Parametric Variational Principle of Viscoplastic Lubrication Model

1992 ◽  
Vol 114 (4) ◽  
pp. 731-735 ◽  
Author(s):  
C. W. Wu ◽  
W. X. Zhong ◽  
L. X. Qian ◽  
L. C. Hu ◽  
S. M. Sun
Keyword(s):  
Mathematical Model ◽  
Mathematical Method ◽  
Variational Principle ◽  
Original Problem ◽  
Engineering Application ◽  
Tangential Velocity ◽  
Control Vector ◽  
Parametric Variational Principle ◽  
Variational Process ◽  
The Mathematical Model

An effective mathematical method to deal with the viscoplastic lubrication model is presented here by applying the parametric variational principle (Zhong, 1985). The plastic slippage of lubricant would occur at the lubricated surfaces under isothermal lubrication. The boundary tangential velocity, therefore, can be taken as the parametric vector (or the control vector) in variational process. The mathematical model of the original problem is finally reduced to a complementarity problem. The algorithm presented in this paper is simple and reliable and shows promise in engineering application.

Mathematical Model for the Influence of Machine Tool Parts Deformation on Machining Accuracy

2014 ◽  
Vol 556-562 ◽  
pp. 1354-1357
Author(s):  
Li Gong Cui ◽  
Gui Qiang Liang ◽  
Fang Shao
Keyword(s):  
Mathematical Model ◽  
Mathematical Method ◽  
Machine Tool ◽  
Cutting Tool ◽  
Lower Surface ◽  
Design Stage ◽  
Machining Accuracy ◽  
Cutting Point ◽  
The Mathematical Model

This paper presents a mathematical method to analyze the influence of each machine tool part deformation on the machining accuracy. Taking a 3-axis machine tool as an example, this paper divides the machine tool into the cutting tool sub-system and workpiece sub-system. Taking the deformation of lower surface of the machine bed as the research target, the mathematical model of the deformation on the displacement of the cutting point was established. In order to distribute the stiffness of each part, the contribution degree of each part on the machining accuracy was analyzed. Using this mathematical model, the stiffness of each part can be distributed at the design stage of the machine tool, and the machining accuracy of the machine tool can be improved economically.

scholarly journals On the correctness of one model of the Stefan-Type filtration theory

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Mathematical Model ◽  
Original Problem ◽  
Oil And Gas ◽  
Filtration Theory ◽  
Oil And Gas Fields ◽  
Surface Active ◽  
Gas Fields ◽  
Limiting Case ◽  
The Mathematical Model ◽  
Active Substances

In this paper a mathematical model of filtration theory with phase transitions is investigated. When using surface-active substances (surfactants) for the development of oil and gas fields in the reservoir occur sorption processes at the interfaces of individual phases (surfactants and oil, or surfactants and soil). In real processes, a finite time is required for achievement equilibrium. Therefore considering the mathematical model was called the mathematical model with phase relaxation. The solvability of the mathematical model, the limiting transition in relaxation time are investigated. It is proved that in the limiting case, the original problem is a problem of Stefan type.

Bending of Thermoviscoelastic Functionally Graded Materials Beams

2012 ◽  
Vol 503-504 ◽  
pp. 305-308
Author(s):  
Ming Lu Wang ◽  
Gao Feng Wei
Keyword(s):  
Mathematical Model ◽  
Variational Principle ◽  
Laplace Transformation ◽  
Transformation Method ◽  
Functionally Graded ◽  
Plane Section ◽  
Graded Materials ◽  
Set Up ◽  
The Mathematical Model ◽  
Laplace Transformation Method

According to the constitutive relation of linear thermovisoelasticity, with the help of Laplace transformation method and the introduction of structure functions and thermal functions, the mathematical model and its corresponding variational principle for thermoviscoelastic FGM beams are set up on the basis of the assumption that plane section remains plane and normal to the beam axis. Using Laplace transformation method, the deflection and the stress distribution are discussed.

