Mathematical model of the electrocontact heating of steel blanks with square cross section

1979 ◽  
Vol 37 (6) ◽  
pp. 1482-1485
Author(s):  
V. K. Kapustkin ◽  
V. Z. Remnyakov
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Electrocontact Heating

Development of a Mathematical Model for a Workpiece Heating and Cooling in a Protective Medium while Treatment under Pressure

2021 ◽  
Vol 410 ◽  
pp. 115-122
Author(s):  
Victoria V. Devyatiarova ◽  
Eugenia E. Balakhnina ◽  
Lilya M. Valeeva
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Arbitrary Shape ◽  
Thermal Conductivity Coefficient ◽  
Regression Equations ◽  
Heating And Cooling ◽  
Temperature Problem ◽  
Protective Medium ◽  
Computer Calculations ◽  
The Mathematical Model

The paper reviews and develops the mathematical model of plastic flow during the hot-forming processes. A flat non-stationary temperature problem for a cross-section of a long solid (rolled product) of arbitrary shape with different heat transfer conditions along the perimeter of the cross-section was considered. Equations for calculation of the thermal conductivity coefficient and heat capacity of tungsten billets were obtained in the temperature range of 700 - 1500°C, based on the literature data. Analytical dependences in form of regression equations were obtained, allowing for computer calculations of physical specifications of 11x11 mm VA grade tungsten billets in form of temperature functions with accuracy sufficient for practical calculations.

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 Numerical Simulation of the Distribution of In Situ Cigarette Combustion-Generated Particulate Matter

2020 ◽  
Vol 4 (4) ◽  
pp. 59
Author(s):  
Shi Chen ◽  
Hanqing Liu ◽  
Zhiguo Sun ◽  
Hongyong Xie
Keyword(s):  
Mathematical Model ◽  
Particulate Matter ◽  
Cigarette Smoke ◽  
Cross Section ◽  
Constant Pressure ◽  
Particle Diameter ◽  
Axial Position ◽  
Number Density ◽  
Total Particulate Matter

This paper has established a two-dimensional (2D) mathematical model for the generation, growth, and deposition of cigarette total particulate matter (TPM) in the smoldering state. The model has covered the chemical reactions and mass transfer as well as the mechanism of generation, flow, and condensation of particulate matter inside a burning cigarette. Cigarette smoke was generated by puffing under a constant pressure, and the pressure of the filter outlet was −274 Pa. The peak of the concentration of particulate matter was spatially overlapped with the peaks of pyrolysis and oxidation. Pertaining to the cross section of the cigarette at the same axial position, the peak of the diameter of particulate matter along the radial distribution first appeared in the zone near the edge of the cigarette cross section, and then gradually moved to the center of the cigarette with the cigarette smoke moving away from the combustion cone. The maximum number density of particulate matter calculated by the 2D mathematical model at the same axial position of the cigarette and the corresponding particle diameter, as well as the filtration efficiency of the filter rod, are in good accordance with the experimental data reported in previous studies.

Analysis of Synchronization Angle Precision in RCS Measurement and its High Speed Synchronous Pulse Implementation

2013 ◽  
Vol 303-306 ◽  
pp. 493-497
Author(s):  
Dong Chen ◽  
Hua Pei Wang ◽  
Qing Guo
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
High Precision ◽  
High Speed ◽  
Radar Cross Section ◽  
Angle Measurement ◽  
Precision Measurements ◽  
Fixed Angle ◽  
Synchronous Pulse ◽  
Angle Interval

To meet the demand for high precision measurements of radar cross section (RCS) in microwave anechoic chamber, the effect of angle repeatability of position servo system in background cancellation technology is analyzed and its error mathematical model is presented. Then a method of high speed synchronization angle measurement based on CPLD is proposed, which improves the precision of synchronization angle measurement in any fixed angle interval. The experiment results show that this method can effectively solve the accuracy of target RCS when rotating.

scholarly journals Bore formation, evolution and disintegration into solitons in shallow inhomogeneous channels

2003 ◽  
Vol 10 (4/5) ◽  
pp. 407-424 ◽  
Author(s):  
J.-G. Caputo ◽  
Y. A. Stepanyants
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Vries Equation ◽  
Spatial Inhomogeneity ◽  
Hydraulic Jumps ◽  
Variable Depth ◽  
Nonlinear Surface Waves ◽  
Nonlinear Surface ◽  
The Mathematical Model ◽  
Riemann Waves

Abstract. The propagation of nonlinear surface waves in channels of smoothly variable in space cross section is studied theoretically and by means of numerical computations. The mathematical model describing wave evolution is based on the generalized Korteweg-de Vries equation with additional terms due to spatial inhomogeneity and energy dissipation. Specifically we consider channels of variable depth and width. The breaking of Riemann waves and the disintegration of hydraulic jumps into trains of solitons have been examined. The results obtained can be useful in particular for the understanding some peculiarities of bore (mascaret) formation, viscous evolution and disintegration into solitons in inhomogeneous channels or rivers.

