Formula For Thickness Research Articles

Modeling of Multibody Lubrication Dynamics in Cylindrical Roller Bearings

As a typical multibody system, rolling bearing consists of several lubricated frictional pairs that transmit motions and forces among components. In this paper, a multibody lubrication dynamics (MLD) model of cylindrical roller bearings (CRBs) is developed by coupling the bearings dynamics submodel and several lubrication submodels of each frictional pairs in real-time. The lubrication submodels are discretized by using finite difference and solved by numerical iteration methods of Gauss-Seidel with line relaxation and discrete convolution-fast Fourier transform (DC-FFT) technique. Additionally, a parallel algorithm is also designed to enhance the calculation efficiency. Its results are validated by the experimental results in literature and further compared by the results from other dynamics models. It revealed that the film formation alters not only friction but also geometrical constraints and pressure distribution, which may introduce additional load inside bearing and increase rolling friction under high-speed conditions. As the dynamic oil film stiffness and damper are took into account by MLD, the cage has a lower whirl frequency and forces. The curve-fitting formulas of elastohydrodynamic lubrication (EHL) film thickness are overestimates of the thickness value and, thus, change the load distribution and friction between roller and raceway.

A Simplified Non‐Hertzian Wheel‐Rail Adhesion Model Under Interfacial Contaminations Considering Surface Roughness

ABSTRACTThe accuracy and efficiency of the wheel‐rail adhesion model are important to the wheel‐rail rolling contact issues. The purpose of this study is to develop a simplified non‐Hertzian wheel‐rail adhesion model under interfacial contaminations to predict the wheel‐rail adhesion coefficient. Firstly, a non‐Hertzian full elasto‐hydrodynamic lubrication (EHL) model was developed and applied to determine the wheel‐rail contact pressure and film thickness under interfacial contaminations. Then, the empirical formula of central film thickness available to non‐Hertzian wheel‐rail normal contact relating to train speeds, axle loads and material parameters were proposed based on a large number of non‐Hertzian full EHL simulation for smooth surface under interfacial contaminations using linear regression. The empirical non‐Hertzian central film thickness formula and minimum film thickness formula for wheel‐rail contact obtained in this paper show certain differences from the formulas based on Hertzian contact. Using the proposed non‐Hertzian central film thickness formula, a simplified non‐Hertzian wheel‐rail contact adhesion model was developed, and the adhesion coefficient was obtained at different speeds and compared with the field test data. The numerical results showed good agreement with field test data.

Experimental and theoretical study on liquid film thickness of upward annular flow in helically coiled tubes

The liquid film thickness is crucial for studying the thermal hydraulic mechanism of the annular flow region in helically coiled tubes (HCTs). This paper introduces a refined experimental study on the liquid film thickness of annular flow in HCTs, utilizing a newly developed liquid film sensor. The experimental results indicate that the smaller coil diameters and pitches result in thinner average liquid film thicknesses. The average liquid film thickness decreases with increasing superficial gas velocity and decreasing superficial liquid velocity. However, the liquid film thickness at different circumferential positions on the cross-section of the tube exhibits varying sensitivities to superficial gas and liquid velocities. The experimental data reveal that the existing typical correlation formula for the average liquid film thickness of annular flow in straight tubes does not apply to HCTs. Consequently, a new prediction model is proposed for the average liquid film thickness of the annular flow region in HCTs, based on the modified Froude number, modified Dean number, Ekman number, and Reynolds number. This model comprehensively incorporates the structural characteristics of HCTs and fluid properties, and its validity is verified through the utilization of available and current data in the literature.

