Model Reduction of a Parametrically Excited Drivetrain

2012 ◽  
Author(s):  
Thomas Pumhoessel ◽  
Peter Hehenberger ◽  
Klaus Zeman
Keyword(s):  
Stability Margin ◽  
Original System ◽  
Reduced Model ◽  
Parametrically Excited ◽  
System Parameters ◽  
Additional Stability ◽  
System Equations ◽  
The Difference ◽  
Set Up ◽  
The Stability

The complexity of engineering systems is continuously increasing, resulting in mathematical models that become more and more computationally expensive. Furthermore, in model based design, for example, system parameters are subject of change, and therefore, the system equations have to be evaluated repeatedly. Hence, there is a need for providing reduced models which are as compact as possible, but still reflect the properties of the original model in a satisfactory manner. In this contribution, the reduction of differential equations with time-periodic coefficients, termed as parametrically excited systems, is investigated using the method of Proper Orthogonal Decomposition (POD). A reduced model is set up based on the solution of the original system for a certain parametric combination resonance of the difference type, resulting in an additional stability margin of the trivial solution. It is shown that the POD reduced model approximates the stability behavior of the original system much better than a modally reduced model even if system parameters are subject of change.

A Study of the Effect of Mixed Cores on the Stability of BWRs

2010 ◽  
Author(s):  
Jose March-Leuba ◽  
Weidong Wang ◽  
Tai L. Huang
Keyword(s):  
Pressure Drop ◽  
Natural Circulation ◽  
Strong Dependence ◽  
Stability Margin ◽  
Fuel Type ◽  
Stability Margins ◽  
Full Power ◽  
Set Up ◽  
The Stability ◽  
Fuel Elements

Cores loaded with a mixture of fuel types are known to reduce stability margins. Mixed fuel cores have become more common as utilities change fuel suppliers, or when fuel vendors upgrade their fuel designs to take advantage of improved thermal and mechanical margins. This paper studies some of the physical processes that reduce the stability of mixed cores. A number of runs have been performed using the LAPUR6 stability code to evaluate the effect on mixed cores on the stability of a typical BWR. To this end, two fuel types have been set up with two different single-phase to two-phase pressure drop ratios by artificially adjusting the spacer and inlet orifice friction coefficients. The flow and pressure drop characteristics of both fuels have been matched at full flow, full power conditions. All manufacturers match the pressure drop of new fuels so that the flow distributions among the new and old fuel elements operating at the same power are approximately constant. The critical power ratio and thermo-mechanical criteria are typically limiting at full power; therefore matching the flow performance at full power maximizes the margin to these criteria. Stability is of concern at low flows, especially at natural circulation, where the thermal-hydraulic conditions are significantly different from full flow and power. Our simulations show that even if two fuel elements are perfectly matched at full flow, the axial void fraction distribution changes significantly when the flow is reduced to natural circulation conditions and the two fuel elements are not fully thermal-hydraulically compatible at the reduced flows. Basically, the two fuel types set up two separate natural circulation lines, and one of the fuel types essentially starves the other from flow. Since stability has such a strong dependence with channel flow, the reactor stability is controlled by the fuel type that has the smaller flow at natural circulation. A counterintuitive result of this study shows that, in general, loading a more stable fuel type into a mixed core has the opposite effect, and the stability margin of that mixed core is lower until the new, more stable fuel becomes dominant. Because of the burnable Gadolinium in most modern BWR fuels, the highest reactivity fuel elements are the once-burned. Loading a more stable fuel type starves the flow of the high-reactivity older fuel, reducing the stability margin.

scholarly journals Methodology for calculating rope drums for stability

2021 ◽  
pp. 83
Author(s):  
Nаtalya Fidrovska ◽  
Viktoria Nesterenko ◽  
Ruslan Karavan
Keyword(s):  
Critical Load ◽  
Stability Margin ◽  
External Pressure ◽  
Shell Shape ◽  
Metal Consumption ◽  
Safety And Reliability ◽  
The Difference ◽  
The Stability ◽  
Stability Issues ◽  
Good Agreement

