Damping and synchronising torques contributed by a voltage regulator to a synchronous generator: a quantitative assessment

In the paper, the total damping and synchronising torques, which determine the dynamic stability of a synchronous generator in a power system, have been traced to their origin. The positive and negative components released or consumed by the voltage regulator, and by the various windings of the machine, have been isolated, with the object of making a quantitative assessment of the effects of various gains and time constants on the dynamic stability of a synchronous machine under different operating conditions. The analysis is based on the properties of quadratic invariance in tensor calculus. An alternative solution by network analysis has also been provided to establish the validity of the tensor approach.

Effect of nanoclay content and compatibilizer on viscoelastic properties of montmorillonite/polypropylene nanocomposites

This paper deals with preparation of nanocomposites using modified nanoclay (organoclay) and polypropylene (PP), with, and without compatibilizer (m-TMI-g-PP) to study the effects of modified nanoclay and compatibilizer on viscoelastic properties. Nanocomposites were prepared in two steps; compounding of master batch of nanoclay, polypropylene and m-TMI-g-PP in a torque rheometer and blending of this master-batch with polypropylene in a twin-screw extruder in the specific proportions to yield 3-9% nanoclay by weight in the composite. Dynamic Mechanical Analysis (DMA) tests were carried out to investigate the viscoelastic behavior of virgin polypropylene and nanocomposites. The dynamic mechanical properties such as storage modulus (E'), loss modulus (E `') and damping coefficient (tand) of PP and nano-composites were investigated with and without compatibilizer in the temperature range of -40 degrees C to 140 degrees C at a step of 5 degrees C and frequency range of 5 Hz to 100 Hz at a step of 10 Hz. Storage modulus and loss modulus of the nano-composites was significantly higher than virgin polypropylene throughout the temperature range. Storage modulus of the composites increased continuously with increasing nano-content from 3% to 9%. Composites prepared with compatibilizer exhibited inferior storage modulus than the composites without compatibilizer. Surface morphology such as dispersion of nanoclay in the composites with and without compatibilizer was analyzed through Atomic Force Microscope (AFM) that explained the differences in viscoelastic behavior of composites. (C) 2011 Elsevier Ltd. All rights reserved.

Internal defect and process parameter analysis during friction stir welding of Al 6061 sheets

Welding parameters like welding speed, rotation speed, plunge depth, shoulder diameter etc., influence the weld zone properties, microstructure of friction stir welds, and forming behavior of welded sheets in a synergistic fashion. The main aims of the present work are to (1) analyze the effect of welding speed, rotation speed, plunge depth, and shoulder diameter on the formation of internal defects during friction stir welding (FSW), (2) study the effect on axial force and torque during welding, (c) optimize the welding parameters for producing internal defect-free welds, and (d) propose and validate a simple criterion to identify defect-free weld formation. The base material used for FSW throughout the work is Al 6061T6 having a thickness value of 2.1 mm. Only butt welding of sheets is aimed in the present work. It is observed from the present analysis that higher welding speed, higher rotation speed, and higher plunge depth are preferred for producing a weld without internal defects. All the shoulder diameters used for FSW in the present work produced defect-free welds. The axial force and torque are not constant and a large variation is seen with respect to FSW parameters that produced defective welds. In the case of defect-free weld formation, the axial force and torque are relatively constant. A simple criterion, (a,tau/a,p)(defective) > (a,tau/a,p)(defect free) and (a,F/a,p)(defective) > (a,F/a,p)(defect free), is proposed with this observation for identifying the onset of defect-free weld formation. Here F is axial force, tau is torque, and p is welding speed or tool rotation speed or plunge depth. The same criterion is validated with respect to Al 5xxx base material. Even in this case, the axial force and torque remained constant while producing defect-free welds.

Prediction of the stiffness of nanoclay-polypropylene composites using a monte carlo finite element analysis approach

The present work deals with the prediction of stiffness of an Indian nanoclay-reinforced polypropylene composite (that can be termed as a nanocomposite) using a Monte Carlo finite element analysis (FEA) technique. Nanocomposite samples are at first prepared in the laboratory using a torque rheometer for achieving desirable dispersion of nanoclay during master batch preparation followed up with extrusion for the fabrication of tensile test dog-bone specimens. It has been observed through SEM (scanning electron microscopy) images of the prepared nanocomposite containing a given percentage (3–9% by weight) of the considered nanoclay that nanoclay platelets tend to remain in clusters. By ascertaining the average size of these nanoclay clusters from the images mentioned, a planar finite element model is created in which nanoclay groups and polymer matrix are modeled as separate entities assuming a given homogeneous distribution of the nanoclay clusters. Using a Monte Carlo simulation procedure, the distribution of nanoclay is varied randomly in an automated manner in a commercial FEA code, and virtual tensile tests are performed for computing the linear stiffness for each case. Values of computed stiffness modulus of highest frequency for nanocomposites with different nanoclay contents correspond well with the experimentally obtained measures of stiffness establishing the effectiveness of the present approach for further applications.

