Search results for: drilling rotation.

Authors: A.N. Ilia Anisa, Abdurahman H.Nour

Abstract:

The influence of viscosity on droplet diameter for water-in-crude oil (w/o) emulsion with two different ratios; 20-80 % and 50-50 % w/o emulsion was examined in the Brookfield Rotational Digital Rheometer. The emulsion was prepared with sorbitan sesquiolate (Span 83) act as emulsifier at varied temperature and stirring speed in rotation per minute (rpm). Results showed that the viscosity of w/o emulsion was strongly augmented by increasing volume of water and decreased the temperature. The changing of viscosity also altered the droplet size distribution. Changing of droplet diameter was depends on the viscosity and the behavior of emulsion either Newtonian or non-Newtonian.

Keywords: Diameter, phase ratio, viscosity, water-in-crude oil(w/o).

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Authors: Abdullah Alnutayfat, Alexander Sutin, Dong Liu

Abstract:

Wind turbine has become one of the most popular energy production methods. However, failure of blades and maintenance costs evolve into significant issues in the wind power industry, so it is essential to detect the initial blade defects to avoid the collapse of the blades and structure. This paper aims to apply modulation of high-frequency blade vibrations by low-frequency blade rotation, which is close to the known Vibro-Acoustic Modulation (VAM) method. The high-frequency wideband blade vibration is produced by the interaction of the surface blades with the environment air turbulence, and the low-frequency modulation is produced by alternating bending stress due to gravity. The low-frequency load of rotational wind turbine blades ranges between 0.2-0.4 Hz and can reach up to 2 Hz for strong wind. The main difference between this study and previous ones on VAM methods is the use of a wideband vibration signal from the blade's natural vibrations. Different features of the VAM are considered using a simple model of breathing crack. This model considers the simple mechanical oscillator, where the parameters of the oscillator are varied due to low-frequency blade rotation. During the blade's operation, the internal stress caused by the weight of the blade modifies the crack's elasticity and damping. The laboratory experiment using steel samples demonstrates the possibility of VAM using a probe wideband noise signal. A cycle load with a small amplitude was used as a pump wave to damage the tested sample, and a small transducer generated a wideband probe wave. The received signal demodulation was conducted using the Detecting of Envelope Modulation on Noise (DEMON) approach. In addition, the experimental results were compared with the modulation index (MI) technique regarding the harmonic pump wave. The wideband and traditional VAM methods demonstrated similar sensitivity for earlier detection of invisible cracks. Importantly, employing a wideband probe signal with the DEMON approach speeds up and simplifies testing since it eliminates the need to conduct tests repeatedly for various harmonic probe frequencies and to adjust the probe frequency.

Keywords: Damage detection, turbine blades, Vibro-Acoustic Structural Health Monitoring, SHM, Detecting of Envelope Modulation on Noise.

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Authors: S. Chikhi, M. Batouche, H. Shout

Abstract:

In this paper, we combine a probabilistic neural method with radial-bias functions in order to construct the lithofacies of the wells DF01, DF02 and DF03 situated in the Triassic province of Algeria (Sahara). Lithofacies is a crucial problem in reservoir characterization. Our objective is to facilitate the experts' work in geological domain and to allow them to obtain quickly the structure and the nature of lands around the drilling. This study intends to design a tool that helps automatic deduction from numerical data. We used a probabilistic formalism to enhance the classification process initiated by a Self-Organized Map procedure. Our system gives lithofacies, from well-log data, of the concerned reservoir wells in an aspect easy to read by a geology expert who identifies the potential for oil production at a given source and so forms the basis for estimating the financial returns and economic benefits.

Keywords: Classification, Lithofacies, Probabilistic formalism, Reservoir characterization, Well-log data.

