Elastohydrodynamic Lubrication Theory Research Articles

Design analysis of Pericyclic Mechanical Transmission system

The Pericyclic Mechanical Transmission (PMT) system is a high reduction ratio, high tooth contact ratio, and nutating/rotating gear mechanism which incorporates meshing conjugate face-gear pairs. The PMT kinematics, gear tooth load capacity, bearing load capacity, and mesh efficiency are investigated in this paper. The gear train kinematics and the reduction ratio formulas are identified initially. The tooth load capacities of the meshing conjugate face-gear pairs are calculated analytically as a function of gear tooth loads and dimensions. The dynamics of the nutating gear and the overturning moments produced by nutation are formulated. The effect of gear mesh loads and overturning moment on the bearing load capacity is investigated based on the Hertzian contact stress of the most heavily loaded rolling element. PMT mesh efficiency is first estimated based on Elastohydrodynamic Lubrication (EHL) theory. Then, an analytical formula is developed to approximate the mesh efficiency without lengthy EHL computations. Finally, 760HP level helicopter transmission design spaces are investigated at different reduction ratios. The PMT system shows substantial gear weight improvement without sacrificing efficiency.

Analysis of Lubricating Performance for Involute Gear Based on Dynamic Loading Theory

An integrated model for gear pair that combines the dynamic load with the mixed elastohydrodynamic lubrication (EHL) theory is proposed in this paper covering the film squeeze effect as well as the friction force generated from the rough surfaces. Comparisons between the two models of load which are, respectively, based on minimum elastic potential energy (MEPE) criterion and dynamic motion equations built up in this paper are discussed. The results show that at low speed the loads calculated by the two models are similar. However, with increasing speed, the load exhibits dynamic characteristics gradually and reaches the highest value at resonant speed. Besides, the effects of the helix angle and the lubricant viscosity are also analyzed. Increasing the ambient viscosity could intensify the film stiffness and viscous damping. Gear with larger helix angle could weaken the impact phenomenon at the shift points where one tooth-pair disengages. Moreover, it is symmetric with regard to the pressure and film thickness across the face width for spur gear. Differently, the pressure for helical gear has a higher value at the dedendum of pinion where the film becomes thinner. In addition, speeding up the pinion would generally result in higher dynamic load and film pressure but thicker film thickness.

The Multi-Objective Optimization for Cycloidal Gear Drive Based on the Elastohydrodynamic Lubrication Theory

For improving the designed quality of the cycloidal gear planetary drive, the paper derives a calculation formula of the minimum film thickness, which is between cycloidal gear teeth, based on elastohydrodynamic lubrication theory and gear geometry. A mathematical model for constrained multi-objective optimization is established and the model satisfies three constrains:maximize minimum film thickness between gear teeth( minimize the reciprocal ), minimize average value of m points’s absolute error value on active section that is between the tooth curves of positive shift optimal combination and tooth curves of rotated angle’s modification, minimize the total volume of gear drive. The paper abandons traditional designed method of the multi-objective optimization , improves two-objective particle swarm optimization and offers a new designed model for constrained three-objective optimization. The example is analyzed and the optimization program is complied using Matlab. The optimization’s process and result shows that the method of improved constrained multi-objective particle swarm optimization could effectively improve the products’ synthesize economical and technical indexes.

Super-smooth surface fabrication technique and experimental research

Wheel polishing, a new optical fabrication technique, is proposed for super-smooth surface fabrication of optical components in high-precision optical instruments. The machining mechanism and the removal function contours are investigated in detail. The elastohydrodynamic lubrication theory is adopted to analyze the deformation of the wheel head, the pressure distribution, and the fluid film thickness distribution in the narrow machining zone. The pressure and the shear stress distributions at the interface between the slurry and the sample are numerically simulated. Practical polishing experiments are arranged to analyze the relationship between the wheel-sample distance and the machining rate. It is demonstrated in this paper that the wheel-sample distance will directly influence the removal function contours. Moreover, ripples on the wheel surface will eventually induce the transverse prints on the removal function contours. The surface roughness of fused silicon is reduced to less than 0.5 nm (rms) from initial 1.267 nm (rms). The wheel polishing technique is feasible for super-smooth surface fabrication.

