Search results for: static transfer switch

Authors: C.B. Vishwakarma

Abstract:

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.

Keywords: Modified pole clustering, order reduction, padeapproximation, stability, transfer function.

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Authors: A. Brener, B. Balabekov, N. Zhumataev

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In the paper we submit the non-local modification of kinetic Smoluchowski equation for binary aggregation applying to dispersed media having memory. Our supposition consists in that that intensity of evolution of clusters is supposed to be a function of the product of concentrations of the lowest orders clusters at different moments. The new form of kinetic equation for aggregation is derived on the base of the transfer kernels approach. This approach allows considering the influence of relaxation times hierarchy on kinetics of aggregation process in media with memory.

Keywords: Binary aggregation, Media with memory, Non-local model, Relaxation times

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Authors: F. Lemfeld, K. Frana

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This article deals with the numerical simulation of the floor heating convector in 3D. Presented convector can operate in two modes – cooling mode and heating mode. This initial numerical simulation is focused on cooling mode of the convector. Models with different temperature of the fins are compared and three various shapes of the fins are examined as well. The objective of the work is to predict air flow and heat transfer inside convector for further optimalization of these devices. For the numerical simulation was used commercial software Ansys Fluent.

Keywords: Cooling output, floor heating convector, numericalsimulation, optimalization.

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Authors: Z. Saleh, E. J. Avital, T. Korakianitis

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The effect of the blade tip geometry of a high pressure gas turbine is studied experimentally and computationally for high speed leakage flows. For this purpose two simplified models are constructed, one models a flat tip of the blade and the second models a cavity tip of the blade. Experimental results are obtained from a transonic wind tunnel to show the static pressure distribution along the tip wall and provide flow visualization. RANS computations were carried to provide further insight into the mean flow behavior and to calculate the discharge coefficient which is a measure of the flow leaking over the tip. It is shown that in both geometries of tip the flow separates over the tip to form a separation bubble. The bubble is higher for the cavity tip while a complete shock wave system of oblique waves ending with a normal wave can be seen for the flat tip. The discharge coefficient for the flat tip shows less dependence on the pressure ratio over the blade tip than the cavity tip. However, the discharge coefficient for the cavity tip is lower than that of the flat tip, showing a better ability to reduce the leakage flow and thus increase the turbine efficiency.

Keywords: Gas turbine, blade tip leakage flow, transonic flow.

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Authors: Shooshpasha I., Kiakojoori M., Mirzagoltabar R. A.

Abstract:

High building constructions are increasing in south beaches of the Caspian Sea because of tourist attractions and limitation of residential areas. According to saturated alluvial fields transfer of load from high structures to the soil by piles is inevitable. In spite of most of these piles are under compression forces, tension piles are used in special conditions. Few studies have been conducted because of the limited use of these piles. Tension capacity of openended pipe piles in full scale was tested in this study. The length of the bored piles was 420 up to 480 cm and all were in 120 cm diameter. The results of testing 7 piles were compared with the results of relations given by researches.

Keywords: piles, tension capacity, sand, shaft friction

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Authors: N. Bachok, N. L. Aleng, N. M. Arifin, A. Ishak, N. Senu

Abstract:

The problem of laminar fluid flow which results from the shrinking of a permeable surface in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the mass suction parameter S, Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. It was found that the reduced Nusselt number is decreasing function of each dimensionless number.

Keywords: Boundary layer, Nanofluid, Shrinking sheet, Brownian motion, Thermophoresis, Similarity solution.

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Authors: Chang Su Woo, Hyun Sung Park

Abstract:

Useful lifetime evaluation of railpads were very important in design procedure to assure the safety and reliability. It is, therefore, necessary to establish a suitable criterion for the replacement period of rail pads. In this study, we performed properties and accelerated heat aging tests of rail pads considering degradation factors and all environmental conditions including operation, and then derived a lifetime prediction equation according to changes in hardness, thickness, and static spring constants in the Arrhenius plot to establish how to estimate the aging of rail pads. With the useful lifetime prediction equation, the lifetime of e-clip pads was 2.5 years when the change in hardness was 10% at 25°C; and that of f-clip pads was 1.7 years. When the change in thickness was 10%, the lifetime of e-clip pads and f-clip pads is 2.6 years respectively. The results obtained in this study to estimate the useful lifetime of rail pads for high speed trains can be used for determining the maintenance and replacement schedule for rail pads.

