Search results for: Cylindrical/Surrounded gate (SGT/CGT) MOSFET

Authors: Omer F. Can, Nevin Celik

Abstract:

In this study, a semi-cylinder obstacle placed in a channel is handled to determine the effect of flow and heat transfer around the obstacle. Both faces of the semi-cylinder are used in the numerical analysis. First, the front face of the semi-cylinder is stated perpendicular to flow, than the rear face is placed. The study is carried out numerically, by using commercial software ANSYS 11.0. The well-known κ-ε model is applied as the turbulence model. Reynolds number is in the range of 104 to 105 and air is assumed as the flowing fluid. The results showed that, heat transfer increased approximately 15 % in the front faze case, while it enhanced up to 28 % in the rear face case.

Keywords: External flow, semi-cylinder obstacle, heat transfer, friction.

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: Meshless spectrally convergent, partial differential equations, extended arithmetic precision, no branching.

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Authors: Zulhelmi Zakaria, Shuja A. Abbasi

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A new approach has been used for optimized design of multipliers based upon the concepts of Vedic mathematics. The design has been targeted to state-of-the art field-programmable gate arrays (FPGAs). The multiplier generates partial products using Vedic mathematics method by employing basic 4x4 multipliers designed by exploiting 6-input LUTs and multiplexers in the same slices resulting in drastic reduction in area. The multiplier is realized on Xilinx FPGAs using devices Virtex-5 and Virtex-6.Carry Chain Adder was employed to obtain final products. The performance of the proposed multiplier was examined and compared to well-known multipliers such as Booth, Carry Save, Carry ripple, and array multipliers. It is demonstrated that the proposed multiplier is superior in terms of speed as well as power consumption.

Keywords: Multiplier, Vedic Mathematics, LUTs, FPGAs.

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Authors: Hong Li, Linfeng Li, Jianping Hu

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With rapid technology scaling, the proportion of the static power consumption catches up with dynamic power consumption gradually. To decrease leakage consumption is becoming more and more important in low-power design. This paper presents a power-gating scheme for P-DTGAL (p-type dual transmission gate adiabatic logic) circuits to reduce leakage power dissipations under deep submicron process. The energy dissipations of P-DTGAL circuits with power-gating scheme are investigated in different processes, frequencies and active ratios. BSIM4 model is adopted to reflect the characteristics of the leakage currents. HSPICE simulations show that the leakage loss is greatly reduced by using the P-DTGAL with power-gating techniques.

Keywords: Leakage reduction, low power, deep submicronCMOS circuits, P-type adiabatic circuits.

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Authors: Ali Reza Pouladkhan, Jalil Emadi, Hamed Habibolahiyan

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This paper presents an exact solution and a finite element method (FEM) for a Piezoceramic Rod under static load. The cylindrical rod is made from polarized ceramics (piezoceramics) with axial poling. The lateral surface of the rod is traction-free and is unelectroded. The two end faces are under a uniform normal traction. Electrically, the two end faces are electroded with a circuit between the electrodes, which can be switched on or off. Two cases of open and shorted electrodes (short circuit and open circuit) will be considered. Finally, a finite element model will be used to compare the results with an exact solution. The study uses ABAQUS (v.6.7) software to derive the finite element model of the ceramic rod.

Keywords: Finite element method, Ceramic rod; Axial poling, Normal traction, Short circuit, Open circuit.

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Authors: Barzin Gavtash, Khalid Hussain, Mohammad Layeghi, Saeed Sadeghi Lafmejani

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This research aims at modeling and simulating the effects of nanofluids on cylindrical heat pipes thermal performance using the ANSYS-FLUENT CFD commercial software. The heat pipe outer wall temperature distribution, thermal resistance, liquid pressure and axial velocity in presence of suspended nano-scaled solid particle (i.e. Cu, Al2O3 and TiO2) within the fluid (water) were investigated. The effect of particle concentration and size were explored and it is concluded that the thermal performance of the heat pipe is improved when using nanofluid as the system working fluid. Additionally, it was observed that the thermal resistance of the heat pipe drops as the particle concentration level increases and particle radius decreases.