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Authors: Jan Flusser

Abstract:

This paper aims to present a survey of object recognition/classification methods based on image moments. We review various types of moments (geometric moments, complex moments) and moment-based invariants with respect to various image degradations and distortions (rotation, scaling, affine transform, image blurring, etc.) which can be used as shape descriptors for classification. We explain a general theory how to construct these invariants and show also a few of them in explicit forms. We review efficient numerical algorithms that can be used for moment computation and demonstrate practical examples of using moment invariants in real applications.

Keywords: Object recognition, degraded images, moments, moment invariants, geometric invariants, invariants to convolution, moment computation.

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Authors: Keshav Pujeri, Pranesh Jain, Krutibas Panda

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Significant changes in oil and gas drilling have emphasized the need to verify the integrity and reliability of drill stem components. Defects are inevitable in cast components, regardless of application; but if these defects go undetected, any severe defect could cause down-hole failure. One such defect is shrinkage porosity. Castings with lower level shrinkage porosity (CB levels 1 and 2) have scattered pores and do not occupy large volumes; so pressure testing and helium leak testing (HLT) are sufficient for qualifying the castings. However, castings with shrinkage porosity of CB level 3 and higher, behave erratically under pressure testing and HLT making these techniques insufficient for evaluating the castings- integrity. This paper presents a case study to highlight how the radiography technique is much more effective than pressure testing and HLT.

Keywords: Casting Defects, Interconnects, Leak Check, Pressure Test, Radiography.

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Authors: A. Lauvray, F. Poulhaon, P. Michaud, P. Joyot, E. Duc

Abstract:

Additive Friction Stir Manufacturing, or AFSM, is a new industrial process that follows the emergence of friction-based processes. The AFSM process is a solid-state additive process using the energy produced by the friction at the interface between a rotating non-consumable tool and a substrate. Friction depends on various parameters like axial force, rotation speed or friction coefficient. The feeder material is a metallic rod that flows through a hole in the tool. There is still a lack in understanding of the physical phenomena taking place during the process. This research aims at a better AFSM process understanding and implementation, thanks to numerical simulation and experimental validation performed on a prototype effector. Such an approach is considered a promising way for studying the influence of the process parameters and to finally identify a process window that seems relevant. The deposition of material through the AFSM process takes place in several phases. In chronological order these phases are the docking phase, the dwell time phase, the deposition phase, and the removal phase. The present work focuses on the dwell time phase that enables the temperature rise of the system due to pure friction. An analytic modeling of heat generation based on friction considers as main parameters the rotational speed and the contact pressure. Another parameter considered influential is the friction coefficient assumed to be variable, due to the self-lubrication of the system with the rise in temperature or the materials in contact roughness smoothing over time. This study proposes through a numerical modeling followed by an experimental validation to question the influence of the various input parameters on the dwell time phase. Rotation speed, temperature, spindle torque and axial force are the main monitored parameters during experimentations and serve as reference data for the calibration of the numerical model. This research shows that the geometry of the tool as well as fluctuations of the input parameters like axial force and rotational speed are very influential on the temperature reached and/or the time required to reach the targeted temperature. The main outcome is the prediction of a process window which is a key result for a more efficient process implementation.

Keywords: numerical model, additive manufacturing, frictional heat generation, process

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Authors: A.V. Hoseini, A. Bidi, M. H. Pol, M.Jalali azizpour

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In this paper stress and strain for two rotating thin wall cylinder fitted together with initial interference and overlap are computed. Also stress value for variation of initial interference is calculated. At first problem is considered without rotation and next angular velocity increased from 0 to 50000 rev/min and stress in each stage is calculated. The important point is that when stress become very small in magnitude the angular velocity is critical and two cylinders will separate. The critical speed i.e. speed of separation is calculated in each step.

