A Mathematical Model Relating Softening Point to Penetration Applicable to a Wide Range of Road Asphalts

1979 ◽  
Vol 18 (3) ◽  
pp. 230-232 ◽  
Author(s):  
A. M. Abushihada ◽  
Y. Al-Farkh
Keyword(s):  
Mathematical Model ◽  
Softening Point ◽  
Wide Range ◽  
Road Asphalts

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

Robust sideslip angle observer of commercial vehicles based on cornering stiffness estimation using neural network

2022 ◽  
pp. 095440702110724
Author(s):  
Chenyu Zhou ◽  
Liangyao Yu ◽  
Yong Li ◽  
Jian Song
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Stability Control ◽  
Estimation Accuracy ◽  
Accurate Estimation ◽  
Commercial Vehicles ◽  
Sideslip Angle ◽  
The Neural Network ◽  
Wide Range ◽  
The Mathematical Model

Accurate estimation of sideslip angle is essential for vehicle stability control. For commercial vehicles, the estimation of sideslip angle is challenging due to severe load transfer and tire nonlinearity. This paper presents a robust sideslip angle observer of commercial vehicles based on identification of tire cornering stiffness. Since tire cornering stiffness of commercial vehicles is greatly affected by tire force and road adhesion coefficient, it cannot be treated as a constant. To estimate the cornering stiffness in real time, the neural network model constructed by Levenberg-Marquardt backpropagation (LMBP) algorithm is employed. LMBP is a fast convergent supervised learning algorithm, which combines the steepest descent method and gauss-newton method, and is widely used in system parameter estimation. LMBP does not rely on the mathematical model of the actual system when building the neural network. Therefore, when the mathematical model is difficult to establish, LMBP can play a very good role. Considering the complexity of tire modeling, this study adopted LMBP algorithm to estimate tire cornering stiffness, which have simplified the tire model and improved the estimation accuracy. Combined with neural network, A time-varying Kalman filter (TVKF) is designed to observe the sideslip angle of commercial vehicles. To validate the feasibility of the proposed estimation algorithm, multiple driving maneuvers under different road surface friction have been carried out. The test results show that the proposed method has better accuracy than the existing algorithm, and it’s robust over a wide range of driving conditions.

Probabilistic Model of the Reflectivity of Construction Materials of the Agroindustrial Complex

2021 ◽  
Vol 3 (44) ◽  
pp. 111-115
Author(s):  
Tat’yana R. Gallyamova ◽  
Keyword(s):  
Mathematical Model ◽  
Energy Consumption ◽  
Reflection Coefficient ◽  
Probabilistic Method ◽  
Construction Materials ◽  
Research Purpose ◽  
Visible Range ◽  
Industrial Complex ◽  
Large Area ◽  
Wide Range

When developing modern lighting technologies for objects of the agro-industrial complex, the problem arises of assessing the contribution of reflected light to the normalized illumination. The reflective properties of the surfaces of materials are characterized by a reflection coefficient ρ, which reaches a value of 0.7. This allows us to consider the reflective surfaces as an additional light source and the possibility of reducing energy consumption costs. (Research purpose) The research purpose is in developing a mathematical model that allows us to estimate the spectral reflection coefficient ρ(λ) of materials of construction technologies of the agro-industrial complex in the ultraviolet and visible spectral regions. (Materials and methods) That the disadvantage of various models is the lack of an analytical method for calculating the reflection coefficient in a wide range of wavelengths. We used a probabilistic method to overcome this disadvantage. (Results and discussion) The developed mathematical model makes it possible to estimate the reflection coefficient of the rough surface of materials in a wide range of the spectrum. For concrete, the area of agreement between theory and experiment is in the wavelength range from 250 to 1000 nm. The saturation mode predicted by the theory (the independence of the reflection coefficient from the wavelength) at a reflection coefficient of 0.4 is consistent with the experimental values in the visible range of the spectrum for construction materials of the agro-industrial complex, in particular, gray textured concrete, gray facade paint, light wood, gray silicate brick, new plaster without whitewash. (Conclusions) In the case of normal light incidence, the developed mathematical model allows us to theoretically estimate the reflection coefficient of the rough surfaces of construction technologies of the agro-industrial complex. The proposed model can be used in the development and design of a system of technological lighting of large-area premises (for example, when keeping birds on the floor), as well as for developing recommendations for reducing the energy consumption of existing lighting systems.

