Pressure Distribution Function Research Articles

A neural-network potential for aluminum

Aluminum and its alloys are most often used as structural materials due to their specific properties, such as low weight, low energy consumption for remelting and the possibility of almost complete processing. This paper utilizes machine learning, specifically the Behler-Parrinello neural network scheme, to develop a powerful potential for studying the underlying mechanisms of deformation, fracture, and defect formation. By surpassing the limitations of first principles calculations, the application of machine-learned potentials (MLP) becomes highly advantageous for describing pure aluminum (Al) in its solid and liquid phases. Specifically, from the generated potential equilibrium, thermodynamic, elastic, and vibrational properties of face-centered cubic (fcc) Al are obtained in very good agreement especially with density functional theory (DFT) results as well as with previous calculations using existing semi-empirical potentials, such as EAM and MEAM, recent machine-learned potentials, and experimental data. Furthermore, our potential proves to accurately reproduce defect formation energies such as previously computed and measured stacking-fault energy curves. Finally, stacking fault profiles as well as key quantities of the liquid phase such as the melting point at ambient pressure, temperature-dependent densities, and radial distribution functions are also calculated in very good agreement with the results from previous theoretical and experimental investigations. Nevertheless, our investigation goes beyond previous studies in proving excellent agreement with experimental data especially of the specific heat and the melting point at very high pressures. The competitive analysis performed in this work thus clearly demonstrates the validity and accuracy of the generated machine-learned potential to describe a wide range of properties of Al at various temperatures and pressures and thereby lays ground for future applications.

Nonlinear Dynamic Analysis and Forecasting of Symmetric Aerostatic Cavities Bearing Systems

Symmetric Aerostatic Cavities Bearing (SACB) systems have attracted increasing attention in the field of high-precision machinery, particularly rotational mechanisms applied at ultra-high speeds. In an air bearing system, the air bearing serves as the main support, and the load-carrying capacity is not as high as that of oil film bearings. However, the aero-spindle can operate at considerably high rotational speeds with relatively lower heat generated from rotation compared with that of oil film bearings. In addition, the operating environment of air bearings does not easily cause the rotor to deform. Hence, through adequate design, air pressure systems exhibit a certain level of stability. In general, the pressure distribution function of air bearings exhibits strong nonlinearity when there are changes in the rotor mass or rotational speed, or when the bearing system is inadequately designed. These issues may lead to instabilities in the rotor, such as unpredictable nonperiodic movements, rotor collisions, or even chaotic movements under certain parameters. In this study, rotor oscillation was analyzed using the maximum Lyapunov exponent to identify whether chaotic behavior occurred. Machine learning methods were then used to establish models and predict the rotor behavior. Especially, random forest and extreme gradient boosting were combined to develop a new model and confirm whether this model offered higher prediction performance and more accurate results in predicting tendencies with considerable changes compared with other models. The results can be effectively used to predict the SACB system and prevent nonlinear behavior from occurring.

Modeling and braking analyses of longitudinal-vertical coupling towbarless aircraft taxiing system

The variation of tire vertical load has effects on the vehicle braking performance, which may lead to the misjudgment of braking distance and increasement of the accident risks. In order to evaluate the braking distance of the towbarless aircraft taxiing system (TLATS) accurately, a longitudinal-vertical coupling model of the TLATS is established, in which the effects of the vertical vibration on braking dynamics is considered. An 11-degrees of freedom (DOF) dynamic model of the TLATS, which consists of the system longitudinal motion, vertical vibration, and an advanced Lugre tire model, is proposed. The tire vertical dynamic loads are obtained by calculating system vibration differential equations as the input for the Lugre tire model, in which an arbitrary pressure distribution function over the contact patch and load related parameters are used. The Lugre tire model parameters are identified based on the virtual experiment results in ADAMS/Car software through a multi-objective optimization (MOO) method. The proposed tire model is more accurate by comparing with the models using other pressure distribution functions. The advanced Lugre model is integrated into the longitudinal-vertical coupling dynamic model of the TLATS, and the fuzzy PID control method is used to achieve the optimal slip rate during the braking procedure. The tire friction and TLATS’s braking performances in terms of the slip rate, braking speed and braking distance are compared between the coupling and uncoupling models under different traction velocities and the road excitations when a same fuzzy control method is used for the system braking. The results show that the proposed longitudinal-vertical coupling TLATS dynamic model could assess the braking behaviors of the TLATS more accurately than the simplified uncoupling model, which could decrease the potential safety risk of the aircraft towing operation on the airport apron.

