Search results for: Friction coefficients

Authors: A. Chaikittiratana, S. Koetniyom, S. Lakkam

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The feasibility of applying a simple and cost effective sliding friction testing apparatus to study the friction behaviour of a clutch facing material, effected by the variation of temperature and contact pressure, was investigated. It was found that the method used in this work was able to give a convenient and cost effective measurement of friction coefficients and their transitions of a clutch facing material. The obtained results will be useful for the development process of new facing materials.

Keywords: Static/kinetic friction, sliding friction testing apparatus, contact pressure and temperature dependent of friction coefficients.

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Authors: G.Ashwini, A.T.Eswara

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This paper examines the forced convection flow of incompressible, electrically conducting viscous fluid past a sharp wedge in the presence of heat generation or absorption with an applied magnetic field. The system of partial differential equations governing Falkner - Skan wedge flow and heat transfer is first transformed into a system of ordinary differential equations using similarity transformations which is later solved using an implicit finite - difference scheme, along with quasilinearization technique. Numerical computations are performed for air (Pr = 0.7) and displayed graphically to illustrate the influence of pertinent physical parameters on local skin friction and heat transfer coefficients and, also on, velocity and temperature fields. It is observed that the magnetic field increases both the coefficients of skin friction and heat transfer. The effect of heat generation or absorption is found to be very significant on heat transfer, but its effect on the skin friction is negligible. Indeed, the occurrence of overshoot is noticed in the temperature profiles during heat generation process, causing the reversal in the direction of heat transfer.

Keywords: Heat generation / absorption, MHD Falkner- Skan flow, skin friction and heat transfer

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Authors: M. Azadbakht, N. Tajari, R. Alimoradzade

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Knowing pea pods mechanical resistance against dynamic forces are important for design of combine harvester. In pea combine harvesters, threshing is accomplished by two mechanical actions of impact and friction forces. In this research, the effects of initial moisture content and needed impact and friction energy on threshing of pea pods were studied. An impact device was built based on pendulum mechanism. The experiments were done at three initial moisture content levels of 12.1, 23.5 and 39.5 (%w.b.) for both impact and friction methods. Three energy levels of 0.088, 0.126 and 0.202 J were used for impact method and for friction method three energy levels of 0.784, 0.930 and 1.351 J. The threshing percentage was measured in each method. By using a frictional device, kinetic friction coefficients at above moisture contents were measured 0.257, 0.303 and 0.336, respectively. The results of variance analysis of the two methods showed that moisture content and energy have significant effects on the threshing percentage.

Keywords: Pea pod, Energy, Friction, Impact, Initial moisture content, Threshing.

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Authors: Mohammad Fuad Mohammad Naser, Faycal Ikhouane

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LuGre friction model is an ordinary differential equation that is widely used in describing the friction phenomenon for mechanical systems. The importance of this model comes from the fact that it captures most of the friction behavior that has been observed including hysteresis. In this paper, we study some aspects related to the hysteresis behavior induced by the LuGre friction model.

Keywords: Hysteresis, LuGre model, operator, (strong) consistency.

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Authors: Marcus Walter, Norbert Nitzsche, Dirk Odenthal, Steffen M¨uller

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This contribution presents a friction estimator for industrial purposes which identifies Coulomb friction in a steering system. The estimator only needs a few, usually known, steering system parameters. Friction occurs on almost every mechanical system and has a negative influence on high-precision position control. This is demonstrated on a steering angle controller for highly automated driving. In this steering system the friction induces limit cycles which cause oscillating vehicle movement when the vehicle follows a given reference trajectory. When compensating the friction with the introduced estimator, limit cycles can be suppressed. This is demonstrated by measurements in a series vehicle.

Keywords: Friction estimation, friction compensation, steering system, lateral vehicle guidance.

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Authors: Maziar Ramezani, Zaidi Mohd Ripin

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In a metal forming process, the friction between the material and the tools influences the process by modifying the stress distribution of the workpiece. This frictional behaviour is often taken into account by using a constant coefficient of friction in the finite element simulations of sheet metal forming processes. However, friction coefficient varies in time and space with many parameters. The Stribeck friction model is investigated in this study to predict springback behaviour of AA6061-T4 sheets during V-bending process. The coefficient of friction in Stribeck curve depends on sliding velocity and contact pressure. The plane-strain bending process is simulated in ABAQUS/Standard. We compared the computed punch load-stroke curves and springback related to the constant coefficient of friction with the defined friction model. The results clearly showed that the new friction model provides better agreement between experiments and results of numerical simulations. The influence of friction models on stress distribution in the workpiece is also studied numerically

Keywords: Friction model, Stress distribution, V-bending.

