Mathematical Model of Heat Treatment and Its Computer Simulation

Computer simulation on heat treatment is the foundation of intelligent heat treatment. The simulations of temperature field, phase transformation, stress/strain complicate quenching operation were realized by using the model of three dimensional non linear finite element method and the treatment methods of abruptly changing interface conditions. The simulation results basically fit those measured in experiments. The intelligent sealed multipurpose furnace production line has been developed based on the combination of computer simulation on gaseous carburizing and computer control technology. More than 3000 batches of workpieces have been processed on this production line, and all are up to standard. The application of computer simulation technology can significantly improve the loading ability and relia bility of nitriding and carburizing workpieces, reduce heat treatment distortion, and shorten carburizing duration. It is recommended that the reliable product design without redundancy should be performed with the combination of the CAD of mechanical products, the CAE of materials selection and heat treatment, and the dynamic evaluation technology of product reliability.

RESEARCH ON THE SELECTION OF FRICTION MODELS IN THE FINITE ELEMENT SIMULATION OF WARM EXTRUSION

During the process of finite element simulation of precision warm forging, the selection of friction models has a direct effect on the precision accuracy of finite element simulation results. Among all the factors which influence the selection of friction models, the distribution rule of normal stress at the tool-workpiece interface is a key one. To find out the distribution rule of normal stress at the tool-workpiece interface, this paper has made a systematic research on three typical plastic deformation processes: forward extrusion, backward extrusion, and lateral extrusion by a method of finite element simulation. Then on the base of synthesizing and correcting traditional friction models, a new general friction model which is fit for warm extrusion is developed at last.

Mathematical modeling of induction heating of discard substitution block for billet hot extrusion process

A magnetic and temperature field-coupled mathematical model is proposed to calculate the induction heating process of a discard substitution block for billet hot extrusion process. The mathematical model is validated by comparing simulation results with temperature measurements recorded during physical modeling. Based on systematical analysis of calculation results, a quantitative sawtooth induction power curve was proposed to realize the aim of achieving the best distributed temperature field in the block within the shortest induction time.

Dynamic Factor Method of Computing Dynamic Mathematical Model for System Simulation

The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor.

Mathematical and Numerical Modelling of Copper Tube Extrusion after Optimizing Geometrical and Operating Parameters

This study aimed to optimize cross-sectional area of the extruder and the flow rate of the material through the extruder. Extrusion process was first modelized using the continuum mechanics method before being simulated with the commercial software LS-DYNA using the Johnson-Cook model based on the finite element method after optimization of the factors with simplex algorithm. The study was carried out on a connecting rod: diameter of 145 mm, cross-section of 1.65 m2, length of 0.25 m, volume of 0.41 m3 and a mass of 37 kg. Optimum parameters obtained were temperature of 850℃, flow rate of 0.237 m/s, die diameter of 19.2 mm, pin diameter of 14 mm, extrusion strength of 565.6 kN and press pressure of 245 GPa. From these factors, a blank was obtained with external and internal diameters of 19.2 and 14 mm respectively over a length of 28 m with a thickness of 2.6 mm. Simulation using LS-DYNA software resulted in a difference in values of 7.4% between optimization and simulation when the difference of 2.4% was found between modelling and simulation. These values make the process optimal for industrial application to improve the extrusion requirements of copper tubes.

Using Pipeline Instructions by Parallel Simulation of Mathematical Models

Simulation is an important and useful technique helping users understand and model real life systems. Once built, the models can run proving realistic results. This supports making decisions on a more logical and scientific basis. The paper introduces method of simulation, and describes various types of its application. The authors used the method of analysis of the creation and implementation of the programme code. The authors compared parallel instruction of computing defined to pipelined instructions. The power of simulation is that a common model can be used to design a large variety of systems. An important aspect of the simulation method is that a simulation model is designed to be repeated in actual computer systems, especially in multicore processors. For this reason, it is important to minimize average waiting time for fetch and decode stage instructions. The objective of the research is to prove that the parallel operation of programme code is faster than sequential operation code on the multi processor architecture. The system modeling uses methods and simulation on the parallel computer systems is very precise. The time benefit gained in simulation of mathematical model on the pipeline processor is higher than the one in simulation of mathematical model on the multi processors computer system.

Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived. The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool, such as mass flow rates, flow coefficients, effiux angles and steady state flow forces under different operating conditions. At last, the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test. It is presented that the bottom arc of sloping U-shape notch （ABU） should not be omitted when it is required to accurately calculate the orifice area of ABU. Although the theoretical flow area of plain bottom sloping U-shape notch （PBU） is larger than that of ABU at the same opening, the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening, while the simulated flow force of PBU is larger than that of ABU at the same opening. Therefore, it should be prior to adapt the ABU when designing the spool with proportional character.

Numerical Simulation of a Mathematical Model for Dry/Wet-Spun Nascent Hollow Fiber Membrane

In an effort to find the effect of mass transfer, surface tension and drag forces on the velocity distribution, the mathematical model of the velocity profile of a nascent hollow fiber during membrane formation in the air gap region was numerically simulated by using the Runge-Kutta method (fourth-order method). The effect of mass transfer on velocity distribution based on the complicated function (G(Cs h)) was presented and the effects of a complicated function were studied in two cases: in the first case, G(Cs h) was constant; in the second, G(Cs h) was variable. The latter was done by varying with the concentration of solvent in a nascent hollow fiber through the air-gap region. One empirical equation was used to describe this change and the predicted values had a better agreement with the experimental values. To verify the model hypotheses, hollow fiber membranes were spun from 20∶80 polybenzimidazole/polyetherimide dopes with 25.6 wt% solid in N, N-dimethylacetamide (DMAc) using water as the external and internal coagulants. Based on the experimental results of dry-jet wet-spinning process for the fabrication of hollow fiber membranes, it is found that the model calculated values were in a good agreement with the experimental values.

Mathematical model of determination of die bearing length in design of aluminum profile extrusion die

Based on the finite element simulation of profile extrusion process, the effect of local extrusion ratio, die bearing area and the distance between extrusion cylindrical center and local die orfice center on mental flow velocity was investigated. The laws of deformed metal flow on profile extrusion process were obtained. The smaller the local extrusion ratio, the faster the metal flow velocity; the smaller the area of die bearing, the faster the metal flow velocity; the smaller the distance of position of local die orifice(the closer the distance of position of local die orifice from extrusion cylindrical axis), the faster the metal flow velocity. The effect of main parameters of die structure on metal flow velocity was integrated and the mathematical model of determination of die bearing length in design of aluminum profile extrusion die was proposed. The calculated results with proposed model were well compared with the experimental results. The proposed model can be applied to determine die bearing length in design of aluminum profile extrusion die.

Numerical Simulation Analysis of a Mathematical Model of Circadian Pacemaker Neurons

Sim and Forger have proposed a mathematical model of circadian pacemaker neurons in the suprachiasmatic nucleus (SCN). This model, which has been formulated on the Hodgkin-Huxley mo-del, is described by a system of nonlinear ordinary differential equations. An important feature of the SCN neurons observed in electrophysiological recording is spontaneous repetitive spiking, which is reproduced using this model. In the present study, numerical simulation analysis of this model was performed to evaluate variations in two system parameters of this model: the maximal conductance of calcium current (gCa) and the maximal conductance of sodium current (gNa). Simulation results revealed the spontaneous repetitive spiking states of the model in the (gCa, gNa)-pa-rameter space.