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

scholarly journals Investigation on membrane fouling in ultrafiltration of latex solution

2021 ◽  
Author(s):  
Amira Abdelrasoul
Keyword(s):  
Mathematical Model ◽  
Molecular Weight ◽  
Power Consumption ◽  
Membrane Fouling ◽  
Membrane Surface ◽  
Operating Conditions ◽  
Specific Power ◽  
Pore Sizes ◽  
Wide Range ◽  
Different Types

The low-pressure membrane applications are considered to be the most effective and sustainable methods of addressing environmental problems in treating water and wastewater that meets or exceed stringent environmental standards. Nevertheless, membrane fouling is one of the primary operational concerns that is currently hindering a more widespread application of ultrafiltration (UF) with a variety of contaminants. Membrane fouling leads to higher operating costs, higher energy demand, reduced membrane life time, and increased cleaning frequency. As a consequence, an efficient and well-planned UF process is becoming a necessity for consistent and long-term monetary returns. Examining the source and mechanisms of foulant attachment to the membrane’s surface is critical when it comes to the research of membrane fouling and its potential practical implementation. A mathematical model was developed in this study in order to predict the amount of fouling based on an analysis of particle attachments. This model was developed using both homogeneous and heterogeneous membranes, with a uniform and non-uniform pore sizes for the UF of simulated latex effluent with a wide range of particle size distribution. The objective of this mathematical model was to effectively identify and address the common shortcomings of previous fouling models, and to account for the existing chemical attachments in membrane fouling. The mathematical model resulting from this study was capable of accurately predicting the mass of fouling retained by the membrane and the increase in transmembrane pressure (TMP). In addition, predictive models of fouling attachments were derived and now form an extensive set of mathematical models necessary for the prediction of membrane fouling at a given operating condition, as well as, the various membrane surface charges. Polycarbonate and Polysulfone flat membranes, with pore sizes of 0.05 μm and a molecular weight cut off of 60,000 respectively, were used in the experimental designs under a constant feed flow rate and a cross-flow mode in UF of the simulated latex paint effluent. The TMP estimated from the model agreed with the experimentally measured values at different operating conditions, mostly within 5.0 - 8.0 % error, and up to 13.0% error for the uniform, and non-uniform pore size membranes, respectively. Furthermore, different types of membranes with a variety of molecular weight cut-off (MWCO) values were tested so as to evaluate the accuracy of the models for a generalized application. In addition , a power consumption model, incorporating fouling attachment as well as chemical and physical factors in membrane fouling, was developed in order to ensure accurate prediction and scale-up. Innovative remediation techniques were likewise developed and applied in order to minimize membrane fouling, enhance the membrane performance, and save energy. Fouling remediation methodologies included the pre-treating of the latex effluent, so as to limit its fouling propensity by using different types of surfactants as cationic and anionic, in addition to the pH change. The antifouling properties of the membranes were improved through the implementation of the membrane pH treatment and anionic surfactant treatment. Increasing the ionic strength of latex effluent or enhancing the membrane surface hydrophilicity facilitated a significant increase in the cumulative permeate flux, a substantial decrease in the total mass of fouling, and a noticeable decrease in the specific power consumption.

scholarly journals Mathematical modeling and algorithm for calculation of thermocatalytic process of producing nanomaterial

2021 ◽  
Vol 23 (3) ◽  
pp. 1590
Author(s):  
Bakhtiyar Ismailov ◽  
Zhanat Umarova ◽  
Khairulla Ismailov ◽  
Aibarsha Dosmakanbetova ◽  
Saule Meldebekova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Phase ◽  
Nonlinear Effects ◽  
Operating Characteristics ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Wide Range ◽  
The Laplace Transform ◽  
Complex Mathematical Model

