Film Thickness Equation Research Articles

ANALYSIS OF THE MIXED ELASTOHYDRODYNAMIC LUBRICATION CHARACTERISTICS OF DOUBLE CIRCULAR ARC GEARS CONSIDERING MICRO-MORPHOLOGY

Different machining methods result in diverse morphologies on the surface of gears. Under mixed lubrication, the friction and contact behavior of the real morphology interface becomes more complex. This study aims to analyze the influence of different process tooth surface micro-morphologies on the lubrication performance of the meshing area of double circular arc gears. Focusing on elastohydrodynamic lubrication (EHL) characteristics of the double circular arc gears as the research object, the study involved measuring the three-dimensional morphology of the meshing position of the double circular arc gears. Non-Gaussian simulation technology was then used to characterize the micromorphology of the tooth surface resulting from different processes (i.e. hobbing process and skiving process). The tooth surface suction speed was determined based on the meshing characteristics of double circular arc gears. Based on the theory of point contact EHL, Reynolds equation and film thickness equation considering micromorphology were derived, and numerical solutions were obtained using the multi-grid method. A point contact EHL model for double circular arc gears was established considering the micromorphology of tooth surfaces in different processes. Results show that, the oil film pressure is positively correlated with rotational speed and torque. The oil film thickness is positively correlated with rotational speed, and negatively correlated with input torque. The negative of micro-morphology on the tooth surface on the lubrication performance could lead to an increase in pressure fluctuations and the absence of the second pressure peak. The uneven distribution of oil film and the lager roughness value could result in obvious fluctuations. The lubrication performance of the contact area in the gear hobbing process is superior to that in the gear skiving process. This study lays the foundation for further exploring the coupling characteristics between the double circular arc gear transmission system and elastic fluid dynamic lubrication. Keywords: Double circular arc gears, Point contact, Mixed EHL, Lubrication characteristics, Micro- morphology.

Research on the lubrication performance of circular tilting pad thrust bearings for large wind turbines

AbstractIn view of the large temperature rise and impact load of thrust bearings in the main shaft system of large wind turbines, this article takes the circular tilting pad thrust bearings in large wind turbines as the research object, and analyses the basic theory of bearing lubrication. The lubrication performance calculation model established for this bearing includes the Reynolds equation, energy equation, film thickness equation, and elastic deformation equation. Theoretically analysing and calculating the lubrication performance of the circular tilting pad thrust bearing, the key performance parameters have identified such as minimum film thickness (hmin), temperature rise (ΔT), power consumption (W), and flow rate (Q). The calculation results show that the eccentricity ratio has a significant impact on the lubrication performance of the circular tilting pad thrust bearing. When both radial and circumferential eccentricity ratios are around 0.5, the bearing exhibits a high temperature rise, leading to a potential risk of bearing burnout. The results also show that at a radial eccentricity ratio of approximately 0.54, the minimum film thickness reaches its maximum value of 10.34 μm. Similarly, at a circumferential eccentricity ratio of about 0.60, the minimum film thickness reaches its peak value of 21.89 μm. This indicates that the eccentricity ratio plays a crucial role in the lubrication performance. In addition, the lubrication performance of the bearing under varying loads has been calculated at a speed of 9.5 r/min. The results demonstrated that the applied load significantly impacts the thrust bearing's performance. The findings elucidate the critical role of considering the eccentricity ratio and operational external load during the bearing design process. This study validates the potential of replacing rolling bearings with sliding bearings in wind turbine main shafts. It also provides a theoretical reference for the future design of sliding bearings.

