scholarly journals Combustion synthesis of metal carbides: Part I. Model development

2005 ◽  
Vol 20 (5) ◽  
pp. 1257-1268 ◽  
Author(s):  
A.M. Locci ◽  
A. Cincotti ◽  
F. Delogu ◽  
R. Orrù ◽  
G. Cao
Keyword(s):  
Mathematical Model ◽  
Combustion Synthesis ◽  
Model Development ◽  
Pure Metal ◽  
Metal Carbides ◽  
Reaction Products ◽  
High Temperature Synthesis ◽  
Suitable Combination ◽  
Definition Of ◽  
Population Balances

The definition of a rigorous theoretical framework for the appropriate physico-chemical description of self-propagating high-temperature synthesis (SHS) processes represents the main goal of this work which is presented in two sequential articles. In this article, a novel mathematical model to simulate SHS processes is proposed. By adopting a heterogeneous approach for the description of mass transfer phenomena, the model is based on appropriate mass and energy conservation equations for each phase present during the system evolution. In particular, it takes microstructural evolution into account using suitable population balances and properly evaluating the differentdriving forces from the relevant phase diagram. The occurrence of phase transitionsis treated on the basis of the so-called enthalpy approach, while a conventional nucleation-and-growth mechanistic scenario is adopted to describe quantitatively the formation of reaction products. The proposed mathematical model may be applied to the case of combustion synthesis processes involving a low melting point reactant and a refractory one, as for the synthesis of transition metal carbides from pure metal and graphite. Thus, the model can be profitably used to gain a deeper insight into the microscopic elementary phenomena involved in combustion synthesis processes through a suitable combination of experimental and modeling investigations, as it may be seen in Part II of this work [J. Mater. Res. 20, 1269 (2005)].

Combustion Synthesis of NiTi – TiC Composites with Controlled Porosity for Biomedical Applications

2003 ◽  
Vol 800 ◽  
Author(s):  
Douglas E. Burkes ◽  
Guglielmo Gottoli ◽  
John J. Moore ◽  
Hu Chun Yi ◽  
Reed A. Ayers
Keyword(s):  
Combustion Synthesis ◽  
Orthopedic Implants ◽  
Functionally Graded ◽  
Nickel Titanium ◽  
Synthesis Process ◽  
Matrix Composites ◽  
Reaction Products ◽  
High Temperature Synthesis ◽  
Commercial Applications ◽  
Image Position

ABSTRACTCombustion synthesis, or Self-propagating High- temperature Synthesis (SHS), is currently being used by the Center for Commercial Applications of Combustion in Space (CCACS) at the Colorado School of Mines to produce advanced porous materials for several important applications. These materials include ceramic, inter- metallic, and metal- matrix composites that can be used for orthopedic implants, heat exchanger and damping systems and micro-and macro-filter applications. Functionally graded materials, both in porosity and composition, can be produced using a range of combustion synthesis reactions systems. There are multiple factors that contribute to the final SHS product, e.g. reactant stoichiometry, initial relative density and pre-heat. The synthesis of nickel-titanium (NiTi) intermetallic compounds and composites is of considerable interest due to the ability to create a porous, shape memory and super-elastic alloy with high corrosion resistance. The synthesis effects of adding a carbon reactant so as to modify the reaction products and reaction exothermicity have been studied through the use of two different reaction stoichiometries involving elemental nickel, titanium and carbon. This paper outlines the synthesis of NiTi intermetallic composites based on the following SHS chemical reaction:The effect of the carbon reactant and the initial sample green density on the apparent porosity, bulk density, pore size and pore distribution of the final materials has been studied and is presented within this paper. A NiTi- TiC intermetallic ceramic composite has been synthesized that is functionally graded in both composition and porosity: the latter grading being due to buoyancy and gas evolution effects. Proposed kinetic mechanisms that drive this synthesis process and control the graded structure are discussed in detail.

scholarly journals Combustion synthesis of metal carbides: Part II. Numerical simulation and comparison with experimental data

2005 ◽  
Vol 20 (5) ◽  
pp. 1269-1277 ◽  
Author(s):  
A.M. Locci ◽  
A. Cincotti ◽  
F. Delogu ◽  
R. Orrù ◽  
G. Cao
Keyword(s):  
Experimental Data ◽  
Combustion Synthesis ◽  
Quantitative Description ◽  
Scale Model ◽  
Metal Carbides ◽  
Fitting Procedure ◽  
High Temperature Synthesis ◽  
Complex Picture ◽  
Model Reliability ◽  
Physical And Chemical

Based on the general theoretical model proposed in Part I of this work [J. Mater. Res. 20, 1257 (2005)], a series of numerical simulations related to the self-propagating high-temperature synthesis in the Ti–C system is presented. A detailed and quantitative description of the various physical and chemical processes that take place during combustion synthesis processes is provided in Part II of this work. In particular, the proposed mathematical description of the system has been discussed by highlighting the relation between system macroscopic behavior obtained experimentally with the modeled phenomena taking place at the microscopic scale. Model reliability is tested by comparison with suitable experimental data being nucleation parameters adopted for the fitting procedure. The complex picture emerging as a result of the model sophistication indicates that the rate of conversion is essentially determined by the rate of nucleation and growth. In addition, comparison between model results and experimental data seems to confirm the occurrence of heterogeneous nucleation in product crystallization.

