints developed in V. Mak and N. Boland [Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs, Technical Report TR M05/03, School of Information Technology, Deakin University, 2005] are, under appropriate conditions, facet-defining for the RATS polytope.

Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs

The asymmetric travelling salesman problem with replenishment arcs (RATSP), arising from work related to aircraft routing, is a generalisation of the well-known ATSP. In this paper, we introduce a polynomial size mixed-integer linear programming (MILP) formulation for the RATSP, and improve an existing exponential size ILP formulation of Zhu [The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994] by proposing two classes of stronger cuts. We present results that under certain conditions, these two classes of stronger cuts are facet-defining for the RATS polytope, and that ATSP facets can be lifted, to give RATSP facets. We implement our polyhedral findings and develop a Lagrangean relaxation (LR)-based branch-and-bound (BNB) algorithm for the RATSP, and compare this method with solving the polynomial size formulation using ILOG Cplex 9.0, using both randomly generated problems and aircraft routing problems. Finally we compare our methods with the existing method of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427]. It turns out that both of our methods are much faster than that of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427], and that the LR-based BNB method is more efficient for problems that resemble the aircraft rotation problems.

Modelling factors of square tubes in high speed bending situations

Accurate finite element crash simulations of side impact depend upon a thorough understanding of dynamic tube bending. There is a need to understand the dynamic bending mode of square sections (equivalent of automotive structural parts) to obtain a greater confidence in CAE. This work varied strain rate and material definitions, such as Cowper-Symonds vs Zerilli-Armstrong, as well as initial velocity and yield strength. The results show that most of the plastic work is done between strains rates of 30 ¿ 300/s and strains up to 0.3. Peak strain rates were marginally above 1000/s with maximum strain greater than 1. When the strain rate definition and material model were modified, it was shown that a higher yield stress produced a higher reaction force. These results would suggest that the strain rate sensitivity needs to be carefully identified for accurate crash simulations.

New insights in asymmetric tetraorganodistannoxane ladder formation. A NMR-spectroscopic and crystallographic study

The syntheses of the asymmetrically substituted tetraorganodistannoxanes [t-Bu₂(X)SnOSn(Y)(CH₂SiMe₃)₂1₂ (1, X = Y = OH; 2, X = Cl, Y = OH; 3, X = Y = Cl) are reported and their structures in solution and in the solid state are characterized by multinuclear NMR spectroscopy and single crystal X-ray analyses. In toluene, the tetrahydroxy-substituted derivative 1 is in equilibrium with the organotin oxides cyclo-[t-Bu₂Sn{OSn(CH₂SiMe₃)₂}₂O] (4), cyclo[(Me₃SiCH₂)₂Sn(OSnt-Bu₂)₂O] (5), and cyclo-(t-Bu₂SnO)₃, and some additional, undefined species containing pentacoordinated tin atoms. In contrast, the dihydroxydichloro-substituted derivative 2 is inert in solution.

Sequential technology adoption with asymmetric firms

We analyse the incentives and welfare implications of costly technology adoption in a two-period duopoly model where firms have different amounts of capital. We also extend our framework to an open economy set-up and examine the relationship between trade and technology adoption. Our findings are as follows. First, no monotone relationship exists between the threshold cost of adoption and capital shares. Second, an unequal distribution of capital, despite lessening competition, can increase total surplus. Third, trade generally encourages adoption of modern technology unless the share of capital for the adopters is too low.

Simulation of three-point bending test of titanium foam for biomedical applications

Using Titanium (Ti) foam as an implant material is a new approach for biomedical applications and it is important to understand the mechanical behaviors of this new foam material. In the present study, the bending of the Ti foam has been simulated and compared against recently published data [1]. FE Analysis has been performed by Abaqus software. Stiffness and Yield strength of foams between 50% (cortical bone) to 80% (cancellous bone) porosity range were considered. This study showed that crushable foam material model in Abaqus, which has developed primarily for Aluminum (Al) foam alloys, is also valid for Ti Foam before any crack or damage occurs in the sample.

Examining the asymmetric behaviour of macroeconomic aggregates in Asian economies

The goal of this paper is to test for asymmetric behaviour of macroeconomic aggregates for three Asian economies; namely, Malaysia, Hong Kong and Korea. Whether macroeconomic aggregates can be characterised as asymmetric has important implications for policy-making and econometric modelling including forecasting. We examine two forms of asymmetries; specifically deepness, which arises when a detrended time series contains an asymmetric distribution, and steepness, which arises when the first difference of a series contains an asymmetric distribution. Overall, our findings suggest that for all three countries, the bulk of the series display asymmetry behaviour.