Effect of surface roughness on lubrication performance of water-lubricated bearing for energy recovery turbocharger

In this study, the lubrication performance of the water-lubricated bearing of the energy recovery turbocharger was studied considering the surface roughness. By simulating the rough surface of the bearing with the Weierstrass-Mandelbrot function and combining the water film thickness equation, Reynolds average equation, Greenwood-Tripp contact model and motion equation, the theoretical model of water-lubricated bearing is established and its solution is developed. The variational rules for the hydrodynamic pressure and force, asperity contact pressure and force, and other performance parameters of the water lubricated bearings during start-up and stable operation were obtained by solving this model, and the effect of different surface roughness on the start-up performance and steady operation lubrication performance is studied. The results show that the hydrodynamic force increases rapidly and the asperity contact force sharp decreases during the early start-up stage, and the smaller the surface roughness, the faster the hydrodynamic increase and asperity contact force decrease. The thickness distribution and pressure distribution of water film with different surface roughness have slight differences in stable operation. Therefore, the surface roughness has an important effect on the lubrication performance of the water lubricated bearing in the start-up stage, but has little effect on the stable operation.

Numerical simulation of wall shear stress and boundary layer flow from jetting cavitation bubble on unheated and heated surfaces

The physics of wall shear stress and boundary layer flow from jetting cavitation bubbles on unheated and heated surfaces was investigated numerically using a homogeneous mixture model based on a fully compressible Navier–Stokes solver. A spatial–temporal shear stress map and velocity field on unheated surfaces under several standoffs were considered first. Complex boundary layer flow, including separation vortex caused by an adverse pressure gradient and the generation of a thermal boundary layer because of skin friction with the shear flow, was discussed in detail. The tendency of different maximum shear stress for each standoff section was discussed with liquid film thickness and jet velocity. Also, we suggested maximum shear stress correlation equation for minimum film thickness and wall impact pressure as dimensionless form. As an expansion of previous studies, we examined bubble collapse–induced wall shear stress on a heated surface under various surface temperatures. The peak shear stress decreased with the lower Prandtl number flow. In the collapse phase, surface cooling by downward microjet and heat transfer with ring vortex were also captured. Consequently, we suggested correlation equations for primary and secondary peak shear stresses as function of Prandtl number and confirmed that the boundary layer flow including heat transfer can be well simulated.

Thermohydrodynamic Lubrication Characteristics of Piston Rings in Diesel Engine Considering Transient Heat Transfer under the Parameterized Surface Texture of Cylinder Liners

The cylinder liner and piston ring form the most crucial friction pair in the diesel engine, contributing 35–40% of its overall friction losses. Recent research indicates that transient heat transfer significantly affects piston ring lubrication. However, the impact of such a transfer on varying surface textures and lubrication traits remains unclear. This paper takes the piston ring–cylinder liner of a certain diesel engine as the research object, which is based on a two-dimensional averaged Reynolds function and Greenwood–Tripp micro convex body contact model; establishes a numerical calculation model of the transient heat fluid lubrication characteristics of a vertical piston ring–cylinder liner assembly by combining the oil film thickness equation, energy equation, lubricating oil viscosity–temperature, and viscosity pressure characteristics; avoids large errors associated with assuming different temperature values for lubricants; and also uses the cylinder liner surface texturing technique to examine the effects of surface texturing on lubrication properties in the presence of transient thermal fluids. The findings indicate that employing transient thermal fluid for determining the mean value of the oil film temperature in isothermal lubrication calculations yields comparable values for minimum oil film thickness and frictional power consumption, while the friction power consumption calculated by the transient thermal fluid is slightly lower. The depth of the recesses on the surface of the cylinder liner should be minimized, while the radius of the texture should be maximized, taking into consideration the current circumstances. Compared with a cylindrical texture, a spherical texture achieves lower friction with good lubrication indexes.

Static performance analysis of gas foil thrust bearings under inclined thrust disc considering the slip flow effect

As one of the important components in air compressors for fuel cell vehicles, the static performance of the gas foil thrust bearings greatly affects the operating stability of the rotor system. In actual operation, thrust disc tilt and the slip flow effect often occur, which will change the characteristics of bearings. Therefore, this paper focuses on the static performance of gas foil thrust bearings under tilting conditions with account of the slip flow effect. Firstly, the gas film thickness equation is established when the thrust disc is inclined, and the Reynolds equation is modified by the boundary slip conditions. Secondly, the load capacity and friction torque of bearings are solved by the finite difference method and successive over-relaxation method. Finally, the sensitivity of rigid and elastic bearings to tilt angles is analyzed by comparing the static characteristics under tilting conditions. The results show that the load capacity will be overestimated without considering the slip flow effect, and the tilting of the thrust disc increases both the load capacity and friction torque. Furthermore, compared with rigid bearings, elastic foil bearings have better adaptability to tilting conditions, which is conducive to the stable operation of the rotor system.

