Analytical model of pass-by-pass strain in rod (or bar) rolling and its applications to prediction of austenite grain size

Rod rolling is a process where the deformation state of the workpiece between the work rolls is quite different from the strip rolling process. However, in most microstructure evolution models, the simple area strains (natural logarithm of the area reduction ratio) multiplied by a constant have been used to compute pass-by-pass evolution of austenite grain size (AGS) in rod (or bar) rolling, without any verification. The strains at a given pass play a crucial role in determining the recrystallization behavior (static or dynamic). In this study, an analytical model that calculates the pass-by-pass strain and strain rate in rod rolling has been developed and verified by conducting four-pass (oval–round) bar and plate rolling experiments. Numerical simulations have then been carried out for the four-pass rolling sequence using the area strain model and the new analytical model, focusing on the effect of the method for calculating the strain on the recrystallization behavior and evolution of AGS. The AGS predicted was compared with those obtained from hot torsion tests. It is shown that the analytical model developed in this study is more appropriate in the analysis of bar (or rod) rolling. It was found that the recrystallization behavior and evolution of AGS during this process were influenced significantly by the calculation method for the deformation parameters (strain and strain rate). The pass-by-pass strain obtained from the simple area strain model is inadequate to be used as an input to the equations for recrystallization and AGS evolution under these rolling conditions.

An analytical model on the propagation of modern email worms

Email worms propagate across networks by taking advantage of email relationships. Modeling the propagation of email worms can help predict their potential damages and develop countermeasures. We propose a novel analytical model on the propagation process of modern reinfection email worms. It relies on probabilistic analysis, and thus can provide a steady and reliable assessment on the propagation dynamics. Additionally, by introducing virtual users to represent the repetitious spreading process, the proposed model overcomes the computational challenge caused by reinfection processes. To demonstrate the benefits of our model, we conduct a series of experimental evaluation. The results show that our novel approach achieves a greater accuracy and is more suitable for modeling modern email worms than previous models.

Analytical model to locate the fluidisation interface in a solid-gas vacuum fluidised bed

Vacuum fluidised beds have a distinct advantage of being operated with reduced mass consumption of the fluidising media. However, a low quality of fluidisation reduces the opportunity to utilise the bubbling regime in vacuum fluidised beds. Fluidisation maps are often used to depict the interface between the quiescent, bubbling and slugging regimes inside a fluidised bed. Such maps have been obtained by visual observations of the fluidisation interface in transparent fluidised beds. For beds which are visually inaccessible fluidisation maps are difficult to obtain. The present work therefore attempts to model the interface travel in a vacuum fluidised bed. The pressure gradient due to the bed weight has been determined to be a main contributor for fluidisation/defluidisation under vacuum. A simple analytical model based on the pressure gradient (PG model) is developed to predict the interface location in a vacuum fluidised bed. For a segregated bed, the Gibilaro-Rowe (GR) model is modified and used to predict the jetsam layer growth along with the fluidisation interface. The predictions are compared with the experimental data for minimally and highly segregated particles and it is seen that for non-segregated powders the predictions are quite accurate. Lack of sufficient knowledge of bubble characteristics, however, impeded accurate prediction of the jetsam growth especially at high flow rates. However, an approximate complete fluidisation interface is successfully predicted using the GR-PG model. © 2014 Elsevier B.V.

An analytical model for optimal spectrum leasing under constraints of quality of service in CRNs

Cognitive radio improves spectrum efficiency and mitigates spectrum scarcity by allowing cognitive users to opportunistically access idle chunks of the spectrum owned by licensed users. In long-term spectrum leasing markets, secondary network operators make a decision about how much spectrum is optimal to fulfill their users' data transmission requirements. We study this optimization problem in multiple channel scenarios. Under the constrains of expected user admission rate and quality of service, we model the secondary network into a dynamic data transportation system. In this system, the spectrum accesses of both primary users and secondary users are in accordance with stochastic processes, respectively. The main metrics of quality of service we are concerned with include user admission rate, average transmission delay and stability of the delay. To quantify the relationship between spectrum provisioning and quality of service, we propose an approximate analytical model. We use the model to estimate the lower and upper bounds of the optimal amount of the spectrum. The distance between the bounds is relatively narrow. In addition, we design a simple algorithm to compute the optimum by using the bounds. We conduct numerical simulations on a slotted multiple channel dynamic spectrum access network model. Simulation results demonstrate the preciseness of the proposed model. Our work sheds light on the design of game and auction based dynamic spectrum sharing mechanisms in cognitive radio networks.

A microstructure based analytical model for tensile twinning in a rod textured Mg alloy

Abstract A model for tensile twinning during the compression of rod textured magnesium is developed based on the idea that these twins nucleate at grain boundaries and that when the twin number density per grain is low these twins readily give rise to the formation of other 'interaction' twins in adjacent grains. Experimental observations of twin aspect ratios measured at a single grain size and twin number densities measured over four grain sizes were used to determine model material parameters. Using these, the model provides reasonable predictions for the observed magnitudes and trends for the following observations:Effect of grain size and stress on twin volume fraction, fractional twin length and the fraction of twin contact.Effect of grain size on the yield stress.Effect of grain size on the general shape of the stress-strain curve at low strains. A parametric study shows the model to be quite robust but that it is particularly sensitive to the value of the exponent assumed for the twin nucleation rate law. It is seen that preventing the formation of interaction twins provides an important avenue for hardening and that the flow stress is also particularly sensitive to the relaxation of the twin back stresses. The model shows the importance of taking microstructure into account when modelling twinning.

