Film Thickness Modulations in Starved Elastohydrodynamically Lubricated Contacts Induced by Time-Varying Lubricant Supply

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
C. H. Venner ◽  
G. Popovici ◽  
P. M. Lugt ◽  
M. Organisciak

Many elastohydrodynamically lubricated contacts in practical applications, e.g., in bearings, operate in the starved lubrication regime. As a result their performance is sensitive to variations of the lubricant layers present on the surfaces, which form the supply to the contact. Their shape is often determined by previous overrollings of the track and also by replenishment mechanisms and various migration effects. Variations of the layers induced in the direction of rolling lead to a time-varying lubricant supply to the contact. In this paper, by means of numerical simulations using a starved lubrication model, the film thickness modulations in the center of the contact induced by a harmonically varying inlet supply have been investigated. First, for a given load condition and layer wavelength, the effect of the nominal layer thickness (degree of starvation) and the layer variation amplitude is illustrated. Subsequently, using results for different load conditions, wavelengths, and degrees of starvation, it is shown that the response of the contact to such variations is determined by a nondimensional parameter, which represents the ratio of the entrainment length of the contact to the wavelength of the induced variation, and by the degree of starvation. A simple formula is presented for use in engineering predicting the ratio of the amplitude of the film modulations in the center of the contact to the amplitude of the layer variations in the inlet.

Author(s):  
C H Venner ◽  
A A Lubrecht

In this article, the problem of predicting the film thickness in so-called narrow or slender elliptic contacts is revisited. In particular, the variation of the minimum film and central film thickness and their ratio with load and ellipticity are studied. It is shown that the minimum film tends to decrease linearly with increasing ellipticity. The central film thickness, until a certain threshold, decreases very slowly, and then decreases linearly too, with a slope independent of the Hertzian pressure. The ratio central to minimum film thickness is not a constant and varies strongly with ellipticity and load conditions. In this article, it is shown that the ratio of central to minimum film thickness is a linear function of a single nondimensional parameter which has the physical meaning of the ratio of the length of the inlet pressure sweep to the relative width of the contact. Results for narrow contacts published in the engineering literature when represented as a function of this parameter exhibit the same trend. The behaviour is the consequence of the same unifying mechanism that, in the last decade, was discovered to determine aspects of behaviour in elasto-hydrodynamically lubricated (EHL) contacts under time varying conditions, such as surface waviness deformation. For these problems, the single parameter dependence facilitated the development of simple engineering tools (e.g. to predict the roughness deformation). The observation in this article that the ratio central to minimum film thickness is also governed by this parameter opens new perspectives to develop a simple computational engineering tool to predict central and minimum film thickness in EHL contacts.


Author(s):  
A Félix-Quiñonez ◽  
G E Morales-Espejel

A simplified semi-analytical solution for the film thickness fluctuations in the normal-approach problem of elastohydrodynamic lubrication (EHL) contacts has been obtained. The model is based on an inlet analysis to include squeeze-film effects together with the variation of lubricant entrainment speed that is induced by the changes of contact radius as the load oscillates. The results obtained are in excellent agreement with numerical solutions and suggest that the fluctuations in entrainment speed are the main cause for the observed film modulations. The modified semi-analytical solution seems applicable in many practical cases. The amplitude of the film thickness fluctuations produced by fluctuations in the load is in this way related to a single parameter.


Author(s):  
G E Morales-Espejel

The effects of time-varying normal approach on the film formation of rolling elastohydrodynamically lubricated (EHL) contacts are studied by means of an inlet analysis. A modified Ertel—Grubin scheme is used to calculate the variation of central film thickness as a response of time-varying normal approach. The inlet shape approximation from Crook is used to derive simple analytical and semi-analytical solutions for the calculation of central film thickness and inlet pressures for situations of prescribed normal rigid-body displacement or prescribed load variation. The methodology is also adopted to model the pressure and clearance wave transport phenomenon shown earlier only with the use of full numerical solutions.


