scholarly journals Interdependence of friction, wear, and noise: A review

Friction ◽  
2021 ◽  
Author(s):  
Kevin Lontin ◽  
Muhammad Khan
Keyword(s):  
Mathematical Models ◽  
Friction And Wear ◽  
Review Paper ◽  
Acoustic Noise ◽  
Friction Noise ◽  
Mathematical Expressions ◽  
Mechanical Contacts ◽  
Exact Relationship ◽  
Modelling Approach ◽  
Frictional Noise

AbstractPhenomena of friction, wear, and noise in mechanical contacts are particularly important in the field of tribomechanics but equally complex if one wants to represent their exact relationship with mathematical models. Efforts have been made to describe these phenomena with different approaches in past. These efforts have been compiled in different reviews but most of them treated friction, wear mechanics, and acoustic noise separately. However, an in-depth review that provides a critical analysis on their interdependencies is still missing. In this review paper, the interdependencies of friction, wear, and noise are analysed in the mechanical contacts at asperitical level. The origin of frictional noise, its dependencies on contact’s mechanical properties, and its performance under different wear conditions are critically reviewed. A discussion on the existing mathematical models of friction and wear is also provided in the last section that leads to uncover the gap in the existing literature. This review concludes that still a comprehensive analytical modelling approach is required to relate the interdependencies of friction, noise, and wear with mathematical expressions.

Formation of laser-induced periodic surface structures on different materials: fundamentals, properties and applications

2020 ◽  
Vol 9 (1-2) ◽  
pp. 11-39 ◽  
Author(s):  
Stephan Gräf
Keyword(s):  
Friction And Wear ◽  
Review Paper ◽  
Laser Wavelength ◽  
Single Step ◽  
Surface Structures ◽  
Direct Writing ◽  
Periodic Surface ◽  
Experimental Approaches ◽  
Ordered Nanostructures ◽  
Physical Background

AbstractThe use of ultra-short pulsed lasers enables the fabrication of laser-induced periodic surface structures (LIPSS) on various materials following a single-step, direct-writing technique. These specific, well-ordered nanostructures with periodicities in the order of the utilised laser wavelength facilitate the engineering of surfaces with functional properties. This review paper discusses the physical background of LIPSS formation on substrates with different material properties. Using the examples of structural colours, specific wetting states and the reduction of friction and wear, this work presents experimental approaches that allow to deliberately influence the LIPSS formation process and thus tailor the surface properties. Finally, the review concludes with some future developments and perspectives related to forthcoming applications of LIPSS-based surfaces are discussed.

scholarly journals A categorical perspective towards aerodynamic models for aeroelastic analyses of bridge decks

2019 ◽  
Vol 6 (3) ◽  
pp. 181848 ◽  
Author(s):  
I. Kavrakov ◽  
D. Legatiuk ◽  
K. Gürlebeck ◽  
G. Morgenthal
Keyword(s):  
Mathematical Models ◽  
Category Theory ◽  
Structural Engineering ◽  
Model Comparison ◽  
Model Assessment ◽  
Adequate Description ◽  
Categorical Approach ◽  
Abstract Approach ◽  
Huge Variety ◽  
Modelling Approach

Reliable modelling in structural engineering is crucial for the serviceability and safety of structures. A huge variety of aerodynamic models for aeroelastic analyses of bridges poses natural questions on their complexity and thus, quality. Moreover, a direct comparison of aerodynamic models is typically either not possible or senseless, as the models can be based on very different physical assumptions. Therefore, to address the question of principal comparability and complexity of models, a more abstract approach, accounting for the effect of basic physical assumptions, is necessary. This paper presents an application of a recently introduced category theory-based modelling approach to a diverse set of models from bridge aerodynamics. Initially, the categorical approach is extended to allow an adequate description of aerodynamic models. Complexity of the selected aerodynamic models is evaluated, based on which model comparability is established. Finally, the utility of the approach for model comparison and characterization is demonstrated on an illustrative example from bridge aeroelasticity. The outcome of this study is intended to serve as an alternative framework for model comparison and impact future model assessment studies of mathematical models for engineering applications.

scholarly journals System analysis of friction and wear processes when using fullerene compositions in lubricants

2021 ◽  
Vol 101 (3) ◽  
pp. 15-25
Author(s):  
A. Kravtsov ◽  
Keyword(s):  
Mathematical Models ◽  
Friction And Wear ◽  
System Analysis ◽  
Contact Problems ◽  
Correct Choice ◽  
Design Parameters ◽  
Technological Parameters ◽  
Surface Layers ◽  
Multi Scale ◽  
The Coefficient Of Friction

