Search results for: Process parameter

Authors: Bandaris Shankar, Yohannes Yirga

Abstract:

In this paper, the problem of heat and mass transfer in unsteady MHD boundary-layer flow of nanofluids over stretching sheet with a non uniform heat source/sink is considered. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations and solved numerically using Keller box method. The velocity, temperature, and concentration profiles were obtained and utilized to compute the skin-friction coefficient, local Nusselt number, and local Sherwood number for different values of the governing parameters viz. solid volume fraction parameter, unsteadiness parameter, magnetic field parameter, Schmidt number, space-dependent and temperature-dependent parameters for heat source/sink. A comparison of the numerical results of the present study with previously published data revealed an excellent agreement.

Keywords: Manetohydrodynamics, nanofluid, non-uniform heat source/sink, unsteady.

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

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In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: Diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix.

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Authors: Anuchit Uchaipichat

Abstract:

A comprehensive program of laboratory testing on a compacted kaolin in a modified triaxial cell was perform to investigate the influence of hydraulic hysteresis on effective stress in unsaturated soils. The test data are presented on a range of constant suction shear tests along wetting and drying paths. The values of effective stress parameter χ at different matric suction were determined using the test results. The effect of hydraulic hysteresis phenomenon on the effective stress was observed. The values of effective stress parameter χ obtained from the experiments were compared with those obtained from the expressions proposed in literature.

Keywords: Unsaturated soils, Hydraulic hysteresis, Effectivestress

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Authors: Yongping Ren, Zongli Li, Fan Zhang

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A new nonlinear PID controller and its stability analysis are presented in this paper. A nonlinear function is deduced from the similarities between the control effort and the electric-field effect of a capacitor. The conventional linear PID controller can be modified into a nonlinear one by this function. To analyze the stability of the nonlinear PID controlled system, an idea of energy equivalence is adapted to avoid the conservativeness which is usually arisen from some traditional theorems and Criterions. The energy equivalence is naturally related with the conceptions of Passivity and T-Passivity. As a result, an engineering guideline for the parameter design of the nonlinear PID controller is obtained. An inverted pendulum system is tested to verify the nonlinear PID control scheme.

Keywords: Nonlinear PID controller, stability, gain equivalence, dissipative, T-Passivity.

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Authors: Oladeinde Mobolaji Humphrey, Akpobi John

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A mathematical model for the hydrodynamic lubrication of parabolic slider bearings with couple stress lubricants is presented. A numerical solution for the mathematical model using finite element scheme is obtained using three nodes isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations were solved using Gauss Quadrature to obtain a finite number of stiffness matrices. The global system of equations was obtained for the bearing and solved using Gauss Seidel iterative scheme. The converged pressure solution was used to obtain the load capacity of the bearing. Parametric studies were carried out and it was shown that the effect of couple stresses and profile parameter are to increase the load carrying capacity of the parabolic slider bearing. Numerical experiments reveal that the magnitude of the profile parameter at which maximum load is obtained increases with decrease in couple stress parameter. The results are presented in graphical form.

Keywords: Finite element, numerical, parabolic slider.

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Authors: Khairuddin Bin Osman, Ngo Boon Kiat, A. Hamid Bin hamidon, Khairul Azha Bin A. Aziz, Hazli Rafis Bin Abdul Rahman, Mazran Bin Esro

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Conventional industrial monitoring systems are tedious, inefficient and the at times integrity of the data is unreliable. The objective of this system is to monitor industrial processes specifically the fluid level which will measure the instantaneous fluid level parameter and respond by text messaging the exact value of the parameter to the user when being enquired by a privileged access user. The development of the embedded program code and the circuit for fluid level measuring are discussed as well. Suggestions for future implementations and efficient remote monitoring works are included.

Keywords: Industrial monitoring system, text messaging, embedded programming.

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Authors: Johannes Nywlt, Julian Becker, Sebastian Bertsch

Abstract:

Due to high dynamics in current markets the expectations regarding logistics increase steadily. However, the complexity and variety of products and production make it difficult to understand the interdependencies between logistical objectives and their determining factors. Therefore specific models are needed to meet this challenge. The Logistic Operating Curves Theory is such a model. With its aid the basic correlations between the logistic objectives can be described. Within this model the capacity flexibility represents an important parameter. However, a proper mathematical description for this parameter is still missing. Within this paper such a description will be developed in order to make the Logistic Operating Curves Theory more accurate.

