# Hydrodynamic Lubrication Regime

27.08.2022

Hydrodynamic Lubrication:

Lubrication in any system at a sliding interface can be classified based on the amount of lubricant present at the interface. According to the stribeck curve (the plot of coefficient of friction (COF) and Hersey number), the region belonging to respective lubrication is termed as the lubricated regimes which can be classified into three categories. They are hydrodynamic, mixed, and boundary lubrication regimes. The stribeck curve with the different lubrication regimes is shown in Fig-1. In these three lubrication regimes, the hydrodynamic lubrication regime plays an important role in most of the practical applications such as journal bearings, pad bearings, etc [1].

Fig-1 Stribeck curve with different lubrication regimes [2].

# Definition:

The hydrodynamic lubrication regime is formed when there is no contact between the surfaces at the sliding interface and there is a gap of separation at the interface due to thick lubricant film formation. In the case of bearings, hydrodynamic lubrication occurs mainly when the rotation speeds are high and relatively low bearing loads. The thick lubricant film formed at the surface keeps the surfaces apart due to the force called hydrodynamic lift. This kind of lubrication helps in providing better tribological properties and improves the frictional behaviors of the mechanical components in most conditions. The schematic representation of the hydrodynamic regime is shown in the Fig-2.

Fig-2 hydrodynamic lubrication regime [3].

# Conditions for formation of the hydrodynamic regime:

The important feature of the hydrodynamic lubricated regime is the fluid film formation, and this film formation needs favorable conditions, it is schematically shown in Fig-3. The hydrodynamic regime is favored by mainly two conditions they are:

1. The two surfaces at the interface should move relative to each other for the formation of the lubricating film at the constant loading conditions.
2. The two surfaces at the interface should be at an angle for the formation of the lubricating film, because when any of the surfaces at an interface is elevated at an angle to another then there is a pressure developed between the surface resulting in the formation of the lubricating film.

Fig-3 the conditions of hydrodynamic lubrication regime [4].

# Reynolds theory on hydrodynamic lubrication:

The theoretical analysis of hydrodynamic lubrication was studied by Osborne Reynolds. Certain assumptions were made in order to derive the equation where he considered the lubricating fluid is a Newtonian fluid. The flow of the lubricant fluid must be laminar, the fluid inertia is neglected, and keeping the fluid density constant. The viscosity of the fluid is maintained constant throughout the generated fluid film with no slip at the boundaries. The body forces are also neglected, and the pressure is maintained constant throughout the film [5].

Considering these following conditions, the flow layers is proportional to the velocity gradient in the direction perpendicular to the flow. The equation can be written as;

τ = η (∂v/∂y)

Where τ is the shear stress, η is the dynamic viscosity of the oil, v is the linear velocity of the laminar layer and y is the axis perpendicular to the flow direction.

# Physical characteristics of the hydrodynamic lubrication:

The thickness of the lubricant film in case of the hydrodynamic lubrication is a very important factor that must be considered to improve the efficiency of the mechanical components working under this regime. The two important physical parameters affecting this lubricant film thickness are the fluid velocity and the load acting on the contact interface.

1. Fluid velocity: The thickness of the lubricant film increases with the increase in the speed of the fluid. In the case of journal bearings, the fluid velocity depends on the velocity of the journal or rider. The relative velocity increases towards a decrease in the eccentricity of journal bearing centers. This is accompanied by the greater lubricant film thickness.
2. Load: The increase in the load at the contact interface of the surfaces tends to decrease the film thickness of the lubricant films. The increase in load increases the pressure which acts in all directions that tends to squeeze the oil out of the ends of the bearings. Also, the increase in pressure increases the viscosity of the fluid which in turn reduces the film thickness.

# Hydrodynamic pressure between two nonparallel surfaces:

The hydrodynamic pressure can vary by varying the orientation of any of the surfaces at the interface leading to different pressure generation. This leads to various applications; the effects of change in pressure are shown in Fig-4. The different orientation shows different effects of the pressure, these effects can be classified as a wedge, stretch and squeeze effects.

1. Wedge effect: In case of the wedge effect the pressure generation takes place due to the flow of fluid from the larger end to the smaller end leading to the wedge-shaped fluid film formation as shown in Fig-4 (a).
2. Stretch effect: In case of the stretch effect, the pressure generation takes place due to the change in the velocity of the flow of fluid at different places of flow, this effect is shown in Fig-4 (b).
3. Squeeze effect: In case of the squeeze effect, the pressure generation takes place due to the change in the film thickness because of the change in the surface gap between the interface. This effect is shown in the Fig-4 (c)

Fig-4 Mechanism of pressure generation. a wedge effect, b stretch effect, c squeeze effect [6].

# Research on hydrodynamic lubrication:

Hydrodynamic lubrication is used in most applications which helps in reducing friction and increases the tribological performance of the materials. The optimization and the improvement of hydrodynamic lubrication play an important role in different applications. There are many surface modification techniques such as surface texturing which are implemented on the material’s surface to enhance the hydrodynamic lubrication. M.S. Uddin et.al., studied the enhancement of the hydrodynamic lubrication by surface texturing on the parallel slider surfaces. The importance of the geometric patterns has been shown in their study, the new optimum star-like texture reduced the COF by 80%, 64.39%, 19.32%, and 16.14%, as compared to ellipse, chevron, triangle, and circle, respectively [7]. Determining the properties of the lubricating film to improve the efficiency of the hydrodynamic lubrication is another important field. In a study, Jing Han et.al., studied the hydrodynamic lubrication of micro dimple textured surfaces using three-dimensional CFD. It was found that the dimensionless optimum micro dimple depth increases with the increase of the width and decreases with the increase of the Reynolds in the range of 0.80–2.00, which is responsible for the largest load-carrying capacity and the smallest friction coefficient [8].

EHL Calculators:

EHL Film Thickness Calculator (Central and Minimum): Line (Cylindircal) Contact

EHL Film Thickness Calculator (Central and Minimum): Elliptical (Point) Contact

References:

I am currently working as a Postgraduate Researcher at the University of Leeds, where I am actively involved in research activities. Prior to this, I successfully completed my master's degree through the renowned Erasmus Mundus joint program, specializing in Tribology and Bachelor's degree in Mechanical Engineering from VTU in Belgaum, India. Further I handle the social media pages for Tribonet and I have my youtube channel Tribo Geek.

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