Keywords: Thin walled cylinder, high angular velocity, twofitted thin walled

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Authors: E. F. P. Leme, L. J. R. Lopez, D. G. Goroso

Abstract:

In this paper as showed a non-invasive 3D eye tracker for optometry clinical applications. Measurements of biomechanical variables in clinical practice have many font of errors associated with traditional procedments such cover test (CT), near point of accommodation (NPC), eye ductions (ED), eye vergences (EG) and, eye versions (ES). Ocular motility should always be tested but all evaluations have a subjective interpretations by practitioners, the results is based in clinical experiences, repeatability and accuracy don-t exist. Optometric-lab is a tool with 3 (tree) analogical video cameras triggered and synchronized in one acquisition board AD. The variables globe rotation angle and velocity can be quantified. Data record frequency was performed with 27Hz, camera calibration was performed in a know volume and image radial distortion adjustments.

Keywords: Eye Tracking, strabismus, eye movements, optometry.

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Authors: G. Bhushan

Abstract:

Multilobe bearings are found to be more stable than circular bearings. A three lobe bearing also possesses good stability characteristics. Sometimes the line of action of the load does not pass through the axis of a bearing and is shifted on either side by a few degrees. Load orientation is one of the factors that affect the stability of a three lobe bearing. The effect of load orientation on the stability of a three-lobe has been discussed in this paper. The results show that stability of a three-lobe bearing supporting either rigid or flexible rotor is increased for the positive values of load orientation i.e. when the load line is shifted in the opposite direction of rotation.

Keywords: Thee-lobe bearing, load orientation, finite element method.

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Authors: Jaqueline M. R. Vieira

Abstract:

Different strategies and tools are available at the oil and gas industry for detecting and analyzing tension and possible fractures in borehole walls. Most of these techniques are based on manual observation of the captured borehole images. While this strategy may be possible and convenient with small images and few data, it may become difficult and suitable to errors when big databases of images must be treated. While the patterns may differ among the image area, depending on many characteristics (drilling strategy, rock components, rock strength, etc.). In this work we propose the inclusion of data-mining classification strategies in order to create a knowledge database of the segmented curves. These classifiers allow that, after some time using and manually pointing parts of borehole images that correspond to tension regions and breakout areas, the system will indicate and suggest automatically new candidate regions, with higher accuracy. We suggest the use of different classifiers methods, in order to achieve different knowledge dataset configurations.

Keywords: Brazil, classifiers, data-mining, Image Segmentation, oil well visualization, classifiers.

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Authors: Yuxin Chen, Qingyun Di, C. Dinis da Gama

Abstract:

In projects like waterpower, transportation and mining, etc., proving up the rock-mass structure and hidden tectonic to estimate the geological body-s activity is very important. Integrating the seismic results, drilling and trenching data, CSAMT method was carried out at a planning dame site in southwest China to evaluate the stability of a deformation. 2D and imitated 3D inversion resistivity results of CSAMT method were analyzed. The results indicated that CSAMT was an effective method for defining an outline of deformation body to several hundred meters deep; the Lung Pan Deformation was stable in natural conditions; but uncertain after the future reservoir was impounded. This research presents a good case study of the fine surveying and research on complex geological structure and hidden tectonic in engineering project.

Keywords: CSAMT Surveying, Deformation Stability.

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Authors: Hui Liu, Haiyang Quan

Abstract:

This paper To get the angle value with a MEMS rate gyroscope in some specific field, the usual method is to make an integral operation to the rate output, which will lead the error cumulating effect. So the rate gyro is not suitable. MEMS rate integrating gyroscope (MRIG) will solve this problem. A DSP system has been developed to implement the control arithmetic. The system can measure the angle of rotation directly by the control loops that make the sensor work in whole-angle mode. Modeling the system with MATLAB, desirable results of angle outputs are got, which prove the feasibility of the control arithmetic.

Keywords: Rate gyroscope, Rate integrating gyroscope, Whole angle mode, MATLAB modeling, DSP control.