Keywords: Capacity flexibility, Production controlling, Production logistics, Production management.

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Authors: Yasusi Kanada

Abstract:

When printing a plate (or dish) by an FDM 3D printer, the process normally requires support material, which causes several problems. This paper proposes a method for forming thin plates without using wasteful support material. This method requires several extraordinary parameter values when slicing plates. The experiments show that the plates can, for the most part, be successfully formed using a conventional slicer and a 3D printer; however, seams between layers spoil them and the quality of printed objects strongly depends on the slicer.

Keywords: Fused deposition modeling (FDM), 3D printing, Support-less, Layer seam, Slicer.

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Authors: R.Muthuvelayudham, T.Viruthagiri

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Response Surface Methodology (RSM) is a powerful and efficient mathematical approach widely applied in the optimization of cultivation process. Cellulase enzyme production by Trichoderma reesei RutC30 using agricultural waste rice straw and banana fiber as carbon source were investigated. In this work, sequential optimization strategy based statistical design was employed to enhance the production of cellulase enzyme through submerged cultivation. A fractional factorial design (26-2) was applied to elucidate the process parameters that significantly affect cellulase production. Temperature, Substrate concentration, Inducer concentration, pH, inoculum age and agitation speed were identified as important process parameters effecting cellulase enzyme synthesis. The concentration of lignocelluloses and lactose (inducer) in the cultivation medium were found to be most significant factors. The steepest ascent method was used to locate the optimal domain and a Central Composite Design (CCD) was used to estimate the quadratic response surface from which the factor levels for maximum production of cellulase were determined.

Keywords: Banana fiber, Cellulase, Optimization, Rice straw

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Authors: Rajiv Kumar, Arthanariee A. M.

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Image segmentation is the process to segment a given image into several parts so that each of these parts present in the image can be further analyzed. There are numerous techniques of image segmentation available in literature. In this paper, authors have been analyzed the edge-based approach for image segmentation. They have been implemented the different edge operators like Prewitt, Sobel, LoG, and Canny on the basis of their threshold parameter. The results of these operators have been shown for various images.

Keywords: Edge Operator, Edge-based Segmentation, Image Segmentation, Matlab 10.4.

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Authors: S. Abdollahi Pour, M. Saneei

Abstract:

This paper propose a new circuit design which monitor total leakage current during standby mode and generates the optimal reverse body bias voltage, by using the adaptive body bias (ABB) technique to compensate die-to-die parameter variations. Design details of power monitor are examined using simulation framework in 65nm and 32nm BTPM model CMOS process. Experimental results show the overhead of proposed circuit in terms of its power consumption is about 10 μW for 32nm technology and about 12 μW for 65nm technology at the same power supply voltage as the core power supply. Moreover the results show that our proposed circuit design is not far sensitive to the temperature variations and also process variations. Besides, uses the simple blocks which offer good sensitivity, high speed, the continuously feedback loop.

Keywords: leakage current, leakage power monitor, body biasing, low power

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Authors: P. Sawitri, S. Cdr. Sittha, T. Kritsana

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Flow forming is widely used in many industries, especially in defence technology industries. Pressure vessels requirements are high precision, light weight, seamless and optimum strength. For large pressure vessels, flow forming by 3 rollers machine were used. In case of long range rocket motor case flow forming and welding of pressure vessels have been used for manufacturing. Due to complication of welding process, researchers had developed 4 meters length pressure vessels without weldment by 4 rollers flow forming machine. Design and preparation of preform work pieces are performed. The optimization of flow forming parameter such as feed rate, spindle speed and depth of cut will be discussed. The experimental result shown relation of flow forming parameters to quality of flow formed tube and prototype pressure vessels have been made.

Keywords: Flow forming, Pressure vessel, four rollers, feed rate, spindle speed, cold work.

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

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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: Shuimiao Wan, Chao Yuan, Baoguang Tian

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In this paper, a linear mixed model which has two random effects is broken up into two models. This thesis gets the parameter estimation of the original model and an estimation’s statistical qualities based on these two models. Then many important properties are given by comparing this estimation with other general estimations. At the same time, this paper proves the analysis of variance estimate (ANOVAE) about σ2 of the original model is equal to the least-squares estimation (LSE) about σ2 of these two models. Finally, it also proves that this estimation is better than ANOVAE under Stein function and special condition in some degree.

Keywords: Linear mixed model, Random effects, Parameter estimation, Stein function.