PEEK (Polyether-ether-ketone) Based Cervical Total Disc Arthroplasty: Contact Stress and Lubrication Analysis

This paper presents a theoretical analysis of the maximum contact stress and the lubrication regimes for PEEK (Polyether-ether-ketone) based self-mating cervical total disc arthroplasty. The NuNec® cervical disc arthroplasty system was chosen as the study object, which was then analytically modelled as a ball on socket joint. A non-adhesion Hertzian contact model and elastohydrodynamic lubrication theory were used to predict the maximum contact stress and the minimum film thickness, respectively. The peak contact stress and the minimum film thickness between the bearing surfaces were then determined, as the radial clearance or lubricant was varied. The obtained results show that under 150 N loading, the peak contact stress was in the range 5.9 – 32.1 MPa, well below the yield and fatigue strength of PEEK; the calculated minimum film thickness ranged from 0 to 0.042 µm and the corresponding lambda ratio range was from 0 to 0.052. This indicates that the PEEK based cervical disc arthroplasty will operate under a boundary lubrication regime, within the natural angular velocity range of the cervical spine.

PEEK (Polyether-ether-ketone) Based Cervical Total Disc Arthroplasty: Contact Stress and Lubrication Analysis

This paper presents a theoretical analysis of the maximum contact stress and the lubrication regimes for PEEK (Polyether-ether-ketone) based self-mating cervical total disc arthroplasty. The NuNec® cervical disc arthroplasty system was chosen as the study object, which was then analytically modelled as a ball on socket joint. A non-adhesion Hertzian contact model and elastohydrodynamic lubrication theory were used to predict the maximum contact stress and the minimum film thickness, respectively. The peak contact stress and the minimum film thickness between the bearing surfaces were then determined, as the radial clearance or lubricant was varied. The obtained results show that under 150 N loading, the peak contact stress was in the range 5.9 – 32.1 MPa, well below the yield and fatigue strength of PEEK; the calculated minimum film thickness ranged from 0 to 0.042 µm and the corresponding lambda ratio range was from 0 to 0.052. This indicates that the PEEK based cervical disc arthroplasty will operate under a boundary lubrication regime, within the natural angular velocity range of the cervical spine.

Research on the Performance of Space Liquid Lubrication System with Oil-Storage

The gravity oil feed method dose not suit for microgravity environment as the same way dose for ground lubrication system. It is the key problem to be solved that how to supply the oil to friction surface in space liquid lubrication system. It analyzed the lubricating manner. A space liquid lubrication system was designed based on a principle of using deformation energy to supply oil. In the analysis of its basic structure and operating principle, the film calculation mode was established based on the elastohydrodynamic lubrication theory. The lubricating performance was simulated by ANSYS finite element analysis software in microgravity. The calculation results show that: in the microgravity, it could achieve elastohydrodynamic lubrication on friction surface in this lubrication system. When the oil supply hole diameter is 2mm, the film-thickness ratio changes between 1.91 and 4.28. It belongs to elastohydrodynamic lubrication. The hole diameter decreases, the film thickness reduces. The minimum film-thickness ratio is 0.93 when the temperature changes widely from -50°C~+80°C. It belongs to boundary lubrication state.

Research on Web-Based Elastohydrodynamic Lubrication Oil Theory of Rolling Bearing Type Planetary Friction Transmission Mechanism

Service mode and dynamic network interfere techniques are analyzed. An elastohydrodynamic lubrication oil thickness theory of rolling bearing type planetary friction transmission mechanism system based on web is presented.Elastohydrodynamic lubrication theory is adopted in rolling bearing type planetary friction transmission mechanism in this paper. Research indicates that elastohydrodynamic oil file lubrication can be realized while mechanical parts with connection between points or lines run under certain conditions. At the same time, surface disrepair of the parts has relation to lubrication state. Minimal oil film thickness formula is deduced based on the elastohydrodynamic lubrication theory. It is a part of He’nan Scientific Committee science and technology research projects 《research on collaborative design and manufacturing technique in gear manufacturing based on network and multi-Agent》

Dynamic Analysis for Investigation of Fluid Resistance for Ball Bearings

Though the rolling ball bearing greatly contributes to decrease the friction energy of the machine movement, we require the development of lower friction torque technology of ball bearing to achieve more efficient machine. Especially, the fluid resistance makes an important role when the ball bearing is soaked in lubricant. Estimation of the loss of torque by the fluid resistance brings the reduction in the design cost. Therefore, in our research, it aims to develop the simulation technology of the fluid resistance by the ALE (Arbitrary Lagrangian and Eulerian) Finite Element Method. As the first step, we have established the simulation technology of movement analysis for the only ball bearing. In this report, we did the movement analysis numerical simulation of the ball bearing that considered the contact ellipse and EHL (Elastohydrodynamic Lubrication) Theory. As the result, we improved validity of the analysis from the perspective of the contact reaction force.