. The problems of the stability of rope drums are quite urgent. The rope drum is in most cases a thin-walled shell, which, under the influence of external pressure from the rope, can lead to loss of stability. The stability issues of the drum shell, which is loaded with rope turns, are very important, because the safety and reliability of the rope hoist is directly related to them The studies carried out made it possible to obtain a new method for calculating the stability of cylindrical shells, which takes into account not only the length of the shell, but also the rigidity of the connection with the head. In addition, a calculation formula was obtained to determine the critical pressure of the oval shell, which gives a fairly good agreement with the experiments of American scientists. The work also considered the effect of the difference in wall thickness on the critical load of the drum. The studies carried out made it possible to conclude that the parameters of the rope drums make it possible to completely eliminate the need to install rings and stiffeners. Also as a result of research it was found that the shell of the crane drum under the influence of a radial load cannot lose stability. Studies have shown that in all cases the stability margin of the rope drum shell is greater than the strength margin. In this case, the load created by the rope wound on the drum is considered, with the ratios of the radius of the drum and the rope typical for crane construction. In addition, a coefficient was established that takes into account the elasticity of the shell-head joint. The studies carried out have shown that such initial deviations of the drum shell shape as ovality do not give a significant increase in the critical load. The results obtained are quite important, since they allow reducing the metal consumption of the rope drum shell and at the same time ensuring its reliable operation. A decrease in metal consumption is achieved by reducing the thickness of the shell and the absence of the need to install rings and stiffeners. This will lead to a decrease in metal consumption and energy consumption of the crane itself, and also simplifies the technology of manufacturing a rope drum.

scholarly journals High-quality thermodynamic data on the stability changes of proteins upon single-site mutations

2016 ◽  
Author(s):  
Fabrizio Pucci ◽  
Raphaël Bourgeas ◽  
Marianne Rooman
Keyword(s):  
Thermal Stability ◽  
Point Mutations ◽  
Experimental Information ◽  
Thermodynamic Quantities ◽  
High Quality ◽  
Melting Temperatures ◽  
The Difference ◽  
Set Up ◽  
The Stability ◽  
The Impact

We have set up and manually curated a dataset containing experimental information on the impact of amino acid substitutions in a protein on its thermal stability. It consists of a repository of experimentally measured melting temperatures (Tm) and their changes upon point mutations (∆Tm) for proteins having a well-resolved X-ray structure. This high-quality dataset is designed for being used for the training or benchmarking of in silico thermal stability prediction methods. It also reports other experimentally measured thermodynamic quantities when available,i.e.the folding enthalpy (∆H) and heat capacity (∆CP) of the wild type proteins and their changes upon mutations (∆∆H and ∆∆CP), as well as the change in folding free energy (∆∆G) at a reference temperature. These data are analyzed in view of improving our insights into the correlation between thermal and thermodynamic stabilities, the asymmetry between the number of stabilizing and destabilizing mutations, and the difference in stabilization potential of thermostable versus mesostable proteins.

scholarly journals A non-linear difference equation with two parameters. II

1985 ◽  
Vol 27 (2) ◽  
pp. 145-166 ◽  
Author(s):  
A. Brown
Keyword(s):  
Difference Equation ◽  
Linear Difference Equation ◽  
Anomalous Behaviour ◽  
Three Solutions ◽  
Unstable Solutions ◽  
The Difference ◽  
Set Up ◽  
The Stability ◽  
Image Position ◽  
Two Parameters

AbstractThe paper discusses solutions of period 4 for the difference equationwhere k and m are real parameters, with k > 0. For given values of k and m there are at most three solutions with period 4 and equations are set up to determine the elements of these solutions and the stability of each solution. Only real solutions are considered. The procedure that is used to find these solutions allows unstable solutions to be identified as well as stable solutions.In a previous paper, solutions of period 2 and period 3 were examined for this equation and there was evidence of anomalous behaviour in the way the stability intervals occurred. Some preliminary information about solutions of period 4 was mentioned in the discussion. The present paper provides more complete results, which confirm the anomalous behaviour and give a better idea of how the stability criterion changes for different families of solutions. These results are used to indicate the variety of behaviour that can be found for one-parameter systems by imposing suitable conditions on m and k.

Suboptimal Bilinear Routh Approximant for Discrete Systems

2004 ◽  
Vol 128 (3) ◽  
pp. 742-745 ◽  
Author(s):  
Younseok Choo
Keyword(s):  
Impulse Response ◽  
Approximation Method ◽  
Order Reduction ◽  
Original System ◽  
Discrete Systems ◽  
Reduced Model ◽  
The Stability

Recently an improved bilinear Routh approximation method has been suggested for the order reduction of discrete systems. In the method, the last α and β parameters of a reduced model were replaced by new parameters so that the impulse response energy of an original system is also preserved in the reduced model without destroying the stability preserving and time-moments matching properties. In this paper a new and simple improvement is proposed from which one can find a suboptimal bilinear Routh approximant. Compared to the previous result, the approach of this paper has an advantage that the improvement is always guaranteed.

scholarly journals Analytical Solutions and Collision Stability Analysis of Solitary Waves in a Pre-compressed One-dimensional Granular Crystal

2021 ◽  
Author(s):  
Zhi-Guo Liu ◽  
Jinliang Zhang ◽  
Yue-Sheng Wang ◽  
Guoliang Huang
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Solitary Wave Solution ◽  
Original System ◽  
Bilinear Method ◽  
One Dimensional ◽  
Balance Principle ◽  
The Difference ◽  
Granular Crystal ◽  
The Stability