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Authors: Seyed Hamid Mirmohammad Sadeghi, Raffaella Sesana, Daniela Maffiodo

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This study presents a procedure for friction calculation of column electric power steering (C-EPS) system which affects handling and comfort in driving. The friction losses estimation is obtained from experimental tests and mathematical calculation. Parts in C-EPS mainly involved in friction losses are bearings and worm gear. In the theoretical approach, the gear geometry and Hertz law were employed to measure the normal load and the sliding velocity and contact areas from the worm gears driving conditions. The viscous friction generated in the worm gear was obtained with a theoretical approach and the result was applied to model the friction in the steering system. Finally, by viscous friction coefficient and Coulomb friction coefficient, values of friction in worm gear were calculated. According to the Bearing Company and the characteristics of each bearing, the friction torques due to load and due to speed were calculated. A MATLAB Simulink model for calculating the friction in bearings and worm gear in C-EPS were done and the total friction value was estimated.

Keywords: Friction, worm gear, column electric power steering system, Simulink, bearing, electric power steering, EPS.

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Authors: Rafał Urbaniak, Robert Kłosowiak, Michał Ciałkowski, Jarosław Bartoszewicz

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The Chair of Thermal Engineering at Poznan University of Technology has been conducted research works on the possibilities of using carbon nanostructures in energy and mechanics applications for a couple of years. Those studies have provided results in a form of co-operation with foreign research centres, numerous publications and patent applications. Authors of this paper have studied the influence of multi-walled carbon nanostructures on changes in static friction arising when steel surfaces were moved. Tests were made using the original test stand consisting of automatically controlled inclined plane driven by precise stepper motors. Computer program created in the LabView environment was responsible for monitoring of the stand operation, accuracy of measurements and archiving the obtained results. Such a solution enabled to obtain high accuracy and repeatability of all conducted experiments. Tests and analysis of the obtained results allowed us to determine how additional layers of carbon nanostructures influenced on changes of static friction coefficients. At the same time, we analyzed the potential possibilities of applying nanostructures under consideration in mechanics.

Keywords: Carbon nanotubes, static friction, dynamic friction.

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Authors: D. Singh, R. Yousefi, M. Boroushaki

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Intelligent deep-drawing is an instrumental research field in sheet metal forming. A set of 28 different experimental data have been employed in this paper, investigating the roles of die radius, punch radius, friction coefficients and drawing ratios for axisymmetric workpieces deep drawing. This paper focuses an evolutionary neural network, specifically, error back propagation in collaboration with genetic algorithm. The neural network encompasses a number of different functional nodes defined through the established principles. The input parameters, i.e., punch radii, die radii, friction coefficients and drawing ratios are set to the network; thereafter, the material outputs at two critical points are accurately calculated. The output of the network is used to establish the best parameters leading to the most uniform thickness in the product via the genetic algorithm. This research achieved satisfactory results based on demonstration of neural networks.

Keywords: Deep-drawing, Neural network, Genetic algorithm, Sheet metal forming.

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Authors: Maziar Ramezani, Thomas Neitzert, Timotius Pasang

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This paper aims at experimental and numerical investigation of springback behavior of sheet metals during L-bending process with emphasis on Stribeck-type friction modeling. The coefficient of friction in Stribeck curve depends on sliding velocity and contact pressure. The springback behavior of mild steel and aluminum alloy 6022-T4 sheets was studied experimentally and using numerical simulations with ABAQUS software with two types of friction model: Coulomb friction and Stribeck friction. The influence of forming speed on springback behavior was studied experimentally and numerically. The results showed that Stribeck-type friction model has better results in predicting springback in sheet metal forming. The FE prediction error for mild steel and 6022-T4 AA is 23.8%, 25.5% respectively, using Coulomb friction model and 11%, 13% respectively, using Stribeck friction model. These results show that Stribeck model is suitable for simulation of sheet metal forming especially at higher forming speed.