Keywords: CFD, Heat Pipe, Nanofluid, Thermal resistance

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Authors: B. Tomczyk, R. Mania

Abstract:

Thin linear-elastic cylindrical circular shells having a micro-periodic structure along two directions tangent to the shell midsurface (biperiodic shells) are object of considerations. The aim of this paper is twofold. First, we formulate an averaged nonasymptotic model for the analysis of parametric vibrations or dynamical stability of periodic shells under consideration, which has constant coefficients and takes into account the effect of a cell size on the overall shell behavior (a length-scale effect). This model is derived employing the tolerance modeling procedure. Second we apply the obtained model to derivation of frequency equation being a starting point in the analysis of parametric vibrations. The effect of the microstructure length oh this frequency equation is discussed.

Keywords: Micro-periodic shells, mathematical modeling, length-scale effect, parametric vibrations

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Authors: M.A. Kamely, S.M. Kamil, C.W. Chong

Abstract:

A mathematical model of the surface roughness has been developed by using response surface methodology (RSM) in grinding of AISI D2 cold work tool steels. Analysis of variance (ANOVA) was used to check the validity of the model. Low and high value for work speed and feed rate are decided from design of experiment. The influences of all machining parameters on surface roughness have been analyzed based on the developed mathematical model. The developed prediction equation shows that both the feed rate and work speed are the most important factor that influences the surface roughness. The surface roughness was found to be the lowers with the used of low feed rate and low work speed. Accuracy of the best model was proved with the testing data.

Keywords: Mathematical Modeling, Response surfacemethodology, Surface roughness, Cylindrical Grinding.

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Authors: Z.A. Jaffery, Vinay Kumar Chandna, Sunil Kumar Chaudhary

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This paper present a MATLAB-SIMULINK model of a single phase 2.5 KVA, 240V RMS controlled PV VSI (Photovoltaic Voltage Source Inverter) inverter using IGBTs (Insulated Gate Bipolar Transistor). The behavior of output voltage, output current, and the total harmonic distortion (THD), with the variation in input dc blocking capacitor (Cdc), for linear and non-linear load has been analyzed. The values of Cdc as suggested by the other authors in their papers are not clearly defined and it poses difficulty in selecting the proper value. As the dc power stored in Cdc, (generally placed parallel with battery) is used as input to the VSI inverter. The simulation results shows the variation in the output voltage and current with different values of Cdc for linear and non-linear load connected at the output side of PV VSI inverter and suggest the selection of suitable value of Cdc.

Keywords: DC Blocking capacitor, IGBTs, PV VSI, THD.

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Authors: Hamed Bazrafshan, Saeideh Dabirnia, Zahra Alipour Tesieh, Samaneh Alavi, Bahram Dabir

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In this study, the removal of pollutants of a real produced water sample from an oil reservoir (a light oil reservoir), using a photocatalytic degradation process in a cylindrical glass reactor, was investigated. Using TiO2 and Ag-TiO2 in slurry form, the photocatalytic degradation was studied by measuring the Chemical Oxygen Demand (COD) parameter, qualitative analysis, and GC-MS. At first, optimization of the parameters on photocatalytic degradation of hydrocarbon pollutants in real produced water, using TiO2 nanoparticles as photocatalysts under UV light, was carried out applying response surface methodology. The results of the design of the experiment showed that the optimum conditions were at a catalyst concentration of 1.14 g/lit and pH of 2.67, and the percentage of COD removal was 72.65%.

Keywords: Photocatalyst, Ag-doped, TiO2, produced water, nanoparticles.