Keywords: Rail pads, accelerated test, Arrhenius plot, useful lifetime prediction.

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Authors: Reza Sedaghati, Mojtaba Hakimzadeh, Mohammad Hasan Raouf, Mostafa Mirzadeh

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Nowadays the growth of distributed generation within the bulk power system is feasible by using the optimal control of the transmission lines power flow. Static Synchronous Compensators (STATCOM) is effective for improving voltage stability but it can only exchange reactive power with the power grid. The integration of Superconducting Magnetic Energy Storage (SMES) with a STATCOM can extend the traditional STATCOM capabilities to four-quadrant bulk power system power flow control and providing exchange both the active and reactive power related to the STATCOM with the ac network. This paper shows how the SMES system can be connected to the ac system via the DC bus of a STATCOM and also analyzes how the integration of STATCOM and SMES allows the bus voltage regulation and power oscillation damping (POD) to be achieved simultaneously. The dynamic performance of the integrated STATCOM-SMES is evaluated through simulation by using PSCAD/EMTDC software and the compensation effectiveness of this integrated compensator is shown.

Keywords: STATCOM-SMES compensator, Power Oscillation Damping (POD), stabilizing, signal, voltage.

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Authors: Ionel Zagan, Vasile Gheorghita Gaitan

Abstract:

The development of CPUs and of real-time systems based on them made it possible to use time at increasingly low resolutions. Together with the scheduling methods and algorithms, time organizing has been improved so as to respond positively to the need for optimization and to the way in which the CPU is used. This presentation contains both a detailed theoretical description and the results obtained from research on improving the performances of the nMPRA (Multi Pipeline Register Architecture) processor by implementing specific functions in hardware. The proposed CPU architecture has been developed, simulated and validated by using the FPGA Virtex-7 circuit, via a SoC project. Although the nMPRA processor hardware structure with five pipeline stages is very complex, the present paper presents and analyzes the tests dedicated to the implementation of the CPU and of the memory on-chip for instructions and data. In order to practically implement and test the entire SoC project, various tests have been performed. These tests have been performed in order to verify the drivers for peripherals and the boot module named Bootloader.

Keywords: Hardware scheduler, nMPRA processor, real-time systems, scheduling methods.

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Authors: Hee Suk Seo, Tae Kyung Kim

Abstract:

Adapting wireless devices to communicate within grid networks empowers us by providing range of possibilities.. These devices create a mechanism for consumers and publishers to create modern networks with or without peer device utilization. Emerging mobile networks creates new challenges in the areas of reliability, security, and adaptability. In this paper, we propose a system encompassing mobility management using AAA context transfer for mobile grid networks. This system ultimately results in seamless task processing and reduced packet loss, communication delays, bandwidth, and errors.

Keywords: Mobile Grid, AAA, Mobility Management.

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Authors: M. Baryshev, D.Vainauska, S. Kozireva, A.Karpovs

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Liposomal magnetofection is the most powerful nonviral method for the nucleic acid delivery into the cultured cancer cells and widely used for in vitro applications. Use of the static magnetic field condition may result in non-uniform distribution of aggregate complexes on the surface of cultured cells. To prevent this, we developed the new device which allows to concentrate aggregate complexes under dynamic magnetic field, assisting more contact of these complexes with cellular membrane and, possibly, stimulating endocytosis. Newly developed device for magnetofection under dynamic gradient magnetic field, “DynaFECTOR", was used to compare transfection efficiency of human liver hepatocellular carcinoma cell line HepG2 with that obtained by lipofection and magnetofection. The effect of two parameters on transfection efficiency, incubation time under dynamic magnetic field and rotation frequency of magnet, was estimated. Liposomal magnetofection under dynamic gradient magnetic field showed the highest transfection efficiency for HepG2 cells.