Selection and thermodynamic analysis of a turbocharger for a producer gas-fuelled multi-cylinder engine

The current work addresses the use of producer gas, a bio-derived gaseous alternative fuel, in engines designed for natural gas, derived from diesel engine frames. Impact of the use of producer gas on the general engine performance with specific focus on turbo-charging is addressed. The operation of a particular engine frame with diesel, natural gas and producer gas indicates that the peak load achieved is highest with diesel fuel (in compression ignition mode) followed by natural gas and producer gas (both in spark ignite mode). Detailed analysis of the engine power de-rating on fuelling with natural gas and producer gas indicates that the change in compression ratio (migration from compression to spark ignited mode), difference in mixture calorific value and turbocharger mismatch are the primary contributing factors. The largest de-rating occurs due to turbocharger mismatch. Turbocharger selection and optimization is identified as the strategy to recover the non-thermodynamic power loss, identified as the recovery potential (the loss due to mixture calorific value and turbocharger mismatch) on operating the engine with a fuel different from the base fuel. A turbocharged after-cooled six cylinder, 5.9 l, 90 kWe (diesel rating) engine (12.2 bar BMEP) is available commercially as a naturally aspirated natural gas engine delivering a peak load of 44.0 kWe (6.0 bar BMEP). The engine delivers a load of 27.3 kWe with producer gas under naturally aspirated mode. On charge boosting the engine with a turbocharger similar in configuration to the diesel engine turbocharger, the peak load delivered with producer gas is 36 kWe (4.8 bar BMEP) indicating a de-rating of about 60% over the baseline diesel mode. Estimation of knock limited peak load for producer gas-fuelled operation on the engine frame using a Wiebe function-based zero-dimensional code indicates a knock limited peak load of 76 kWe, indicating the potential to recover about 40 kWe. As a part of the recovery strategy, optimizing the ignition timing for maximum brake torque based on both spark sweep tests and established combustion descriptors and engine-turbocharger matching for producer gas-fuelled operation resulted in a knock limited peak load of 72.8 kWe (9.9 bar BMEP) at a compressor pressure ratio of 2.30. The de-rating of about 17.0 kWe compared to diesel rating is attributed to the reduction in compression ratio. With load recovery, the specific biomass consumption reduces from 1.2 kg/kWh to 1.0 kg/kWh, an improvement of over 16% while the engine thermal efficiency increases from 28% to 32%. The thermodynamic analysis of the compressor and the turbine indicates an isentropic efficiency of 74.5% and 73%, respectively.

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Analysis of asymmetrical cold rolling with varying coefficients of friction

In this research, asymmetrical cold rolling was produced by the difference in the coefficient of friction between rolls and sheets rather than the difference of roll radius or rotation speeds. The influence of friction coefficient ratio on the cross shear deformation, rolling pressure and torque was investigated using slab analysis. The results showed that the shear deformation zone length increased with the increase of the friction coefficient ratio. The rolling force decreased only under the condition that the friction coefficient ratio increased while the sum of the friction coefficients was held constant. As the reduction per pass was increased, the shear deformation zone length increased and the rolling force also increased. An increase of the front tension resulted in a decrease of the shear deformation zone length. An increase of back tension, however, led to an increase of the shear deformation zone length. The reduction of rolling torque for the work roll with higher surface roughness was greater than that for the work roll with lower surface roughness. (C) 2002 Elsevier Science B.V. All rights reserved.

Dynamic-response of a laminated plate with friction damping

Nonlinear Fluid Damping In Structure-Wake Oscillators In Modeling Vortex-Induced Vibrations

A Nonlinear Fluid Damping (NFD) in the form of the square-velocity is applied in the response analysis of Vortex-induced Vibrations (VIV). Its nonlinear hydrodynamic effects oil the coupled wake and structure oscillators are investigated. A comparison between the coupled systems with the linear and nonlinear fluid dampings and experiments shows that the NFD model can well describe response characteristics, such as the amplification of body displacement at lock-in and frequency lock-ill, both at high and low mass ratios. Particularly, the predicted peak amplitude of the body in the Griffin plot is ill good agreement with experimental data and empirical equation, indicating the significant effect of the NFD on the structure motion.

Some problems in nonlinear elasticity

Two separate problems are discussed: axisymmetric equilibrium configurations of a circular membrane under pressure and subject to thrust along its edge, and the buckling of a circular cylindrical shell.