scholarly journals Plastic Deformation of Metal Tubes Subjected to Lateral Blast Loads

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kejian Song ◽  
Yuan Long ◽  
Chong Ji ◽  
Fuyin Gao
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Plastic Flow ◽  
Cross Section ◽  
Circular Tube ◽  
Circular Tubes ◽  
Simply Supported ◽  
Different Dimensions ◽  
Thin Walled ◽  
Wave Induced

When subjected to the dynamic load, the behavior of the structures is complex and makes it difficult to describe the process of the deformation. In the paper, an analytical model is presented to analyze the plastic deformation of the steel circular tubes. The aim of the research is to calculate the deflection and the deformation angle of the tubes. A series of assumptions are made to achieve the objective. During the research, we build a mathematical model for simply supported thin-walled metal tubes with finite length. At a specified distance above the tube, a TNT charge explodes and generates a plastic shock wave. The wave can be seen as uniformly distributed over the upper semicircle of the cross-section. The simplified Tresca yield domain can be used to describe the plastic flow of the circular tube. The yield domain together with the plastic flow law and other assumptions can finally lead to the solving of the deflection. In the end, tubes with different dimensions subjected to blast wave induced by the TNT charge are observed in experiments. Comparison shows that the numerical results agree well with experiment observations.

Hydraulic Transport of Sand/Shell Mixtures

2011 ◽  
Author(s):  
Robert C. Ramsdell ◽  
Sape A. Miedema ◽  
Arno M. Talmon
Keyword(s):  
Mathematical Model ◽  
Critical Velocity ◽  
Cross Section ◽  
Settling Velocity ◽  
Hydraulic Transport ◽  
Erosion Process ◽  
Large Area ◽  
Small Cross Section ◽  
Horizontal Cross Section ◽  
Sand Particles

When considering pumping shells through a pipeline we have to consider that the shells are not spherical, but more discs shaped. When shells settle they will settle like leaves where the biggest cross section is exposed to the drag. But when they settle, they will settle in the same orientation, flat on the sediment, so the sides of the shells are exposed to the horizontal flow in the pipeline. Since the side cross section is much smaller than the horizontal cross section, a much higher velocity is required to make them erode and go back into suspension. The settling velocity is much smaller because of the large area of the cross section. Even when the slurry velocity exceeds the settling velocity, there will always be some shells that will reach the bottom of the pipe due to the combination of settling velocity and turbulence. Once these shells are on top of the sediment they are hard to remove by erosion, because they lay flat on the surface and have a small cross section that is exposed to the flow compared with the weight of the shell. So although their settling velocity is much lower than equivalent sand particles, the erosion velocity is much higher. If we look at the beach in an area with many shells, we can always see the shells on top of the sand, covering the sand. In fact the shells are shielding the sand from erosion, because they are hard to erode. The bigger shells will also shield the smaller pieces, because the smaller pieces settle faster. Compare this with leaves falling from a tree, the bigger leaves, although heavier, will fall slower, because they are exposed to higher drag. The same process will happen in the pipeline. Shells settle slower than sand grains, so they will be on top of the bed (if there is a bed), just like on the beach. Since they are hard to erode, in fact they protect the bed from being eroded, even if the line speed is increased. The combination of high erosion velocity and the shell ‘protecting’ the bed means that even a small amount of shells can lead to relatively thick bed in the pipeline. But there will always be velocities above the bed that will make the shells erode. The paper describes the settling and erosion process of shells and the consequences of this on the critical velocity when pumping a sand/shell mixture through a pipeline. A mathematical model of the processes involved will be presented.

Optimization Design for Luffing Mechanism of Portal Slewing Crane

2014 ◽  
Vol 577 ◽  
pp. 305-309
Author(s):  
Zhong Hua Luo
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Optimization Design ◽  
Maximum Force ◽  
Optimization Result ◽  
Mechanism Optimization ◽  
Cross Section Area ◽  
Section Area ◽  
Minimum Amplitude ◽  
Comprehensive Study

This paper conducts a comprehensive study on the optimization design for luffing mechanism of portal slewing crane. First, displacement formulae are derived of crampon hinge point of the luffing mechanism. Secondly, mathematical model is established for luffing mechanism optimization design of portal slewing crane, according to the mechanism characteristics, and, with an aim of making crampon hinge end point to move horizontally, and of satisfying the value of maximum and minimum amplitude, and of saving material, etc. Finally, program of optimization design is compiled for the luffing mechanism of portal slewing crane. The luffing mechanism of M4022 portal slewing crane is optimized, and the optimization result is satisfactory. This paper makes it possible to obtain not only each rod length and cross-section area, but also obtain the counterbalance weight and the each rod maximum force of the luffing mechanism.

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