scholarly journals Analytic approximation of the Debye function

2020 ◽  
Vol 49 ◽  
pp. 96-110
Author(s):  
Konstantin Vladimirovich Khishchenko ◽  
◽  
Keyword(s):  
Closed Form ◽  
High Temperatures ◽  
Equations Of State ◽  
Analytic Approximation ◽  
Thermodynamic Models ◽  
Relative Deviation ◽  
Debye Function ◽  
Limiting Behavior ◽  
Maximum Relative Deviation

An expression in a closed form is proposed for the approximation of the Debyefunction used in thermodynamic models of solids. This expression defines an analytic functionthat has the same limiting behavior as the Debye function at low and high temperatures. Theapproximation gives the maximum relative deviation from the value of the Debye function lessthan 0.001. The proposed expression can be useful in the equations of state of solids in a widetemperature range.

scholarly journals Measurement of the (p, ρ, T) Behavior of Liquid MEA and DEA at Temperatures from (293.15 to 423.15) K and Pressures up to 90 MPa

2021 ◽  
Vol 42 (5) ◽  
Author(s):  
Christian W. Scholz ◽  
Roland Span
Keyword(s):  
Equations Of State ◽  
Oscillation Period ◽  
Argon Atmosphere ◽  
Relative Uncertainty ◽  
Relative Deviation ◽  
Density Measurements ◽  
Maximum Relative Deviation ◽  
Data Points ◽  
Temperature And Pressure ◽  
Mono Ethanolamine

AbstractDensities in the homogeneous liquid phase of (mono-)ethanolamine (MEA) and diethanolamine (DEA) were investigated using a commercially available high-pressure vibrating-tube densimeter (VTD). Due to the melting point of the experimental materials, the setup of the VTD had to be modified by an insulated housing of the entire piping including the pressure pump. The insulated housing could be heated up by a temperature-controlled heating fan. The liquid samples with a purity of (0.9994 or 0.9950) mole fraction, respectively, were decanted within an inert protective argon atmosphere and further degassed by several freeze–pump–thaw cycles. Density measurements were carried out at temperatures between (293, respectively, 313 and 423) K and at pressures between (5 and 90) MPa. The resulting 140, respectively, 120 (p, ρ, T) data points, explicitly extend the published database for MEA and DEA, with regards to pressure. A comparison with the currently used equations of state for MEA and DEA revealed a maximum relative deviation of – 0.18 % for MEA and – 0.41 % for DEA, each at the highest investigated temperature and pressure. Considering the measurement uncertainties in temperature, pressure, and oscillation period, as well as uncertainties resulting from the calibration and from the impurities of the sample, the combined expanded relative uncertainty (k = 2) in density varied from (0.1027 to 0.1038) % and from (0.1104 to 0.1130) %, respectively. The VTD was previously calibrated by comprehensive measurements of water and helium and had been further validated by measurements with pure propane.

Neural network modeling as an efficient approach to predict the density of ionic liquids/ethanol binary systems

2017 ◽  
Vol 16 (04) ◽  
pp. 1750031 ◽  
Author(s):  
Mostafa Lashkarbolooki
Keyword(s):  
Neural Network ◽  
Ionic Liquids ◽  
Binary Data ◽  
Binary Systems ◽  
Statistical Error ◽  
Percentage Error ◽  
Neural Network Modeling ◽  
Ann Model ◽  
Relative Deviation ◽  
Maximum Relative Deviation

Ionic liquids (ILs) especially their mixtures are of high interest within the different scientific societies due to their amazing properties. In this regard, a number of attempts have been made to measure, correlate, estimate and calculate the properties of ILs in the neat or mixture forms. Among the different possible predictive methods, artificial neural networks (ANNs) are widely used because of their unique and amazing capabilities for prediction of different parameters. With respect to this paper, a feed-forward ANN model is proposed to model the densities of different binary mixtures of ILs/ethanol. The proposed network is trained and tested with 1078 binary data points gathered by mining into the different published literatures. The data gathered from previously published literatures are separated into two different subsets namely training and testing. The statistical error analysis has shown that the proposed neural network correlated the binary densities with the overall mean absolute percentage error (MAPE), average relative deviation percentage error (ARD%), minimum relative deviation percent (RDmin%), maximum relative deviation Percent (RDmax%) and correlation coefficient ([Formula: see text] of 1.5%, [Formula: see text]0.1%, [Formula: see text]13.0%, 15.0% and 0.9712, respectively.