<p>At present, when constructing a mathematical description of the pyrolysis reactor, partial differential equations for the components of the gas phase and the catalyst phase are used. In the well-known works on modeling pyrolysis, the obtained models are applicable only for a narrow range of changes in the process parameters, the geometric dimensions are considered constant. The article poses the task of creating a complex mathematical model with additional terms, taking into account nonlinear effects, where the geometric dimensions of the apparatus and operating characteristics vary over a wide range. An analytical method has been developed for the implementation of a mathematical model of catalytic pyrolysis of methane for the production of nanomaterials in a continuous mode. The differential equation for gaseous components with initial and boundary conditions of the third type is reduced to a dimensionless form with a small value of the peclet criterion with a form factor. It is shown that the laplace transform method is mainly suitable for this case, which is applicable both for differential equations for solid-phase components and calculation in a periodic mode. The adequacy of the model results with the known experimental data is checked.</p>

scholarly journals Investigation on membrane fouling in ultrafiltration of latex solution

2021 ◽  
Author(s):  
Amira Abdelrasoul
Keyword(s):  
Mathematical Model ◽  
Molecular Weight ◽  
Power Consumption ◽  
Membrane Fouling ◽  
Membrane Surface ◽  
Operating Conditions ◽  
Specific Power ◽  
Pore Sizes ◽  
Wide Range ◽  
Different Types

The low-pressure membrane applications are considered to be the most effective and sustainable methods of addressing environmental problems in treating water and wastewater that meets or exceed stringent environmental standards. Nevertheless, membrane fouling is one of the primary operational concerns that is currently hindering a more widespread application of ultrafiltration (UF) with a variety of contaminants. Membrane fouling leads to higher operating costs, higher energy demand, reduced membrane life time, and increased cleaning frequency. As a consequence, an efficient and well-planned UF process is becoming a necessity for consistent and long-term monetary returns. Examining the source and mechanisms of foulant attachment to the membrane’s surface is critical when it comes to the research of membrane fouling and its potential practical implementation. A mathematical model was developed in this study in order to predict the amount of fouling based on an analysis of particle attachments. This model was developed using both homogeneous and heterogeneous membranes, with a uniform and non-uniform pore sizes for the UF of simulated latex effluent with a wide range of particle size distribution. The objective of this mathematical model was to effectively identify and address the common shortcomings of previous fouling models, and to account for the existing chemical attachments in membrane fouling. The mathematical model resulting from this study was capable of accurately predicting the mass of fouling retained by the membrane and the increase in transmembrane pressure (TMP). In addition, predictive models of fouling attachments were derived and now form an extensive set of mathematical models necessary for the prediction of membrane fouling at a given operating condition, as well as, the various membrane surface charges. Polycarbonate and Polysulfone flat membranes, with pore sizes of 0.05 μm and a molecular weight cut off of 60,000 respectively, were used in the experimental designs under a constant feed flow rate and a cross-flow mode in UF of the simulated latex paint effluent. The TMP estimated from the model agreed with the experimentally measured values at different operating conditions, mostly within 5.0 - 8.0 % error, and up to 13.0% error for the uniform, and non-uniform pore size membranes, respectively. Furthermore, different types of membranes with a variety of molecular weight cut-off (MWCO) values were tested so as to evaluate the accuracy of the models for a generalized application. In addition , a power consumption model, incorporating fouling attachment as well as chemical and physical factors in membrane fouling, was developed in order to ensure accurate prediction and scale-up. Innovative remediation techniques were likewise developed and applied in order to minimize membrane fouling, enhance the membrane performance, and save energy. Fouling remediation methodologies included the pre-treating of the latex effluent, so as to limit its fouling propensity by using different types of surfactants as cationic and anionic, in addition to the pH change. The antifouling properties of the membranes were improved through the implementation of the membrane pH treatment and anionic surfactant treatment. Increasing the ionic strength of latex effluent or enhancing the membrane surface hydrophilicity facilitated a significant increase in the cumulative permeate flux, a substantial decrease in the total mass of fouling, and a noticeable decrease in the specific power consumption.