The system-structural approach in researches of processes of friction and wear at application of fullerene compositions in lubricants is proved in the work. It is proposed to use a multilevel approach to study and model the processes of deformation of the surface layers of movable and fixed triboelements and the formation on energy-activated surfaces of wear-resistant structures containing fullerene molecules. The essence of the approach is to use multi-scale research methods to build mathematical models within a single research structure. Due to the fact that tribosystems differ in the integrity of the interconnected elements included in them, it is assumed that all processes occur at three hierarchical levels. At this level, they interact with each other and exchange energy and matter. Input and output flows in studies of tribosystems are formulated. It is shown that the input streams include design parameters of the tribosystem, technological parameters, operating parameters. These parameters form the flow of matter, energy and information, which is the input effect on the tribosystem. The output flow from the tribosystem are the parameters: volumetric wear rate I, dimension m3/hour; friction losses, which are estimated by the coefficient of friction f, dimensionless quantity. The output stream is the information flow of the tribosystem. When solving contact problems, this allows to take into account not only the level of stresses, but also the speed of deformation in the materials of the surface layers, as well as the depth of deformation, which in the models will take into account the volume of deformed material.Depending on the tasks and requirements for their solution, the use of different methodological approaches for modeling is justified. It is shown that the application of mathematical models in the modeling of tribological processes depends on the correct choice of technical constraints that determine the range of optimal solutions

scholarly journals Investigation of a new effective bacterium for cellulosic degradation

2021 ◽  
Author(s):  
Weining Lin
Keyword(s):  
Growth Rate ◽  
Mathematical Models ◽  
Incubation Temperature ◽  
Biogas Production ◽  
Substrate Utilization ◽  
Gas Production ◽  
Biomass Growth ◽  
Growth Substrate ◽  
Wide Range ◽  
Modelling Approach

Clostridium phytofermentans, a newly isolated mesophilic anaerobic bacterium from forest soil, has received considerable attention for its potential application in producing ethanol directly from cellulose. This microorganism produces ethanol, acetate, CO₂ and H₂ as major metabolites from cellulose. Potential applications of this research include the transformation of waste materials into valuable products, such as fuels and organic acids. As an initial part of a multi-staged project, this study is to focus on the characerization of this microorganism growth and to verify the bacterium kinetics, including biomass growth, substrate utilization, and gas production. A series of batch fermentation experiments using cellulose substrate (GS-2C) was performed under the incubation temperature of 37°C. To investigate the effects of pH and substrate concentration (S₀) on growth, 12 trial experiments were conducted with various controlled pH values (7.0 to 8.5) and with various initial cellulose concentration settings (0.1 to 6.0 g/L). Our experimental results showed that the optimal growth condition for C. phytofermentans in batch culture was at pH = 8.4 amd S₀ = 6.0 g/L. Under such condition, the maximum growth rate of 0.37h⁻¹ was observed. Comparing results with other celluloytic clostridium studies, relatively high biomass growth rate using C. phytofermentans is confirmed by our experiments. Mathematical models, using a combination modelling approach with the logistic equation. Monod model, and Luedeking-Piret model, were developed for biomass growth, substrate degradation, and biogas production, respectively, base on our experiment results. This study demonstrated the determination of the four parameters (µmax, Ks, Y, and Smin), which can describe satisfactorily growth or degradation phenomena, using the proposed integration modelling approach. The experiments conducted under wide range conditions, such as changing pH and S₀, not only provide insight into growth kinetics but also provide an opportunity to evaluate the performance of the mathematical models and understand their limitations. This leads to look for improvement or modification to the models. It is foreseen that the findings in this study will enhance the overall understanding of the kinetics of growth and substrate utilization and product formation of this bacterium, and provide important information on the design of the bench-scale anaerobic bioreactor for future studies.

Design and Implementation of Smart Electricity with Monitor Integrating Forecasting and Status Estimation Functions and the Relevant Simulation Based on MATLAB

2014 ◽  
Vol 685 ◽  
pp. 350-357 ◽  
Author(s):  
Chao Dong Zhang ◽  
Shou Wen Ji ◽  
Shu Ping Dang
Keyword(s):  
Smart Grid ◽  
Mathematical Models ◽  
Demand Forecasting ◽  
The State ◽  
Power Network ◽  
Design And Implementation ◽  
Electricity Use ◽  
Mathematical Expressions ◽  
Simulation Based ◽  
Overall Performance

