scholarly journals Research on Mathematical Model of Composite Micromachining of Laser and Electrolysis Based on the Electrolyte Fluid

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Aixi Sun ◽  
Bo Hao ◽  
Yulan Hu ◽  
Dewei Yang
Keyword(s):  
Mathematical Model ◽  
Laser Processing ◽  
New Technology ◽  
Machining Process ◽  
Laser Machining ◽  
Machining Accuracy ◽  
Metallic Materials ◽  
Two Phase ◽  
Processing Accuracy ◽  
The Mathematical Model

A new technology of composite micromachining of laser and electrolysis is presented through a combination of technological advantages of laser processing and electrolytic machining. The implication of its method is that laser processing efficiently removes metallic materials and that pulse electrolytic machining removes recast layer and controls shape precisely. Machining accuracy and efficiency can be improved. The impacts that electrolyte fluid effectively cools the microstructure edge in the laser machining process and that gas-liquid two-phase flow makes the electrolyte conductivity produce uneven distribution in the electrolytic processing are considered. Some approximate assumptions are proposed on the actual conditions of machining process. The mathematical model of composite micromachining of laser and electrolysis based on the electrolyte fluid is built. The validity of the model can be verified by experimentation. The experimental results show that processing accuracy meets accuracy requirements which are ±0.05 mm. Machining efficiency increases more than 20 percent compared to electrolytic processing.

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.

Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid

2016 ◽  
Vol 693 ◽  
pp. 837-842
Author(s):  
Fu Yi Xia ◽  
Li Ming Xu ◽  
De Jin Hu
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Abrasive Particle ◽  
Influence Factors ◽  
Machining Process ◽  
Quadric Surface ◽  
Precision Grinding ◽  
Cup Wheel ◽  
The Mathematical Model ◽  
Trajectory Equation

A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

On the correctness of a phenomenological model of equilibrium phase transitions in a deformable elastic medium

1992 ◽  
Vol 3 (2) ◽  
pp. 181-191
Author(s):  
A. M. Meirmanov ◽  
N. V. Shemetov
Keyword(s):  
Mathematical Model ◽  
Continuous Medium ◽  
Equilibrium Phase ◽  
Elastic Solid ◽  
Complementary Energy ◽  
Structure Of Solutions ◽  
Two Phase ◽  
Pure Phase ◽  
The Mathematical Model ◽  
Uniqueness Of A Solution

In this paper we investigate the mathematical model of the equilibrium of a finite volume in ℝn (n = 1,2, 3) of a two-phase continuous medium, under the assumption that each pure phase is an isotropic elastic solid. The main results in this paper are:(i) the existence and uniqueness of a solution of this mathematical model;(ii) a discussion of the stress-strain law associated with the free energy of this two-phase continuous medium, which is multiple-valued due to the non-smoothness of the Gibbs potential (complementary energy);(iii) a description of the structure of solutions in plane strain.

scholarly journals Modeling and Analysis of Magnetic Nanoparticles Injection in Water-Oil Two-Phase Flow in Porous Media under Magnetic Field Effect

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed F. El-Amin ◽  
Ahmed M. Saad ◽  
Amgad Salama ◽  
Shuyu Sun
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Porous Media ◽  
Magnetic Nanoparticles ◽  
Additional Term ◽  
Flow In Porous Media ◽  
Phase System ◽  
Two Phase ◽  
The Mathematical Model ◽  
Nanoparticles Suspension

In this paper, the magnetic nanoparticles are injected into a water-oil, two-phase system under the influence of an external permanent magnetic field. We lay down the mathematical model and provide a set of numerical exercises of hypothetical cases to show how an external magnetic field can influence the transport of nanoparticles in the proposed two-phase system in porous media. We treat the water-nanoparticles suspension as a miscible mixture, whereas it is immiscible with the oil phase. The magnetization properties, the density, and the viscosity of the ferrofluids are obtained based on mixture theory relationships. In the mathematical model, the phase pressure contains additional term to account for the extra pressures due to fluid magnetization effect and the magnetostrictive effect. As a proof of concept, the proposed model is applied on a countercurrent imbibition flow system in which both the displacing and the displaced fluids move in opposite directions. Physical variables, including water-nanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat concentrations of deposited nanoparticles, are investigated under the influence of the magnetic field. Two different locations of the magnet are studied numerically, and variations in permeability and porosity are considered.

