Mathematical Model of Thermal Deformation in Precision Measurement and its Application

2011 ◽  
Vol 411 ◽  
pp. 287-291
Author(s):  
Xiao Li Ma ◽  
Huai Bo Qiang ◽  
Xiao Zhou Feng
Keyword(s):  
Mathematical Model ◽  
Expansion Coefficient ◽  
Thermal Deformation ◽  
Steady Temperature ◽  
Shape Factors ◽  
Temperature Changes ◽  
Cylindrical Shaft ◽  
Volume Expansion Coefficient ◽  
Geometric Size ◽  
Material Line

As everyone knows, the temperature changes can cause the changes of mechanical geometric size. The thermal deformation obtained by traditional calculation formulas are approximate and linear, used in low precision requirement, however, if applied in high precision field, it is very limited. In this paper, by using the relations between crystal material line expansion coefficient and volume expansion coefficient, we will establish the thermal deformation mathematical model of cylindrical shaft and hole parts in the steady temperature, the model will consider the effects of the shape factors of parts on thermal deformation.

scholarly journals P-Cu alloy as anode materials for lithium ion batteries: a first-principles study

2021 ◽  
Vol 245 ◽  
pp. 03003
Author(s):  
Zhaowen Huang ◽  
Benjing Chen ◽  
Jingyang Li ◽  
Lingzhi Zhao
Keyword(s):  
Expansion Coefficient ◽  
First Principles ◽  
Volume Expansion ◽  
Anode Materials ◽  
Formation Energy ◽  
Lithium Ion ◽  
Lithium Intercalation ◽  
First Principle ◽  
Cu Alloy ◽  
Volume Expansion Coefficient

In this paper, based on the first principle method, the mechanism of lithium intercalation and deintercalation of P-Cu alloy as anode material of lithium-ion battery was studied. The results followed that the volume expansion coefficient of Li-P-Cu is small, 59.4650% for Li2PCu3 and 61.4071% for Li2P2Cu, indicating that the introduction of Cu can effectively inhibit the volume expansion of phosphorus. And PCu3 is superior to P2Cu in terms of volume expansion coefficient and lithium intercalation formation energy and good conductivity.

scholarly journals Technological Forecasting of Deformations in Flat Parts

2020 ◽  
Vol 3 (1) ◽  
pp. 1-12
Author(s):  
Tatiana N. Ivanova ◽  
Witold Biały ◽  
Jiři Fries ◽  
Victor Nordin
Keyword(s):  
Expansion Coefficient ◽  
Linear Expansion ◽  
Plate Thickness ◽  
Heat Removal ◽  
Quality Parameters ◽  
Grinding Wheel ◽  
Linear Expansion Coefficient ◽  
Plate Material ◽  
Thermal Deformations ◽  
Geometric Size

AbstractThe deformation of a part occurring in the process of grinding directly influences its exploitation and quality parameters. The instability of shape and size, which occurs due to an imbalance of residual stress, can be the one of the major causes of deformation of a part. The decrease in stress slows down the deformation process. Considering the regularities of heat source intensity dependence on the grinding modes, it can be asserted that with increasing grinding depth and grinding wheel hardness, the value increases and it decreases with a growth in a speed of the part and the use of cooling. The higher the heat removal is and the better lubricant properties of the liquid are, the more significant the decrease in is. Changing these values allows regulation of the residual stresses. As a result of the research on determination of deformations, it is recommended to reduce thermal deformations by considering the geometric size of a plate to be machined, linear expansion coefficient of plate material and an allowance for nonflatness from thermal deformations. The value of nonflatness from thermal deformations is directly proportional to linear expansion coefficient of plate material and its square overall dimensions. At the same time, the value of nonflatness is inversely proportional to the plate thickness.

scholarly journals Liquid–liquid gravity displacement in a vertical fracture during drilling: Experimental study and mathematical model

2019 ◽  
Vol 38 (2) ◽  
pp. 533-554
Author(s):  
Dong Xiao ◽  
Yingfeng Meng ◽  
Xiangyang Zhao ◽  
Gao Li ◽  
Jiaxin Xu
Keyword(s):  
Mathematical Model ◽  
Drilling Fluid ◽  
Effective Means ◽  
Fluid Density ◽  
Shape Factors ◽  
Fracture Width ◽  
Factors Affecting ◽  
Double Substrate ◽  
Fracture Height ◽  
Liquid Displacement

Gravity displacement often occurs when drilling a vertical fractured formation, causing a downhole complexity with risk of blowout and reservoir damage, well control difficulty, drilling cycle prolongation, and increased costs. Based on an experimental device created for simulating the gravity displacement, various factors affecting the displacement quantity were quantitatively evaluated by simulating the fracture width, asphalt viscosity, drilling fluid density, and viscosity under different working conditions, and a liquid–liquid displacement law was obtained. Using the theories of rock mechanics, fluid mechanics, and seepage mechanics, based on conformal mapping, as well as a fracture-pore double substrate fluid flow model, we established a steady-state mathematical model of fractured formation liquid–liquid gravity displacement by optimizing the shape factors and using a combination of gravity displacement experiments to verify the feasibility of the mathematical model. We analyzed the influence of drilling fluid density, fracture height and length, and asphalt viscosity on displacement rate, and obtained the corresponding laws. The results show that when the oil–fluid interface is stable, the fracture width is the most important factor affecting the gravity displacement, and plugging is the most effective means of managing gravity displacement.