Author(s):  
Grienggrai Rajchakit ◽  
Ramalingam Sriraman ◽  
Rajendran Samidurai

Abstract This article discusses the dissipativity analysis of stochastic generalized neural network (NN) models with Markovian jump parameters and time-varying delays. In practical applications, most of the systems are subject to stochastic perturbations. As such, this study takes a class of stochastic NN models into account. To undertake this problem, we first construct an appropriate Lyapunov–Krasovskii functional with more system information. Then, by employing effective integral inequalities, we derive several dissipativity and stability criteria in the form of linear matrix inequalities that can be checked by the MATLAB LMI toolbox. Finally, we also present numerical examples to validate the usefulness of the results.


1989 ◽  
Vol 111 (2) ◽  
pp. 246-251 ◽  
Author(s):  
Ping Pan ◽  
B. J. Hamrock

The film thickness and pressure in elastohydrodynamically lubricated conjunctions have been evaluated numerically for a rather complete range of operating parameters (dimensionless load, speed, and materials parameters) normally experienced in practical applications. From the film thickness and pressure throughout the conjunction a number of performance parameters were evaluated. By curve fitting the data, formulas were obtained that allow easy evaluation of the amplitude and location of the pressure spike, the minimum and central film thicknesses, the value of ρeHe, and the center of pressure.


1996 ◽  
Vol 75 (1) ◽  
pp. 60-74 ◽  
Author(s):  
D. L. Weeks ◽  
M. P. Aubert ◽  
A. G. Feldman ◽  
M. F. Levin

1. We analyzed the rapid adaptation of elbow movement to unexpected changes in external load conditions at the elbow joint. The experimental approach was based on the lambda model, which defines control variables (CVs) setting the positional frames of reference for recruitment of flexor and extensor motoneurons. CVs may be specified by the nervous system independently of the current values of output variable such as electromyographic (EMG) activity, muscle torques, and kinematics. The CV R specifies the referent joint angle (R) at which the transition of flexor to extensor activity or vice versa can be observed during changes in the actual joint angle, theta, elicited by an external force. The other CV, the coactivation (C) command, instead of a single transition angle, defines an angular range in which flexor and extensor muscles may be simultaneously active (if C > 0) or silent (if C < 0). Changes in the R command result in shifts in the equilibrium state of the system, a dynamic process leading to EMG modifications resulting in movement or isometric force production if movement is obstructed. Fast movements are likely produced by combining the R command with a positive C command, which provides movement stability and effective energy dissipation, diminishing oscillations at the end of movement. 2. According to the model, changes in the load characteristic (e.g., from a 0 to a springlike load) influence the system's equilibrium state, leading to a positional error. This error may be corrected by a secondary movement produced by additional changes in R and C commands. In subsequent trials, the system may reproduce the CVs specified after correction in the previous trial. This behavior is called the recurrent strategy. It allows the system to adapt to the new load condition in the subsequent trials without corrections (1-trial adaptation). Alternatively, the system may reproduce the CVs specified before correction (invariant strategy). If the movement was perturbed only in a single trial, the invariant strategy allows the system to reach the target in the subsequent trials without corrections. 3. To test the assumption on the dominant role of the recurrent strategy in rapid adaptation of movement to new load conditions, we performed experiments in which subjects (n = 6) used a pivoting manipulandum and made fast 60 degrees movements to a target. After a random number of trials (5-10) with no load, we introduced opposing (experiment 1), assisting (experiment 2), or randomly varied opposing or assisting loads (experiment 3) for 5-10 trials before unexpectedly switching loads again (14-18 switches in total). The opposing or assisting torque was created by position feedback to a torque motor and was a linear function of the displacement of the manipulandum form the initial position (springlike load). Subjects were instructed to correct positional errors as soon as possible to reach the target. The EMG activity of two elbow flexors (biceps brachii and brachioradialis) and two elbow extensors (triceps brachii and anconeus), elbow position, velocity, and torque were recorded. Kinematic and EMG patterns were compared with those obtained in similar experiments in which subjects were instructed not to correct errors. 4. In 94% of the trials in which a change in the load occurred, the primary movement was in error and was followed by a corrective secondary movement. In primary movements, both the phasic and tonic levels of EMG activity as well as the kinematics were load dependent, implicating reflex and intramuscular mechanisms in the adaptation of muscle forces counteracting external loads. These mechanisms, however, were not sufficient to eliminate positional errors. 5. An undershoot error occurred in trials with an opposing load after those with no load or in trials with no load after those with an assisting load. After adaptation to a new load condition, a sudden return to the previous load condition resulted in an error of the oppo