Mathematical Modeling of Impingement of an Air Jet in a Liquid Bath

2010 ◽  
Vol 1276 ◽  
Author(s):  
J. Solórzano-López ◽  
R. Zenit ◽  
M. A. Ramírez-Argáez
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Free Surface ◽  
Gas Flow ◽  
Two Phase ◽  
Arc Furnaces ◽  
Air Jet ◽  
Image Velocimetry ◽  
Oxygen Gas ◽  
The Mathematical Model

AbstractPhysical and mathematical modeling of jet-bath interactions in electric arc furnaces represent valuable tools to obtain a better fundamental understanding of oxygen gas injection into the furnace. In this work, a 3D mathematical model is developed based on the two phase approach called Volume of Fluid (VOF), which is able to predict free surface deformations and it is coded in the commercial fluid dynamics software FLUENTTM. Validation of the mathematical model is achieved by measurements on a transparent water physical model. Measurements of free surface depressions through a high velocity camera and velocity patterns are recorded through a Particle Image Velocimetry (PIV) Technique. Flow patterns and depression geometry are identified and characterized as function of process parameters like distance from nozzle to bath, gas flow rate and impingement angle of the gas jet into the bath. A reasonable agreement is found between simulated and experimental results.

Regularity of Dust Distributing in Fully Mechanized Caving Face and Negative Pressure Spray Dust-Settling Technology

2012 ◽  
Vol 246-247 ◽  
pp. 624-628 ◽  
Author(s):  
Wen Nie ◽  
Wei Min Cheng
Keyword(s):  
Mathematical Model ◽  
Negative Pressure ◽  
Lagrangian Model ◽  
Dust Particles ◽  
Phase Flow ◽  
Dust Pollution ◽  
Two Phase ◽  
Fluent Software ◽  
The Mathematical Model ◽  
Hydraulic Supports

The mathematical model of solving two-phase flow of gas and dust particles was built by established the k-ε equation. Moreover, by basing on Eulerian-Lagrangian model and using FLUENT software, the diffusion rule of dust pollution in full-mechanized caving face was confirmed. Based on negative pressure spray dust-settling mechanism, negative pressure spray technology was developed between hydraulic supports, in drawing opening position and shearer, and it was determined by the optimal spray pressure for 4 MPa. After negative pressure spray technology was applied in fully mechanized caving face, the dust concentration was down significantly.

scholarly journals A SIMPLIFIED OXIDATION MODEL FOR TWO-PHASE FLOW IN POROUS MEDIA

2002 ◽  
Vol 1 (2) ◽  
pp. 09
Author(s):  
J. C. Da Mota ◽  
A. J. De Souza ◽  
D. Marchesin ◽  
P. W. Teixeira
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Wave Structure ◽  
Thermal Recovery ◽  
Flow In Porous Media ◽  
Low Temperature Oxidation ◽  
Two Phase ◽  
Temperature Oxidation ◽  
Physical Effects ◽  
The Mathematical Model

This paper describes a simplified mathematical model for thermal recovery by oxidation for flow of oxygen and oil in porous media. Some neglected important physical effects include gravity, compressibility and heat loss to the rock formation, but heat longitudinal conduction and capillary pressure difference between the phases are considered. The mathematical model is obtained from the mass balance equations for air and oil, energy balance and Darcy's law applied to each phase. Based on this model some typical features in low temperature oxidation concerning the wave structure are captured. Numerical simulations showing saturations and temperature profiles are reported.

scholarly journals Modelling and thermodynamic analysis of ejector flow for application at design and off design operating conditions in an ejector air conditioner

2021 ◽  
Vol 12 (3) ◽  
pp. 3455-3467
Author(s):  
Anoop Kumar. M Et.al
Keyword(s):  
Mathematical Model ◽  
Heat Input ◽  
Flow Analysis ◽  
Cooling Capacity ◽  
Two Phase ◽  
Entrainment Ratio ◽  
Air Conditioning System ◽  
The Mathematical Model ◽  
Minimum Quality