An ordinary differential equation governing the circular membrane is imbedded in a family of n-dimensional nonlinear equations. Phase plane methods are used to examine the number of solutions corresponding to a parameter which generalizes the thrust, as well as other parameters determining the shape of the nonlinearity and the undeformed shape of the membrane. It is found that in any number of dimensions there exists a value of the generalized thrust for which a countable infinity of solutions exist if some of the remaining parameters are made sufficiently large. Criteria describing the number of solutions in other cases are also given.

Donnell-type equations are used to model a circular cylindrical shell. The static problem of bifurcation of buckled modes from Poisson expansion is analyzed using an iteration scheme and pertubation methods. Analysis shows that although buckling loads are usually simple eigenvalues, they may have arbitrarily large but finite multiplicity when the ratio of the shell's length and circumference is rational. A numerical study of the critical buckling load for simple eigenvalues indicates that the number of waves along the axis of the deformed shell is roughly proportional to the length of the shell, suggesting the possibility of a "characteristic length." Further numerical work indicates that initial post-buckling curves are typically steep, although the load may increase or decrease. It is shown that either a sheet of solutions or two distinct branches bifurcate from a double eigenvalue. Furthermore, a shell may be subject to a uniform torque, even though one is not prescribed at the ends of the shell, through the interaction of two modes with the same number of circumferential waves. Finally, multiple time scale techniques are used to study the dynamic buckling of a rectangular plate as well as a circular cylindrical shell; transition to a new steady state amplitude determined by the nonlinearity is shown. The importance of damping in determining equilibrium configurations independent of initial conditions is illustrated.

Avaliação in vitro da variação do torque de remoção de parafusos para fixação de pilares protéticos submetidos a ciclos de parafusamento e desparafusamento

O afrouxamento dos parafusos protéticos é descrito na literatura como uma das complicações mais frequentes das próteses sobre implantes. Durante sua confecção, os profissionais sentem necessidade de remover várias vezes as próteses e/ou componentes protéticos, soltando e re-apertando os parafusos repetidamente. O principal objetivo deste trabalho foi avaliar a variação do torque de remoção de parafusos de fixação de pilares protéticos a implantes osteointegráveis após sucessivos ciclos de parafusamento e desparafusamento. Outro objetivo foi avaliar a influência do hexágono da base do pilar no torque de remoção dos parafusos. Para isso, foram utilizados 20 implantes de plataforma regular com hexágono externo e 20 pilares protéticos sextavados, que foram parafusados aos implantes com um parafuso de titânio, aplicando-se a este um torque de 32Ncm, por meio de um torquímetro digital. Os conjuntos implante/pilar/parafuso foram divididos em dois grupos: (1) pilares cujo hexágono da base foram removidos e (2) pilares convencionais, com hexágono na base. Cada conjunto recebeu uma restauração provisória e foi submetido a ciclagem mecânica por 15 minutos. Depois, os parafusos foram removidos, medindo-se o torque de remoção. Esta sequência foi repetida dez vezes e então o parafuso foi trocado por outro sem uso, e mais um ciclo foi realizado. Uma análise de regressão linear demonstrou nos dois grupos uma queda do torque de remoção do parafuso ao longo dos repetidos ciclos de inserção/remoção. A comparação entre os coeficientes da regressão nos dois grupos não revelou diferença entre eles. Também não houve diferença entre as médias das 5 últimas repetições e o 11 ciclo, com o parafuso novo. Concluiu-se que (1) repetidos parafusamentos e desparafusamentos promoveram a diminuição progressiva do torque de remoção dos parafusos, (2) a troca do parafuso por outro sem uso após dez ciclos de inserção/remoção não aumentou sua resistência ao afrouxamento, e (3) a remoção do hexágono da base do pilar protético não exerceu nenhum efeito sobre o torque de remoção do parafuso.

SteelConverter and Caltech VirtualShaker: Rapid Nonlinear Cloud-Based Structural Model Conversion and Analysis

STEEL, the Caltech created nonlinear large displacement analysis software, is currently used by a large number of researchers at Caltech. However, due to its complexity, lack of visualization tools (such as pre- and post-processing capabilities) rapid creation and analysis of models using this software was difficult. SteelConverter was created as a means to facilitate model creation through the use of the industry standard finite element solver ETABS. This software allows users to create models in ETABS and intelligently convert model information such as geometry, loading, releases, fixity, etc., into a format that STEEL understands. Models that would take several days to create and verify now take several hours or less. The productivity of the researcher as well as the level of confidence in the model being analyzed is greatly increased.