Enhancing the heat transfer in CuO-MWCNT oil hybrid nanofluid flow in a pipe

In this study, three-dimensional steady-state laminar flow simulations were conducted in a horizontal pipe using CuO and multi-walled carbon nanotubes (MWCNT) nanoparticles with engine oil as the base fluid. Various nanoparticle volume fractions were examined under a constant heat flux boundary condition applied to the pipe wall. The main goal was to assess and compare the effects of different nanoparticle volume concentrations, including CuO and MWCNT in ratios of 1:1 and 1:2, on convective heat transfer. A second-order discretisation method was employed for solving the equations, and the SIMPLE algorithm was used for pressure–velocity coupling in the CFD code. The study focused on the impact of nanoparticle volume fraction on the convective heat transfer coefficient and the Nusselt number at a Reynolds number of 750. The findings indicate that increasing the nanoparticle volume fraction enhances both the convective heat transfer coefficient and the Nusselt number, with MWCNT having a more pronounced effect compared to CuO. Specifically, adding 2% CuO increases the heat transfer coefficient by 65%, while a mixture of 1% CuO and 1% MWCNT boosts it by 75%. The thermal boundary layer thickness also grows with higher nanoparticle concentrations, with 1% CuO and 3% CuO increasing the thickness by 1.5% and 3.6%, respectively. A formula for the thermal boundary layer thickness in CuO-oil nanofluids is provided based on volume fraction, and a scale analysis of the average heat transfer coefficient confirms that the simulation results are consistent with this analysis.

The association of temporalis muscle thickness with post-stroke dysphagia based on swallowing kinematic analysis

Background/purposePost-stroke dysphagia (PSD) is a common functional deficit after stroke. Temporal muscle thickness (TMT) had been proven to be an independent factor for PSD. However, the relationship between TMT and PSD based on quantitative swallowing kinematic analysis remains unexplored. We aimed to investigate the association between TMT and PSD using videofluoroscopic swallow study (VFSS). MethodWe retrospectively recruited stroke patients from May 2015 to March 2020 in the tertiary referral hospital. A total of 83 patients with dysphagia met all the enrollment criteria and were included in the study. TMT was measured by non-contrast brain computed tomography (CT) images. Parameters of VFSS were obtained, including penetration-aspiration scale (PAS), oral transit time (OTT), pharyngeal transit time (PTT) and swallowing trigger time (STT) in four standardized barium formulas respectively. The association between TMT and variables of VFSS were analyzed by adjusted linear and logistic multivariate regression models. Subgroup analysis based on age, sex, and premorbid modified Rankin Scale (mRS) stratification was conducted. ResultsTMT was significantly correlated with gender and premorbid mRS as the confounders. Univariate regression showed smaller TMT (p = 0.010) and poorer premorbid mRS (p = 0.018) was associated with prolonged PTT of the thick formula; lesser TMT was associated with prolonged PTT of the paste formula (p = 0.037). Multivariate analyses after confounder-adjustment demonstrated TMT was an independent indicator for PTT in the thick formula (p = 0.028). ConclusionsTMT was associated with swallowing kinematic changes in patients diagnosed with PSD. TMT is an independent indicator for delayed pharyngeal stage in the thick standardized formula during deglutition in PSD patients.

Optimizing the Thickness Uniformity of Magnetron Sputtering Deposited Films on a Large-Scale Curved Workpiece Surface

This study prepared magnetron-sputtering deposition film on a large-scale curved workpiece with a favorable thickness uniformity using a rectangular target cathode. For a substrate rotation structure with eccentric rotation/revolution composite motion, the geometrical model of the thickness distribution of the coating film on a large substrate was established in combination with the principle of rectangular cathode magnetron sputtering. The integral formula of the film thickness was derived, and various film thickness distribution patterns under different parameters were simulated. According to the present research results, the film thickness distribution can be optimized by adjusting the revolution-to-rotation radius and eccentric ratios. At an eccentric distance of 400 mm and a radius ratio of 2.78, the most favorable uniformity degree of 0.87 was obtained, which was controlled by the motion path of the fixed point on the substrate. The proposed approach helps to obtain large-scale films with favorable uniformity on the substrate.