Keywords: Friction, L-bending, Springback, Stribeck curves.

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Authors: S. Djebali, S. Larbi, A. Bilek

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The present work aims at contributing to the study of the complex phenomenon of wear of pin on disc contact in dry sliding friction between two material couples (bronze/steel and unsaturated polyester virgin and charged with graphite powder/steel). The work consists of the determination of the coefficient of friction, the study of the influence of the tribological parameters on this coefficient and the determination of the mass loss and the wear rate of the pin. This study is also widened to the highlighting of the influence of the addition of graphite powder on the tribological properties of the polymer constituting the pin. The experiments are carried out on a pin-disc type tribometer that we have designed and manufactured. Tests are conducted according to the standards DIN 50321 and DIN EN 50324. The discs are made of annealed XC48 steel and quenched and tempered XC48 steel. The main results are described here after. The increase of the normal load and the sliding speed causes the increase of the friction coefficient, whereas the increase of the percentage of graphite and the hardness of the disc surface contributes to its reduction. The mass loss also increases with the normal load. The influence of the normal load on the friction coefficient is more significant than that of the sliding speed. The effect of the sliding speed decreases for large speed values. The increase of the amount of graphite powder leads to a decrease of the coefficient of friction, the mass loss and the wear rate. The addition of graphite to the UP resin is beneficial; it plays the role of solid lubricant.

Keywords: Friction coefficients, mass loss, wear rate, bronze, polyester, graphite.

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Authors: Ashutosh Kumar Singh, Anand Mohan

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This paper deals with efficient computation of probability coefficients which offers computational simplicity as compared to spectral coefficients. It eliminates the need of inner product evaluations in determination of signature of a combinational circuit realizing given Boolean function. The method for computation of probability coefficients using transform matrix, fast transform method and using BDD is given. Theoretical relations for achievable computational advantage in terms of required additions in computing all 2n probability coefficients of n variable function have been developed. It is shown that for n ≥ 5, only 50% additions are needed to compute all probability coefficients as compared to spectral coefficients. The fault detection techniques based on spectral signature can be used with probability signature also to offer computational advantage.

Keywords: Binary Decision Diagrams, Spectral Coefficients, Fault detection

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Authors: T. Tchawe Moukam, N. Ngongang François, D. Thomas, K. Bienvenu, T. -Toko Dénis

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Since the expression of the coefficient of friction by Colebrook-White which turns out to be an implicit equation, equations have been developed to facilitate their applicability. In this work, this equation was applied to the penstock of the Three Gorges dam in order to observe the evolution of the turbulent boundary layer and the friction along the walls. Thus, the study is being carried out using a 3D digital approach in FLUENT in order to take into account the wall effects. It appears that according to the position of the portions, we have a variation in the evolutions of the turbulent friction and of the values of the boundary layer. We also observe that the inclination of the pipe has a significant influence on this turbulent friction; similarly, one could not make a fair evaluation of the latter without specifying the choice and location of the wall.

Keywords: Hydroelectric dam, penstock, turbulent friction, boundary layer, CFD.

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Authors: Mario Mastriani

Abstract:

We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.

Keywords: Compression, denoising, projections, wavelets.

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Authors: S. K. Tiwari, Dinesh Kumar Shukla, R. Chandra

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Friction stir welding is a solid state joining process. High strength aluminum alloys are widely used in aircraft and marine industries. Generally, the mechanical properties of fusion welded aluminum joints are poor. As friction stir welding occurs in solid state, no solidification structures are created thereby eliminating the brittle and eutectic phases common in fusion welding of high strength aluminum alloys. In this review the process parameters, microstructural evolution, and effect of friction stir welding on the properties of weld specific to aluminum alloys have been discussed.

Keywords: Aluminum alloys, Friction stir welding (FSW), Microstructure, Properties.

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Authors: G. Revathi, P. Saikrishnan

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In the present analysis an unsteady laminar forced convection water boundary layer flow is considered. The fluid properties such as viscosity and Prandtl number are taken as variables such that those are inversely proportional to temperature. By using quasi-linearization technique the nonlinear coupled partial differential equations are linearized and the numerical solutions are obtained by using implicit finite difference scheme with the appropriate selection of step sizes. Non-similar solutions have been obtained from the starting point of the stream-wise coordinate to the point where skin friction value vanishes. The effect non-uniform mass transfer along the surface of the cylinder through slot is studied on the skin friction and heat transfer coefficients.