Identifying the influence of design parameters of a hydrostatic bearing in an aircraft fuel pump on its static characteristics

The object of this study is hydrostatic processes in the sliding bearings of gear-type aviation fuel pumps. The problem of the influence of the design parameters of the fuel pump bearing on its static characteristics was solved. Load-bearing capacity, lubricant consumption, and operating temperature conditions were considered as static characteristics. The determination of these characteristics was based on the pressure distribution function in the working fluid layer. An option was adopted with two load-bearing chambers located on the working surface of the hydrostatic bearing. Three options for the circumferential arrangement of chambers relative to the line of action of the external load were studied. A quantitative assessment of the effect of increasing the temperature of the working fluid on the consumption of lubricant and bearing capacity is given. It has been established that with an increase in the angle of position of chambers relative to the line of action of the external load, the flow rate of the working fluid in the bearing increases, and its load-bearing capacity decreases. With a clearance in the bearing of 0.0225 mm, with an increase in the angle of the chambers from 30° to 40°, the flow of working fluid through the bearing increases by approximately 1.64 times. When the gap increases to 0.0425 mm and the angle of the chambers changes from 30° to 40°, the flow rate of the working fluid increases by approximately 1.2 times. The load-bearing capacity of the bearing with an increase in the chamber position angle from 30° to 40° decreases with a gap of 0.0225 mm by approximately 1.6 times, and with a gap of 0.0425 mm by approximately 1.93 times. An increase in the temperature of the working fluid leads to a decrease in the load-bearing capacity of the bearing by 2.5 % and an increase in the flow rate of the working fluid in the bearing by 4.6 %. The results allow for more rational design of hydrostatic bearings for fuel gear pumps.

Revealing the influence of structural and operational parameters of a hydrostatic bearing in a gear-type fuel pump on its main characteristics

The object of this study is hydrostatic processes in the sliding supports of gear-type fuel pumps. The problem solved was the influence of the structural and operational parameters of hydrostatic bearings of the fuel pump on their static characteristics. The carrying capacity and consumption of the lubricant were considered as static characteristics. The characterization was based on the function of distributing the pressure in the lubricant layer. It was determined from the joint solution of the Reynolds equations and the balance of costs. The carrying capacity of the bearing was determined by the numerical integration of the pressure distribution function in the lubricant layer. The lubricant consumption was determined by the calculated pressures in the chambers. Variants of the working surface of the bearing with two and three carrying chambers were considered. Due to the fact that the load in the pump acts in one direction during operation, the scheme of the working surface of the bearing with two carrying chambers was adopted. The fluid consumption of such a bearing was less compared to a bearing with three carrying chambers. One of the parameters that significantly affect the carrying capacity of the bearing is the diameter of the nozzle installed at the inlet to the chambers. It has been established that the dependence of the carrying capacity of a hydrostatic bearing on the diameter of the nozzle is nonlinear. With an increase in the diameter of the nozzle from 1 mm to 2.3 mm, the carrying capacity of the bearing increased by about 2.83 times. The extraction of fuel for the operation of the hydrostatic bearing was 1 % of the fuel pumped by the pump. The results make it possible to recommend hydrostatic bearings as shaft supports for gear-type fuel pumps and can be used for practical calculations

Contact Pressure Distribution and Pressure Correction Methods of Bolted Joints under Mixed-Mode Loading