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Authors: M.Somjarod, V. Tanawat, l. Weerawat

Abstract:

The understanding of knee movement during swing importance for golf swing improving and preventing injury. Thirty male professional and amateur golfers were assigned to swing time by time for 3 times. Data from a vedio-based motion capture were used to compute knee joint movement variables. The results showed that professional and amateur golfers were significantly in left knee flexion angle at the impact point and mid follow through phase. Nevertheless, left knee external rotation in both groups was also significant. The right knee were no significant different in all variable. However, pattern of knee joint movement are also likely between professional and amateur golfers.

Keywords: Golfer, Knee joint, Movement, Swing

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Authors: Xiangming Ge, Bing Pan, Wei He, Hao Chen, Yong Zhou, Jiayao Wu, Weijiang Chu

Abstract:

How the extraction and penetration of spudcan affect the performance of the adjacent pile foundation supporting the jacket platform was studied in the program FLAC3D depending on a wind farm project in Bohai sea. The simulations were conducted at the end of the spudcan penetration, which induced a pockmark in the seabed. The effects of the distance between the pile foundation and the pockmark were studied. The displacement at the mudline arose when the pockmark was closer. The bearing capacity of this jacket platform with deep pile foundations has been less influenced by the process of spudcan penetration, which can induce severe stresses on the pile foundation. The induced rotation was also satisfied with the serviceability constraints.

Keywords: Offshore foundation, pile-soil interaction, spudcan penetration, FLAC3D.

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Authors: Jincan Li, Mingyu Gao, Zhiwei He, Yuxiang Yang, Zhongfei Yu, Yuanyuan Liu

Abstract:

Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories.

Keywords: 6-DOF robots, motion planning, trigonometric function, kinematic constraints

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

Abstract:

Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: Gravity gradient, accelerometer, gravity gradient sensor, single-axis rotation modulation.

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Authors: I. Zohourkari, M. Zohoor

Abstract:

In this paper, an erosion-based model for abrasive waterjet (AWJ) turning process is presented. By using modified Hashish erosion model, the volume of material removed by impacting of abrasive particles to surface of the rotating cylindrical specimen is estimated and radius reduction at each rotation is calculated. Different to previous works, the proposed model considers the continuous change in local impact angle due to change in workpiece diameter, axial traverse rate of the jet, the abrasive particle roundness and density. The accuracy of the proposed model is examined by experimental tests under various traverse rates. The final diameters estimated by the proposed model are in good accordance with experiments.

Keywords: Abrasive, Erosion, impact, Particle, Waterjet, Turning.

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Authors: A. Rouili

Abstract:

Cantilever L-shaped walls are known to be relatively economical as retaining solution. The design starts by proportioning the wall dimensions for which the stability is checked for. A ratio between the lengths of the base and the stem, falling between 0.5 to 0.7 ensure in most case the stability requirements, however, the displacement pattern of the wall in terms of rotations and translations, and the lateral pressure profile, do not have the same figure for all wall’s proportioning, as it is usually assumed. In the present work the results of a numerical analysis are presented, different wall geometries were considered. The results show that the proportioning governs the equilibrium between the instantaneous rotation and the translation of the wall-toe, also, the lateral pressure estimation based on the average value between the at-rest and the active pressure, recommended by most design standards, is found to be not applicable for all walls.

Keywords: Cantilever wall, proportioning, numerical analysis.

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Authors: M. Ovinis, D. Kerr, K. Bouazza-Marouf, M. Vloeberghs

Abstract:

In this paper, the feasibility of using machine vision to assess task completion in a surgical intervention is investigated, with the aim of incorporating vision based inspection in robotic surgery systems. The visually rich operative field presents a good environment for the development of automated visual inspection techniques in these systems, for a more comprehensive approach when performing a surgical task. As a proof of concept, machine vision techniques were used to distinguish the two possible outcomes i.e. satisfactory or unsatisfactory, of three primary surgical tasks involved in creating a burr hole in the skull, namely incision, retraction, and drilling. Encouraging results were obtained for the three tasks under consideration, which has been demonstrated by experiments on cadaveric pig heads. These findings are suggestive for the potential use of machine vision to validate successful task completion in robotic surgery systems. Finally, the potential of using machine vision in the operating theatre, and the challenges that must be addressed, are identified and discussed.