Mathematical Model of Flat Surface Machining Inaccuracies due to Elastic Strains of Technological System

2018 ◽  
pp. 1-14 ◽  
Author(s):  
I. I. Kravchenko
Keyword(s):  
Mathematical Model ◽  
Vector Field ◽  
Model Development ◽  
Technological System ◽  
Mutual Arrangement ◽  
Real Surface ◽  
Main Bearing ◽  
Flat Surfaces ◽  
Internal Surfaces ◽  
Elastic Strains

The paper considers the mathematical model development technique to build a vector field of the shape deviations when machining flat surfaces of shell parts on multi-operational machines under conditions of anisotropic rigidity in technological system (TS). The technological system has an anisotropic rigidity, as its elastic strains do not obey the accepted concepts, i.e. the rigidity towards the coordinate axes of the machine is the same, and they occur only towards the external force. The record shows that the diagrams of elastic strains of machine units are substantially different from the circumference. The issues to ensure the specified accuracy require that there should be mathematical models describing kinematic models and physical processes of mechanical machining under conditions of the specific TS. There are such models for external and internal surfaces of rotation [2,3], which are successfully implemented in practice. Flat surfaces (FS) of shell parts (SP) are both assembly and processing datum surfaces. Therefore, on them special stipulations are made regarding deviations of shape and mutual arrangement. The axes of the main bearing holes are coordinated with respect to them. The joints that ensure leak tightness and distributed load on the product part are closed on these surfaces. The paper deals with the analytical construction of the vector field F, which describes with appropriate approximation the real surface obtained as a result of modeling the process of machining flat surfaces (MFS) through face milling under conditions of anisotropic properties.

Optimization Control of the Bullwhip Effect in Supply Chain Inventory

2014 ◽  
Vol 945-949 ◽  
pp. 3187-3190
Author(s):  
Hai Dong ◽  
Jin Hua Liu ◽  
Liang Yu Liu
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Control Theory ◽  
Inventory Control ◽  
Pid Controller ◽  
Bullwhip Effect ◽  
Control Gain ◽  
Optimization Control ◽  
Suitable Combination ◽  
The Mathematical Model

The bullwhip effect was caused by fuzzy demand among the enterprises. In order to reduce this effect, control theory was applied to solve the inventory in supply chain. Firstly, inventory control in supply chain and the bullwhip effect was researched. Secondly, a kind of proportional integral differential (PID) controller was developed for inventory control in a three-level supply chain, and the mathematical model of the PID controller for inventory control was presented. Finally, the results show that the PID controller can evidently alleviate the bullwhip effect and inventory fluctuations under the suitable combination of control gain.

scholarly journals Immediately mathematical model of maneuverability of the items of the administration

2019 ◽  
Vol 9 (3) ◽  
Author(s):  
Volodymyr Kotsyuruba ◽  
Ruslan Cherevko
Keyword(s):  
Mathematical Model ◽  
Traditional Approach ◽  
Armed Forces ◽  
Control Points ◽  
Military Operations ◽  
The Reformation ◽  
Definition Of ◽  
The Cost ◽  
Military Units ◽  
Current Stage

At the current stage of the reformation of the Armed Forces of Ukraine in the context of the operation of the United Nations (Anti-Terrorist Operation (ATO)), there was a need to increase the effectiveness of the use of troops without increasing the cost of the resource. In the context of increasing capabilities of the armies of the leading countries in the world to investigate and defeat the forces of the opposite side, the problem of maintaining and restoring combat capability in the course of hostilities is very acute. One of the important components that determines combat capability is the maneuverability of the control points (PU). In the course of the defense, the problem of increasing the survivability of the PU system is important because the forces of the opposite side, with the onset of aggression, will try, first of all, to dismantle the PU using modern means of defeat and the massive use of high-precision weapons (WTZ), as well as aircraft and artillery strikes, electronic information and information fight, the use of sabotage and reconnaissance groups and tactical airborne troops to disrupt the control of defending troops. Important importance of the ability to timely carry out maneuver (organized movement) of PU and its elements into a new area in the preparation and in the course of military operations. The traditional approach to ensuring the survivability of PU does not allow to ensure the proper stability of their functioning. There is an objective necessity in the development of such a mathematical model of maneuverability, which in its characteristics would meet the dynamically increasing requirements of the control system of troops in the difficult conditions of projected operations. To ensure the quality management of military units, various measures to ensure the survivability of PU are considered. The article outlines approaches to the definition of indicators of estimation of maneuverability of PU and methods of their calculation. The research is carried out in modern conditions of combat operations, taking into account the movement of the line of the combat collision of the parties and the disclosure of the PU to the enemy's intelligence.

scholarly journals Development of a mathematical model for calculating the process of crushing hard rocks by explosions of cylindrical charges of explosives

2020 ◽  
Vol 5 ◽  
pp. 30-32
Author(s):  
Norov Yunus Dzhumaevich ◽  
Mehmonov Maksud Rabbonokul ugli
Keyword(s):  
Mathematical Model ◽  
Rock Mass ◽  
Mechanism Of Action ◽  
Mathematical Description ◽  
Granulometric Composition ◽  
Rock Fragmentation ◽  
Hard Rocks ◽  
Definition Of ◽  
The Relationship

The article presents a developed mathematical model for calculating the granulometric composition of the blasted rock mass based on the mechanism of action of an explosion in rocks, a mathematical description of the determination of natural units (blocks) in the rock mass, the relationship between the degree of rock fragmentation and the size of the units and the definition of sections of the controlled pressure zone.

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