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Authors: Ahmed Chalak Shakir, GuXuemai, Jia Min

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Recently, wireless sensor networks have been paid more interest, are widely used in a lot of commercial and military applications, and may be deployed in critical scenarios (e.g. when a malfunctioning network results in danger to human life or great financial loss). Such networks must be protected against human intrusion by using the secret keys to encrypt the exchange messages between communicating nodes. Both the symmetric and asymmetric methods have their own drawbacks for use in key management. Thus, we avoid the weakness of these two cryptosystems and make use of their advantages to establish a secure environment by developing the new method for encryption depending on the idea of code conversion. The code conversion-s equations are used as the key for designing the proposed system based on the basics of logic gate-s principals. Using our security architecture, we show how to reduce significant attacks on wireless sensor networks.

Keywords: logic gates, code conversions, Gray-code, and clustering.

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Authors: A. Tavangari, N. Salehzadeh

Abstract:

In the crack growth analysis, the Stress Intensity Factor (SIF) is a fundamental prerequisite. In the present study, the mode I stress intensity factor (SIF) of three-dimensional penny- Shaped crack is obtained in an isotropic elastic cylindrical medium with arbitrary dimensions under arbitrary loading at the top of the cylinder, by the semi-analytical method based on the Rayleigh-Ritz method. This method that is based on minimizing the potential energy amount of the whole of the system, gives a very close results to the previous studies. Defining the displacements (elastic fields) by hypothetical functions in a defined coordinate system is the base of this research. So for creating the singularity conditions at the tip of the crack the appropriate terms should be found.

Keywords: Penny-shaped crack, Stress intensity factor, Fracture mechanics, Ritz method.

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Authors: Sara Kamalisiahroudi, Jun Huang, Zhe Li, Jianbo Zhang

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Two types of commercial cylindrical lithium ion batteries (Panasonic 3.4 Ah NCR-18650B and Samsung 2.9 Ah INR-18650), were investigated experimentally. The capacities of these samples were individually measured using constant current-constant voltage (CC-CV) method at different ambient temperatures (-10°C, 0°C, 25°C). Their internal resistance was determined by electrochemical impedance spectroscopy (EIS) and pulse discharge methods. The cells with different configurations of parallel connection NCR-NCR, INR-INR and NCR-INR were charged/discharged at the aforementioned ambient temperatures. The results showed that the difference of internal resistance between cells much more evident at low temperatures. Furthermore, the parallel connection of NCR-NCR exhibits the most uniform temperature distribution in cells at -10°C, this feature is quite favorable for the safety of the battery pack.

Keywords: Batteries in parallel connection, internal resistance, low temperature, temperature difference, current distribution.

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Authors: Semih Demir, Anil Celebi

Abstract:

Circuit switched networks widely used until the end of the 20^th century have been transformed into packages switched networks. Time Division Multiplexing over Internet Protocol (TDMoIP) is a system that enables Time Division Multiplexing (TDM) traffic to be carried over packet switched networks (PSN). In TDMoIP systems, devices that send TDM data to the PSN and receive it from the network must operate with the same clock frequency. In this study, it was aimed to implement clock synchronization process in Field Programmable Gate Array (FPGA) chips using time information attached to the packages received from PSN. The designed hardware is verified using the datasets obtained for the different carrier types and comparing the results with the software model. Field tests are also performed by using the real time TDMoIP system.

Keywords: Clock recovery on TDMoIP, FPGA, MATLAB reference model, clock synchronization.

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Authors: Morteza Khaleghi Meybodi, Hossein Bisadi

Abstract:

Explosive forming is one of the unconventional techniques in which, most commonly, the water is used as the pressure transmission medium. One of the newest methods in explosive forming is gas detonation forming which uses a normal shock wave derived of gas detonation, to form sheet metals. For this purpose a detonation is developed from the reaction of H2+O2 mixture in a long cylindrical detonation tube. The detonation wave goes through the detonation tube and acts as a blast load on the steel blank and forms it. Experimental results are compared with a finite element model; and the comparison of the experimental and numerical results obtained from strain, thickness variation and deformed geometry is carried out. Numerical and experimental results showed approximately 75 – 90 % similarity in formability of desired shape. Also optimum percent of gas mixture obtained when we mix 68% H2 with 32% O2.