Keywords: Machine vision, robotic surgery, visual inspection.

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Authors: Sang-Hong Park

Abstract:

This paper proposes an efficient method to classify inverse synthetic aperture (ISAR) images. Because ISAR images can be translated and rotated in the 2-dimensional image place, invariance to the two factors is indispensable for successful classification. The proposed method achieves invariance to translation and rotation of ISAR images using a combination of two-dimensional Fourier transform, polar mapping and correlation-based alignment of the image. Classification is conducted using a simple matching score classifier. In simulations using the real ISAR images of five scaled models measured in a compact range, the proposed method yields classification ratios higher than 97 %.

Keywords: Radar, ISAR, radar target classification, radar imaging.

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Authors: Basman Elhadidi, Islam Elqatary, Osama Mohamady, Hesham Othman

Abstract:

An active slat is developed to increase the lift and delay the separation for a DU96-W180 airfoil. The active slat is a fixed slat that can be closed, fully opened or intermittently opened by a rotating vane depending on the need. Experimental results show that the active slat has reduced the mean pressure and increased the mean velocity on the suction side of the airfoil for all positive angles of attack, indicating an increase of lift. The experimental data and numerical simulations also show that the direction of actuator vane rotation can influence the mixing of the flow streams on the suction side and hence influence the aerodynamic performance.

Keywords: Active slat, flow control.

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Authors: Fridhi Hadia, Soua Wadhah, Hidouri Ammar, Omri Ahmed

Abstract:

In this paper, the effect of the intake temperature (IT) and intake pressure (IP) on ignition timing and pollutants emission of Homogeneous Charge Compression Ignition (HCCI) engine is investigated. Numerical computations are performed using the CHEMKIN computer code. The numerical temperature obtained using different boundary conditions is compared to published data and a good agreement is assigned. Results show that the HCCI combustion engine is significantly improved by increasing the IT. With a value of IT lower than 390 K, combustion cannot occur. However, with an IT greater than 420 K, the cylinder pressure decreases. An optimum crank rotation angle is achieved by using IT of 420 K. So, we can conclude that the variation of the IT and IP influence notably the emission concentration.

Keywords: HCCI engine, CEMKIN, intake temperature, intake pressure.

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Authors: O. Mahian, A. B. Rahimi, A. Kianifar, A. Jabari Moghadam

Abstract:

In this study, the numerical solution of unsteady flow between two concentric rotating spheres with suction and blowing at their boundaries is presented. The spheres are rotating about a common axis of rotation while their angular velocities are constant. The Navier-Stokes equations are solved by employing the finite difference method and implicit scheme. The resulting flow patterns are presented for various values of the flow parameters including rotational Reynolds number Re , and a blowing/suction Reynolds number Rew . Viscous torques at the inner and the outer spheres are calculated, too. It is seen that increasing the amount of suction and blowing decrease the size of eddies generated in the annulus.

Keywords: Concentric spheres, numerical study, suction andblowing, unsteady flow, viscous torque.

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Authors: Yoshimoto Kurihara, Tad Gonsalves

Abstract:

Currently, in the field of object posture estimation, there is research on estimating the position and angle of an object by storing a 3D model of the object to be estimated in advance in a computer and matching it with the model. However, in this research, we have succeeded in creating a module that is much simpler, smaller in scale, and faster in operation. Our 6D pose estimation model consists of two different networks – a classification network and a regression network. From a single RGB image, the trained model estimates the class of the object in the image, the coordinates of the object, and its rotation angle in 3D space. In addition, we compared the estimation accuracy of each camera position, i.e., the angle from which the object was captured. The highest accuracy was recorded when the camera position was 75°, the accuracy of the classification was about 87.3%, and that of regression was about 98.9%.

