프로파일링한 테이퍼 로울러의 탄성유체윤활 해석

The rollers and/or races in cylindrical and tapered roller bearings should be profiled to relieve high edge stress concentrations caused by their finite lengths and misalignment. In this study, a numerical analysis was performed to investigate the elastohydrodynamic lubrication (EHL) of a Lundberg profile-type cylindrical roller. A finite difference method with fully nonuniform grids and the Newton-Raphson method were used to present detailed EHL pressure distributions and film shapes, as well as the variations in the minimum and central film thicknesses with the profile modification coefficient. In the Lundberg profile, the maximum pressure and minimum film thickness always occurred near the edges. Proper modification of the Lundberg profile considerably increased the minimum film thickness.

A numerical solution to the problem of thermal elastotydrodynamic lubrication of line contacts was obtained by using a finite-difference formulation. The solution procedure consists of simultaneous solution of the thermal Reynolds equation, the elasticity equation, and the energy equation subject to appropriate boundary conditions. Pressure distribution, film shape, and temperature distribution were obtained for fully flooded conjunctions, a paraffinic lubricant, and various dimensionless speed parameters while the dimensionless load and materials parameters were held constant. Reduction in the minimum film thickness due to thermal effects (as a ratio of thermal to isothermal minimum film thickness) is given by a simple formula as a function of the thermal loading parameter, Q: Plots of pressure distribution, films shape, temperature distribution, and flow are shown for some representative cases.

Comparison of Exact and Sommerfeld Solution for the Pressure of a Journal Bearing

The 2D VOF (volume of fluid) model is introduced in this paper to simulate rapid filling process in pressurized water conveyance pipeline with trapped air mass. The movement of gas-water interface, pressure distribution, maximum pressure and position of its occurrence during filling process are modeled and analyzed. According to results, sudden pressure increase caused by water striking on pipe wall could happen, and is sensitively influenced by geometry parameters of pipeline. When occurrence time of water striking on pipe wall is prior or close to that of maximum air pressure, maximum pressure of is obviously greater than maximum air pressure numerically. With increase of diameter of pipeline, maximum pressure of increases gradually, and phenomenon becomes clearer when inlet pressure is higher. Obviously, above-drawn conclusions are essentially different from those based on one- dimensional model, such as the maximum air pressure is maximum pressure of system and the maximum pressure changes with diameter of pipeline but slightly, which are caused by inherent limitations of simplification and basic assumptions of one-dimensional model.

The effect of the significant variables on solutions to the problem of isothermal lubrication of elastic rollers is examined. It is found that for realistic materials, speeds, and loads, the outlet pressure peak predicted by Grubin (4) is always present. The magnitude of this pressure peak may exceed the maximum Hertzian pressure. It varies only slightly with load, but markedly with speed and materials. The influence of these variables on the shape of the outlet pressure curve explains the difference between Petrusevich's results (5) and those presented earlier by the authors. The stress concentrations produced near the surface by the outlet pressure peak would have a significant effect on the fatigue life of rolling elements. It is found that the centre-line film thickness varies hardly at all with load, significantly with material properties and considerably with the product of speed and inlet viscosity. Pressure distributions and film shapes are presented for five cases to illustrate the influence of load, speed, and materials. In addition, maximum principal stress differences are shown for two solutions.

A new very high-order finite-difference method for linear stability analysis and bi-orthogonal decomposition of hypersonic boundary layer flow

In this paper a full numerical solution for the thermoelastohydrodynamic problem in elliptical contacts is presented, and the method of computation is also described. The film pressure, thickness, and film shape, the three dimensional temperature distribution within both the film and the bounding solids, as well as the coefficients of the sliding and rolling frictions have all been determined for different rolling velocities and slide-roll ratios. The results obtained indicate the film temperature increases as the rolling velocity or slide-roll ratio increases. The effects of thermal action on the pressure distribution, the film shape and thickness, and the friction factors are also given. The problem studied in this paper is steady-state, the lubricant is assumed to be Newtonian.

Analysis of the thermal elastohydrodynamic lubrication of a finite line contact

Numerical and experimental analyses were carried out to investigate the static characteristics of liquid annular seals with helical grooves in a seal stator. In the numerical analysis, the momentum equations with turbulent coefficients and the continuity equation, which were averaged across the film thickness, were numerically solved to obtain the leakage flow rate and the pressure distributions in the seal clearance. To accurately define the location of the step between the groove and the land regions in the calculation domain, these governing equations were expressed using an oblique coordinate system in which the directions of coordinate axes coincided with the circumferential direction and the direction along the helical grooves. The numerical analysis included the effects of both fluid inertia and energy loss due to expansion during the passage of fluid from the land region to the helical groove region and that due to contraction from the groove region to the land region. In the experimental analysis, the leakage flow rate and the fluid-film pressure distributions in the seal clearance were measured for the helically grooved seals with different helix angles of the helical groove. The numerical results of leakage flow rate and pressure distributions agree reasonably with the experimental results, which demonstrates the validity of the numerical analysis. The leakage flow rate of the helically grooved seals was influenced by two factors: fluid energy loss during passage through the step between the groove and the land, and the pumping effect by which the spinning motion of the rotor pushes the flow back upstream along the helical grooves. Under a low range of rotor spinning velocity, the leakage flow rate decreased with helix angle because the effect of fluid energy loss in the steps was significant. By contrast, under a high range of spinning velocity, the quantitative difference in the leakage flow rate due to the helix angle decreased compared to that under a low range because the reduction in the leakage flow rate due to the pumping effect was pronounced for a larger helix angle. The effects of helix angle and rotor spinning velocity on the leakage flow rate are explained qualitatively using a simplified model.