The dynamic response of complex equipment under mixed-mode loading is significant for structural design. Bolted joints are the primary connection mode of subsystem assembly, and the degradation of bolted joints may reduce the safety and reliability of the equipment. The Iwan model is widely used to describe the degradation of bolted joints, which has been continuously revised and experimentally verified. The classic Iwan model is a static model that lacks predictive ability. The latest dynamic Iwan model can predict the softening process and reveal the physical mechanism of degradation. However, the function of dynamic pressure distribution needs to be determined for the model solution. We analyzed the contact boundary and pressure distribution under mixed-mode loading with the finite element method (FEM) and proposed the dynamic functions. Secondly, we put forward two correction methods to compensate for the loss of preload caused by simplification and to achieve consistency between the pressure distribution function and the contact boundary function. Finally, the influence of discrete order on the correction of pressure distribution was analyzed. The results show that the constraint method is more suitable for the modification of the pressure distribution. The research results can be applied to the solution of the dynamic Iwan model.

Greenhouse Natural Ventilation Models: How Do We Develop with Chinese Greenhouses?

Greenhouse technology has advanced over the past few decades in terms of environmental control (e.g., indoor temperature, relative humidity, and CO2 concentration). Ventilation is an effective way to adjust the indoor climate. Natural ventilation has gained significant research attention recently because of its low energy requirement. To evaluate the ventilation effectiveness, the ventilation rate is often used. This review summarizes the published review papers related to greenhouse ventilation. Ventilation models are reported under different conditions, including wind-induced, buoyancy-induced, and combined effects-induced ventilation in greenhouses. The influencing factors are described, such as the wind and buoyancy strength and distribution, greenhouse geometry, and vent arrangement. Various methods assessing natural ventilation in greenhouses are introduced, consisting of tracer gas techniques, the pressure difference method, the energy balance method, the emptying fluid-filling box method, and numerical simulation. The values of the key coefficients deduced and used in the literature are listed. This paper reports what has been done in the world and where we can start to develop dynamic ventilation models for solar and tunnel-type greenhouses in China. Further valuable investigations are discussed. The pressure distribution function in greenhouses with horizontal openings, a model for cross-ventilation induced by combined wind and buoyancy force, and an analytical plant-considered ventilation model with higher applicability are described. To ensure the accuracy of the ventilation models, other environmental variables, especially geography-dependent ones, can be added. More criteria are suggested to evaluate the ventilation performance rather than the ventilation rate to provide a comprehensive assessment.

An atomistic approach to study the dynamic and structural response in 2D nanofiller reinforced polyethylene nanocomposites under ultra-short shock pulse loading

An atomistic model was developed to systematically investigate the shock propagation and its attenuation behavior in two-dimensional (2D) nanofiller reinforced polyethylene (PE) nanocomposites. Under the framework of non-equilibrium molecular dynamics, an explicit ultra-short shock pulse with an impact velocity of 1.0 km/s was applied on the mono- and bi-crystalline 2D nanofiller reinforced PE nanocomposites. Their dynamic and structural responses were captured in terms of particle velocity, mean pressure, kinetic energy, and radial distribution function (RDF). The trends depicted that the energy dissipated from graphene (GNS) and boron nitride nanosheet (BNNS) reinforced PE nanocomposites were 30.69% and 24.92%, respectively, whereas the energy dissipation improves up to 45.33% and 41.77% for bi-crystalline GNS and bi-crystalline BNNS, respectively. Higher energy dissipation in GNS reinforced PE nanocomposites can be attributed to extreme impedance mismatch and superior interfacial interaction energy between GNS and PE chains.

Theoretical Research on Grouting in Deep Loose Layers Based on the Cylindrical Diffusion Model of Radial Tube Flow

Grouting in deep, loose layers are a complex process in which many modes such as infiltration, splitting, and compaction coexist. It is of great significance to establish a realistic, simplified physical model to study the law of slurry diffusion. Herein, a cylindrical diffusion model of radial tube flow is established, and the control differential equations of both the Bingham slurry diffusion velocity in a single tube and the diffusion velocity of the radial tube flow are deduced. Additionally, the calculation formulas for the diffusion radius and slurry pressure distribution function are obtained. The rationality of the theory is verified by combining our results with those of the field grouting test of the Guotun coal mine. The results show that the cylindrical diffusion model of radial tube flow can successfully characterize the slurry diffusion law of grouting in a deep, loose layer. The slurry pressure attenuation shows distinguishable stages: within the first 30% of the diffusion radius, the slurry pressure decreased sharply by approximately 70%, and the slurry pressure decreases slowly in the later stages. Furthermore, the diffusion radius has a nonlinear, negative correlation with the height of the grouting section and the comprehensive injection rate of formation; the change rate is relatively more gradual, and there are no distinguishable stages. The research results provide a theoretical basis for reasonably determining the grouting parameters of deep, loose layers in the future.