Dynamic States Specific Analysis for Belt Conveyor Based on FDM

2013 ◽  
Vol 278-280 ◽  
pp. 27-30
Author(s):  
Xiao Shen ◽  
Qun Wang ◽  
Zhou Yu Fu ◽  
Shuo Wei Bai ◽  
Zhao Yang Sun
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Mathematical Method ◽  
Finite Element ◽  
Continuous Model ◽  
Belt Conveyor ◽  
Specific Analysis ◽  
Simulation Results ◽  
The Mathematical Model ◽  
Dynamic States

There are two common research methods on the dynamic states model of belt conveyor in China at present. The mathematical model is built by finite element method then it is solved by numerical method. And the continuous model is built when the belt is treated as elastic body then it is solved by mathematical method. This paper puts forward the establishment of continuous model, the model is solved by FDM and the simulation results are given.

The Study of the Initial State of Cable-Net Structure Reflector for the FAST

2012 ◽  
Author(s):  
Yu Liu ◽  
Feng Gao
Keyword(s):  
Mathematical Model ◽  
Variational Principle ◽  
Nonlinear Equations ◽  
Layer By Layer ◽  
Initial State ◽  
Main Cable ◽  
Highly Nonlinear ◽  
Node Location ◽  
Set Up ◽  
The Mathematical Model

By using the variational principle to set up the mathematical model of the reflector for the FAST, we can get the node location of the cable-net and tension of the main cable by solving highly nonlinear equations of the mathematical model. A new layer-by-layer substitution approach has been proposed for solving the highly nonlinear equations, through the calculation and simulation it verifies the correctness of this method.

Nonlinear Regression Analysis for Programming and Engineering Application

2013 ◽  
Vol 846-847 ◽  
pp. 1080-1083
Author(s):  
Qing Lan Qi ◽  
Shao Xiong Zhang
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Nonlinear Regression ◽  
Regression Coefficient ◽  
Engineering Application ◽  
Least Square Method ◽  
Least Square ◽  
Nonlinear Regression Analysis ◽  
Practical Engineering ◽  
The Mathematical Model

Aiming at the calculating the flow of cutthroat flume in Hydraulic Engineering, the test data is processed through the nonlinear regression analysis program which is based on the principle of least square method. With 33 equations of various functions including linear, power function curve and exponential curve to be selected as the mathematical model, the regression analysis is taken through 33 equations. Comparing the regression coefficient from analysis, the optimal mathematical model is selected as the empirical formula, which has great significance in guiding the practical engineering.

scholarly journals Validation of a Mathematical Model Applied to Four Autonomous Communities in Spain to Determine the Number of People Infected by Covid-19

2020 ◽  
Vol 14 (6) ◽  
pp. 110 ◽  
Author(s):  
Gastón Sanglier ◽  
Roberto A. Gónzález ◽  
Sonia Cesteros ◽  
Eduardo J. López
Keyword(s):  
Mathematical Model ◽  
Mathematical Method ◽  
Real Data ◽  
Forecast Errors ◽  
Autonomous Communities ◽  
The Real ◽  
Infected People ◽  
Speed Of Propagation ◽  
The Mathematical Model ◽  
Coronavirus Infections

In this study, the application of a mathematical method already developed in other articles for the study of the speed of propagation of the number of people infected by Covid-19 has been validated. The proposed mathematical model has been contrasted with models based on quantitative prognostic methods in order to seek its validation. At the same time, the forecast errors of the proposed methods and the mathematical model have been calculated and compared. The results obtained have been applied to the four autonomous communities in Spain with the highest number of coronavirus infections during the study period, obtaining very satisfactory results and achieving very good approximations to the real data on the number of infected people in all the autonomous communities studied. 

Determination of the Maximum Length of the Cooling Pipeline Used in the District Cooling System

2014 ◽  
Vol 1030-1032 ◽  
pp. 1379-1383
Author(s):  
Chao Yi Tan ◽  
Hui Zhu ◽  
Hai Hua Hu ◽  
Gang Chen ◽  
Han Qing Wang
Keyword(s):  
Mathematical Model ◽  
Energy Efficiency ◽  
Cooling System ◽  
Engineering Application ◽  
Maximum Length ◽  
Transportation Energy ◽  
Refrigeration Unit ◽  
High Level ◽  
The Mathematical Model

For the purpose of taking full advantages of the District Cooling System (DCS), the mathematical model was established based on the principle of non-decreasing state of the energy efficiency grade of the refrigeration unit and high level of the transportation energy efficiency of the cooling pipeline. Based on the mathematical model, two formula were derived. One is suitable for the scientific research concerning the length of the DCS, and the other is appropriate for the design in engineering application. The determination of the maximum length of the pipe provides an alternative for the research and design of the DCS, therefore it is worth studying.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

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