Multigrid method for the solution of thermal elastohydrodynamic lubrication point contact problem with surface asperities

The paper presents, the numerical investigation of point contact thermal elasto-hydrodynamic lubrication (EHL) with surface asperities are analyzed. The effect of temperature and surface roughness on fluid film thickness is studied in detail. The governing equations comprises Reynolds, film thickness, load balance and energy equations with appropriate boundary conditions. The second order finite difference approximation is used to discretize the governing equations and the resultant nonlinear system of algebraic equations is solved using Multigrid V-cycle with full approximation scheme (FAS) technique. Multi level multi integration (MLMI) technique is employed to solve the film thickness equation. The obtained results are illustrated in the form of graphs and tables which are comparable with earlier findings. The film thickness profiles shows dimple near to the outlet region due to temperature-viscosity wedge mechanism. Isothermal minimum film thickness is higher than the thermal minimum film thickness. Minimum film thickness is much smaller due to slide to roll ratio is positive ascompared to negative, whereas the behavior of central film thickness is contrast as that of minimum film thickness.

Surface effects on elastohydrodynamic lubrication contact of piezoelectric materials with non-Newtonian fluid

Using surface piezoelectricity theory, this article investigates the elastohydrodynamic lubrication (EHL) line contact of a transversely isotropic piezoelectric half-plane with consideration of the surface effect under a rigid cylindrical punch. The surface effect in the surface piezoelectricity theory is mainly described by the following parameters: surface piezoelectric constant, surface dielectric constant, surface elastic constant, and residual surface stress. The punch is treated as an electrical insulator. The lubricant, whose viscosity and density are dependent on fluid pressure, is chosen as a non-Newtonian fluid. Firstly, by analyzing the frictionless dry contact of piezoelectric materials vith the surface effect, the dry contact pressure distribution and the EHL film thickness equation are obtained. Then, an iterative method is proposed to obtain the fluid pressure and film thickness in the lubricant contact region by calculating the fluid–solid coupled nonlinear equations. The effects of the surface dielectric constant, surface piezoelectric constant, surface elastic constant, residual surface stress, punch radius, entraining velocity, and slide/roll ratio on the film thickness and fluid pressure are examined. Our analysis indicates that the surface effect has an essential effect on the EHL contact behavior of piezoelectric materials at micro-/nano-scales.

Transient tribo-dynamic performance of journal bearings considering wear behavior during start-up

The transient tribo-dynamics and wear model are coupled to study the mixed lubrication-wear behavior during start-up. The coupled numerical model involves the film thickness equation with wear depth and a time-varying wear coefficient to account for the impact of transient mixed lubrication behavior on wear. In this study, the evolution of wear and mixed lubrication performance distribution over time is predicted, and the impact of acceleration mode, acceleration time, external load, lubricant viscosity, and start-up time on the numerical predictions is evaluated. The findings demonstrate that wear behavior, particularly in the analysis of the effects of acceleration mode and acceleration time, has a significant impact on the evaluation of the bearing-rotor system's start-up performance and even changes the determination of optimal parameters. Furthermore, the parametric study demonstrates that wear and mixed lubrication performance are sensitive to the external load and lubricant viscosity. Finally, studies on the effect of start-up times show that proper wear geometry promotes hydrodynamic effects, but severely worn bearing surfaces have a negative effect on start-up.