An analytical model for web-warping in variable width flexible roll forming

The development of ultra/advanced high strength steels (U/AHSS) has challenged traditional forming methods due to their higher strength and reduced formability. An alternative method is flexible roll forming, which allows the manufacture of sheet metal of high strength and limited ductility into complex and weight-optimized components. However, one major problem in flexible roll forming is the web-warping defect, which is the deviation in height of the web over the length of the profile. The authors’ previous work developed an analytical model to predict the magnitude of web-warping. That model was purely geometric and neglected the effect of material properties. This work develops an analytical solution for the prediction of web-warping that considers both geometric and material parameters. The model results were validated by comparison with numerical and experimental results. The impact of this new model will be the ability to provide a rapid initial design assessment before an intensive numerical analysis of flexible roll forming is conducted.

Analytical communication networks model for enterprise grid computing

This paper addresses the problem of performance analysis based on the communication modeling of large-scale heterogeneous distributed systems, with an emphasis on enterprise Grid computing systems. The study of communication layers is important, as the overall performance of a distributed system often critically hinges on the effectiveness of this part. We propose an analytical model that is based on probabilistic analysis and queuing networks. The proposed model considers the processor as well as network heterogeneity of the enterprise Grid system. The model is validated through comprehensive simulations, which demonstrate that the proposed model exhibits a good degree of accuracy for various system sizes, and under different working conditions.

Analytical interconnection networks model for multi-cluster computing systems

This paper addresses the problem of interconnection networks performance modeling of large-scale distributed systems with emphases on multi-cluster computing systems. The study of interconnection networks is important because the overall performance of a distributed system is often critically hinged on the effectiveness of its interconnection network. We present an analytical model that considers stochastic quantities as well as processor heterogeneity of the target system. The model is validated through comprehensive simulation, which demonstrates that the proposed model exhibits a good degree of accuracy for various system sizes and under different operating conditions.

A comprehensive analytical subdomain model and its field solutions for surface-mounted permanent magnet machines

This paper presents a comprehensive analytical subdomain model together with its field solutions for predicting the magnetic field distributions in surface-mounted permanent magnet (PM) machines. The tooth tips and slotting effects during open-circuit, armature reaction, and on-load conditions are considered when deriving the model and developing its solutions. The model derivations and field solutions are extended from a previous model, and can be applied to PM machines with any combinations of slot and pole numbers and any magnetization patterns in the magnets. This model is initially formulated according to Laplace's and Poisson's equations in 2-D polar coordinates by the separation of variables technique in four subdomains, such as magnet, airgap, winding slots, and slot-openings. The field solution of each subdomain is obtained applying the appropriate boundary conditions and interface conditions between every two subdomains, respectively, which can precisely account for the mutual influence between slots. Finite element analysis (FEA) is later deployed to validate the analytical results in a surface-mounted PM machine that has nonoverlapping winding arrangement. For validation purposes, PM machines having 3-slot/2-pole with parallel magnetization and 12-slot/10-pole with either parallel or radial magnetizations are used for comparisons. Computation of global quantities for the motor which include the phase back-EMF and cogging torque is also included. The results indicate that the proposed analytical model can accurately predict the magnetic field distributions in each subdomain and the motor's global quantities, which are in good agreement with those obtained from the FEA.

Analytical performance modeling of the enterprise grid computing

This paper addresses the problem of performance modeling of large-scale heterogeneous distributed systems with emphases on enterprise grid computing systems. To this end, we present an analytical model that can be employed to explore the effectiveness of different design approaches so that one can have an intelligent choice during design and evaluation a cost-effective large-scale heterogeneous distributed computing system. The model is validated through comprehensive simulation.

Analytical network modeling of heterogeneous large-scale cluster systems

The study of the communication networks for distributed systems is very important, since the overall performance of these systems is often depends on the effectiveness of its communication network. In this paper, we address the problem of networks modeling for heterogeneous large-scale cluster systems. We consider the large-scale cluster systems as a typical cluster of clusters system. Since the heterogeneity is becoming common in such systems, we take into account network as well as cluster size heterogeneity to propose the model. To this end, we present an analytical network model and validate the model through comprehensive simulation. The results of the simulation demonstrated that the proposed model exhibits a good degree of accuracy for various system organizations and under different working conditions.

Analytical modeling of communication latency in multi-cluster systems

This paper addresses the problem of performance modeling of large-scale distributed systems with emphasis on communication networks in heterogeneous multi-cluster systems. The study of interconnection networks is important because the overall performance of a distributed system is often critically hinged on the effectiveness of this part. We present an analytical model to predict message latency in multi-cluster systems in the presence of processor heterogeneity. The model is validated through comprehensive simulation, which demonstrates that the proposed model exhibits a good degree of accuracy for various system sizes and under different operating conditions.

An analytical approach to predict web-warping and longitudinal strain in flexible roll formed sections of variable width

To reduce weight and improve passenger safety there is an increased need in the automotive industry to use Ultra High Strength Steel (UHSS) for structural and crash components. However, the application of UHSS is restricted by their limited formability and the difficulty of forming them in conventional stamping. An alternative method of manufacturing structural auto body parts from UHSS is the flexible roll forming process, which allows the manufacture of metal sheet with high strength and limited ductility into complex and weight-optimized components. One major problem in the flexible roll forming of UHSS is the web-warping defect, which is the deviation in height of the web area over the length of the profile. It has been shown that web-warping is strongly dependant to the permanent longitudinal strain formed in the flange of the part. Flexible roll forming is a continuous process with many roll stands, which makes numerical analysis extremely time intensive and computationally expensive. An analytical model of web-warping is therefore critical to improve design efficiency during the early process design stage before FEA is applied. This paper establishes for the first time an analytical model for the prediction of web-warping for the flexible roll forming of a section with variable width. The model is based on evaluating longitudinal edge strain in the flange of the part. This information is then used in combination with a simple geometrical model to investigate the relationship between web-warping and longitudinal strain with respect to process parameters.