Keywords: AlexNet, Deep learning, image recognition, 6D posture estimation.

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Authors: Rajendra K. Ray, H. V. R. Mittal

Abstract:

A numerical study is made of laminar, unsteady flow behind a rotationally oscillating circular cylinder using a recently developed higher order compact (HOC) scheme. The stream function vorticity formulation of Navier-Stokes (N-S) equations in cylindrical polar coordinates are considered as the governing equations. The temporal behaviour of vortex formation and relevant streamline patterns of the flow are scrutinized over broad ranges of two externally specified parameters namely dimensionless forced oscillating frequency Sf and dimensionless peak rotation rate αm for the Reynolds-s number Re = 200. Excellent agreements are found both qualitatively and quantitatively with the existing experimental and standard numerical results.

Keywords: HOC, Navier-Stokes, non-uniform polar grids, rotationally oscillating cylinder.

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Authors: Ahmed T. Farid, Muhammed Rizwan

Abstract:

Geotechnical study for evaluating soil or rock permeability is a highly important parameter. Permeability values for rock formations are more difficult for determination than soil formation as it is an effect of the rock quality and its fracture values. In this research, the prediction of in situ permeability of limestone rock formations was predicted. The limestone rock permeability was evaluated using Lugeon tests (in-situ packer permeability). Different sites which spread all over the Riyadh region of Saudi Arabia were chosen to conduct our study of predicting the in-situ permeability of limestone rock. Correlations were deducted between the values of in-situ permeability of the limestone rock with the value of the rock quality designation (RQD) calculated during the execution of the boreholes of the study areas. The study was performed for different ranges of RQD values measured during drilling of the sites boreholes. The developed correlations are recommended for the onsite determination of the in-situ permeability of limestone rock only. For the other sedimentary formations of rock, more studies are needed for predicting the actual correlations related to each type.

Keywords: Packer, permeability, rock, quality.

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Authors: W. Paraguassu, S. Guerini, C. M. R. Remédios, P. T. C. Freire

Abstract:

High Pressure Raman scattering measurements of KDP:Mn were performed at room temperatures. The X-ray powder diffraction patterns taken at room temperature by Rietveld refinement showed that doped samples of KDP-Mn have the same tetragonal structure of a pure KDP crystal, but with a contraction of the crystalline cell. The behavior of the Raman spectra, in particular the emergence of a new modes at 330 cm-1, indicates that KDP:Mn undergoes a structural phase transition with onset at around 4 GP. First principle density-functional theory (DFT) calculations indicate that tetrahedral rotation with pressure is predominantly around the c crystalline direction. Theoretical results indicates that pressure induced tetrahedral rotations leads to change tetrahedral neighborhood, activating librations/bending modes observed for high pressure phase of KDP:Mn with stronger Raman activity.

Keywords: Dipotassium molybdate, High pressure, Raman scattering, Phase transition, ab initio

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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

Abstract:

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: Khaled Alenezi, Talal Alhajri, M. M. Tahir, Mohamed Ragaee K. Badr, S. O. Bamaga

Abstract:

The population growth in the world requires an increase in demand of residential and housing construction. Using lightweight construction materials such as cold formed steel sections and ferrocement could be an alternate solution to foster the construction industry. In this study, a new composite column is introduced. It consists of cold formed steel section and ferrocement jacket. The ferrocement jacket was constructed using self-compacting mortar with two wire steel mesh of 550 MPa yield strength. Experimental push out tests was conducted to investigate the strength capacities and behavior of proposed shear connectors namely, bolt, bar-angle and self-drilling screw shear connectors. It was found that bolt connector showed the best behavior followed by bar-angle. Also, it was concluded that the ferrocement could be used to strength and improve the behavior of cold formed steel column.

Keywords: Cold formed steel, composite column, push out test, shear connector, ferrocement, strengthen method.

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

Abstract:

In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: Explicit group method, finite difference, Helmholtz equation, rotated grid, standard grid.

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