With the development and proliferation of smart grid and the relevant techniques, smart the electricity monitor is increasingly important for improving the overall performance of power network. With a number of new attributes, the smart electricity monitor is significantly different from these conventional electricity meters. For example, it actively provides the information for the management, reliability and maintainability purposes and acts as an irreplaceable component in the power network. In this paper, we mainly focus on the design and implementation of the smart grid which integrates a series of innovative functions, for example demand forecasting and status estimation. Specifically, the research backgrounds pertaining to this field will be briefly introduced and the state-or-the-art mathematical models related to both demand forecasting and status estimation will be constructed accordingly. Also, to investigate their feasibility and efficiency, a set of simulations based on MATLAB will be conducted and the simulated results will be presented. Finally, a complete and innovative prototype of smart electricity use monitor integrating forecasting and status estimation functions can be constructed, verified and analysed in depth by both of mathematical expressions and simulated results.

Rotordynamic Performance of Hybrid Air Foil Bearings With Regulated Hydrostatic Injection

2017 ◽  
Author(s):  
Behzad Zamanian Yazdi ◽  
Daejong Kim
Keyword(s):  
Friction And Wear ◽  
Heat Dissipation ◽  
Load Capacity ◽  
Substantial Improvement ◽  
Maximum Speed ◽  
Foil Bearings ◽  
The Past ◽  
Foil Bearing ◽  
Current Modelling ◽  
Modelling Approach

Air foil bearing (AFB) technology has made substantial advancement during the past decades and found its applications in various small turbomachinery. However, rotordynamic instability, friction and drag during the start/stop, and thermal management are still challenges for further application of the technology. Hybrid air foil bearing (HAFB), utilizing hydrostatic injection of externally pressurized air into the bearing clearance, is one of the technology advancements to the conventional AFB. Previous studies on HAFBs demonstrate the enhancement in the load capacity at low speeds, reduction or elimination of the friction and wear during starts/stops, and enhanced heat dissipation capability. In this paper, the benefit of the HAFB is further explored to enhance the rotordynamic stability by employing a controlled hydrostatic injection. This paper presents the analytical and experimental evaluation of the rotordynamic performance of a rotor supported by two three-pads HAFBs with the controlled hydrostatic injection, which utilizes the injections at particular locations to control eccentricity and attitude angle. The simulations in both time domain orbit simulations and frequency-domain modal analyses indicate a substantial improvement of the rotor-bearing performance. The simulation results were verified in a highspeed test rig (maximum speed of 70,000 rpm). Experimental results agree with simulations in suppressing the subsynchronous vibrations but with a large discrepancy in the magnitude of the subsynchronous vibrations, which is a result of the limitation of the current modelling approach. However, both simulations and experiments clearly demonstrate the effectiveness of the controlled hydrostatic injection on improving the rotordynamic performance of AFB.

scholarly journals A Bayesian machine scientist to aid in the solution of challenging scientific problems

2020 ◽  
Vol 6 (5) ◽  
pp. eaav6971 ◽  
Author(s):  
Roger Guimerà ◽  
Ignasi Reichardt ◽  
Antoni Aguilar-Mogas ◽  
Francesco A. Massucci ◽  
Manuel Miranda ◽  
...  
Keyword(s):  
Social Sciences ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Mathematical Models ◽  
Real Data ◽  
Mathematical Expressions ◽  
The Social ◽  
The World ◽  
Out Of Sample

Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social sciences. However, to deal with increasing amounts of data, we need “machine scientists” that are able to extract these models automatically from data. Here, we introduce a Bayesian machine scientist, which establishes the plausibility of models using explicit approximations to the exact marginal posterior over models and establishes its prior expectations about models by learning from a large empirical corpus of mathematical expressions. It explores the space of models using Markov chain Monte Carlo. We show that this approach uncovers accurate models for synthetic and real data and provides out-of-sample predictions that are more accurate than those of existing approaches and of other nonparametric methods.

Methodology for Identification of the Coolant Thermalhydraulic Regimes in the Core of Nuclear Reactors

2002 ◽  
Author(s):  
L. G. Sharaevsky ◽  
E. I. Sharaevskaya ◽  
E. D. Domashev ◽  
A. P. Arkhypov ◽  
V. N. Kolochko
Keyword(s):  
Mathematical Models ◽  
Acoustic Noise ◽  
Dynamic Pressure ◽  
Random Processes ◽  
Correct Identification ◽  
Experimental Measurements ◽  
Bayes Classifier ◽  
The Core ◽  
Fuel Assemblies ◽  
Neutron Noise