Dynamic Characterization of Grease-Lubricated Ball Screws

According to the lubrication characteristics of grease and lubrication mechanism, concerning the Hamrock-Dowson minimum film thickness formula, this paper analyses the trend and size of oil film thickness change of grease-lubricated ball screw sub under different aviation working conditions to identify the lubrication status. ABAQUS software is used to carry out dynamic simulation and the friction coefficient is selected according to the lubrication state and Stribeck curve to define the contact conditions to obtain the friction torque change curve and the fluctuation curve of axial velocity of the nut under different aerospace working conditions. Finally, a test bench is set up to test and calculate the friction torque of grease-lubricated ball screws to analyze the influence of different aviation working conditions on the dynamic characteristics of grease-lubricated ball screws and to investigate the reasons for the change of dynamic characteristics.

Analysis of the thickness of the outburst prevention layer in karst tunnels under the control of compressive faults

In order to solve the problem of the safe thickness between concealed karst caves and tunnels under the influence of compressive faults, a simplified calculation model of the safe thickness under three working conditions is constructed. Based on the cusp catastrophe theory, the analytical formulas of the safe thickness between concealed karst cave and tunnel are derived. On this basis, based on the finite difference method, the evolution law of the maximum displacement of rock slabs under different cave water pressures is revealed, the criterion of “when the maximum displacement of the rock slab exceeds the thickness of the rock slab, the water inrush caused by the strength failure of the rock slab occurs in the tunnel” has been established, and the rationality and effectiveness of this criterion have been verified. When the compressive fault is located in the middle of the rock slab, the difference between the theoretical thickness of the rock slab and the maximum displacement of the rock slab is only 0.26 m, the simplified model can accurately determine the thickness of the anti-outburst rock slab. When the compressive fault is located in a quarter of the length of the rock slab, the simplified model also has strong applicability. Research has shown that when the cave water pressure is small, the rock slab displacement increases approximately linearly with the increase of cave water pressure; When the water pressure increases to a certain extent, the cave water pressure and rock slab displacement show a nonlinear correlation, and the rock slab deformation enters the plastic stage; The spatial location of faults has a significant impact on the applicability of analytical formulas, when the fault is located in the middle of the rock slab, the influence of the deformation of the fault itself on the stability of the rock slab should be considered; For the working condition where the karst cave above the tunnel, the theoretical thickness of the rock slab has a certain linear relationship with the length of the rock beam, the corresponding theoretical thickness of the rock slab when the fault is located at other locations can be determined according to the linear relationship; When the location of the fault moves from the middle of the anti-outburst rock slab to the root of the anti-outburst rock slab, for working condition three, the theoretical safety thickness required for the fault located in the upper part of the rock slab is slightly greater than that required for the symmetric position. The research methods and results of this paper have certain reference and application value for similar research and engineering problems.

A Fast Calculation Approach for Elastohydrodynamic Finite Line Contacts Applicable to Online Calculations of Rolling Bearing Models

Abstract Finite line contacts in rolling element bearings are usually under the regime of elastohydrodynamic lubrication (EHL). To obtain deeper insights into bearing performance, it is necessary to directly couple EHL contact models into bearing models. However, the existing EHL contact models are either too time consuming to be employed in the bearing model or too simplified to consider tilting contact behaviors and actual roller profiles. A fast calculation approach for EHL finite line contacts is proposed by combining the empirical film thickness formulas that have been developed for decades and an improved slicing technique that considers the coupling behaviors between slices. The proposed approach can not only predict the contact stiffness (normal contact stiffness and tilting contact stiffness) and contact states (contact pressure and film thickness) accurately but also is universal for different profiled contacts and material properties. The proposed approach costs only a few milliseconds for a single load case, which enables it to be directly employed in bearing models. Besides, the proposed approach is more of a framework, the use of which can be extended by involving different film thickness formulas and correction factors to consider complicated EHL behaviors such as thermal effects, shear thinning effects, surface roughness, lubricant starvation, and so on.