Author(s):  
Fadi Ali ◽  
Ivan Křupka ◽  
Martin Hartl

This study presents experimental results on the effect of out-of-contact lubricant channeling on the tribological performance of nonconformal contacts under starved lubrication. Channeling of lubricant was carried out by adding a slider with a limited slot for scraping the displaced lubricant on one of mating surfaces (ball). Thus, the scraped lubricant is forced to flow back into the depleted track through the limited slot resulting in robust replenishment. The measurements have been conducted using optical tribometer (ball-on-disc) equipped with a digital camera and torque sensor. The effect of lubricant channeling was compared to the original contact condition by means of measuring friction and film thickness. The results show that the out-of-contact lubricant channeling leads to a significant enhancement of film thickness and friction reduction under starved conditions. Indeed, the starved elastohydrodynamic lubrication contacts transformed to the fully flooded regime after introducing the flow reconditioning. Moreover, the film thickness decay over time, which is common with starved elastohydrodynamic lubrication contacts, has not been observed in the case of lubricant channeling. However, the beneficial effect of lubricant channeling diminishes as the original contact condition tends to the fully flooded regime. The results of this study can be easily implemented in practical applications such as radial and thrust rolling-element bearings.


1988 ◽  
Vol 32 (15) ◽  
pp. 981-984
Author(s):  
Gerard C. Jorna ◽  
Michael F. Mohageg ◽  
Harry L. Snyder

This study determined the perceived safety and comfort of an alternating tread stair and a conventional ships ladder. The alternating tread stair and the conventional ships ladder were also compared with respect to travel time and missteps. Subjects in military uniform ascended and descended both the alternating tread stair and the conventional ships ladder under load and no-load conditions. In the load condition subjects performed trials while carrying a 9-kg tool box, and in the no-load condition trials were performed without the tool box. Results indicate that the alternating tread stair is perceived to be safer and more comfortable to use. Moreover, the alternating tread stair had significantly fewer missteps.


2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Wei Pu ◽  
Dong Zhu ◽  
Jiaxu Wang

In this study, a modified mixed lubrication model is developed with consideration of machined surface roughness, arbitrary entraining velocity angle, starvation, and cavitation. Model validation is executed by means of comparison between the obtained numerical results and the available starved elastohydrodynamic lubrication (EHL) data found from some previous studies. A comprehensive analysis for the effect of inlet oil supply condition on starvation and cavitation, mixed EHL characteristics, friction and flash temperature in elliptical contacts is conducted in a wide range of operating conditions. In addition, the influence of roughness orientation on film thickness and friction is discussed under different starved lubrication conditions. Obtained results reveal that inlet starvation leads to an obvious reduction of average film thickness and an increase in interasperity cavitation area due to surface roughness, which results in significant increment of asperity contacts, friction, and flash temperature. Besides, the effect of entrainment angle on film thickness will be weakened if the two surfaces operate under starved lubrication condition. Furthermore, the results show that the transverse roughness may yield thicker EHL films and lower friction than the isotropic and longitudinal if starvation is taken into account. Therefore, the starved mixed EHL model can be considered as a useful engineering tool for industrial applications.


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