Keywords: Dynamic magnetic field, Lipofection, Magnetofection

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Authors: Tarek M. Alguhane, Ayman H. Khalil, M. N. Fayed, Ayman M. Ismail

Abstract:

Early pre-code reinforced concrete structures present undetermined resistance to earthquakes. This situation is particularly unacceptable in the case of essential structures, such as healthcare structures and pilgrims' houses. Amongst these, an existing old RC building in Madinah city (KSA) is seismically evaluated with and without infill wall and their dynamic characteristics are compared with measured values in the field using ambient vibration measurements (AVM). After updating the mathematical models for this building with the experimental results, three dimensional pushover analysis (Nonlinear static analysis) was carried out using commercial structural analysis software incorporating inelastic material properties for concrete, infill and steel. The purpose of this analysis is to evaluate the expected performance of structural systems by estimating, strength and deformation demands in design, and comparing these demands to available capacities at the performance levels of interest. The results summarized and discussed.

Keywords: Seismic Assessment, Pushover Analysis, Ambient vibration, Modal update.

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Authors: Dong-Chul Lee, Byung-Kwan Oh, Se-Woon Choi, Hyo-Sun Park

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The unanticipated brittle fracture of connection of the steel moment resisting frame (SMRF) occurred in 1994 the Northridge earthquake. Since then, the researches for the vulnerability of connection of the existing SMRF and for rehabilitation of those buildings were conducted. This paper suggests performance-based optimal seismic retrofit technique using connection upgrade. For optimal design, a multi-objective genetic algorithm(NSGA-II) is used. One of the two objective functions is to minimize initial cost and another objective function is to minimize lifetime seismic damages cost. The optimal algorithm proposed in this paper is performed satisfying specified performance objective based on FEMA 356. The nonlinear static analysis is performed for structural seismic performance evaluation. A numerical example of SAC benchmark SMRF is provided using the performance-based optimal seismic retrofit technique proposed in this paper

Keywords: connection upgrade, performace-based seismicdesign, seismic retrofit, multi-objective optimization

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Authors: Y. C. Mao, G. S. Chen

Abstract:

Bicycle configuration is not as large as those of motorcycles or automobiles, while it indeed composes a complicated dynamic system. People-s requirements on comfortability, controllability and safety grow higher as the research and development technologies improve. The shock absorber affects the vehicle suspension performances enormously. The absorber takes the vibration energy and releases it at a suitable time, keeping the wheel under a proper contact condition with road surface, maintaining the vehicle chassis stability. Suspension design for mountain bicycles is more difficult than that of city bikes since it encounters dynamic variations on road and loading conditions. Riders need a stiff damper as they exert to tread on the pedals when climbing, while a soft damper when they descend downhill. Various switchable shock absorbers are proposed in markets, however riders have to manually switch them among soft, hard and lock positions. This study proposes a novel design of the bicycle shock absorber, which provides automatic smooth tuning of the damping coefficient, from a predetermined lower bound to theoretically unlimited. An automatic quick releasing valve is involved in this design so that it can release the peak pressure when the suspension fork runs into a square-wave type obstacle and prevent the chassis from damage, avoiding the rider skeleton from injury. This design achieves the automatic tuning process by innovative plunger valve and fluidic passage arrangements without any electronic devices. Theoretical modelling of the damper and spring are established in this study. Design parameters of the valves and fluidic passages are determined. Relations between design parameters and shock absorber performances are discussed in this paper. The analytical results give directions to the shock absorber manufacture.

Keywords: Modelling, Simulation, Bicycle, Shock Absorber, Damping, Releasing Valve

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Authors: E. Fehling, P. Capewell

Abstract:

In recent years, the importance of masonry glued by polyurethane adhesive has increased. In 2021, the Institute of Structural Engineering of the University of Kassel was commissioned to carry out quasi-static in-plane shear tests on prefabricated brick masonry panel systems with 2K PUR adhesive in order to investigate the load-bearing behavior during earthquakes. In addition to the usual measurement of deformations using displacement transducers, all tests were documented using an optical measuring system, which was used to determine the surface strains and deformations of the test walls. To compare the results with conventional mortar walls, additional reference tests were carried out on test specimens with thin-bed mortar joints. This article summarizes the results of the test program and provides a comparison between the load-bearing behavior of masonry bonded with polyurethane adhesive and thin-bed mortar in order to enable realistic non-linear modeling.

Keywords: Glued Masonry, in-plane tests, shear resistance, polyurethane adhesive.