Theoretical Research on Sand Penetration Grouting Based on Cylindrical Diffusion Model of Tortuous Tubes

The penetration paths of grouts in sand layers are tortuous, and there is no reasonable penetration grouting theory at present. By employing tortuous circular tubes as the internal penetration pore channels of the sand layer, the cylindrical diffusion model is established for sand-layer penetration grouting. First, the permeability of porous media and average penetration velocity of Bingham slurry were deduced by considering tortuosity. Second, based on the penetration continuity equation, the active steady-state penetration differential equation of Bingham slurry and the pressure distribution function of slurry in the diffusion region were obtained. Finally, combined with the indoor penetration grouting test results, the attenuation law of slurry pressure and the influencing factors of diffusion radius were discussed. The results show that the cylindrical diffusion model of tortuous tubes can better characterize the diffusion process of penetration grouting in the sand layer. The stop condition for diffusion during penetration grouting is the reduction of the pressure gradient of the slurry to its starting value. The slurry pressure attenuation has obvious stages. The slurry pressure attenuation is faster in the area close to the grouting tube. At 50% of the maximum diffusion radius, the pressure attenuation is 70.01~75.41% of the total pressure attenuation within the diffusion region. Increasing the grouting pressure and permeability coefficient and reducing the slurry viscosity ratio can greatly increase the slurry diffusion radius. These results provide a theoretical basis for determining sand grouting parameters in the future.

Точное решение основного уравнения акустики для развивающейся по двум направлениям волны давления

The authors proceed from the hyperbolic equation for acoustic pressure. Using the integral Fourier transform along the axial coordinate, an equation in partial derivatives for the kernel of this transformation is found. This equation contains only one spatial coordinate and time. Applying the integral Laplace transform in time to the last equation, we obtain an ordinary differential equation with respect to the radial coordinate for the corresponding image. It turns out that the solution of the last equation is the well-known Macdonald function. For this function, it was possible to find the original image according to Laplace. All this made it possible to write an integral formula for the pressure in a sound wave. If the function of the initial pressure distribution along the pipe axis is taken in the form of a Gaussian impulse, then the integrals included in the representation of the desired solution are taken explicitly. As a result, we obtain an explicit compact formula for the acoustic pressure distribution in the axisymmetric case. It is convenient to use this formula to analyze the distribution of sound disturbances both along the pipe axis and in the radial direction. Therefore, the results are presented as isobars in the (z, r) plane corresponding to different times.

Particle paths in equatorial flows

<p style='text-indent:20px;'>We investigate particle trajectories in equatorial flows with geophysical corrections caused by the earth's rotation. Particle trajectories in the flows are constructed using pairs of analytic functions defined over the labelling space used in the Lagrangian formalism. Several classes of flow are investigated, and the physical regime in which each is valid is determined using the pressure distribution function of the flow, while the vorticity distribution of each flow is also calculated and found to be effected by earth's rotation.</p>

A novel analytical study on the buckling of cylindrical shells subjected to arbitrarily distributed external pressure

A completely new analytical method to solve the fourth-order governing partial differential equations with variable coefficients is proposed for the buckling of cylindrical shells subjected to distributed external pressure. Unlike the present energy method in literatures, pressure distribution needs not be assumed beforehand and be simple, which is arbitrary in this manuscript. The present novel method makes the buckling analysis for the complicated external pressure distributions (including discontinuous loads) possible. Furthermore, general buckling load formulas related to geometrical sizes of the shell and pressure distribution functions are obtained by the combined perturbation method and Fourier series expansion for the first time. The first and second order asymptotic terms of buckling loads are directly given for the purpose of engineering application. Based on the presented method, three types of external pressure loads (namely, linear liquid pressure, wind type pressure and discontinuous stepwise external pressure)are considered. Validity and accuracy are demonstrated by comparing with the results in published literatures for linear liquid pressure and wind type pressure, and it is also the first time to derive the buckling load for a shell under discontinuous stepwise external pressure. Parametric discussion is also performed to investigate the effects of load distribution types and parameters on buckling resistance capacity.