Finite-difference (FD) schemes have been used widely for solving wave equations in seismic exploration. However, the conventional FD schemes hardly guarantee high accuracy at both small and large wavenumbers. In this paper, we propose an optimal time-space domain FD scheme for acoustic vertical transversely isotropic (VTI) wave modeling. The optimal FD coefficients for the second-order spatial derivatives are derived by approaching the time-space domain dispersion relation of acoustic VTI wave equations with the combination of the Taylor-series expansion and the sampling interpolation. We perform numerical dispersion analyses and acoustic VTI modeling using the optimal time-space domain FD scheme. The numerical dispersion analyses show that the optimal FD scheme has smaller dispersion than the conventional FD scheme at large wavenumbers, and also preserves high accuracy at small wavenumbers. The acoustic VTI modeling examples also demonstrate that the optimal time-space domain FD scheme has greater accuracy compared with the conventional time-space domain FD scheme for the same modeling parameters.

Paper VII(iv) A full E.H.L. solution for line contacts under slidding-rolling condition with a non-Newtonian rheological model

Determining lubricant film thickness between contacting bodies under elastohydrodynamic (EHD) conditions is often simulated by using a ball/cylinder and transparent disc apparatus together with an interferometry technique. The simulated contact will have a point or elliptic shape and the light used can be white or monochromatic. The interference pattern is normally photographed with a regular camera or a video camera and the pictures are then evaluated by the naked eye of the observer. In most cases, only central or minimum thicknesses are evaluated. In this paper an image processing method for the analysis of film thickness is presented. This method makes it possible to extract considerably more information about film thickness fluctuations than is achievable by the naked eye. The method primarily matches hue (but also saturation and intensity values) from digitized colour interferometric images of the unknown film shapes with calibration values obtained with known geometric shapes. The method is shown to work well in the range from 95 up to 700 nm with white light and makes the results unbiased by the observer. Furthermore, absolute film thickness can be evaluated without prior knowledge about the fringe order in the interferogram.

On the impingement heat transfer of an oblique free surface plane jet

Numerical analysis is performed to study the transient behavior of EHL finite line contact of a cylindrical roller and flat plane under load impulse. In the present work, effect of pressure on the density and viscosity of lubricant is considered. Finite difference method is used to discretize the governing equations. Multilevel Multi-integration method is used to calculate the elastic deformation. Moreover, Multigrid method is implemented to accelerate the convergence process. Uniqueness of this finite line contact analysis is that it provides an ability to determine the transient behavior of lubricated contact even at the edges of roller. Results show that the load impulse causes squeezing and separation movement within the contact that develops film dimple and pressure ripples at the inlet region, which propagate towards the exit region due to the entrainment motion. It is noticed that the time taken by oil film [Formula: see text] to travel the Hertzian contact width and the time period [Formula: see text] of load impulse decides the behavior of lubricated contacts. Firstly, under a relatively heavy load when the contact width is large enough so that [Formula: see text], then a significant rise in central film thickness (CFT), central minimum film thickness (CMFT) and minimum film thickness (MFT) occurs after the execution of load impulse. Further, under the light load generating a relatively small contact width such that [Formula: see text], then comparatively a small rise in CFT occurs right during the load impulse. Lastly, for a given load if the time period of impulse [Formula: see text] is large enough satisfying the condition [Formula: see text], then a considerable reduction in CFT, CMFT and MFT takes place during the application of load impulse. Moreover, as compare to other cases, for [Formula: see text] the steady state condition is reestablished after a relatively more number of time cycles. It is observed that the maximum pressure and MFT occurs at the contact edges of roller which can be controlled by a proper choice of the radius of end profile [Formula: see text].

In soldier pile retaining wall systems, the surface facing, commonly a shotcrete layer, is typically designed as a one-way slab subjected to a uniform lateral earth pressure. However, this conventional assumption neglects the soil arching phenomenon, which can substantially modify the actual pressure distribution and lead to conservative and uneconomical designs. Previous studies have primarily relied on simplified analytical formulations or limited physical models, and the combined influence of soil micro-mechanical properties and geometric configuration has not been comprehensively evaluated. To address this gap, this study numerically investigates the influence of soil arching on the lateral earth pressure distribution behind the wall facing using two numerical approaches: the finite difference method (FDM) and a coupled discrete–continuum approach (Combined DEM–FDM). Analyses were performed using the FLAC and PFC software packages, considering variations in inter-particle friction coefficient, particle rolling resistance, pile spacing, shotcrete thickness, and applied stress level. The results reveal that soil arching induces a non-uniform pressure distribution between adjacent piles, where the lateral earth pressure decreases linearly from the pile location to about one-fourth of the pile spacing and then remains nearly constant toward the midspan. Increasing the pile spacing, rolling resistance, and inter-particle friction significantly intensifies the arching effect and reduces the maximum bending moment in the wall facing, while increasing the shotcrete thickness leads to a more uniform pressure distribution and a reduced arching effect. The influence of stress level on the pressure distribution was found to be negligible. The outcomes of both FDM and DEM–FDM analyses show excellent agreement, confirming the reliability of the proposed numerical approach. Overall, considering the soil arching effect substantially reduces the predicted bending moment compared to the conventional uniform pressure assumption, suggesting a potential for more economical retaining wall designs.