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Authors: H. Shayeghi, M. Mahdavi, A. Kazemi

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Transmission network expansion planning (TNEP) is a basic part of power system planning that determines where, when and how many new transmission lines should be added to the network. Up till now, various methods have been presented to solve the static transmission network expansion planning (STNEP) problem. But in all of these methods, transmission expansion planning considering network adequacy restriction has not been investigated. Thus, in this paper, STNEP problem is being studied considering network adequacy restriction using discrete particle swarm optimization (DPSO) algorithm. The goal of this paper is obtaining a configuration for network expansion with lowest expansion cost and a specific adequacy. The proposed idea has been tested on the Garvers network and compared with the decimal codification genetic algorithm (DCGA). The results show that the network will possess maximum efficiency economically. Also, it is shown that precision and convergence speed of the proposed DPSO based method for the solution of the STNEP problem is more than DCGA approach.

Keywords: DPSO algorithm, Adequacy restriction, STNEP.

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Authors: Noor Fadiya Mohd Noor

Abstract:

The hydromagnetic flow of a Maxwell fluid past a vertical stretching sheet with thermophoresis is considered. The impact of chemical reaction species to the flow is analyzed for the first time by using the homotopy analysis method (HAM). The h-curves for the flow boundary layer equations are presented graphically. Several values of wall skin friction, heat and mass transfer are obtained and discussed.

Keywords: homotopy, MHD, thermophoresis, chemical reaction, Maxwell

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Authors: S. Nazhan, Hassan K. Al-Musawi, Khalid A. Humood

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This paper reports on an experimental investigation into the influence of current modulation on the properties of a vertical-cavity surface-emitting laser (VCSEL) with a direct square wave modulation. The optical output power response, as a function of the pumping current, modulation frequency, and amplitude, is measured for an 850 nm VCSEL. We demonstrate that modulation frequency and amplitude play important roles in reducing the VCSEL’s power consumption for optical generation. Indeed, even when the biasing current is below the static threshold, the VCSEL emits optical power under the square wave modulation. The power consumed by the device to generate light is significantly reduced to > 50%, which is below the threshold current, in response to both the modulation frequency and amplitude. An operating VCSEL device at low power is very desirable for less thermal effects, which are essential for a high-speed modulation bandwidth.

Keywords: VCSELs, optical power generation, power consumption, square wave modulation.

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Authors: Edward Guillén, Stephanne Rodríguez, Jhordany Rodríguez

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Throughput enhancement can be achieved with two main approaches. The first one is by the increase of transmission rate and the second one is reducing the control traffic. This paper focuses on how the throughput can be enhanced by increasing Maximum Transmission Unit -MTU. Transmission of larger packets can cause a throughput improvement by reducing IP overhead. Analysis results are obtained by a mathematical model and simulation tools with a main focus on wireless channels.

Keywords: 802.11, Maximum Transfer Unit, throughput enhancement, wireless networks.

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Authors: Sultan Daud, John P. Forth, Nikolaos Nikitas

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The current study aims to highlight the loading characteristics impact on the time evolution (focusing particularly on long term effects) of the deformation of realized reinforced concrete beams. Namely the tension stiffening code provisions (i.e. within Eurocode 2) are reviewed with a clear intention to reassess their operational value and predicting capacity. In what follows the experimental programme adopted along with some preliminary findings and numerical modeling attempts are presented. For a range of long slender reinforced concrete simply supported beams (4200 mm) constant static sustained and repeated cyclic loadings were applied mapping the time evolution of deformation. All experiments were carried out at the Heavy Structures Lab of the University of Leeds. During tests the mid-span deflection, creep coefficient and shrinkage strains were monitored for duration of 90 days. The obtained results are set against the values predicted by Eurocode 2 and the tools within an FE commercial package (i.e. Midas FEA) to yield that existing knowledge and practise is at times over-conservative.

Keywords: Eurocode2, midas fea, repeated, sustained loading.