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Authors: Masoud Mohammadpour, Blair Carlson, Radovan Kovacevic

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The quality of laser welded-brazed (LWB) joints were strongly dependent on the main process parameters, therefore the effect of laser power (3.2–4 kW), welding speed (60–80 mm/s) and wire feed rate (70–90 mm/s) on mechanical strength and surface roughness were investigated in this study. The comprehensive optimization process by means of response surface methodology (RSM) and desirability function was used for multi-criteria optimization. The experiments were planned based on Box– Behnken design implementing linear and quadratic polynomial equations for predicting the desired output properties. Finally, validation experiments were conducted on an optimized process condition which exhibited good agreement between the predicted and experimental results. AlSi3Mn1 was selected as the filler material for joining aluminum alloy 6022 and hot-dip galvanized steel in coach peel configuration. The high scanning speed could control the thickness of IMC as thin as 5 µm. The thermal simulations of joining process were conducted by the Finite Element Method (FEM), and results were validated through experimental data. The Fe/Al interfacial thermal history evidenced that the duration of critical temperature range (700–900 °C) in this high scanning speed process was less than 1 s. This short interaction time leads to the formation of reaction-control IMC layer instead of diffusion-control mechanisms.

Keywords: Laser welding-brazing, finite element, response surface methodology, multi-response optimization, cross-beam laser.

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Authors: Wookyong Kwon, Sangmoon Lee

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In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: Model predictive control, sampled-data control, linear parameter varying systems, LPV.

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Authors: C.S. Jawalkar, Apurbba Kumar Sharma, Pradeep Kumar

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Electro Chemical Discharge Machining (ECDM) is an emerging hybrid machining process used in precision machining of hard and brittle non-conducting materials. The present paper gives a critical review on materials machined by ECDM under the prevailing machining conditions; capability indicators of the process are reported. Some results obtained while performing experiments in micro-channeling on soda lime glass using ECDM are also presented. In these experiments, Tool Wear (TW) and Material Removal (MR) were studied using design of experiments and L–4 orthogonal array. Experimental results showed that the applied voltage was the most influencing parameter in both MR and TW studies. Field emission scanning electron microscopy (FESEM) results obtained on the microchannels confirmed the presence of micro-cracks, primarily responsible for MR. Chemical etching was also seen along the edges. The Energy dispersive spectroscopy (EDS) results were used to detect the elements present in the debris and specimens.

Keywords: ECDM, applied-voltage, FESEM, EDS.

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Authors: Abduladheem A. Ali, Easa A. Abd

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The robot is a repeated task plant. The control of such a plant under parameter variations and load disturbances is one of the important problems. The aim of this work is to design Geno-Fuzzy controller suitable for online applications to control single link rigid robot arm plant. The genetic-fuzzy online controller (indirect controller) has two genetic-fuzzy blocks, the first as controller, the second as identifier. The identification method is based on inverse identification technique. The proposed controller it tested in normal and load disturbance conditions.

Keywords: Fuzzy network, genetic algorithm, robot control, online genetic control, parameter identification.

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Authors: P. C. Chiu, Jehnming Lin

Abstract:

In this study, a 50-W CO₂ laser was used for the clad of 304L powders on the stainless steel substrate with a temperature sensor and image monitoring system. The laser power and cladding speed and focal position were modified to achieve the requirement of the workpiece flatness and mechanical properties. The numerical calculation is based on ANSYS to analyze the temperature change of the moving heat source at different surface positions when coating the workpiece, and the effect of the process parameters on the bath size was discussed. The temperature of stainless steel powder in the nozzle outlet reacting with the laser was simulated as a process parameter. In the experiment, the difference of the thermal conductivity in three-dimensional space is compared with single-layer cladding and multi-layer cladding. The heat dissipation pattern of the single-layer cladding is the steel plate and the multi-layer coating is the workpiece itself. The relationship between the multi-clad temperature and the profile was analyzed by the temperature signal from an IR pyrometer.

Keywords: Laser cladding, temperature, profile, microstructure.

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Authors: K. Jafar, R. Nazar, A. Ishak, I. Pop

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The present analysis considers the steady stagnation point flow and heat transfer towards a permeable shrinking sheet in an upper-convected Maxwell (UCM) electrically conducting fluid, with a constant magnetic field applied in the transverse direction to flow and a local heat generation within the boundary layer, with a heat generation rate proportional to (T-T)^p Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results are obtained for the flow and thermal fields for various values of the stretching/shrinking parameter λ, the magnetic parameter M, the elastic parameter K, the Prandtl number Pr, the suction parameter s, the heat generation parameter Q, and the exponent p. The results indicate the existence of dual solutions for the shrinking sheet up to a critical value λ_c whose value depends on the value of M, K, and s. In the presence of internal heat absorption (Q<0)  the surface heat transfer rate decreases with increasing p but increases with parameters Q and s when the sheet is either stretched or shrunk.