It has always been a major goal of Caltech to spread the knowledge created here to other universities. However, due to the complexity of STEEL it was difficult for researchers or engineers from other universities to conduct analyses. While SteelConverter did help researchers at Caltech improve their research, sending SteelConverter and its documentation to other universities was less than ideal. Issues of version control, individual computer requirements, and the difficulty of releasing updates made a more centralized solution preferred. This is where the idea for Caltech VirtualShaker was born. Through the creation of a centralized website where users could log in, submit, analyze, and process models in the cloud, all of the major concerns associated with the utilization of SteelConverter were eliminated. Caltech VirtualShaker allows users to create profiles where defaults associated with their most commonly run models are saved, and allows them to submit multiple jobs to an online virtual server to be analyzed and post-processed. The creation of this website not only allowed for more rapid distribution of this tool, but also created a means for engineers and researchers with no access to powerful computer clusters to run computationally intensive analyses without the excessive cost of building and maintaining a computer cluster.

In order to increase confidence in the use of STEEL as an analysis system, as well as verify the conversion tools, a series of comparisons were done between STEEL and ETABS. Six models of increasing complexity, ranging from a cantilever column to a twenty-story moment frame, were analyzed to determine the ability of STEEL to accurately calculate basic model properties such as elastic stiffness and damping through a free vibration analysis as well as more complex structural properties such as overall structural capacity through a pushover analysis. These analyses showed a very strong agreement between the two softwares on every aspect of each analysis. However, these analyses also showed the ability of the STEEL analysis algorithm to converge at significantly larger drifts than ETABS when using the more computationally expensive and structurally realistic fiber hinges. Following the ETABS analysis, it was decided to repeat the comparisons in a software more capable of conducting highly nonlinear analysis, called Perform. These analyses again showed a very strong agreement between the two softwares in every aspect of each analysis through instability. However, due to some limitations in Perform, free vibration analyses for the three story one bay chevron brace frame, two bay chevron brace frame, and twenty story moment frame could not be conducted. With the current trend towards ultimate capacity analysis, the ability to use fiber based models allows engineers to gain a better understanding of a building’s behavior under these extreme load scenarios.

Following this, a final study was done on Hall’s U20 structure [1] where the structure was analyzed in all three softwares and their results compared. The pushover curves from each software were compared and the differences caused by variations in software implementation explained. From this, conclusions can be drawn on the effectiveness of each analysis tool when attempting to analyze structures through the point of geometric instability. The analyses show that while ETABS was capable of accurately determining the elastic stiffness of the model, following the onset of inelastic behavior the analysis tool failed to converge. However, for the small number of time steps the ETABS analysis was converging, its results exactly matched those of STEEL, leading to the conclusion that ETABS is not an appropriate analysis package for analyzing a structure through the point of collapse when using fiber elements throughout the model. The analyses also showed that while Perform was capable of calculating the response of the structure accurately, restrictions in the material model resulted in a pushover curve that did not match that of STEEL exactly, particularly post collapse. However, such problems could be alleviated by choosing a more simplistic material model.

Analog methods of nonlinear vibration analysis

This thesis presents methods by which electrical analogies can be obtained for nonlinear systems. The accuracy of these methods is investigated and several specific types of nonlinear equations are studied in detail.

In Part I a general method is given for obtaining electrical analogs of nonlinear systems with one degree of freedom. Loop and node methods are compared and the stability of the loop analogy is briefly considered.

Parts II and III give a description of the equipment and a discussion of its accuracy. Comparisons are made between experimental and analytic solutions of linear systems.

Part IV is concerned with systems having a nonlinear restoring force. In particular, solutions of Duffing's equation are obtained, both by using the electrical analogy and also by approximate analytical methods.

Systems with nonlinear damping are considered in Part V. Two specific examples are chosen: (1) forced oscillations and (2) self-excited oscillations (van der Pol’s equation). Comparisons are made with approximate analytic solutions.

Part VI gives experimental data for a system obeying Mathieu's equation. Regions of stability are obtained. Examples of subharmonic, ultraharmonic, and ultrasubharmonic oscillat1ons are shown.

Towards identification of a general model of damping

Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. In spite of a large amount of research, understanding of damping mechanisms is not well developed. A major reason for this is that unlike inertia and stiffness forces it is not in general clear what are the state variables that govern the damping forces. The most common approach is to use `viscous damping' where the instantaneous generalized velocities are the only relevant state variables. However, viscous damping by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model. This paper is devoted to develop methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure. The method uses experimentally identified complex modes and complex natural frequencies and does not a-priori assume any fixed damping model (eg., viscous damping) but seeks to determine parameters of a general damping model described by the so called `relaxation function'. The proposed method and several related issues are discussed by considering a numerical example of a linear array of damped spring-mass oscillators.