Simulation of Inking System Based on Elastohydrodynamic Lubrication

the inking system is one of the important components of an offset printing machine and an inking system with good performances is the necessary condition for high quality printing. In this paper, the Reynolds equation for ink transfer was deducted on the basis of the elastohydrodynamic lubrication theory and the relation model between parameters of the roller, speed, pressure and ink thickness in gap of rollers was established by applying the Hertz contact theory, so as to obtain the minimum film thickness equation in gaps of rollers. The influences of roller speed, pressure and size on ink thickness in gaps of rollers were analyzed. In addition, the ink transfer model was modified under the condition of considering retention of ink in gaps of rollers by using Roland700 as the object and the influences of printing speed on inking characteristics were analyzed by applying the method of computer simulation. The results showed that the longer was the inking stabilization time of the system was, the higher the printing speed was.

Film formation of yogurt under confined condition

The yogurt film confined within a nanogap was investigated by the thin film interferometry between two solid surfaces. Significantly thick film was found even under a low speed, which indicated yogurt might have excellent lubrication performance. The film thickness was much higher than the prediction of elastohydrodynamic lubrication theory. Experiment results indicated that the thick confined film of yogurt can be induced by the adhesion of organic material, which can sustain high pressure without being extruded under low speed. The effect of the rolling speed on film thickness shows that the lubrication under a high rolling speed tends to be the elastohydrodynamic lubrication. Copyright © 2011 John Wiley & Sons, Ltd.

Development and validation of a rigid–flexible coupled dynamic valve-train model

A rigid–flexible coupled dynamics model has been developed to analyse the dynamic behaviour of a pushrod valve-train system of an internal combustion engine. The elastic vibration mechanism of each flexible component is described in a floating reference frame. The mechanical impacts in a valve-train system at the opening and closing events of the valve are affected by the contact stiffness and damping of contact components. The contact force model for the cam–tappet interface was developed based on the elasto-hydrodynamic lubrication theory of finite line conjunction. The finite-difference method is used to solve the rigid–flexible coupled dynamic equations. The algorithm of finite difference and the boundary conditions have been carefully selected to solve the fourth-order Bernoulli–Euler beam equation. Experiments were conducted on a motor-driven valve-train system from a four-cylinder diesel engine. The measured valve displacement, acceleration, and contact forces showed excellent consistency with the predicted results. The rigid–flexible coupled dynamics model has shown improved accuracy compared to the lumped rigid mass system in analysing the dynamic performance of the valve-train system.

The effects of inhomogeneous boundary dilution on the coating flow of an anti-HIV microbicide vehicle.

A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when topically applied, significantly inhibits sexual HIV transmission to women [Karim et al., Science 329, 1168 (2010)]. However, the gel for this drug and anti-HIV microbicide gels in general have not been designed using an understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model spreading of microbicide gels [Szeri et al., Phys. Fluids 20, 083101 (2008)]. This should incorporate the full rheological behavior of a gel, including how rheological properties change due to contact with, and dilution by, ambient vaginal fluids. Here, we extend our initial analysis, incorporating the effects of gel dilution due to contact with vaginal fluid produced at the gel-tissue interface. Our original model is supplemented with a convective-diffusive transport equation to characterize water transport into the gel and, thus, local gel dilution. The problem is solved using a multi-step scheme in a moving domain. The association between local dilution of gel and rheological properties is obtained experimentally, delineating the way constitutive parameters of a shear-thinning gel are modified by dilution. Results show that dilution accelerates the coating flow by creating a slippery region near the vaginal wall akin to a dilution boundary layer, especially if the boundary flux exceeds a certain value. On the other hand, if the diffusion coefficient of boundary fluid is increased, the slippery region diminishes in extent and the overall rate of gel spreading decreases.

Investigation of dynamic characteristics of a valve train system

A valve train dynamics model of internal combustion engine has been developed using the kineto-elastodynamics method. The dynamics behavior for flexible components such as the valve springs in the valve train system was described by the wave equation. The contact force at the cam/tappet interface was estimated by the elasto-hydrodynamic lubrication theory of finite line conjunction. Component submodels were integrated into the whole valve train model by coupling the corresponding contact and friction forces, and solved simultaneously considering transient effect of lubrication, as well as the torsional and bending vibrations of camshaft. Experimental validation was performed on a motored test rig. The predicted results agree well with experiments at difference camshaft speeds. The effects of the bending deflection and torsional vibration of camshaft on performance of the valve train system were also studied.

Research on Dual-Cones CVT Based on EHL

A novel configuration of CVT that contains two cones located in the same shaft face to face is researched about the traction performance under high speed based on the theory of elastohydrodynamic lubrication(EHL). The effects of load, radii of curvature and slip-roll ratio on the traction characteristics and power transmission are analyzed. The results show that with increasing load the traction coefficient enhances close to linearly where the load is not heavy and the minimum film thickness decreases linearly when the inner wheel radii of curvature less than 0.085m. The leftmost position could transmit higher power. The power transmitted improves slightly as slip-roll ratio enhances in an appropriate range.