Keywords: Boundary layer, heat transfer, non-similar solution, non-uniform mass, unsteady flow.

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Authors: Samir A. Emam, Ali El Domiaty

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Friction-stir welding has received a huge interest in the last few years. The many advantages of this promising process have led researchers to present different theoretical and experimental explanation of the process. The way to quantitatively and qualitatively control the different parameters of the friction-stir welding process has not been paved. In this study, a refined energybased model that estimates the energy generated due to friction and plastic deformation is presented. The effect of the plastic deformation at low energy levels is significant and hence a scale factor is introduced to control its effect. The predicted heat energy and the obtained maximum temperature using our model are compared to the theoretical and experimental results available in the literature and a good agreement is obtained. The model is applied to AA6000 and AA7000 series.

Keywords: Friction-stir welding, Energy, Aluminum Alloys.

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Authors: Hamed Sanei, Mohammad Bagher Ayani

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Optimizations of Plate Heat Exchangers (PHS) have received great attention in the past decade. In this study, heat transfer and pressure drop coefficients are compared for rectangular and circular PHS employing numerical simulations. Plates are designed to have equivalent areas. Simulations were implemented to investigate the efficiency of PHSs considering heat transfer, friction factor and pressure drop. Amount of heat transfer and pressure drop was obtained for different range of Reynolds numbers. These two parameters were compared with aim of F "weighting factor correlation". In this comparison, the minimum amount of F indicates higher efficiency. Results reveal that the F value for rectangular shape is less than circular plate, and hence using rectangular shape of PHS is more efficient than circular one. It was observed that, the amount of friction factor is correlated to the Reynolds numbers, such that friction factor decreased in both rectangular and circular plates with an increase in Reynolds number. Furthermore, such simulations revealed that the amount of heat transfer in rectangular plate is more than circular plate for different range of Reynolds numbers. The difference is more distinct for higher Reynolds number. However, amount of pressure drop in circular plate is less than rectangular plate for the same range of Reynolds numbers which is considered as a negative point for rectangular plate efficiency. It can be concluded that, while rectangular PHSs occupy more space than circular plate, the efficiency of rectangular plate is higher.

Keywords: Chevron corrugated-plate heat exchanger, heat transfer, friction factor, Reynolds numbers.

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Authors: Esther T. Akinlabi, Stephen A. Akinlabi

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Friction Stir Welding (FSW) is a solid state welding process invented and patented by The Welding Institute (TWI) in the United Kingdom in 1991 for butt and lap welding of metals and plastics. This paper highlights the benefits of friction stir welding process as an energy efficient and a green technology process in the field of welding. Compared to the other conventional welding processes, its benefits, typical applications and its use in joining similar and dissimilar materials are also presented.

Keywords: Dissimilar materials, Friction Stir Welding, Green technology, similar materials.

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Authors: Ibrahim F. Jasim, Najah F. Jasim

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The problem of controlling a two link robotic manipulator, consisting of a rotating and a prismatic links, is addressed. The actuations of both links are assumed to have unknown dead zone nonlinearities and friction torques modeled by LuGre friction model. Because of the existence of the unknown dead zone and friction torque at the actuations, unknown parameters and unmeasured states would appear to be part of the overall system dynamics that need for estimation. Unmeasured states observer, unknown parameters estimators, and robust adaptive control laws have been derived such that closed loop global stability is achieved. Simulation results have been performed to show the efficacy of the suggested approach.

Keywords: Adaptive Robust Control, Dead Zone, Friction Torques, Robotic Manipulators.

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Authors: Lingaraju Dumpala, Laxmi Mohan Kumar Chintada, Devadas Deepu, Pravin Kumar Yadav

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Friction stir welding is the new-fangled and cutting-edge technique in welding applications; it is widely used in the fields of transportation, aerospace, defense, etc. For thriving significant welding joints and properties of friction stir welded components, it is essential to carry out this advanced process in a prescribed systematic procedure. At this moment, Underwater Friction Stir Welding (UFSW) Process is the field of interest to do research work. In the continuous assessment, the study of UFSW process is to comprehend problems occurred in the past and the structure through which the mechanical properties of the welded joints can be value-added and contributes to conclude results an acceptable and resourceful joint. A meticulous criticism is given on how to modify the experimental setup from NFSW to UFSW. It can discern the influence of tool materials, feeds, spindle angle, load, rotational speeds and mechanical properties. By expending the DEFORM-3D simulation software, the achieved outcomes are validated.