Numerical Study on the Bearing Capacity of Lubricant Film in Journal Bearing with Micro-textured Surface

For studying the hydrodynamic lubrication performance of micro-textured radial journal bearings, a numerical model of hydrodynamic lubrication for journal bearings was established first. Solve the established numerical model using FDM, and the lubricant film pressure distribution and static characteristics of bearings were obtained. Considering the processing cost and feasibility of the processing technology, the cylindrical texture arranged in the radial of the bearing shell surface is applied, the lubricant film thickness equation considering the micro-texture is introduced into the Reynolds equation. According to the height and distribution density of microstructure, the bearing capacity parameters were obtained. The load-carrying capacity of micro structure journal bearing is significantly higher than that of plain bearing. In this paper, a practical model with cylindrical micro-textured surface is given for journal bearing applications with high capacity demand.

Newton-GMRES-Method for the Scritinization of electric double layer and surface roughness on EHL line contact problem

The electric double layer phenomenon exists on the solid interface under the water-liquid condition. The water molecules are ionized and adhered in the interface forming the sturn layer is a diffused layer in which molecules can move with the movement of bulk of molecules. Because of these two characteristics, the boundary layer of water molecules is called the electric double layer. The aim of present study is to explore the impact of two fraction surfaces of electric double layer (EDL) on a thin water lubricating film on an elastohydrodynamic lubrication (EHL) line contact problem with a sinusoidal surface roughness. The governing modified Reynolds and film thickness equations are based on mathematical model of electro-viscosity of asymmetrical electrical double layer is analyzed numerically. The viscosity-pressure relation of water and theoretical evaluation pertaining to the effect of electric double layer on film-thickness and pressure distribution of EHL with water film of line contact problem is discussed in detail. The effect of zeta potential on film thickness and pressure is determined using Newton’s-GMRES method with Daubechies D6 wavelet as a pre-conditioner. The results predict that, EDL has less impact on pressure distribution and significant impact on film thickness. The obtained results are compared with results of Dowson and Higginson which are comparable.

Numerical Solution for Thermal Elastohydrodynamic Lubrication of Line Contact with Couple Stress Fluid as Lubricant

In this paper, the detail analysis of the influence of thermal and non-Newtonian aspects of lubricant (couple stress fluid) on EHL line contact as a function of slide-roll ratio is presented. The novel low complexity FAS(Full approximation scheme), of Multigrid scheme, with Jacobi dipole and Gauss Seidel relaxationis used for the solution of coupled equations viz.modified Reynolds equation, film thickness equation and energy equation satisfying appropriate boundary conditions. The analysis reveals the combined influence of non-Newtonian, thermal and slide-roll ratio (of bearing movingwith different speeds) on pressure, film thickness and pressure spike covering wide range of physical parameters of interest. Results show that pressure spike is strongly influenced by thermal, slide-roll ratio and non-Newtonian character of lubricant with negligible effect on overall pressure distribution. Also, minimum film thickness is slightly altered and it increases with increase in couple stress parameter. These findings confirm the importance of non-Newtonian and thermal effects in the study of EHL.

Impact of partial surface waviness on the tribological performance of hydrodynamic journal bearing

AbstractIn this paper, the static performance analysis of journal bearing having full and partial surface waviness has been presented. The surface waviness is to be considered in the full, first half, second half, and pressure‐increasing and decreasing regions of the bearing for analysis. The effect of surface waviness is considered by modifying the lubricant flow governing Reynolds equation with the film thickness equation and it is solved with the finite element method to get performance parameters like bearing load capacity, friction coefficient, and so forth operating under eccentricity ratios range of 0.2–0.8. The waviness geometrical parameters like waviness numbers and amplitudes are also considered in circumferential, axial, and both directions in the selected regions. The maximum performance has been found for waviness in the full and pressure‐increasing region in the circumferential direction at a high eccentricity ratio.