Keywords: Magnetohydrodynamic (MHD), boundary layer flow, UCM fluid, stagnation point, shrinking sheet.

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Authors: Moonjung Kim, Chang-Ho Hyun, Won-Ho Kim

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In this paper, the signal transmission analysis of the semicircle-shaped via structure for the differential pairs is presented in the frequency range up to 10 GHz. In order to improve the signal transmission properties in the differential pairs, single via is separated centrally into two semicircle-shaped sections, which are interconnected with the traces of differential pairs respectively. This via structure make possible to route differential pairs using only one via. In addition, it can improve impedance discontinuity around its region and then enhance the signal transmission properties in the differential pairs. The electrical analysis such as S-parameter calculation and eye diagram simulation has been performed to investigate the improvement of the signal transmission property in the differential pairs with new via structure.

Keywords: Differential pairs, signal transmission property, via, S-parameter.

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Authors: K. Shoylekova, K. Grigorova

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The Petri nets are the first standard for business process modeling. Most probably, it is one of the core reasons why all new standards created afterwards have to be so reformed as to reach the stage of mapping the new standard onto Petri nets. The paper presents a business process repository based on a universal database. The repository provides the possibility the data about a given process to be stored in three different ways. Business process repository is developed with regard to the reformation of a given model to a Petri net in order to be easily simulated. Two different techniques for business process simulation based on Petri nets - Yasper and Woflan are discussed. Their advantages and drawbacks are outlined. The way of simulating business process models, stored in the Business process repository is shown.

Keywords: Business process repository, Petri nets, Simulation, Woflan, Yasper.

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Authors: Mohammad Ehson Rangiha, Bill Karakostas

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Social Business Process Management (SBPM) promises to overcome limitations of traditional BPM by allowing flexible process design and enactment through the involvement of users from a social community. This paper proposes a meta-model and architecture for socially driven business process management systems. It discusses the main facets of the architecture such as goalbased role assignment that combines social recommendations with user profile, and process recommendation, through a real example of a charity organization.

Keywords: Business Process Management, Goal-Based Modelling, Process Recommendation Social Collaboration, Social BPM.

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Authors: C. Perez, O. Reinoso, N. Garcia, J. M. Sabater, L. Gracia

Abstract:

For high-speed control of robots, a good knowledge of system modelling is necessary to obtain the desired bandwidth. In this paper, we present a cartesian robot with a pan/tilt unit in end-effector (5 dof). This robot is implemented with powerful direct drive AC induction machines. The dynamic model, parameter identification and model validation of the robot are studied (including actuators). This work considers the cartesian robot coupled and non linear (contrary to normal considerations for this type of robots). The mechanical and control architecture proposed in this paper is efficient for industrial and research application in which high speed, well known model and very high accuracy are required.

Keywords: Robot modelling, parameter identification and validation, AC servo-motors.

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Authors: Ö. Tolga Altınöz

Abstract:

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].

Keywords: Adaptive backstepping, inverted pendulum, nonlinear adaptive control.

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Authors: Mou-Yuan Liao, Chien-Wei Wu, Chien-Hua Lin

Abstract:

Process capability index Cpk is the most widely used index in making managerial decisions since it provides bounds on the process yield for normally distributed processes. However, existent methods for assessing process performance which constructed by statistical inference may unfortunately lead to fine results, because uncertainties exist in most real-world applications. Thus, this study adopts fuzzy inference to deal with testing of Cpk . A brief score is obtained for assessing a supplier’s process instead of a severe evaluation.

Keywords: Process capability analysis, quality control.

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Authors: S. Bangphan, P. Bangphan, T. Boonkang

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Quality control helps industries in improvements of its product quality and productivity. Statistical Process Control (SPC) is one of the tools to control the quality of products that turning practice in bringing a department of industrial engineering process under control. In this research, the process control of a turning manufactured at workshops machines. The varying measurements have been recorded for a number of samples of a rice polished cylinder obtained from a number of trials with the turning practice. SPC technique has been adopted by the process is finally brought under control and process capability is improved.