Keywords: Underwater friction stir welding, al alloys, mechanical properties, normal friction stir welding.

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Authors: Jacques J. Scheepers, Edison Muzenda

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This work focused on the interactions which occur between ester solvents and alcohol solutes. The alcohols selected ranged from the simplest alcohol (methanol) to C10-alcohols, and solubility predictions in the form of infinite dilution activity coefficients were made using the Modified UNIFAC Dortmund group contribution model. The model computation was set up on a Microsoft Excel spreadsheet specifically designed for this purpose. It was found that alcohol/ ester interactions yielded an increase in activity coefficients (i.e. became less soluble) with an increase in the size of the ester solvent molecule. Furthermore, activity coefficients decreased with an increase in the size of the alcohol solute. The activity coefficients also decreased with an increase in the degree of unsaturation of the ester hydrocarbon tail. Tertiary alcohols yielded lower activity coefficients than primary alcohols. Finally, cyclic alcohols yielded higher activity coefficients than straight-chain alcohols until a point is reached where the trend is reversed, referred to as the ‘crossover’ point.

Keywords: Activity coefficients, alcohols, esters, solubility, van der Waals, UNIFAC.

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Authors: Huai-Feng Wang, Meng-Lin Lou, Ru-Lin Zhang

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One good analysis method in seismic response analysis is direct time integration, which widely adopts Rayleigh damping. An approach is presented for selection of Rayleigh damping coefficients to be used in seismic analyses to produce a response that is consistent with Modal damping response. In the presented approach, the expression of the error of peak response, acquired through complete quadratic combination method, and Rayleigh damping coefficients was set up and then the coefficients were produced by minimizing the error. Two finite element modes of soil layers, excited by 28 seismic waves, were used to demonstrate the feasibility and validity.

Keywords: Rayleigh damping, modal damping, damping coefficients, seismic response analysis.

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Authors: Saeid Saryazdi, Hossein Nezamabadi-pour

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A new blind gray-level watermarking scheme is described. In the proposed method, the host image is first divided into 4*4 non-overlapping blocks. For each block, two first AC coefficients of its Hadamard transform are then estimated using DC coefficients of its neighbor blocks. A gray-level watermark is then added into estimated values. Since embedding watermark does not change the DC coefficients, watermark extracting could be done by estimating AC coefficients and comparing them with their actual values. Several experiments are made and results suggest the robustness of the proposed algorithm.

Keywords: Digital Watermarking, Image watermarking, Information Hiden, Steganography.

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Authors: A. Chandrashekar, H. N. Reddappa, B. S. Ajaykumar

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A Friction stir welding tool is a critical component to the success of the process. The tool typically consists of a rotating round shoulder and a threaded cylindrical pin that heats the work piece, mostly by friction, and moves the softened alloy around it to form the joint. In this research work, an attempt has been made to investigate the relationship between FSW variables mainly tool profile, rotating speed, welding speed and the mechanical properties (tensile strength, yield strength, percentage elongation, and micro hardness) of friction stir welded aluminum alloy 5083 joints. From the experimental details, it can be assessed that the joint produced by using Triflute profile tool has contribute superior mechanical and structural properties as compared to Tapered unthreaded & Threaded tool for 1000rpm.

Keywords: Friction stir welding, Tool profile, Rotating speed, Strength, Speed ratio.

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Authors: Abiodun M. Aibinu, Momoh J. E. Salami, Amir A. Shafie, Athaur Rahman Najeeb

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Autoregressive Moving average (ARMA) is a parametric based method of signal representation. It is suitable for problems in which the signal can be modeled by explicit known source functions with a few adjustable parameters. Various methods have been suggested for the coefficients determination among which are Prony, Pade, Autocorrelation, Covariance and most recently, the use of Artificial Neural Network technique. In this paper, the method of using Artificial Neural network (ANN) technique is compared with some known and widely acceptable techniques. The comparisons is entirely based on the value of the coefficients obtained. Result obtained shows that the use of ANN also gives accurate in computing the coefficients of an ARMA system.