Effect of herringbone groove structure parameters on the static performance of gas foil herringbone groove thrust bearings

The application of foil bearings technology into high speed and heavy load turbine machinery with high axial force is limited because of the insufficient load capacity of gas foil thrust bearings. This paper presents a new type gas foil thrust bearing, engraving the herringbone groove on the top foil surface of gas thrust foil bearing, relying on the pumping effect of herringbone grooves, so that the bearing load capacity of gas foil thrust bearings can be further improved by using the secondary pressure boosting effect of herringbone grooves on the basis of taper dynamic pressure effect. The physical models of non-groove gas foil thrust bearing and gas foil herringbone groove thrust bearings are established. The Reynolds equation, gas film thickness equation and foil deformation equation are coupling solved by finite difference method to obtain gas film thickness distribution and gas film pressure distribution for non-groove and herringbone grooves gas foil thrust bearing. The effects of the number of grooves, groove depth, groove width ratio, groove angle of the herringbone groove and the Taper inlet height on the friction torque, bearing load capacity and ultimate load capacity of the herringbone grooves gas foil thrust bearing are researched. Furthermore, when compared to the traditional non-groove gas foil thrust bearing, the optimal herringbone groove structure parameters are obtained, and a feasible method for optimizing the performance of gas foil thrust bearings is proposed.

The Mechanism of Flow Patterns and Rivulet Instability in Gravity-Driven Film Flow on a Porous Wall with Uniform Heating

Properties of porous mediums have significant impacts on the spreading pattern of falling-film along a vertical heated wall. In this paper, we investigate the combined effect of porosity and uniform heating on the flow instability of a falling liquid film. Based on the film thickness equation derived by the long wave theory, linear stability analysis and numerical simulations are given to verify the influences of various dimensionless parameters, and the physical mechanism for the flow instability is explained. With the uniform heating, it is shown that the increasing Marangoni number and Biot number both enhance the rivulet instability because the Marangoni force becomes larger with bigger values of the two numbers. For porous properties, the existence of Darcy number causes the contact line to move faster and results in a destabilizing effect, while a bigger Beavers–Joseph coefficient causes the contact line to move slower and plays a stabilizing role. Increment of porous thickness and the thermal conductivity ratio slightly enhances or impedes the flow instability, respectively, and neither of the two parameters influences the moving speed of the contact lines.

Elastohydrodynamic ultrathin film formation at the start-up of motion under the combined effect of surface force and hydrodynamic action

Purpose The purpose of this study is to investigate the behavior of ultra-thin film formation at the start-up of motion for different acceleration rates and final entrainment speed, including the effect of intermolecular forces; solvation and Van der Waals’ in addition to hydrodynamic action for the elastohydrodynamic lubrication of point contact problems. Design/methodology/approach The equation of motion of the ball is considered to account for the applied force on the ball during the start-up of motion. The Newton–Raphson with Gauss–Seidel iterative method is used to solve the Reynolds, film thickness and load balance equations simultaneously. In addition to hydrodynamic effects, solvation and Van der Waals’ forces are taken into account in the calculation of bearing capacity. Findings The simulation results showed that the effects of acceleration rate are important for ultra-thin film formation at the start-up of motion. Increasing the rate of acceleration results in a higher value of central film thickness during the start-up of motion than the corresponding steady-state film thickness value reached at the final entrainment speed. The effects of intermolecular forces are important to prevent metal-to-metal contact during the inactive period of motion, where a constant value of film thickness is achieved regardless of the value of the acceleration rate or final entrainment speed. Originality/value The behavior of ultra-thin film formation at start-up of motion, including the effect of intermolecular forces; solvation and Van-der-Waals’ along with hydrodynamic action, are evaluated after different acceleration rates and final entrainment speeds.

Transient Elastohydrodynamic Lubrication of Rough Contact Surface for Intermittent Motion