Abstract In this paper, the governing equation in a pre-compressed one-dimensional granular crystal, which was previously discussed by Nesterenko [J. Appl. Mech. Phys. 24, 733 (1983)], is solved analytically. Multiple solitary wave solutions are obtained by using the homogeneous balance principle and Hirota’s bilinear method. We analyze the difference between the original system and the KdV system and examine the collision of solitary waves in some special parameters. The dynamic behavior and stability of the double solitary waves are also studied. We find that the opposite collision between single solitary waves may be stable and thus generate a stable double solitary wave. It is concluded that the collision is a special stable double solitary wave solution. We further propose a possible way to determine the stability of multiple solitary waves qualitatively.

Numerical Investigation on Transverse Maneuverability of a Vectored Underwater Vehicle Without Appendage

2016 ◽  
Vol 28 (3) ◽  
pp. 371-377 ◽  
Author(s):  
Rongmin Zhang ◽  
◽  
Yuan Chen ◽  
Jun Gao
Keyword(s):  
Kinematic Model ◽  
Stability Margin ◽  
Underwater Vehicle ◽  
Euler Method ◽  
Nonlinear Dynamic Model ◽  
Research Attention ◽  
Spherical Parallel Mechanism ◽  
Six Dof ◽  
Set Up ◽  
The Stability

[abstFig src='/00280003/13.jpg' width=""300"" text='Solid model of a vectored underwater vehicle' ] Vectored underwater vehicles (VUVs) are receiving increasing research attention, in part for their maneuverability. In our work, we apply a novel vectored thruster based on a spherical parallel mechanism to an underwater vehicle. We present and calculate the scaling factor based on the vectored thruster’s configuration parameters and set up a six DOF kinematic model. We construct a nonlinear dynamic model of the VUV without appendages using the Newton-Euler method. To demonstrate the VUV’s transverse maneuverability, we set up a perturbation model in a complex domain using Laplacian transformation, and propose the stability margin of vectored propulsion as a maneuverability index. Many numerical examples are provided to verify the maneuverability of the VUV.

Stability Analysis of Parametrically Excited Systems With Time-Delay

2003 ◽  
Author(s):  
Eric A. Butcher ◽  
Haitao Ma ◽  
Ed Bueler ◽  
Victoria Averina ◽  
Zsolt Szabo
Keyword(s):  
Time Delay ◽  
Integral Form ◽  
Original System ◽  
Time Interval ◽  
Linear Difference Equations ◽  
Direct Integral ◽  
Parametrically Excited ◽  
Stability Matrix ◽  
The Stability ◽  
Time Periodic

This paper presents a new technique for studying the stability properties of parametrically excited dynamic systems with time delay modeled by delay-differential equations (DDEs) with time-periodic parameters. By employing a shifted Chebyshev polynomial approximation in each time interval with length equal to the delay period, the dynamic system can be reduced to a set of linear difference equations for the Chebyshev expansion coefficients of the state vector in the previous and current intervals. This defines a linear map which is the “infinite-dimensional Floquet transition matrix U”. Two different formulas for the computation of the approximate U, whose size is determined by the number of polynomials employed, are given. The first one, which results in a numerical stability matrix, uses the direct integral form of the original system in state space form while the second, which can give a symbolic stability matrix in terms of parameters, uses a convolution integral (variation of parameters) formulation. An extension of the method to the case where the delay and parametric periods are commensurate is also available. Numerical and symbolic stability charts are produced for several examples of time-periodic DDEs, including the delayed Mathieu equation and a model for regenerative chatter in impedance-modulated turning. The results indicate that this method is a effective way to study the stability of periodic DDEs.

Use of a Lyophilized Reference Plasma to Compare Coagulation Test Procedures

1975 ◽  
Vol 34 (02) ◽  
pp. 426-444 ◽  
Author(s):  
J Kahan ◽  
I Nohén
Keyword(s):  
Oral Anticoagulant Therapy ◽  
Repeated Measurements ◽  
Test Procedures ◽  
Coagulation Activity ◽  
Close Relationship ◽  
Measured Activity ◽  
Test Materials ◽  
The Difference ◽  
The Stability ◽  
The One

