A three-dimensional mathematical model of electromagnetic casting and testing against a physical model: Part I. The mathematical model

1995 ◽  
Vol 26 (1) ◽  
pp. 1263-1270 ◽  
Author(s):  
D. P. Cook ◽  
J. W. Evans
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Three Dimensional ◽  
Electromagnetic Casting ◽  
The Mathematical Model

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.

Research on cargo-loading optimization based on genetic and fuzzy integration

2021 ◽  
Vol 40 (4) ◽  
pp. 8493-8500
Author(s):  
Yanwei Du ◽  
Feng Chen ◽  
Xiaoyi Fan ◽  
Lei Zhang ◽  
Henggang Liang
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Three Dimensional ◽  
Distribution Center ◽  
Long Time ◽  
Low Efficiency ◽  
Decision Making Model ◽  
The Mathematical Model ◽  
Loading Scheme

With the increase of the number of loaded goods, the number of optional loading schemes will increase exponentially. It is a long time and low efficiency to determine the loading scheme with experience. Genetic algorithm is a search heuristic algorithm used to solve optimization in the field of computer science artificial intelligence. Genetic algorithm can effectively select the optimal loading scheme but unable to utilize weight and volume capacity of cargo and truck. In this paper, we propose hybrid Genetic and fuzzy logic based cargo-loading decision making model that focus on achieving maximum profit with maximum utilization of weight and volume capacity of cargo and truck. In this paper, first of all, the components of the problem of goods stowage in the distribution center are analyzed systematically, which lays the foundation for the reasonable classification of the problem of goods stowage and the establishment of the mathematical model of the problem of goods stowage. Secondly, the paper abstracts and defines the problem of goods loading in distribution center, establishes the mathematical model for the optimization of single car three-dimensional goods loading, and designs the genetic algorithm for solving the model. Finally, Matlab is used to solve the optimization model of cargo loading, and the good performance of the algorithm is verified by an example. From the performance evaluation analysis, proposed the hybrid system achieve better outcomes than the standard SA model, GA method, and TS strategy.

Simulation Investigation on Environment-Induced Pitting Corrosion on the Metal Surface

2021 ◽  
Vol 13 (5) ◽  
pp. 820-828
Author(s):  
Wei Zhang ◽  
Shengli Lv ◽  
Leijiang Yao ◽  
Xiaoyan Tong
Keyword(s):  
Mathematical Model ◽  
Pitting Corrosion ◽  
Three Dimensional ◽  
Corrosion Damage ◽  
Sudden Onset ◽  
Ion Concentration ◽  
Two Dimensional Image ◽  
Aging Aircraft ◽  
Efficient Calculation ◽  
The Mathematical Model

The prediction of corrosion damage is one of effective research methods in the safety inspection of aging aircraft structures. A mathematical model for quantifying corrosion damage is used in this paper to predict the onset of corrosion on structural surfaces exposed to aggressive environments. Based on the finite difference technique, the evolution process of local pitting corrosion on the surface of aluminum alloy in the medium is simulated, which can consider the sudden onset and the randomness of pitting corrosion. The effect of local ion concentration and oxide film damage on subsequent pitting nucleation was analyzed. Based on the efficient calculation program, the effectiveness of the mathematical model is verified by the comparison between the corrosion damage morphology and the experimental data in the literature. The results show a more widespread distribution of subsequent pits because of stronger aggressive ions are released during the life cycle of active pits and the higher diffusion coefficient of the aggressive ions. The three dimensional morphology is generated by image processing method based on the gray value of the two dimensional image of pits.

scholarly journals Bifurcation phenomena and statistical regularities in dynamics of forced impacting oscillator

2019 ◽  
Vol 98 (3) ◽  
pp. 1795-1806 ◽  
Author(s):  
Sergii Skurativskyi ◽  
Grzegorz Kudra ◽  
Krzysztof Witkowski ◽  
Jan Awrejcewicz
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Physical Model ◽  
Dry Friction ◽  
Stepper Motor ◽  
Nonlinear Phenomenon ◽  
Hertz Contact ◽  
Bifurcation Phenomena ◽  
Statistical Regularities ◽  
The Mathematical Model

Abstract The paper is devoted to the study of harmonically forced impacting oscillator. The physical model for oscillator is a cart on a guide connected to the support with springs and excited by the stepper motor. The support also is provided with limiter of motion. The mathematical model for this system is defined with the second-order piecewise smooth differential equation. Model’s nonlinearity is connected with the incorporation of dry friction and generalized Hertz contact law. Analyzing the classical Poincare sections and inter-impact sequences obtained experimentally and numerically, the bifurcations and statistical properties of periodic, multi-periodic, and chaotic regimes were examined. The development of impact-adding regime as a new nonlinear phenomenon when the forcing frequency varies was observed.