Investigations of the static and dynamic characteristics of the precision hydrostatic spindle with mid-thrust bearing under different loads

This paper investigates the static and dynamic characteristics of the precision hydrostatic spindle with a mid-thrust bearing under different working conditions. Firstly, the paper establishes the fluid governing equations of the coupled journal and thrust bearings based on orifice restrictors; and the dynamic and static Reynolds equations are solved using the perturbation and finite difference methods to obtain the steady and transient pressure distribution functions. Then the stiffness and damping characteristics of matrixes of the spindle are obtained by integrating the steady and transient pressure. Furthermore, by establishing the motion equation for the spindle rotor with five degrees of freedom, the quasi-static equilibrium position and stability criterion of the rotor under different working conditions are determined. Finally, the relationships between the dynamic and static characteristics of the spindle and cutting force, rotational speed, and cutting distance are simulated and analyzed. The simulation results show the patterns of variation in performance indices such as stiffness, damping, quasi-static position, and stability of the spindle under different working conditions, which provides important design information to be taken into consideration concerning the precision hydrostatic spindle.

Spectroscopic Investigation of Laser-Produced Strontium Plasma Using Fundamental and Second Harmonics of Nd:YAG Laser

In the present work, our main focus is to find out an optical window where the plasma is optically thin and the plasma parameters can be determined more reliably. The strontium plasma was generated using the fundamental (1064 nm) and the second harmonic (532 nm) of a Q-switched Nd:YAG laser. The spectra were registered using a set of five miniature spectrometers covering the spectral range from 200 to 720 nm. The intensity ratios of some specific lines have been compared with the theoretically calculated intensities to check the validity of optically thin plasma, free from self-absorption and in local thermodynamic equilibrium. In the selected optical window, the electron number densities have been determined from the Stark broadened line profiles, and the excitation temperatures have been calculated using the Boltzmann plot method for 1064- and 532-nm laser wavelengths. The variations in the electron number density and excitation temperature have been studied as a function of laser energy (8-100 mJ), atmospheric pressure (100-600 mbar), and spatial distribution of the plasma plume (0.5-4.0 mm) for both the lasers. The electron number density is found to be higher for the 532-nm laser than the 1064-nm laser, while the excitation temperature is higher for the 1064-nm laser than the 532-nm laser. We have fitted a power law on the experimental data to analyze the varying trends of excitation temperature.

A comprehensive analysis of factors affecting the accuracy of the precision hydrostatic spindle with mid-thrust bearing layout

This paper investigates the influence of rotor coaxiality error on spindle accuracy under different operating conditions in the precision hydrostatic spindle with a mid-thrust bearing structure. Firstly, a linearized model of rotor dynamics equation with five degrees-of-freedom is established based on Newton’s law of motion and angular momentum principle. Then, by solving the Reynolds equation and the flow continuity equation using the mathematical perturbation method, the steady and transient pressure distribution functions of the hydrostatic bearings are obtained; subsequently, the stiffness and damping coefficient matrices of the spindle are determined. Furthermore, the linearized stiffness and damping coefficients are substituted into the rotor dynamics equation to obtain the instantaneous acceleration of the rotor, and the motion trajectory of the rotor is solved iteratively by the Euler method. Finally, the paper studies the influences of different rotor coaxiality, rotating speed, cutting load, oil supply pressure, and oil film clearance on dynamic characteristics, amplitude amplification factor, and radial runout of the spindle by computer simulation. The simulation results show that the spindle runout is more sensitive to rotor coaxiality error and oil film clearance.