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Authors: W. Mughees, M. Al-Ahmad, M. Naeem

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This research involves the design and analysis of pinch-based water/wastewater networks to minimize water utility in the petrochemical and petroleum industries. A study has been done on Tehran Oil Refinery to analyze feasibilities of regeneration, reuse and recycling of water network. COD is considered as a single key contaminant. Amount of freshwater was reduced about 149m3/h (43.8%) regarding COD. Re-design (or retrofitting) of water allocation in the networks was undertaken. The results were analyzed through graphical method and mathematical programming technique which clearly demonstrated that amount of required water would be determined by mass transfer of COD.

Keywords: Minimization, Water Pinch, Water Management, Pollution Prevention.

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Authors: Haider H. Aodah, Yassir Nashaat A. Kareem, Satish Chandra

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The present study explains the effect of aggregate gradation on moisture damage in bituminous mixes. Three types of aggregate gradation and two types of binder; VG-30 and Polymer modified bitumen (PMB-40) are used. Moisture susceptibility tests like retained stability and tensile strength ratio (TSR) and static creep test are conducted on Marshall specimens. The creep test was also conducted for conditioned and unconditioned specimens to observe the effect of moisture on creep behaviour. The results indicate that Marshall stability value is higher in PMB-40 mix than VG-30 mixes. Moisture susceptibility of PMB-40 mixes is low when compared with mix using VG-30. The reduction in retained stability, and indirect tensile strength and increase in creep are evaluated for finer, coarser and normal gradation of aggregate to observe the effect of gradation on moisture susceptibility of mixes. The retained stability is least affected when compared with other moisture susceptibility parameters

Keywords: Aggregate gradation, Creep ratio, Retained stability, Stripping, Tensile strength ratio.

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Authors: Ionel Zagan, Vasile Gheorghita Gaitan

Abstract:

Minimizing the response time to asynchronous events in a real-time system is an important factor in increasing the speed of response and an interesting concept in designing equipment fast enough for the most demanding applications. The present article will present the results regarding the validation of the nMPRA (Multi Pipeline Register Architecture) architecture using the FPGA Virtex-7 circuit. The nMPRA concept is a hardware processor with the scheduler implemented at the processor level; this is done without affecting a possible bus communication, as is the case with the other CPU solutions. The implementation of static or dynamic scheduling operations in hardware and the improvement of handling interrupts and events by the real-time executive described in the present article represent a key solution for eliminating the overhead of the operating system functions. The nMPRA processor is capable of executing a preemptive scheduling, using various algorithms without a software scheduler. Therefore, we have also presented various scheduling methods and algorithms used in scheduling the real-time tasks.

Keywords: nMPRA architecture, pipeline processor, preemptive scheduling, real-time system.

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Authors: Seung-Kyung Kye, Sang-Seung Lee, Dooyong Cho, Sun-Kyu Park

Abstract:

Although many studies on the assembly technology of the bridge construction have dealt mostly with on the pier, girder or the deck of the bridge, studies on the prefabricated barrier have rarely been performed. For understanding structural characteristics and application of the concrete barrier in the modular bridge, which is an assembly of structure members, static loading test was performed. Structural performances as a road barrier of the three methods, conventional cast-in-place(ST), vertical bolt connection(BVC) and horizontal bolt connection(BHC) were evaluated and compared through the analyses of load-displacement curves, strain curves of the steel, concrete strain curves and the visual appearances of crack patterns. The vertical bolt connection(BVC) method demonstrated comparable performance as an alternative to conventional cast-in-place(ST) while providing all the advantages of prefabricated technology. Necessities for the future improvement in nuts enforcement as well as legal standard and regulation are also addressed.

Keywords: Modular Bridge, Concrete Barrier, Bolt Connection

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Authors: Guanqun Shi, Xueqing Zhang

Abstract:

The frequent occurrence of failures in PPP projects which caused great loss has raised attention from the government as well as the concessionaire. PPPs are complex arrangements for its long operation period and multiple players. Many types of risks in PPP projects may cause the project fail. The insurance is an important tool to transfer the risks. Through a comparison and analysis of international government PPP guidelines and contracts as well as the case studies worldwide, we have identified eight main insurance principles, discussed thirteen insurance types in different stages. An overall procedure would be established to improve the practices in PPP projects.

Keywords: Public-private partnerships, insurance, contract, risk.