Keywords: Autoregressive moving average, coefficients, back propagation, model parameters, neural network, weight.

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Authors: Apetsi K. Ampiah, Zhao Xin

Abstract:

Earthquakes over the years have been known to cause devastating damage on buildings and induced huge loss on human life and properties. It is for this reason that engineers have devised means of protecting buildings and thus protecting human life. Since the invention of devices such as the viscous and friction dampers, scientists/researchers have been able to incorporate these devices into buildings and other engineering structures. The viscous damper is a hydraulic device which dissipates the seismic forces by pushing fluid through an orifice, producing a damping pressure which creates a force. In the friction damper, the force is mainly resisted by converting the kinetic energy into heat by friction. Devices such as viscous and friction dampers are able to absorb almost all the earthquake energy, allowing the structure to remain undamaged (or with some amount of damage) and ready for immediate reuse (with some repair works). Comparing these two devices presents the engineer with adequate information on the merits and demerits of these devices and in which circumstances their use would be highly favorable. This paper examines the performance of both viscous and friction dampers under different ground motions. A two-storey frame installed with both devices under investigation are modeled in commercial computer software and analyzed under different ground motions. The results of the performance of the structure are then tabulated and compared. Also included in this study is the ease of installation and maintenance of these devices.

Keywords: Friction damper, seismic, slip load, viscous damper.

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Authors: Antônio P. de Araújo Neto, Ruy D. A. da Silva Neto, Juliana R. de Souza, Salete K. P. de Medeiros, João T. N. de Medeiros

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The tribological test with Pin-On-Disc configuration measures friction and wear properties in dry or lubricated sliding surfaces of a variety of materials and coatings. Polymeric matrix composites loaded with mineral filler were used, 1%, 3%, 10%, 30%, and 50% mass percentage of filler, to reduce the material cost by using mineral tailings. Using a pin-on-disc tribometer to quantify coefficient of friction and wear resistance of the specimens. The parameters known to performing the test were 300 rpm rotation, normal load of 16N and duration of 33.5 minutes. The composite with 10% mineral filler performed better, considering that the wear resistance was good when compared to the other compositions and an average low coefficient of friction, in the order of μ ≤ 0.15.

Keywords: Microcomposites, microparticles tailings of scheelite, PTFE, tribology.

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Authors: Mostafa Makrahy, Nouby Ghazaly, Ahmad Moaaz

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Brakes are one of the most important safety and performance components in automobiles and airplanes. Development of brakes has mainly focused on increasing braking power and stability. Nowadays, brake noise, vibration and harshness (NVH) together with brake dust emission and pad life are very important to vehicle drivers. The main objective of this research is to define the relationship between compressibility of friction materials and their tendency to generate vibration. An experimental study of the friction-induced vibration obtained by the disc brake system of a passenger car is conducted. Three commercial brake pad materials from different manufacturers are tested and evaluated under various brake conditions against cast iron disc brake. First of all, compressibility test for the brake friction material are measured for each pad. Then, brake dynamometer is used to simulate and reproduce actual vehicle braking conditions. Finally, a comparison between the three pad specimens is conducted. The results showed that compressibility have a very significant effect on reduction the vibration occurrence.

Keywords: Automotive brake, friction material, brake dynamometer, compressibility test.

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Authors: Samy E. Oraby, Ayman M. Alaskari

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The importance of machining process in today-s industry requires the establishment of more practical approaches to clearly represent the intimate and severe contact on the tool-chipworkpiece interfaces. Mathematical models are developed using the measured force signals to relate each of the tool-chip friction components on the rake face to the operating cutting parameters in rough turning operation using multilayers coated carbide inserts. Nonlinear modeling proved to have high capability to detect the nonlinear functional variability embedded in the experimental data. While feedrate is found to be the most influential parameter on the friction coefficient and its related force components, both cutting speed and depth of cut are found to have slight influence. Greater deformed chip thickness is found to lower the value of friction coefficient as the sliding length on the tool-chip interface is reduced.

Keywords: Mathematical modeling, Cutting forces, Frictionforces, Friction coefficient and Chip ratio.

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