Thermophysical properties of liquid and supercooled ruthenium measured by noncontact methods

2004 ◽  
Vol 19 (2) ◽  
pp. 590-594 ◽  
Author(s):  
P-F. Paradis ◽  
T. Ishikawa ◽  
S. Yoda
Keyword(s):  
Surface Tension ◽  
Heat Capacity ◽  
Temperature Interval ◽  
Expansion Coefficient ◽  
Thermophysical Properties ◽  
Volume Expansion ◽  
Isobaric Heat Capacity ◽  
Electrostatic Levitation ◽  
Entropy Of Fusion ◽  
Volume Expansion Coefficient

Several thermophysical properties of liquid and supercooled ruthenium were measured using electrostatic levitation. Over the 2225–2775 K temperature interval, the density can be expressed as ρ(T) = 10.75 × 103 – 0.56(T – Tm)(kg ⋅ m−3) with Tm = 2607 K. In addition, the surface tension can be expressed as σ(T) = 2.26 × 103 – 0.24(T – Tm)(mN ⋅ m−1) and the viscosity as η(T) = 0.60 exp[4.98 × 104/(RT)] (mPa ⋅ s) over the 2450–2725 K range. The isobaric heat capacity was estimated as CP(T) = 35.9 + 1.1 × 10−3(T – Tm)[(J/(mol K)] over the 2200–2750 K span by assuming a constant emissivity. The volume expansion coefficient, the enthalpy, and the entropy of fusion were also calculated as 5.2 × 10−5 K−1, 29.2 kJ ⋅ mol−1, and 11.2 J/(mol K).

Brain temperature changes during selective cooling with endovascular intracarotid cold saline infusion: simulation using human data fitted with an integrated mathematical model

2012 ◽  
Vol 5 (2) ◽  
pp. 165-171 ◽  
Author(s):  
Matthew Aaron Harold Neimark ◽  
Angelos Aristeidis Konstas ◽  
Leslie Lee ◽  
Andrew Francis Laine ◽  
John Pile-Spellman ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Brain Temperature ◽  
Saline Infusion ◽  
Temperature Changes ◽  
Cold Saline ◽  
Human Data ◽  
Selective Cooling

scholarly journals Physics Learning Based on Practicum: Factors that Affecting Expansion

2015 ◽  
Vol 6 (3) ◽  
pp. 12-15
Author(s):  
Eduarsyah Eduarsyah ◽  
Devi Astriani .
Keyword(s):  
Expansion Coefficient ◽  
Initial Temperature ◽  
Volume Ratio ◽  
Equilibrium Temperature ◽  
The Body ◽  
Water Volume ◽  
Copper Block ◽  
Physics Learning ◽  
Volume Expansion Coefficient ◽  
Area And Volume

An object when heated will undergo expansion. Expansion of an object is affected by the expansion coefficient, temperature, and type of object substances that cause the length, area, and volume of the object and other objects differently. Based on these concepts, to investigate the comparative increase in the size of the object that is affected by factors that affect the expansion by heating the body until it reaches the equilibrium temperature. As the object under study will use a block of copper and water with each volume to be measured 10-5 m3 added volume ratio. With the initial temperature of each object 20 oC, both substances will be heated up to a temperature of 30oC, 35oC, 40oC, 45oC, dan 50oC. Both substances are then calculated and compared to the increase in volume experimentally and theoretically. After calculation, a score which indicates that the copper block and the water volume is different. Increase the volume of water is greater than the increase in the volume of copper block in each temperature increment. Both these substances are two different substances that have different volume expansion coefficient as well. So we get that expansion coefficient, temperature, and type of object substances have an affect on the expansion that occurs on an object.

scholarly journals Phase Behavior Analysis of CO2 and Formation Oil System

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Lei Tang ◽  
Tongyao Zhang ◽  
Baogang Li ◽  
Lu Zhang ◽  
Dong Han
Keyword(s):  
Molecular Weight ◽  
Liquid Phase ◽  
Expansion Coefficient ◽  
Volume Expansion ◽  
Average Molecular Weight ◽  
Injection Rate ◽  
Co2 Injection ◽  
Bubble Point Pressure ◽  
Volume Expansion Coefficient ◽  
Point Pressure

In this paper, there are nine oil samples to explore the characteristics of formation oil at different CO2 injection rate, and the characteristics include bubble point pressure, volume expansion coefficient, viscosity, density, and average molecular weight, composition of gas and liquid phase, and asphalt sediment. According to the experimental results of early nine oil samples of swelling tests, in high temperature and high pressure conditions, characteristics and changing rules of properties of formation oil, including bubble point pressure, volume expansion coefficient, viscosity, density, and average molecular weight, composition of gas and liquid phase, and asphalt sediment, were evaluated and analyzed at different CO2 injection rate systematically. The research not only can provide guides for petroleum engineers when they need to adjust the injection and production programs, but also can provide comparatively comprehensive experimental rules for researches on enhanced oil recovery (EOR) mechanisms of gas miscible and nonmiscible flooding. Moreover, phase parameters of different formation oil system can be extracted for reservoir numerical simulation.

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