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Authors: Roman Kalvin, Anam Nadeem, Shahab Khushnood

Abstract:

Differential is an integral part of four wheeled vehicle, and its main function is to transmit power from drive shaft to wheels. Differential assembly allows both rear wheels to turn at different speed along curved paths. It consists of four gears which are assembled together namely pinion, ring, spider and bevel gears. This research focused on the spider gear and its static structural analysis using ANSYS. The main aim was to evaluate the distribution of stresses on the teeth of the spider gear. This study also analyzed total deformation that may occur during its working along with bevel gear that is meshed with spider gear. Structural steel was chosen for spider gear in this research. Modeling and assembling were done on SolidWorks for both spider and bevel gear. They were assembled exactly same as in a differential assembly. This assembly was then imported to ANSYS. After observing results that maximum amount of stress and deformation was produced in the spider gear, it was concluded that structural steel material for spider gear possesses greater amount of strength to bear maximum stress.

Keywords: Differential, spider gear, ANSYS, structural steel.

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Authors: Frantisek Bozek, Pavel Budinsky, Ignac Hoza, Alexandr Bozek, Magdalena Naplavova

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A cleaner production project was implemented in a bakery. The project is based on the substitution of the best available technique for an obsolete leaven production technology. The new technology enables production of durable, high-quality leavens. Moreover, 25% of flour as the original raw material can be replaced by pastry from the previous day production which has not been sold. That pastry was previously disposed in a waste incineration plant. Besides the environmental benefits resulting from less waste, lower consumption of energy, reduction of sewage waters quantity and floury dustiness there are also significant economic benefits. Payback period of investment was calculated with help of static method of financial analysis about 2.6 years, using dynamic method 3.5 years and an internal rate of return more than 29%. The supposed annual average profit after taxationin the second year of operation was incompliance with the real profit.

Keywords: Bakery, best available technology, cleaner production, costs, economic benefit, efficiency, energy, environmental benefit, investment, savings.

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Authors: François Chiocchio, Mahshid Gharibpour

Abstract:

Regardless of the extent to which succession management is implemented in the private sector, it is still overlooked in the public sector. Traditional succession management is evolving providing a better alignment between business strategies and HR strategies. Succession management brings sustainable effectiveness for succession programs through career path development, knowledge and skill transfer, job retention, as well as high-potential candidates’ empowerment for upcoming vacancies. By way of a systematic literature review, we bring into focus strategic succession management in public organizations and discuss best ways of implementation. 

Keywords: Succession management, strategic succession management, public organization, succession management model.

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Authors: R. I. Liban, N. Tayşi

Abstract:

This paper deals with a nonlinear finite element analysis to examine the behavior up to failure of cantilever composite steel-concrete beams which are prestressed externally. 'Pre-' means stressing the high strength external tendons in the steel beam section before the concrete slab is added. The composite beam contains a concrete slab which is connected together with steel I-beam by means of perfect shear connectors between the concrete slab and the steel beam which is subjected to static loading. A finite element analysis will be done to study the effects of external prestressed tendons on the composite steel-concrete beams by locating the tendons in different locations (profiles). ANSYS version 12.1 computer program is being used to analyze the represented three-dimensional model of the cantilever composite beam. This model gives all these outputs, mainly load-displacement behavior of the cantilever end and in the middle span of the simple support part.

Keywords: Composite steel-concrete beams, external prestressing, finite element analysis, ANSYS.

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Authors: Azali Saudi, Jumat Sulaiman

Abstract:

Harmonic functions are solutions to Laplace’s equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the computation for obtaining harmonic functions is often too slow particularly when it involves very large environment. This paper presents a two-stage iterative method namely Modified Arithmetic Mean (MAM) method for solving 2D Laplace’s equation. Once the harmonic functions are obtained, the standard Gradient Descent Search (GDS) is performed for path finding of an autonomous vehicle from arbitrary initial position to the specified goal position. Details of the MAM method are discussed. Several simulations of vehicle navigation with path planning in a static known indoor environment were conducted to verify the efficiency of the MAM method. The generated paths obtained from the simulations are presented. The performance of the MAM method in computing harmonic functions in 2D environment to solve path planning problem for an autonomous vehicle navigation is also provided.

Keywords: Modified Arithmetic Mean method, Harmonic functions, Laplace’s equation, path planning.

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