The mathematical model and simulation of the electrostatic suspension system in the vertical direction

In order to research the vibration law of electrostatic suspension systems in the vertical direction, the mathematical model as a nonlinear differential equation is established. A series of simulation is carried out. The results show that the solution of the differential equation is a periodic function. The amplitude becomes bigger with the original velocity increased. The period becomes smaller with the original velocity increasing. The numerical methods are presented to derive the amplitude and the frequency, and the results coincide with that of the simulation. The condition during which the simple harmonic vibration arises is pointed out. The expressions for the amplitude and the period of simple harmonic vibration are derived respectively, and the results are the same with that of the simulation. This study is helpful for researching the vibration characteristics of the electrostatic suspension system. The external disturb should be controlled to lower the amplitude and the frequency of the vibration.

Simulation of a Mathematical Model Minimizing Energy Consumption in SDN Type Networks

Several works by the authors have shown that energy consumption in communication networks does not only depend on the traffic load but on all connected equipment in the network. We have contributed a new mathematical model and a new energy saving strategy with Software Defined Network (SDN) technology [1]. Our Model solution is based on the Modified SPRING Protocol (MSP). In this paper, we simulated our work and compared it to that of the authors [2] and [3]. The OMNET++ simulator was used for our work. Thus, the results of the simulations gave a delay that tends to zero, a packet loss of the order of 10% and a constant jitter of 4% better than the previous authors.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

A 2D discrete mathematical model of a nine-point finite difference scheme is built to simulate tumor-induced angiogenesis. Nine motion directions of an individual endothelial cell and two parent vessels are extended in the present model. The process of tumor-induced angiogenesis is performed by coupling random motility, chemotaxis, and haptotaxis of endothelial cell in different mechanical environments inside and outside the tumor. The results show that nearly realistic tumor microvascular networks with neoplastic pathophysiological characteristics can be generated from the present model. Moreover, the theoretical capillary networks generated in numerical simulations of the discrete model may provide useful information for further clinical research.

SIMULATED MATHEMATICAL MODEL FOR HIGH PRESSURE CYLINDER WALL TEMPERATURE OF HOMEMADE TURBINE

In order to balance the contradiction between the demand of high precision and that of short time interval of model computing for the power plant simulator, a set of simulated mathematical models are constructed. The model describes the cylinder wall temperature located at four key positions of the high pressure cylinder. The simulated model is confirmed to be not only simple but also precise via comparison between the simulated results and the autoptic data of a power plant.

Research and Application Prospect of Computer Simulation on Heat Treatment Process

In this paper, a modified temperature-phase transformation-stress/strain field coupled 3D non-linear mathematical model was used in the computer simulation on heat treatment processes of workpieces including catch jaw, anchor ring, cold roller, large-scale bearing roller, nitriding crank shaft, etc. The simulation on complicated technologies such as pre-cooled quenching, double media quenching, self-tempering, difference temperature heating, nitriding distortion was carried out. The optimum design of heat treatment technology has been realized. The successful application of computer simulation on heat treatment have also been demonstrated.

Experimental optimization and mathematical modeling of supercritical carbon dioxide extraction of essential oil from Pogostemon cablin

The supercritical carbon dioxide extraction was applied to obtain essential oil from Pogostemon cablin in this work.Effect of extraction parameters including temperature,pressure,extraction time and particle size on extraction yield was investigated,and the response surface methodology with a Box–Behnken Design was used to achieve the optimized extraction conditions.The maximum yield of essential oil was 2.4356%under the conditions of extraction temperature 47°C,pressure 24.5 MPa and extraction time 119 min.Moreover,based on the Brunauer–Emmett–Teller theory of adsorption,a mathematical modeling was performed to correlate the measured data.The model shows a function relationship between extraction yield and time by a simple equation with three significantly adjustable parameters.These model parameters have been optimized through simulated annealing algorithm.The predicted data from the mathematical model show a good agreement with the experimental data of the different extraction parameters.