Finite Element Simulation of Bending Stress on Involute Spur Gear Tooth Profiles

2017 ◽  
Vol 30 ◽  
pp. 1-10
Author(s):  
Kolawole Adesola Oladejo ◽  
Dare Aderibigbe Adetan ◽  
Ayobami Samuel Ajayi ◽  
Oluwasanmi Oluwagbenga Aderinola
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Gear Tooth ◽  
Spur Gear ◽  
Bending Stress ◽  
Relative Deviation ◽  
Element Simulation ◽  
Maximum Relative Deviation ◽  
Bending Stresses ◽  
Good Agreement

This study investigated bending stress distribution on involute spur gear tooth profiles with pressure angle of 20 ̊ but different modules 2.5, 4.0 and 6.0 mm, using a finite-element-based simulation package - AutoFEA JL Analyzer. The drafting of the geometry for the three gear tooth profiles were implemented on the platform of VB-AutoCAD customized environment, before importing to the package. These were separately subjected to analysis for bending stresses for a point at the tooth fillet region with appropriate settings of material property, load and boundary conditions. With the same settings, the bending stresses were computed analytically using American Gear Manufacturers Association (AGMA) established equation. The results of the two approaches were in good agreement, with maximum relative deviation of 4.38%. This informed the confidence in the implementation of the package to investigate the variation of bending stress within the gear tooth profile. The simulation revealed decrease in the bending stresses at the investigated regions with increase in the module of the involute spur-gear. The study confirms that Finite element simulation of stresses on gear tooth can be obtained accurately and quickly with the AutoFEA JL Analyzer.

The mechanical parameters modeling of heavy steel plate snake/gradient temperature rolling with the same roll diameters

2020 ◽  
Vol 117 (3) ◽  
pp. 301
Author(s):  
Lian-Yun Jiang ◽  
Tao Zhen ◽  
Guo Yuan ◽  
Jin-Bo Huang ◽  
Yao-Yu Wei ◽  
...  
Keyword(s):  
Shear Zone ◽  
Steel Plate ◽  
Rolling Force ◽  
Slip Zone ◽  
Analytic Model ◽  
Mechanical Parameters ◽  
Ansys Software ◽  
Relative Deviation ◽  
Maximum Relative Deviation ◽  
Rolling Torque

The grains in the center of the heavy steel plate can be refined by the snake/gradient temperature rolling, and the deformation penetration, the microstructure, and the properties of the steel plate will be improved. The existing rolling mechanical models are not suitable for the snake/gradient temperature rolling, so it is necessary to establish the mechanical parameters model of the snake/gradient temperature rolling to instruct production. The yield criterion of rolled material was modified based on the idea of equivalent flow stress. The element stress analyses were carried out based on the uniform normal stress and nonuniform shear stress in the vertical sides of each slab. Then the equilibrium equation of the unit pressure based on the slab method was established on this basis. The deformation region was divided into three layers (the top layer, the bottom layer, and the central layer) and maximum four zones (back slip zone, front slip zone, cross shear zone, and reverse deflection zone) according to the temperature distribution and position of the neutral point, and then the 12 zones were formed during the snake/gradient temperature rolling. The boundary conditions of the existence of the back slip zone, the front slip zone, and the cross shear zone were established according to the relationship between the threading angle and the neutral angle. The accurate mechanical parameters model of the rolling force and rolling torque of the snake/gradient temperature rolling with the same roll diameters was set up on this basis. The ANSYS software has been used in the rolling process simulation by many scholars, and the calculating precision has been verified. So the rolling processes were simulated by the ANSYS software to validate the model precision. The results show that the maximum relative deviation of the rolling force analytic model is less than 7% compared with the numerical method, and the maximum relative deviation of the rolling torque analytic model is less than 11% compared with the measured results. The mechanical parameters model can accurately predict the rolling force and rolling torque during the snake/gradient temperature rolling with the same roll diameters, so as to provide a theoretical basis for the design of rolling mill and the setup of the process parameters.

scholarly journals The Thermodynamic and Kinetic Effects of Sodium Lignin Sulfonate on Ethylene Hydrate Formation