The current study aims to study the characteristics of transient elastohydrodynamic lubrication of smooth and rough surface contacts subjected to intermittent motion for different inactive periods of motion and deceleration/acceleration periods to fulfill an identified need for such conjunction. In this case, the non-steady Reynolds’ equation, the film thickness equation with elastic deformation and taking into account the influence of surface roughness, and the load balance equation are simultaneously solved using the Newton-Raphson with Gauss-Seidel iterations method to determine the film profile and pressure distribution at various time steps. Surface contact of sinusoidal waves is presented with different amplitudes and wavelengths. The results indicated that surface waviness causes random oscillations in pressure and film profiles at different time steps. The greater the amplitude of the waviness, the more pressure and film profile variations occur. The magnitude of the pressure and film profile fluctuations becomes little noticeable as the wavelength of a wavy surface rises. The findings of this investigation also revealed that increasing the inactive duration for wavy surfaces results in zero minimum film thickness and surface contact. Squeezing action is ineffective in conveying loading capacity in this circumstance. The central and maximum pressure heights increase during the stop time interval as stop time increases. The centre film thickness increases at the end of the deceleration phase when the deceleration/acceleration period is reduced, but the minimum film thickness is unaffected. In fact, the minimum film thickness tends to be zero at the end of the deceleration phase, regardless of the deceleration/acceleration period. The central and maximum pressure increase during the stop time interval with the decrease of the deceleration/acceleration period. The difference between the results for smooth and wavy surface contacts is the appearance of fluctuations in film and pressure profiles, as well as the reduction of the film thickness and increase in pressure for the wavy surface when compared to contact with a smooth surface.

Dynamic performance and stability characteristics of a multi pad externally adjustable fluid film bearing

ABSTRACT Due to the recent advances in the development of smart rotating machineries, there is a high demand for automated support bearings with efficient integrated control systems. Existing research studies have indicated that high-end performance can be attained from automated bearings through effective control and modification of the bearing performance parameters. In this study, an innovative journal bearing geometry with multi-control operations is presented. The four controllable bearing pads enclosed in the bearing casing have a novel feature to translate radially and undergo controlled tilt motions. The multi-control bearing system with radial and tilt pad motions will significantly influence the stability responses of the rotorsystem, which is theoretically analysed in this study. To predict the variation in film thickness for varied pad adjustments, a modified film thickness equation is incorporated in the linearised perturbed model for dynamic analysis. A notable variation in dynamic coefficients and stability parameters are observed for negative radial adjustment and tilt angles. Results indicate that negatively adjusted radial and pad tilt motion can generate improved stability margins at higher eccentricities. Data generated on stability margins at specific pad adjustments will be helpful while developing the control system for the actuation mechanism in the experimental setup.

Research on static characteristics of elastic foil gas thrust bearing applied to aeronautical ACM

In air conditioning system for aircraft, air cycle machine (ACM) is the flimsy core component, which is impacted observably by the performance and reliability of elastic foil air-dynamic pressure bearing. It's necessary to have research on static characteristics of elastic foil air-dynamic pressure bearing. Based on finite element analysis (FEA) theory, it’s clearly obtained that discretized fluid lubrication Reynolds equation of foil dynamic pressure bearing by the weighted residual method. Coupled with the elastic deformation of foil calculated by beam element model, foil gas film thickness equation is used to work out static characteristics of elastic foil air-dynamic pressure bearing by iterative calculation. And then, it’s known how the basic parameters of the bearing impact its static characteristics. The result of the method in this paper, is verified that it’s correct by the experiment data in other relevant papers, and it’s appropriate to be used as guidance and reference for the further application of elastic foil bearing in ACM.

Optimization lubrication performance of journal bearings with microtexture

PurposeResearchers have not reached an agreement on which biomimetic shape has the best lubrication performance. This paper aims to study the influence of microtexture size, shape and direction on bearing capacity, end leakage, friction coefficient and wear of oil film.Design/methodology/approachDifferent oil film thickness equations considering the microtexture of bearing surface are gained. The two-dimensional finite difference equation and the calculation equation of wear are established.FindingsThe theoretical research shows that the wear value and the wear ratio when long side is perpendicular to the axial direction of the bearing are generally lower than when the long axis is parallel to the axial direction of bearing. The theoretical and experimental results show that the appropriate microtexture shape, such as circular dimple, crescent-shaped dimple, triangular dimple and fish-shaped dimple can improve effectively the lubrication performance of journal bearing and reduce the friction coefficient.Originality/valueThe research has great significance to reduce friction and improve the wear resistance of equipment.