A continuous and high-efficiency process to separate coal bed methane with porous ZIF-8 slurry:Experimental study and mathematical modelling

Coal bed methane has been considered as an important energy resource.One major difficulty of purifying coal bed methane comes from the similar physical properties of CH_4 and N_2.The ZIF-8/water-glycol slurry was used as a medium to separate coal bed methane by fluidifying the solid adsorbent material.The sorption equilibrium experiment of binary mixture(CH_4/N_2)and slurry was conducted.The selectivity of CH_4 to N_2 is within the range of 2-6,which proved the feasibility of the slurry separation method.The modified Langmuir equation was used to describe the gas-slurry phase equilibrium behavior,and the calculated results were in good agreement with the experimental data.A continuous absorption-adsorption and desorption process on the separation of CH_4/N_2 in slurry is proposed and its mathematical model is also developed.Sensitivity analysis is conducted to determine the operation conditions and the energy performance of the proposed process was also evaluated.Feed gas contains 30 mol%of methane and the methane concentration in product gas is 95.46 mol%with the methane recovery ratio of 90.74%.The total energy consumption for per unit volume of product gas is determined as 1.846 kWh Nm^(-3).Experimental results and process simulation provide basic data for the design and operation of pilot and industrial plant.

A Practical Approach of Developing Mathematical Model for All Speed Governors

The paper introduced a special approach for diesel’s all-speed-governor modeling, which, in some cases, could solve the knotty problem frequently met in computer simulation of diesel propulsion system or diesel generating set. Suppose that it is hard to get a control-oriented governor mathematical model when the general approaches, the analytical approach or the experimental approach, are applied, and that an open-loop step response of the diesel engine and its system is available by means of computer simulation, the critical three parameters of a governor mathematical model, the proportional gain K_p, integral time constant K_i, and derivative time constant K_d, can be determined by use of PID tuning method which are widely applied in industrial process control. This paper discussed the train of thought of the approach, precondition, procedure, several modifications of the classical PID model, and some points for attention. A couple of case studies were given to demonstrate the effectiveness of this approach.

Basic mathematical model for the normal black smoker system and the hydrothermal megaplume formation

A tube model to simulate the normal black smoker system has been built, where the Darcy flow equation, the Ergun equation and the turbulent pipe flow equation are used respectively to describe the dynamic process of different key areas in the hydrothermal circulation system. At the same time, a convection - diffuse Equation for the temperature field is used for describe the exchange of thermal energy and the law of temperature variation. Combining the above facts and using efficient mathematical algorithms and programming with the MatLab programming language, the variation curves of temperature, pressure and mass flow rate are determined, while also the dynamic heat equilibrium and pressure equilibrium within the black smoker system are analyzed. On the basis of the model of the normal black smoker system, a megaplume formation model is further built. For instance, the hydrothermal venting plume on the Juan de Fuca Ridge has been simulated and the simulation results are fairly consistent with Baker＇ s imputed data in 1986. On the basis of the above productive simulation, a series of factors for megaplume formation and the effectiveness of the main parameters of the periodicity of the megaplume formation, temperature and the maximum mass flow rate are systematically discussed. Main conclusions are as follows： The normal black smoker system can evolve into a megaplum eruption. In fact, the passageway of the hydrothermal discharge is blocked by the hydrothermal sediments during the black smoker period, which leads to a hydrothermal fluid accumulation, rise of temperature and increase of buoyancy pressure under the seabed. After a period of 2 - 3 a, the megaplume hydrothermal eruption will occur when the increasing buoyancy pressure is high enough to crack the blockage （cap）. Meanwhile, the temperature of the heat source must exceed 500 ℃, while the highest temperature of the eruption fluid may be high up to 413 ℃, which is fairly consistent with the surveying data. If the temperature of the heat source were to be higher than 500 ℃, then the critical period for the megaplume formation could be obviously curtailed to be less than 1 a, while the critical temperature and the maximum mass flow rate are nearly invariable. As the permeability increases, the maximum mass flow rate increases gradually close to a steady value.

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19in Nigeria Using Atangana-Baleanu Operator

We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.