Keywords: Explosive forming, High strain rate, Gas detonation, Finite element analysis.

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Authors: Y. S. Tai, M. Y. Huang, H. T. Hu

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The commercial finite element program LS-DYNA was employed to evaluate the response and energy absorbing capacity of cylindrical metal tubes that are externally wrapped with composite. The effects of composite wall thickness, loading conditions and fiber ply orientation were examined. The results demonstrate that a wrapped composite can be utilized effectively to enhance the crushing characteristics and energy absorbing capacity of the tubes. Increasing the thickness of the composite increases the mean force and the specific energy absorption under both static and dynamic crushing. The ply pattern affects the energy absorption capacity and the failure mode of the metal tube and the composite material property is also significant in determining energy absorption efficiency.

Keywords: fiber-reinforced metal tubes, energy absorption, axial crushing, impact loading.

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Authors: Abhijit Chandra, Sudipta Chattopadhyay

Abstract:

In this communication, we have made an attempt to design multiplier-less low-pass finite impulse response (FIR) filter with the aid of various mutation strategies of Differential Evolution (DE) algorithm. Impulse response coefficient of the designed FIR filter has been represented as sums or differences of powers of two. Performance of the proposed filter has been evaluated in terms of its frequency response and associated hardware cost. Supremacy of our approach has been substantiated by comparing our result with many of the existing multiplier-less filter design algorithms of recent interest. It has also been demonstrated that DE-optimized filter outperforms Genetic Algorithm (GA) based design by a large margin.  Hardware efficiency of our algorithm has further been validated by implementing those filters on a Field Programmable Gate Array (FPGA) chip.

Keywords: Convergence speed, Differential Evolution (DE), error histogram, finite impulse response (FIR) filter, total power of two (TPT), zero-valued filter coefficient (ZFC).

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Authors: M. Tahar Bouzaher

Abstract:

This numerical study aims to develop a coupled, passive and active control strategy of the flow around a cylinder of diameter D, and Re=4000. The strategy consists to put a cylindrical rod in front of a deforming cylinder. The quasi- elliptical deformation of cylinder follow a sinusoidal law in order to reduce the drag force. To analyze the evolution of unsteady vortices, the Large Eddy Simulation approach is used in this 2D simulation, carried out using ANSYS – Fluent. The movement of deformation is reproduced using an internal subroutine, introduced in the form of a User Defined Function UDF. Two diameters of the rod were tested for a rod placed at a distance L = 3 ×d, with an amplitudes of deformation A = 5%, A = 25% and A = 50% of the cylinder diameter, the frequency of deformation take the values fd = 1fn, 5fn and 8fn, which fn represents the naturel vortex shedding frequency. The results show substantial changes in the flow behavior and for a rod of 6mm (1% D) with amplitude A = 25%, and with a 2fn frequency, drag reduction of 60% was recorded.

Keywords: CFD, Flow separation, control, Boundary layer, rod, Cylinder.

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Authors: F. Lhafiane, A. Elbyed, M. Bouchoum

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The design of Reverse logistics Network has attracted growing attention with the stringent pressures from both environmental awareness and business sustainability. Reverse logistical activities include return, remanufacture, disassemble and dispose of products can be quite complex to manage. In addition, demand can be difficult to predict, and decision making is one of the challenges task in such network. This complexity has amplified the need to develop an integrated architecture for product return as an enterprise system. The main purpose of this paper is to design Multi Agent System (MAS) architecture using the Prometheus methodology to efficiently manage reverse logistics processes. The proposed MAS architecture includes five types of agents: Gate keeping Agent, Collection Agent, Sorting Agent, Processing Agent and Disposal Agent which act respectively during the five steps of reverse logistics Network.

Keywords: Reverse logistics, multi agent system, Prometheus methodology.