Approximate theory of armour perforation by ductile hole expansion

The present study suggests a complete analytical model for armour perforation by ductile hole enlargement process. The new approximate model is applicable for entry, tunnelling and exit phases of a rigid nose-pointed projectile with an arbitrary nose-shape. The theory is based on dividing the target into infinitesimal thin layers, in which a cylindrical hole expansion is assumed. The elastoplastic work that is consumed by the target for infinitesimal projectile advancement is based on the specific cavitation energy and leads to reduction of the projectile kinetic energy. Several equivalent formulae for ballistic limit velocity, and a formula for the ballistic limit thickness are found to be independent of projectile nose-shape and nose length. The approximate model is compared with numerical simulations for AA6061-T651 targets that are impacted by two different ogive nose-shape projectiles at several striking velocities. A small nose-shape effect on the ballistic limit velocity is observed in the numerical simulations and is attributed mainly to the target axial effect and the bulge formation at the target rear surface, which are not considered in the approximate model.

Studies on activity and oxide shell thickness of micron-sized Mg-Al alloy powder

The empirical formula of average oxide thickness of atomized micron-sized aluminum - magnesium alloy powder was proposed. At the same time, the influence of particle size and the ratio of magnesium on samples’ activity was studied. The phase composition, morphology, and oxidation process of the alloy powders were studied by x-ray diffraction, scanning electron microscope/energy-dispersive x-ray, respectively. Study on the change of powder activity was achieved by standard gas volumn method. The results show that the oxide thickness of the atomized micron-sized aluminum - magnesium alloy powder is positively correlated with the particle size, and the activity decreases with the increase of the particle size and the magnesium content.

Effects of a typical shear dependent viscosity on analytical elastohydrodynamic lubrication film thickness predictions: A critical issue for the classical approach

Many engineering estimates of the film thickness in the concentrated contacts of real machines have come from extrapolations of measurements of elastohydrodynamic lubrication film thickness performed in glass on steel elastohydrodynamic rigs. Such estimates are likely to have large errors due to shear dependence of viscosity. The classical film thickness formulas employed have not been validated except for some Newtonian reference liquids at room temperature because the real pressure-viscosity response measured in viscometers has been ignored. A blend of polyalpha olefin base oils with mild shear-thinning has been employed in a line contact calculation to assess the effects of shear-dependent viscosity on the power-law exponents of the classical film thickness formula. The exponents on the pressure-viscosity coefficient and on the elastic modulus of the solids are not sensitive to the non-Newtonian effect. The exponents on ambient pressure viscosity and velocity are slightly reduced by shear-thinning. The exponents on pressure and scale are substantially increased by the shear dependence. The usual practice of measuring film thickness in an elastohydrodynamic rig to obtain an effective “[Formula: see text]-value” to use in a classical Newtonian film thickness formula will overstated the film thickness of a liquid which is shear dependent in the elastohydrodynamic lubrication inlet.

FRACTAL MODEL OF FLOW CURRENT IN MICRO ROUGH CAPILLARY TUBES

Based on the fractal geometry science and the model of flow friction resistance when fluid flows through rough microcapillaries, the formula of diffusion layer thickness and the spatial charge density distribution of the pipe were derived. The relationship between the amount of space charge and the structural parameters of rough elements, relative roughness, liquid conductivity, pipeline diameter, and other physical quantities was discussed. It was found that the height of rough elements is directly proportional to the thickness of the diffusion layer, and also positively proportional to the amount of current. The predicted results of the model are in good agreement with existing models and various published experimental data, verifying the accuracy and reliability of the model.