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3291
Author(s):  
Yiwei Wang ◽  
Lin Wang ◽  
Zhen Hu ◽  
Youli Li ◽  
Qiang Sun ◽  
...  
Keyword(s):  
Formation Rate ◽  
Hydrate Formation ◽  
Solution System ◽  
Relative Deviation ◽  
Thermodynamic Effect ◽  
Maximum Relative Deviation ◽  
Lignin Sulfonate ◽  
The Difference ◽  
Kinetic Effects ◽  
First Time

Hydrate-based technologies (HBTs) have high potential in many fields. The industrial application of HBTs is limited by the low conversion rate of the water into hydrate (RWH), and sodium lignin sulfonate (SLS) has the potential to solve the above problem. In order to make the HBTs in the presence of SLS applied in industry and promote the advances of commercial HBTs, the effect of SLS on the thermodynamic equilibrium hydrate formation pressure (Peq) was investigated for the first time, and a new model (which can predict the Peq) was proposed to quantitatively describe the thermodynamic effect of SLS on the hydrate formation. Then, the effects of pressure and initial SLS concentration on the hydrate formation rate (rR) at different stages in the process of hydrate formation were investigated for the first time to reveal the kinetic effect of SLS on hydrate formation. The experimental results show that SLS caused little negative thermodynamic effect on hydrate formation. The Peq of the ethylene-SLS solution system predicted by the model proposed in this work matches the experimental data well, with an average relative deviation of 1.6% and a maximum relative deviation of 4.7%. SLS increased RWH: the final RWH increased from 57.6 ± 1.6% to higher than 70.0% by using SLS, and the highest final RWH (77.0 ± 2.1%) was achieved when the initial SLS concentration was 0.1 mass%. The rR did not significantly change as RWH increased from 35% to 65% in the formation process in the presence of SLS. The effect of increasing pressure on increasing rR decreased with the increase in RWH when RWH was lower than 30%, and the difference in pressure led to little difference in the rR when RWH was higher than 30%.

Plasticity Model of Extruded Peanuts under Mechanical Pressing

2011 ◽  
Vol 55-57 ◽  
pp. 20-25
Author(s):  
Xiao Zheng ◽  
Ya Xin Zhang ◽  
Guo Xiang Lin ◽  
Zhi Xian Sun
Keyword(s):  
Constitutive Equations ◽  
Inverse Method ◽  
Yield Criterion ◽  
Strain Curve ◽  
Model Parameters ◽  
Plasticity Model ◽  
Stress Strain ◽  
Relative Deviation ◽  
Maximum Relative Deviation ◽  
Mechanical Pressing

The experiments for stress—strain and confined pressing of granular peanuts by uniaxial pressing were carried out. The results show that granular peanuts conform to the model of three power curve. By using of Kuhn`s yield criterion, plasticity constitutive equations of granular peanuts were developed. The model parameters were determined from experimental stress—strain curve using an inverse method. The maximum relative deviation between the measured and the simulated value of strain is 5.4%, and the average relative deviation is 3.5%. Results indicated that the plasticity constitutive equations can describe the plastic deformation for extruded peanut, and Kuhn`s yield criterion can be used as theoretical basis for plasticity model of granular peanuts.<b></b>

Multi-Channel Detection System for Joint Position Based on Optical and Orthogonal Decoding

2013 ◽  
Vol 483 ◽  
pp. 368-373
Author(s):  
Qi Xiang Hu
Keyword(s):  
Joint Angle ◽  
Detection System ◽  
Maximum Error ◽  
Joint Position ◽  
Optical Encoder ◽  
Relative Deviation ◽  
Angle Sensor ◽  
Channel Detection ◽  
Position Detection ◽  
Maximum Relative Deviation

The multi-channel joint position detection system of measuring arm is of high precision, multi-channel and other special characteristic. This system uses hardware called DSPic30F microchip as the processing core. The detection system adopts optical encoder as joint angle sensor and orthogonal decoding and reversible chip HCTL-2032 to multi frequency the detected signal, which greatly reduces the system error and enhances the detection precision. Experiments of joint position detection are realized. Thirty times repeated experiments show that the maximum error is 0.009 °and the maximum relative deviation is 40.9 × 10-3 /%.

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