SummaryIn 4 collaborative trials, involving a varying number of hospital laboratories in the Stockholm area, the coagulation activity of different test materials was estimated with the one-stage prothrombin tests routinely used in the laboratories, viz. Normotest, Simplastin-A and Thrombotest. The test materials included different batches of a lyophilized reference plasma, deep-frozen specimens of diluted and undiluted normal plasmas, and fresh and deep-frozen specimens from patients on long-term oral anticoagulant therapy.Although a close relationship was found between different methods, Simplastin-A gave consistently lower values than Normotest, the difference being proportional to the estimated activity. The discrepancy was of about the same magnitude on all the test materials, and was probably due to a divergence between the manufacturers’ procedures used to set “normal percentage activity”, as well as to a varying ratio of measured activity to plasma concentration. The extent of discrepancy may vary with the batch-to-batch variation of thromboplastin reagents.The close agreement between results obtained on different test materials suggests that the investigated reference plasma could be used to calibrate the examined thromboplastin reagents, and to compare the degree of hypocoagulability estimated by the examined PIVKA-insensitive thromboplastin reagents.The assigned coagulation activity of different batches of the reference plasma agreed closely with experimentally obtained values. The stability of supplied batches was satisfactory as judged from the reproducibility of repeated measurements. The variability of test procedures was approximately the same on different test materials.

In the stability of paints and varnishes for protective and decorative wood finish

2016 ◽  
Author(s):  
Ю.И. Цой
Keyword(s):  
Organic Solvents ◽  
Evaluation Criteria ◽  
Ternary Systems ◽  
Solubility Parameters ◽  
Formaldehyde Resin ◽  
Film Forming ◽  
The Difference ◽  
Molecular Forces ◽  
The Stability ◽  
Thermodynamic Interaction

Задача получения однородного состава ЛКМ сводится к правильному выбору пленкообразователей и соответствующих растворителей и, в случае необходимости, разбавителей и добавок. На основе положений теории растворимости была проведена оценка совместимости компонентов и стабильности таких систем. Критериями оценки были приняты параметры растворимости и термодинамического взаимодействия. Исследовали совместимость алкидных лаков с аминоформальдегидными смолами в бутаноле, и результаты этих исследований представлены в треугольной фазовой диаграмме. Для оценки совместимости смол по результатам расчета параметров термодинамического взаимодействия были построены спинодали для тройных систем. Как показывает анализ результатов проведенных исследований, даже при большой разности ?? = |?12 – ?13| = 0,2 наблюдается небольшая область несовместимости. С уменьшением разности ?? область несовместимости сужается. При ?23 > ?с область несовместимости расширяется как для ? = 0,2, так и для ?? = 0,1 и ?? = 0. Таким образом, для таких систем на совместимость компонентов, в первую очередь, влияет их взаимодействие между собой – чем оно больше, тем лучше они совместимы. Проведенные исследования показали, что парциальные параметры растворимости, учитывающие природу когезионных сил, более объективно характеризуют растворимость пленкообразующих смол в органических растворителях, чем их общий параметр растворимости. Растворимость пленкообразующих алкидных и этерифицированных аминоформальдегидных смол в органических растворителях обусловлена термодинамическим взаимодействием молекулярных сил различной природы. Стабильность смеси алкидной и этерифицированной аминоформальдегидной смолы в бутаноле обусловлена в большей степени термодинамическим взаимодействием молекулярных сил; при этом степень бутанолизации меламиноформальдегидной смолы оказывает наибольшее влияние на стабильность cистемы. Проведенные исследования по стабильности лакокрасочных смесей из различных пленкообразующих смол на основе рассмотренных критериев оценки могут быть использованы для совершенствования технологии защитно-декоративной отделки древесины. The problem of obtaining a homogeneous composition of the coatings is reduced to the proper selection of film-forming agents, and diluent and, if appropriate, diluents and additives. On the basis of the theory of solubility, we have carried out the assessment of the compatibility of the components and stability of such systems. The evaluation criteria were adopted the parameters of the solubility and thermodynamic interaction. Researched the compatibility with alkyd varnishes aminoformaldehyde resin in butanol, and the results of these studies are presented in the triangular phase diagram. To evaluate the compatibility of the resins according to the results of calculation of thermodynamic parameters of interaction were built spinodal for ternary systems. As the analysis of the results of the studies, even when the difference ??|?12 – ?13| = 0,2 there is a small area of incompatibility. With the decrease of the difference ? ? region incompatibility narrows. When ?23> ?с region incompatibility extends to ?? = 0,2, and for ?? = 0.1 and ?? = 0. Thus, for such systems, compatibility of components, primarily, affects their interaction with each other – the further away it is, the better they are compatible. Studies have shown that the partial solubility parameters, which take into account the nature of cohesive forces, more objectively characterize the solubility of film-forming resins in organic solvents than their total solubility parameter. The solubility and film-forming aminoformaldehyde esterified alkyd resins in organic solvents due to thermodynamic interaction of molecular forces of different nature. Тhe stability of the mixture and aminoformaldehyde esterified alkyd resin in butanol is generated largely by thermodynamic forces of molecular interaction; the degree of butanolate melamine-formaldehyde resin has the greatest effect on the stability of the system. Conducted research on the stability of the paint mixtures of various film-forming resins on the basis of the evaluation criteria can be used to improve the technology of protective and decorative wood finish.

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