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Authors: Bhavana Prakash Shrivastava, Kavita Khare

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This paper presents a synthesis and simulation of proposed enhanced buffer. The design provides advantages of both buffer and bufferless network for that two cross bar switches are used. The concept of virtual channel (VC) is eliminated from the previous design by using an efficient flow-control scheme that uses the storage already present in pipelined channels in place of explicit input VCBs. This can be addressed by providing enhanced buffers on the bufferless link and creating two virtual networks. With this approach, VCBs act as distributed FIFO buffers. Without VCBs or VCs, deadlock prevention is achieved by duplicating physical channels. An enhanced buffer provides a function of hand shaking by providing a ready valid handshake signal and two bit storage. Through this design the power is reduced to 15.65% and delay is reduced to 97.88% with respect to virtual channel router.

Keywords: Enhanced buffer, Gate delay, NOC, VCs, VCB.

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Authors: Fathi N. Mayoof

Abstract:

Rolling element bearings are widely used in industry, especially where high load capacity is required. The diagnosis of their conditions is essential matter for downtime reduction and saving cost of maintenance. Therefore, an intensive analysis of frequency spectrum of their faults must be carried out in order to determine the main reason of the fault. This paper focus on a beating phenomena observed in the waveform (time domain) of a cylindrical rolling element bearing. The beating frequencies were not related to any sources nearby the machine nor any other malfunctions (unbalance, misalignment ...etc). More investigation on the spike energy and the frequency spectrum indicated a problem with races of the bearing. Multi-harmonics of the fundamental defects frequencies were observed. Two of them were close to each other in magnitude those were the source of the beating phenomena.

Keywords: Bearing, beating, spike energy, vibration.

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Authors: Jairo A. Muñoz, Alexander Komissarov, Alexander Gromov

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In this investigation, a hypoeutectic AlSi11Cu alloy was printed. This alloy was obtained in powder form with an average particle size of 40 µm. Bars 20 mm in diameter and 100 mm in length were printed with the building direction parallel to the bars' longitudinal direction. The microstructural characterization demonstrated an Al matrix surrounded by a Si network forming a coral-like pattern. The microstructure of the alloy showed a heterogeneous behavior with a mixture of columnar and equiaxed grains. Likewise, the texture indicated that the columnar grains were preferentially oriented towards the building direction, while the equiaxed followed a texture dominated by the cube component. On the other hand, the as-printed material strength showed higher values than those obtained in the same alloy using conventional processes such as casting. In addition, strength and ductility differences were found in the printed material, depending on the measurement direction. The highest values were obtained in the radial direction (565 MPa maximum strength and 4.8% elongation to failure). The lowest values corresponded to the transverse direction (508 MPa maximum strength and 3.2 elongation to failure), which corroborate the material anisotropy.

Keywords: Additive manufacturing, aluminium alloy, melting pools, tensile test.

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Authors: Dogan Ciloglu, Abdurrahim Bolukbasi, Kemal Comakli

Abstract:

In this study, the effect of nanofluids on the pool film boiling was experimentally investigated at saturated condition under atmospheric pressure. For this purpose, four different water-based nanofluids (Al2O3, SiO2, TiO2 and CuO) with 0.1% particle volume fraction were prepared. To investigate the boiling heat transfer, a cylindrical rod with high temperature was used. The rod heated up to high temperatures was immersed into nanofluids. The center temperature of rod during the cooling process was recorded by using a K-type thermocouple. The quenching curves showed that the pool boiling heat transfer was strongly dependent on the nanoparticle materials. During the repetitive quenching tests, the cooling time decreased and thus, the film boiling vanished. Consequently, the primary reason of this was the change of the surface characteristics due to the nanoparticles deposition on the rod-s surface.