A dynamic model to predict the occurrence of skidding in wind-turbine bearings

Despite use of the best in current design practices, high-speed shaft (HSS) bearings, in a wind-turbine gearbox, continue to exhibit a high rate of premature failure. As HSS bearings operate under low loads and high speeds, these bearings are prone to skidding. However, most of the existing methods for analyzing skidding are quasi-static in nature and cannot be used to study dynamic operating conditions. This paper proposes a dynamic model, which includes gyroscopic and centrifugal effects, to study the skidding characteristics of angular-contact ball-bearings. Traction forces between rolling-elements and raceways are obtained using elastohydrodynamic (EHD) lubrication theory. Underlying gross-sliding mechanisms for pure axial loads, and combined radial and axial loads are also studied. The proposed model will enable engineers to improve bearing reliability at the design stage, by estimating the amount of skidding.

The consequences of yield stress on deployment of a non-Newtonian anti-HIV microbicide gel

A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when applied topically, significantly inhibits sexual HIV transmission to women [10]. However the gel for this drug, and anti-HIV microbicide gels in general, have not been designed using full understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model such spreading of microbicide gels, which are inherently non-Newtonian [13,15]. A yield stress is emerging as one of the important properties of microbicide gel vehicle deployment, as this may improve retention within the vaginal canal. On the other hand, a yield stress may decrease the initial extent of the coating flow. Here, we first explain a certain yield stress paradox observed generally in many lubrication flows. Four conditions are determined, via scaling analysis, which mitigate the inconsistency in the use of lubrication theory to analyze the specific problem of elastic wall squeezing flow of yield stress fluid. Parameters characterizing these conditions are obtained experimentally for a test gel. Using them, it is shown that the lubrication approximation may be applied to the elastic wall-squeezing problem for this gel.

Analysis Methods of Power Characteristics for Hydraulic Pressing of the Traction Drive Device

Analysis Methods of Power characteristics for hydraulic pressing of the traction drive device are studied. The operating principle of hydraulic pressing of the traction drive device is analyzed, Probe into the rule of variation of the inner and outer Friction Pairs about the traction coefficient and the transmission ratio, A mathematical model of transmission traction characteristics is built up based of the Elasto-hydrodynamic lubrication theory, to explore the power characteristics of the friction pairs under different slip roll ratio and normal loading force, and the transmission of the input power and output power under different total sliding rate and loading force. The results showed that the transmission power of hydraulic pressing of the traction drive device is increasing when the normal loading force is increasing under some sliding Rate, but the transmission power tend to stable when the shearing stress is close to limiting shearing stress；and with the Sliding Rate increasing the transmission power increase under some normal loading force, but the transmission power eventually tend to stable when the Shearing Stress is close to limiting shearing stress.

Vibrations of a deformable ball rolling on a lubricated rigid half-space

The problem of vertical vibrations of a deformable ball rolling on a lubricated rigid half-space has been stated and numerically solved. It is assumed that the force, which causes the ball’s elastic deformation in the zone of lubricated concentrated contact, is applied to the ball. The problem’s mathematical model is reduced to the system of nonstationary integrodifferential equations and inequalities with initial and boundary conditions. The computational algorithm of the problem’s solution was based on Newton’s method and application of an implicit scheme to approximate nonstationary equations. Vibrational solutions, which describe the behavior of the system consisting of the ball and the lubrication layer both under excitation of the initial conditions and under the excitation force, have been obtained. It is shown that as opposed to the traditional elastohydrodynamic lubrication theory approach, in which contacting bodies are considered as massless ones, taking the ball’s mass and corresponding inertia into account makes it possible to extend the category of obtained solutions and investigate vibrational processes in the contact zone. The results may be used to analyze processes occurring in lubricated concentrated contacts of gears and rolling bearings.

A Review of Elasto-Hydrodynamic Lubrication Theory

The development and understanding of elastohydrodynamic lubrication (EHL) can be traced back to the beginning of the previous century. However, it was not until 1949 that the first real solution of the problem was published. Since then, the technology has evolved enormously. In the current article a summary of these developments is given. Smooth surface EHL has become well established. Numerical methods, analytical solutions, and experimental techniques have become mature. Focus areas of research today are thermal EHL, starved EHL, friction (non-Newtonian lubricants), roughness, and grease. The scope of EHL is so wide that the authors needed select the topics of focus in this article. Therefore, in addition to the general overview of the areas of friction, analytical methods, starved EHL, and grease EHL are highlighted in this article.