The paper deals with one of the acute for the nuclear energy problem of accident regimes of NPPs recognition diagnostics using noise signal diagnostics methodology. The methodology intends transformation of the random noise signals of the main technological parameters at the exit of a nuclear facility (neutron flow, dynamic pressure etc.) which contain the important information about the technical status of the equipment. The effective algorithms for identification of random processes wore developed. After proper transformation its were considered as multidimensional random vectors. Automatic classification of these vectors in the developed algorithms is realized on the basis of the probability function in particular Bayes classifier and decision functions. Till now there no mathematical models for thermalhydraulic regimes of fuel assemblies recognition on the acoustic and neutron noises parameters in the core of nuclear facilities. The two mathematical models for analysis of the random processes submitted to the automatic classification is proposed, i.e. statistical (using Bayes classifier of acoustic spectral density diagnosis signals) and geometrical (on the basis of formation in the featured space of dividing hyperplane). The theoretical basis of the bubble boiling regimes in the fuel assemblies is formulated as identification of these regimes on the basis of random parameters of auto spectral density of acoustic noise (ASD) measured in the fuel assemblies (dynamic pressure in the upper plenum in the paper). The elaborated algorithms allow recognize realistic status of the fuel assemblies. For verification of the proposed mathematical models the analysis of experimental measurements was carried out. The research of the boiling onset and definition of the local values of the flow parameters in the seven-beam fuel assembly (length of 1.3 m, diameter of 6 mm) have shown the correct identification of the bubble boiling regimes. The experimental measurements on real WWER core assemblies were analysed as well. On the basis of model of Bayes classifier for bubble structure of two-phase flow in fuel assemblies of WWBR-440 (intends usage of 28 dimensional accidental realizations of ASD of neutron noise) the reliable identification of the pointed regimes of fuel assemblies in WWERs up to 98% was obtained. On the basis of geometrical mathematical model of identification at essentially more limited volume of teaching sampling the recognition of ASD realizations of the neutron noise of the same both dimensions and quantity of the reliability of correct identification of these parameters was up to 92%. The recognition of the pointed thermalhydraulic parameters was carried out on the basis of experimental research of ASD of acoustic noise parameters of the experimental fuel assembly with electrically heated imitators using the two recognition models — statistical and geometrical. It confirmed high efficiency of the algorithms developed. The average reliability of identification of the first vapor bubbles activation regime at the heat transfer surface was not low then 90%.

Predicting Epistasis from Mathematical Models

1999 ◽  
Vol 7 (1) ◽  
pp. 69-101 ◽  
Author(s):  
Robert B. Heckendorn ◽  
Darrell Whitley
Keyword(s):  
Mathematical Models ◽  
Empirical Evidence ◽  
Sampling Error ◽  
Evaluation Function ◽  
Theoretical Interest ◽  
Exact Computation ◽  
Mathematical Expressions ◽  
Insight Into

Classically, epistasis is either computed exactly by Walsh coefficients or estimated by sampling. Exact computation is usually of theoretical interest since the computation typically grows exponentially with the number of bits in the domain. Given an evaluation function, epistasis also can be estimated by sampling. However this approach gives us little insight into the origin of the epistasis and is prone to sampling error. This paper presents theorems establishing the bounds of epistasis for problems that can be stated as mathematical expressions. This leads to substantial computational savings for bounding the difficulty of a problem. Furthermore, working with these theorems in a mathematical context, one can gain insight into the mathematical origins of epistasis and how a problem's epistasis might be reduced. We present several new measures for epistasis and give empirical evidence and examples to demonstrate the application of the theorems. In particular, we show that some functions display “parity” such that by picking a well-defined representation, all Walsh coefficients of either odd or even index become zero, thereby reducing the nonlinearity of the function.

scholarly journals Estimating the parameters of SIR model of COVID-19 cases in India during lock down periods

2020 ◽  
Author(s):  
DILIP KUMAR BAGAL ◽  
ARATI RATH ◽  
Abhishek Barua ◽  
Dulu Patnaik
Keyword(s):  
Mathematical Models ◽  
Sir Model ◽  
The World ◽  
Near Future ◽  
Day By Day ◽  
Modelling Approach

From the pandemic scenario of COVID-19 disease cases in all over the world, the outbreak prediction becomes very complex for the emerging scientifically research. Several epidemiological mathematical models of spread are increasing day by day to forecast correctly. Here, the classical SIR modelling approach is carried out to study the different parameters of this model in case of India county. This type of approach analyzed by considering different governmental lock down measures in India. There are some assumptions were taken into account for fitting the model in Python simulation in each lock down scenario. The predicted parameters of SIR model showed some improvement in each case of lock down in India. The outcome results showed the extreme interventions should be taken to tackle this type of pandemic situation in near future.

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