Keywords: Rice polished cylinder, statistical process control, control charts, process capability.

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Authors: A. A. Ugla

Abstract:

The present paper aims to investigate the effects of the welding process parameters and cooling state on the weld bead geometry, mechanical properties and microstructure characteristics for weldments of AISI 304L stainless steel. The welding process was carried out using TIG welding with pulsed/non-pulsed current techniques. The cooling state was introduced as an input parameter to investigate the main effects on the structure morphology and thereby the mechanical property. This paper clarifies microstructure- mechanical property relationship of the welded specimens. In this work, the selected pulse frequency levels were 5-500 Hz in order to study the effect of low and high frequencies on the weldment characteristics using filler metal of ER 308LSi. The key findings of this work clarified that the pulse frequency has a significant effect on the breaking of the dendrite arms during the welding process and so strongly influences on the tensile strength and microhardness. The cooling state also significantly affects on the microstructure texture and thereby, the mechanical properties. The most important factor affects the bead geometry and aspect ratio is the travel speed and pulse frequency.

Keywords: Microstructure, mechanical properties, pulse frequency, high pulse frequency, austenitic stainless steel, TIG welding.

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Authors: Mohamed Yousef, Magdy Samuel, Maha El-Meligy, Taher El-Bitar

Abstract:

The present work is dealing with 2% Si-steel alloy. The alloy contains 0.05% C as well as 0.85% Al. The alloy under investigation would be used for electrical transformation purposes. A heating (expansion) - cooling (contraction) dilation investigation was executed to detect the a, a+g, and g transformation temperatures at the inflection points of the dilation curve. On heating, primary a  was detected at a temperature range between room temperature and 687 ^oC. The domain of a+g was detected in the range between 687 ^oC and 746 ^oC. g phase exists in the closed g region at the range between 746 ^oC and 1043 ^oC. The domain of a phase appears again at a temperature range between 1043 and 1105 ^oC, and followed by secondary a at temperature higher than 1105 ^oC. A physical simulation of thermo-mechanical processing on the as-cast alloy was carried out. The simulation process took into consideration the hot flat rolling pilot plant parameters. The process was executed on the thermo-mechanical simulator (Gleeble 3500). The process was designed to include seven consecutive passes. The 1^st pass represents the roughing stage, while the remaining six passes represent finish rolling stage. The whole process was executed at the temperature range from 1100 ^oC to 900 ^oC. The amount of strain starts with 23.5% at the roughing pass and decreases continuously to reach 7.5 % at the last finishing pass. The flow curve of the alloy can be abstracted from the stress-strain curves representing simulated passes. It shows alloy hardening from a pass to the other up to pass no. 6, as a result of decreasing the deformation temperature and increasing of cumulative strain. After pass no. 6, the deformation process enhances the dynamic recrystallization phenomena to appear, where the z-parameter would be high.

Keywords: Si-steel, hot deformability, critical transformation temperature, physical simulation, thermo-mechanical processing, flow curve, dynamic softening.

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Authors: Seksan Chunothaisawat, Pongchanun Luangpaiboon

Abstract:

There are two common types of operational research techniques, optimisation and metaheuristic methods. The latter may be defined as a sequential process that intelligently performs the exploration and exploitation adopted by natural intelligence and strong inspiration to form several iterative searches. An aim is to effectively determine near optimal solutions in a solution space. In this work, a type of metaheuristics called Ant Colonies Optimisation, ACO, inspired by a foraging behaviour of ants was adapted to find optimal solutions of eight non-linear continuous mathematical models. Under a consideration of a solution space in a specified region on each model, sub-solutions may contain global or multiple local optimum. Moreover, the algorithm has several common parameters; number of ants, moves, and iterations, which act as the algorithm-s driver. A series of computational experiments for initialising parameters were conducted through methods of Rigid Simplex, RS, and Modified Simplex, MSM. Experimental results were analysed in terms of the best so far solutions, mean and standard deviation. Finally, they stated a recommendation of proper level settings of ACO parameters for all eight functions. These parameter settings can be applied as a guideline for future uses of ACO. This is to promote an ease of use of ACO in real industrial processes. It was found that the results obtained from MSM were pretty similar to those gained from RS. However, if these results with noise standard deviations of 1 and 3 are compared, MSM will reach optimal solutions more efficiently than RS, in terms of speed of convergence.

Keywords: Ant colony optimisation, metaheuristics, modified simplex, non-linear, rigid simplex.

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