Ejector flow in an ejector air conditioning system using R245fa is analysed for entrainment ratio and potential refrigeration effect, at varying temperature and heat input conditions in  the generator ranging from 60C to 100C and 2kW to 5kW respectively. The effect of varying generator temperature in cooling capacity of the system when the vapour ejectoris operating at design evaporator and condenser temperatures of 10C and 35C respectively is investigated. The mathematical model of the vapour ejector with optimum area ratio is developed and validated. A critical entrainment ratio of 0.385 is obtained corresponding to generator temperature of 100C. When the generator temperature is varied from 60C to 100C, the cooling capacity range from 0.3kW at generator heat input of 2 kW to 1.78 kW at 5 kW heat input. Further, the operation of the system is analysed for off design operating condition corresponding to reduced heat input rate in the generator. In that case the state of primary refrigerant flow in ejector inlet will be two phase and a mathematical model for two-phase ejector flow is developed and validated. Ejector flow analysis revealed the minimum quality of flow at ejector inlet to maintain adequate backpressure for condensation to occur range from 0.72 at 60C to 0.22 at 100C. The corresponding refrigeration refrigeration effect produced is less than the respective designed operation value byits  12.2% to 8%. Further, analysis of the system shows that at least 7 kW heat input at 100C is required to produce 1 ton of cooling effect. Ejector flow in an ejector air conditioning system using R245fa is analysed for entrainment ratio and potential refrigeration effect, at varying temperature and heat input conditions in  the generator ranging from 60C to 100C and 2kW to 5kW respectively. The effect of varying generator temperature in cooling capacity of the system when the vapour ejectoris operating at design evaporator and condenser temperatures of 10C and 35C respectively is investigated. The mathematical model of the vapour ejector with optimum area ratio is developed and validated. A critical entrainment ratio of 0.385 is obtained corresponding to generator temperature of 100C. When the generator temperature is varied from 60C to 100C, the cooling capacity range from 0.3kW at generator heat input of 2 kW to 1.78 kW at 5 kW heat input. Further, the operation of the system is analysed for off design operating condition corresponding to reduced heat input rate in the generator. In that case the state of primary refrigerant flow in ejector inlet will be two phase and a mathematical model for two-phase ejector flow is developed and validated. Ejector flow analysis revealed the minimum quality of flow at ejector inlet to maintain adequate backpressure for condensation to occur range from 0.72 at 60C to 0.22 at 100C. The corresponding refrigeration refrigeration effect produced is less than the respective designed operation value byits  12.2% to 8%. Further, analysis of the system shows that at least 7 kW heat input at 100C is required to produce 1 ton of cooling effect.

scholarly journals Research on the Cutting Principle and Tool Design of Gear Skiving Based on the Theory of Conjugate Surface

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Peng Wang ◽  
Jingcai Li ◽  
Lin Han
Keyword(s):  
Mathematical Model ◽  
Design Principle ◽  
Design Method ◽  
Tool Design ◽  
Theoretical Research ◽  
Machining Accuracy ◽  
Rake Face ◽  
Key Factors ◽  
Flank Face ◽  
The Mathematical Model

Tool design is one of the key factors that restrict the development of gear skiving technology since the design principle does not correspond to the cutting principle. The existing skiving tool cannot achieve ideal machining accuracy and reasonable cutting angles. In view of this, some research has been done in this paper. Firstly, the skiving principle is investigated essentially according to the skiving motions. Then, the principle of tool design is analyzed based on the theory of conjugate surface, and a new tool design method is proposed to match the skiving principle. For this, all the skiving patterns for various kinds of workpieces are enumerated and summarized to abstract a normalized skiving model. Based on this, the mathematical model of the conjugate surface is then derived to lay the foundation for tool design. Then, the design methods of cutting edge, rake face, and flank face are proposed. An example is presented at last, and the cutting simulation is conducted. The result proves that the proposed methods are correct and valid. The theoretical research in this paper could promote the improvement of skiving tools.

scholarly journals A SIMPLIFIED OXIDATION MODEL FOR TWO-PHASE FLOW IN POROUS MEDIA

2002 ◽  
Vol 1 (2) ◽  
Author(s):  
J. C. Da Mota ◽  
A. J. De Souza ◽  
D. Marchesin ◽  
P. W. Teixeira
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Wave Structure ◽  
Thermal Recovery ◽  
Flow In Porous Media ◽  
Low Temperature Oxidation ◽  
Two Phase ◽  
Temperature Oxidation ◽  
Physical Effects ◽  
The Mathematical Model

This paper describes a simplified mathematical model for thermal recovery by oxidation for flow of oxygen and oil in porous media. Some neglected important physical effects include gravity, compressibility and heat loss to the rock formation, but heat longitudinal conduction and capillary pressure difference between the phases are considered. The mathematical model is obtained from the mass balance equations for air and oil, energy balance and Darcy's law applied to each phase. Based on this model some typical features in low temperature oxidation concerning the wave structure are captured. Numerical simulations showing saturations and temperature profiles are reported.

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