Deep hole connector design and oil film pressure study

Aiming at the problem of insufficient rigidity of the tool system and unbalanced radial force during deep hole machining, this paper designs a deep hole connector using the fluid dynamic pressure lubrication principle. The deep hole connector includes double-bridge strain gauges and tiltable tiles, which can increase the rigidity of the tool system by using the oil film support stiffness and offset the unbalanced radial force of synchronous detection by adjusting the oil film pressure in real time. First, the mathematical model of tiltable tile is established, the oil film thickness formula is derived, and the formula of oil film pressure is derived. Then, based on Fluent software, the fluid simulation of the deep hole connector is carried out. The simulation adopts a single-factor experiment method, and the change law of oil film pressure on tiltable tile is analyzed under different conditions, respectively. The results show that during deep hole machining, the oil film pressure can be adjusted by adjusting the parameters of workpiece speed, cutting fluid viscosity, tile tilt angle, and tile wrap angle, and then achieve the purpose of increasing the rigidity of the tool system and offsetting the unbalanced radial force.

A stable analytical expression for magnetotelluric/radiomagnetotelluric impedances in anisotropic layered Earth models

Previous closed-form solutions of impedances on layered Earth models were only available for the anisotropic conductivity case under the plane wave electromagnetic incidence. Here, we have developed a numerically stable impedance formula for both magnetotelluric and radiomagnetotelluric problems in layered media with arbitrarily anisotropic conductivity and dielect permittivity. Maxwell equations are first transformed into a set of coupled second-order partial differential equations with the horizontal components of electric field as the variables. Then, the recursive formula of surface impedance is obtained by using the general solutions of the second-order partial differential equations and the tangential continuity condition of electromagnetic fields at each layer interface. To avoid the numerical overflow in both the nominator and denominator of the recursive impedance formula due to large layer thickness or high working frequency, an artificial exponential function with positive exponential factor is used to regularize both the nominator and denominator. It leads numerically stable recursive formula for any layer thickness and working frequency. At the end, a four layered magnetotelluric model with anisotropic conductivities is adopted to validate the newly derived analytical formula and another two synthetic layered Earth models are used to study the effects of conductive anisotropy and dielectric anisotropy on radiomagnetotelluric responses.

Numerical and analytical flow models in ecological channels with interaction of vegetation and freshwater

Aquatic vegetation interferes with river hydrodynamics, thus affecting the mass transport and energy transfer in an ecosystem. The flow over submerged vegetation is characterized by a complex velocity profile and multiple turbulence structures, which have been usually simulated using cylinders or strips in previous studies. Because the simplified vegetation configuration may hide or amplify some physical processes found in natural conditions, we investigate the velocity distribution and turbulence structure in foliaged vegetation flows using both analytical and numerical approaches. The main innovations and findings can be summarized as follows: 1) numerical and analytical models adopted in this paper accurately simulate the flow velocity profile in vegetated channel; 2) the Karman constant is found to be unsuitable for complex vegetation morphologies, so we proposed adjusted coefficient; 3) an image processing method is adopted to quantify the vegetation morphology accurately; 4) the existing mixing-layer thickness formula is found to be unsuitable for vegetation with leaves, an improved formula is proposed showing high correlation coefficient (0.9562) between measured and predicted data; 5) to ensure applicability to larger-scale hydrodynamic simulations, an analytical expression of Manning’s coefficient is proposed based on an analytical multi-layer flow velocity model. These research findings can provide theoretical support for the design of vegetated river and ecological restoration.

Thermal characteristics and distribution rule of lubrication film of full ceramic ball bearing under different service condition