Mathematical modeling of a generic multi-profile form milling cutter

2012 ◽  
Vol 227 (5) ◽  
pp. 1036-1046 ◽  
Author(s):  
Mohammed Rajik Khan ◽  
Puneet Tandon
Keyword(s):  
Mathematical Model ◽  
Three Dimensional ◽  
Sculptured Surfaces ◽  
Three Dimensional Model ◽  
Machining Time ◽  
Milling Cutter ◽  
Machined Parts ◽  
Rotary Cutting ◽  
Three Dimensional Models ◽  
The Mathematical Model

In order to machine multiple sculptured surfaces with reduced machining time and high accuracy of the machined parts, shape design of a customised multi-point rotary cutting tool needs to be evolved. In the present work, a novel design of a generic multi-profile form milling cutter is developed for machining various multiple sculptured surfaces. This article describes in detail the mathematical model to design an accurate three-dimensional geometry of a generic multi-profile form milling cutter. Use of non-uniform rational B-spline curve(s) and sweep surfaces enables to control the shape of cutting flutes of the generic multi-profile form milling cutter. The article also discusses the methodology to develop a variety of cutters lying in the same conceptual family of multi-profile form milling cutter. To physically visualise the cutter and to show one of the downstream applications once a three-dimensional model of the cutter is available, one of the multi-profile form milling cutters is fabricated. The proposed methodology offers an intuitive high-quality mathematical model for a generic family of multi-profile form milling cutters, which is different from the traditional three-dimensional models.

Computations of Three-Dimensional Gas-Turbine Combustion Chamber Flows

1979 ◽  
Vol 101 (3) ◽  
pp. 326-336 ◽  
Author(s):  
M. A. Serag-Eldin ◽  
D. B. Spalding
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Combustion Process ◽  
Three Dimensional ◽  
Solution Algorithm ◽  
Physical Models ◽  
Turbulence Energy ◽  
Experimental Conditions ◽  
Diffusion Controlled ◽  
The Mathematical Model

The paper presents a mathematical model for three-dimensional, swirling, recirculating, turbulent flows inside can combustors. The present model is restricted to single-phase, diffusion-controlled combustion, with negligible radiation heat-transfer; however, the introduction of other available physical models can remove these restrictions. The mathematical model comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy, its dissipation rate, and the mean square of concentration fluctuations. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variables at all internal grid nodes. The prediction procedure, composed of the mathematical model and its solution algorithm, is applied to predict the fields of variables within a representative can combustor; the results are compared with corresponding measurements. The predicted results give the same trends as the measured ones, but the quantitative agreement is not always acceptable; this is attributed to the combustion process not being truly diffusion-controlled for the experimental conditions investigated.

Calculations of three-dimensional viscous flow in a multiblade centrifugal fan by modelling blade forces

2003 ◽  
Vol 217 (3) ◽  
pp. 287-297 ◽  
Author(s):  
S-J Seo ◽  
K-Y Kim ◽  
S-H Kang
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Complex Flows ◽  
Flow Through ◽  
Volume Method ◽  
The Mathematical Model

A numerical study is presented for Reynolds-averaged Navier-Stokes analysis of three-dimensional turbulent flows in a multiblade centrifugal fan. Present work aims at development of a relatively simple analysis method for these complex flows. A mathematical model of impeller forces is obtained from the integral analysis of the flow through the impeller. A finite volume method for discretization of governing equations and a standard k-ɛ model as turbulence closure are employed. For the validation of the mathematical model, the computational results for velocity components, static pressure, and flow angles at the exit of the impeller were compared with experimental data. The comparisons show generally good agreement, especially at higher flow coefficients.

Modeling and Simulation Analysis of the Twist Drill Conical Grinding Method Based on Pro/E Software

2010 ◽  
Vol 160-162 ◽  
pp. 1680-1684
Author(s):  
Xing Jun Gao ◽  
Qing Liu ◽  
Ping Zou ◽  
Jian Song ◽  
Ping Li
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Three Dimensional ◽  
Fundamental Principle ◽  
Drilling Process ◽  
Twist Drill ◽  
Three Dimensional Modeling ◽  
Grinding Method ◽  
Dimensional Modeling ◽  
The Mathematical Model

The fundamental principle of the twist drill conical grinding method was introduced. The mathematical model of the twist drill was established. Mathematical model to establish drill bit is the geometric design, manufacture, cutting analysis and modeling on the basis of the drilling process. According to the twist drill grinding principle, using Pro/E the three-dimensional modeling of the twist drill was completed, and the feature of the conical grinding method was analyzed.

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