Keywords: Heat transfer, nanofluid, nanoparticles, pool film boiling

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Authors: Pawel P. Czapski, Andrzej Sluzek

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This paper presents preliminary results regarding system-level power awareness for FPGA implementations in wireless sensor networks. Re-configurability of field programmable gate arrays (FPGA) allows for significant flexibility in its applications to embedded systems. However, high power consumption in FPGA becomes a significant factor in design considerations. We present several ideas and their experimental verifications on how to optimize power consumption at high level of designing process while maintaining the same energy per operation (low-level methods can be used additionally). This paper demonstrates that it is possible to estimate feasible power consumption savings even at the high level of designing process. It is envisaged that our results can be also applied to other embedded systems applications, not limited to FPGA-based.

Keywords: Power optimization, FPGA, system-level designing, wireless sensor networks.

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Authors: Kotaro Miura, Makoto Sakamoto, Yuji Tanabe

Abstract:

We focus on internal stress and displacement of an elastic axisymmetric contact problem for indentation of a layer-substrate body. An elastic layer is assumed to be perfectly bonded to an elastic semi-infinite substrate. The elastic layer is smoothly indented with a flat-ended cylindrical indenter. The analytical and exact solutions were obtained by solving an infinite system of simultaneous equations using the method to express a normal contact stress at the upper surface of the elastic layer as an appropriate series. This paper presented the numerical results of internal stress and displacement distributions for hard-coating system with constant values of Poisson’s ratio and the thickness of elastic layer.

Keywords: Indentation, contact problem, stress distribution, coating materials, layer-substrate body.

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Authors: Abdolamir Nekoubin

Abstract:

In this paper effect of stator slots structure and switching angle on a cylindrical single-phase brushless direct current motor (BLDC) is analyzed. BLDC motor with three different structures for stator slots is designed by using RMxprt software and efficiency of BLDC motor for different structures in full-load condition has been presented. Then the BLDC motor in different conditions by using Maxwell 3D software is designed and with finite element method is analyzed electromagnetically. At the end with the use of MATLAB software influence of switching angle on motor performance investigated and optimal angle has been determined. The results indicate that with correct choosing of stator slots structure and switching angle, maximum efficiency can be found.

Keywords: Permanent magnets, Switching angle, BLDC motor

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Authors: Hema Sandhya Jagarlamudi, Mousumi Saha, Pavan Kumar Jagarlamudi

Abstract:

The use of Quantum dots is a promising emerging Technology for implementing digital system at the nano level. It is effecient for attractive features such as faster speed , smaller size and low power consumption than transistor technology. In this paper, various Combinational and sequential logical structures - HALF ADDER, SR Latch and Flip-Flop, D Flip-Flop preceding NAND, NOR, XOR,XNOR are discussed based on QCA design, with comparatively less number of cells and area. By applying these layouts, the hardware requirements for a QCA design can be reduced. These structures are designed and simulated using QCA Designer Tool. By taking full advantage of the unique features of this technology, we are able to create complete circuits on a single layer of QCA. Such Devices are expected to function with ultra low power Consumption and very high speeds.

Keywords: QCA, QCA Designer, Clock, Majority Gate

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Authors: M. A. Kamely, A. Y. Bani Hashim, S. H. Yahaya, H. Sihombing, H. Hazman

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Grinding requires high specific energy and the consequent development of high temperature at tool-workpiece contact zone impairs workpiece quality by inducing thermal damage to the surface. Finishing grinding process requires component to be cut more than one pass. This paper deals with an investigation on the effect of multipass cutting on grinding performance in term of surface roughness and surface defect. An experimental set-up has been developed for this and a detailed comparison has been done with a single pass and various numbers of cutting pass. Results showed that surface roughness increase with the increase in a number of cutting pass. Good surface finish of 0.26μm was obtained for single pass cutting and 0.73μm for twenty pass cutting. It was also observed that the thickness of the white layer increased with the increased in a number of cutting pass.

Keywords: Cylindrical grinding, Multipass cutting, Surface roughness, Surface defect.

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

Abstract:

Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: Identification, Hammerstein-Wiener, optimization, quantization.

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Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan

Abstract:

The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.

Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.

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