Высокотемпературное воздействие газовой струи реагирующих компонентов на фронтальную пластину

The paper introduces the results of measuring and predicting the heat and force effect of jets of high-temperature reacting mixtures on the oxygen-methane, oxygen-alcohol components when acting on the front plate in the near field of the jet. A high-temperature supersonic gas jet flows out of a model chamber with a Laval nozzle into a medium with atmospheric pressure at a degree of off-design ratio of about unity. In the chamber, ignition and stable combustion of a mixture of selected substances occur, the ratio of these substances providing a stagnation temperature in the range of 1900 ... 3400 K. The pressure distribution function on the front plate obtained in the experiment is used. The proposed model of the high-temperature flow effect on the frontal surface can be used to test software systems and determine the levels of thermal effect during sample tests.

Elastic punching of material during flattening of a spherical asperity and restoration of the imprint in unloading

The development of the methodology previously proposed by the authors for determining the displacements of half-space points under the action of an axisymmetric load described by a parabola is presented. It is shown that when the sphere is flattened, the pressure distribution on the contact area is a function of complex shape, which can be represented by a combination of several equations for description in adjacent sections. The knowledge and description of the contact pressure distribution function is of practical importance in solving the issues of elastic punching of the material, the magnitude of the elastic recovery of the contact print during unloading, and determining the curvature of its profile. Equations are proposed for determining displacements inside and outside the contact area when describing the distribution of contact pressure by analytical functions and when using a discrete distribution of contact pressure. The accuracy of the obtained results depends on the rate of the approximating functions to the actual pressure distribution at the contact area. At the same time, the goals of the problems to be solved should be considered. When determining elastic recovery in the center of the contact area, it is sufficient to use a uniform distribution of contact pressure. When determining the profile of the restored contact print and its curvature, increased accuracy of approximating functions is required.

Mechanical behavior of grouted connections under compression-bending loads

A grouted connection (GC) is critical to the transfer of combined axial force and bending moment from an upper tower to a substructure. Meanwhile, the increasing offshore wind turbine capacities and deeper pile foundation locations require robust connection structures. However, it is difficult to completely test the stress in GCs through experiments. So, in this paper, a numerical approach combined with python was adopted to analyze the load transferring mechanism between staggered shear keys mounted. A Parametric (grout thickness, the height-to-spacing ratio of the shear keys, and the length-to-diameter ratio of the tube) study was conducted to determine the effect on the mechanical behavior. In addition, an equation and two coefficients were proposed: the regression function of the contact pressure distribution, the non-uniform coefficient ηsk and the amplification coefficient βsk of the shear keys force. Through an analysis of the composition of the flexural capacity, it was found that shear keys accounts for the largest proportion while the contact pressure took the second place. From the study, programming enriches the post-processing of the numerical simulation, which provides researchers a method to research the GCs through complex calculations. And by the analyzing the parameters and introducing related variables, a deeper understanding of the mechanical performance of GCs has been obtained.

Hydrophobic and Stable MXene-Polymer Pressure Sensors for Wearable Electronics.

Ti3C2Tx MXene has exhibited great potential for use in wearable devices, especially as pressure sensors, due to its lamellar structure, which changes its resistance as a function of interlayer distance. Despite the good performance of the reported pure MXene pressure sensors, their practical applications are limited by moderate flexibility, excessively high MXene conductivity, and environmental effects. To address the above challenges, we incorporated multilayer MXene particles into hydrophobic poly(vinylidene fluoride) trifluoroethylene (P(VDF-TrFE)) and prepared freestanding, flexible, and stable films via spin-coating. These films were assembled into highly sensitive piezoresistive pressure sensors, which show a fast response time of 16 ms in addition to excellent long-term stability with no obvious responsivity attenuation when the sensor is exposed to air, even after 20 weeks. Moreover, the fabricated sensors could monitor human physiological signals such as knee bending and cheek bulging and could be used for speech recognition. The mapping spatial pressure distribution function was also demonstrated by the designed 10 × 10 integrated pressure sensor array platform.