Feeding Mathematical Modeling of Superalloy Vacuum-Electromagnetic Casting and its Application

2012 ◽  
Vol 629 ◽  
pp. 171-175
Author(s):  
Wen Zhong Jin ◽  
Su Fang Li ◽  
Wei Zhang
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
New Technology ◽  
Experimental Results ◽  
Electromagnetic Stirring ◽  
Shrinkage Cavity ◽  
Vacuum Casting ◽  
Electromagnetic Casting ◽  
Wide Range

The new technology of superalloy vacuum-electromagnetic casting was developed and the feeding mathematical model melt in vacuum-electromagnetic casting was established. The availability of mathematical model was approved by the experiments of the IN100 superalloy. The experimental results indicate that the feeding capacity of melt in vacuum casting can be greatly increased by imposing the 50Hz, 60A rotating electromagnetic stirring, which can decrease the central shrinkage cavity in superalloy ingots, so the quality of the superalloy ingots can be wide-range improved.

Release of nitrous oxide (N2O) from denitrifying activated sludge caused by H2S-containing wastewater: quantification and application of a new mathematical model

1998 ◽  
Vol 38 (1) ◽  
pp. 237-246 ◽  
Author(s):  
Barbara Schönharting ◽  
Ruxandra Rehner ◽  
Jörg W. Metzger ◽  
Karlheinz Krauth ◽  
Manfred Rizzi
Keyword(s):  
Mathematical Model ◽  
Nitrous Oxide ◽  
Hydrogen Sulfide ◽  
Activated Sludge ◽  
Sulfide Concentration ◽  
Oxide Reduction ◽  
Strong Inhibition ◽  
Wide Range ◽  
Nitrous Oxide Reduction ◽  
Denitrification Process

A new mathematical model is presented which describes the denitrification process by dynamic material balance equations. In this approach the kinetic rate expressions of the single denitrification steps and the observed strong inhibition of nitrate on nitrite and nitrous oxide reduction are based exclusively on fundamental enzyme kinetics. This allows a prediction of the denitrification process in a wide range of wastewater-relevant nitrate concentrations. The model was successfully applied to the description of the kinetic behavior of a standardized denitrifying activated sludge system. Furthermore the experimentally investigated influence of hydrogen sulfide was quantified by extending the model with a non-competitive inhibition mechanism involving all steps of the denitrification process. The inhibitory effect was related to the free membrane-permeable hydrogen sulfide concentration. This means that the extent of its inhibition depends additionally on the pH-value. Even very low hydrogen sulfide concentrations lead to a strong inhibition of nitrous oxide reduction and therefore to a high release of nitrous oxide from wastewater treatment plants.

The Effect of Gravity and Rotor Configuration on Dry Friction Whip and Safe Rotor/Stator Clearance

2019 ◽  
Author(s):  
Rajiv Kumar Vashisht
Keyword(s):  
Mathematical Model ◽  
Fault Diagnosis ◽  
Dry Friction ◽  
Rotating Machinery ◽  
Degree Of Freedom ◽  
System Response ◽  
Rich Variety ◽  
Wide Range ◽  
Clearance Level ◽  
High Degree

Abstract A mathematical model is developed for a real rotor/stator system with high degrees-of-freedoms, multiple disks, flexible bearing supports and couplings. The safe clearance level for coasting up of the rotor is calculated for a general high degree-of-freedom rotor/stator system. The harmful phenomena of dry friction whip, which is generally observable for simple 2 degree-of-freedom Jeffcott rotors in the absence of gravity only, can be proved to exist (in real rotor/stator systems) even in the presence of gravity for a wide range of clearance levels. In case of Jeffcott rotors, by fixing the clearance and increasing the rotor spin frequency, the response of the system follows the pattern: No rub - Forward Annular Rub (FAR) - Partial Forward Whirl (PFW) - Partial Backward Whirl (PBW) - dry whip (WHIP). In case of a real rotor/stator system, at certain frequencies, the system directly jumps to dry whip. The simulated results show a rich variety of system dynamics including FAR, PFW and WHIP in case of vertical rotors where the effect of gravity is neglected. For horizontal rotors, under the effect of gravity, the system response contains multi-harmonics, chaotic responses and multi-period vibrations. Based on these responses, a robust fault diagnosis strategy can be designed to identify the rubbing action in rotating machinery.

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