PurposeThe study aims to the distribution rule of lubricating oil film of full ceramic ball bearing and improve its performance and life.Design/methodology/approachThe paper established an analysis model based on the fluid–solid conjugate heat transfer theory for full ceramic ball bearings. The distribution of flow, temperature and pressure field of bearings under variable working conditions is analyzed. Meanwhile, the mathematical model of elastohydrodynamic lubrication (EHL) of full ceramic ball bearings is established. The numerical analysis is used to study the influence of variable working conditions on the lubricant film thickness and pressure distribution of bearings. The temperature rise test of full ceramic ball bearing under oil lubrication was carried out to verify the correctness of simulation results.FindingsAs the speed increased, the oil volume fraction in full ceramic ball bearing decreased and the surface pressure of rolling element increased. The temperature rise of full ceramic ball bearings increases with increasing speed and load. The lubricant film thickness of full ceramic ball bearing is positively correlated with speed and negatively correlated with load. The pressure of lubricating film is positively correlated with speed and load. The test shows that the higher inner ring speed and radial load, the higher the steady-state temperature rise of full ceramic ball bearing. The test results are in high agreement with simulation results.Originality/valueBased on the fluid–solid conjugate heat transfer theory and combined with Reynolds equation, lubricating oil film thickness formula, viscosity temperature and viscosity pressure formula. The thermal analysis model and EHL mathematical model of ceramic ball bearings are established. The flow field, temperature field and pressure field distribution of the full ceramic ball bearing are determined. And the thickness and pressure distribution of lubricating oil film in the contact area of full ceramic ball bearing were determined.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-05-2023-0126/

Simulation research on corrosion and thinning characteristics of water wall tubes based on electric field array

During service, the water wall tube will inevitably corrode due to various corrosive gases such as SO2, HCl, H2S, etc. To prevent the occurrence of tube burst accidents caused by thinning and income-pressure resistance of the water wall tube, it is necessary to monitor the wall thickness of the water wall tube row in real-time. This paper proposes an array-based method for monitoring the thickness of the water wall tube row, and the different corrosion characteristics models of the water wall tube row are established by using the finite element analysis software Maxwell. Based on the model, the influence of tube wall thickness and material on measurement accuracy is analyzed by current density distribution and electric field intensity. The error of calculation formula is analyzed by simulating different corrosion conditions of tube wall thinning. The calculation formula of the wall thickness after the corrosion of the water wall tube row and the correction formula of the wall thickness of a single water wall tube with the correction coefficient α of 3 are determined. And put forward to define the ”generalized average thickness” of the water wall corrosion of multiple tubes, and determine the correct formula for calculating the thickness of the water wall tube row with a correction coefficient β of 0.85 to 0.95.

Improving the top coal recovery ratio in longwall top coal caving mining using drawing balance analysis

ABSTRACT The recovery ratio of longwall top coal caving (LTCC) technology is an important measure of its effectiveness. However, the recovery ratio of single-opening sequential caving technology in thick and extra-thick coal seams needs improvement. To address this, an independent cluster-group caving technology is proposed in this study. Four numerical simulation experiments were conducted to compare the recovery ratio and drawing balance of four-opening independent cluster-group caving technology and single-opening sequential caving technology. Results show that the recovery ratio in four-opening independent cluster-group caving technology is approximately 6% higher than in single-opening sequential caving technology when the thickness of the broken gangue layer and the coal seam are the same. Additionally, a judgment formula for the broken immediate roof thickness is provided when the top coal recovery ratio is seriously affected. The independent cluster-group caving technology demonstrates stronger stability and better adaptability under different conditions, as its caving sequence can prevent larger thickness changes and gangue disturbances during the drawing process. Overall, this study highlights the potential of independent cluster-group caving technology to improve the recovery ratio of LTCC technology in thick and extra-thick coal seams.

Thermal Elastohydrodynamic Analysis of a Worm Gear

This study explores the elastohydrodynamic lubrication (EHL) between the contacting tooth flanks of a worm gear with nonconjugate meshing action. The contact is characterized by a slender-like elliptical shape and high sliding. The geometry and contact conditions for the considered worm gear were obtained using tooth contact analysis. Based on that, the complete area of the worm gear contact was analyzed using a validated numerical EHL model considering non-Newtonian, thermal, and transient effects. The geometrical and kinematic design factors that influence EHL film formation in worm gears were identified and discussed. The results show the specific characteristics of worm gear EHL contacts, such as the very slender contact in the tooth root flank area, which diminishes the effect of the entrainment speed on film thickness. EHL film formation could be supported by increasing conformity between the flanks to make the contact less slender. By comparing the film thickness results against analytically obtained ones, relatively large differences were observed except for one formula for minimum film thickness.