Lubrication is fundamental to the operation of all engineering machines.   It is required to minimise friction, wear and also provides a cooling function and a surface protection function.

A liquid film lubrication regime can be hydrodynamic or hydrostatic.  In hydrodynamic bearings the fluid is introduced into the bearing surfaces by the action of the bearing.  In hydrostatic bearing the fluid is introduced under pressure from an external source.

Liquid lubrication in machines is normally hydrodynamic.   An oil film is formed between the two sliding surfaces separating them and providing a low sliding friction.    However this mechanism is only active during the sliding movement.   At the start and at the termination of movement the oil film is not present.   At these times wear can take place.   Hydrodynamic lubrication is present in linear motion (slideways) and in rotational motion (journals).

An important property of a liquid used for lubrication is its viscosity..  The viscosity of a fluid is its resistance to shear.   The friction in a lubricated bearing is directly related to the fluid viscosity.   Notes and links providing viscosity information is provide on this website ....Viscosity

The design of a liquid lubricated bearing system must include cosideration of a number of associated factors as listed below:

It is not possible to address these factors on this page.. Please refer to the links provided below

Petroff's equation provides an friction value for an unloaded journal bearing i.e with the shaft concentric with the journal.  This assumes no end load and does not allow for end leakage..

f = 2 . p ² . (m . n / p ) . r / c

Torque to rotate shaft .. T (Nm)

= W. f .r

= W.[ 2 . p ² . (m . n / p ) . r / c ] . r


= W.[ 2 . p ² . (m . n . L. 2. r / W ) . r / c ] .r    = 4.p ².r³.m . n .L / c

Power to rotate shaft... = T.ω = T.2.p .n

> P (Watts)    = 8 . p ³ .n ² . r ³ . L . m / c
= p ³ .n ² . d ³ . L . m / c

The equivalent power for a rotating thrust bearing ...

P (Watts)   =  2 . p ³ .n ² . m . ( r₂ ⁴ — r₁ ⁴ ) / t

Journal and thrust and linear bearings can be hydrostatic in that the load carrying capacity results from externally generated lubricant pressure.   These type of bearing do not depend on the relative motion of the bearing surfaces for lubrication and so they are effective at zero and very low velocities.  This type of lubrication does not involve the necessity of metal contact during start-up and shut down.

Hydrostatic lubrication systems are generally expensive to engineer and are liable to problems with controlling the lubrication supply

Note; Hydrodynamic Lubrication is extremely complex.   These notes provide only outline explanations of the principles involved...

In hydrodynamic lubrication the fluid is assumed not to slip at the interface with the bearing surfaces i.e. the fluid in contact with the bearing surfaces moves at the same velocity as the surface.   Over the thickness of the fluid there is a velocity gradient depending on the relative movement of the bearing surfaces.  If the bearing surfaces are parallel (or concentric ) the action motion of the lubricant will not result in a pressure which could support any bearing load.   However if the surfaces are at a slight angle the resulting lubrication fluid velocity gradients will be such that a pressure results from the wedging action of the bearing surfaces...  Hydrodynamic lubrication depends upon this effect... Note; This principle is similar to the lift in water skiing / aqua planing ..

The operation of hydrodynamic lubrication in journal bearings is illustrated below.   Before the rotation commences the shaft rests on the bearing surface. When the rotation commences the shaft moves up the bore until an equilibrium condition is reached when the shaft is supported on a wedge of lubricant.  The moving surfaces are then held apart by the pressure generated within the fluid film.   Journal bearings are designed such that at normal operating conditions the continuously generated fluid pressure supports the load with no contact between the bearing surfaces.   This operating condition is known as thick film lubrication and results in a very low operating friction and extremely low bearing load

Boundary lubricating conditions occur when the lubricant film is insufficient to prevent surface contact.  This occurs at rotation start-up, a slow speed operation or if the load is too heavy.   This regime results in bearing wear and a relatively high friction value.  If a bearing is operated under boundary lubricating conditions special lubricants are needed.

The operation of hydrodynamic lubrication for thrust bearings is enabled by various design options including tilting pads, taper lands and step bearings.  The tilting pads provide the most ideal Hydrodynamic lubrication conditions as shown on the figure below..

It is generally desirable to achieve hydrodynamic lubrication in bearings or the following reasons;

Hydrodynamic lubrication depends on at least three of dimensionless numbers ... ( m .n / p ) ,    ( D / h ) ,    and (L/D)

The relationship between the bearing friction coefficient and the bearing modulus is shown in the figure below

A design constraint to keep thick film (full hydrodynamic) is to ensure the bearing modulus (m n /p ) >= 1.09 x 10^-9

McKee established the following relationship using small bearings .  This does not allow for end leakage

f = 19,56 . ( m .n / p ). ( D /C) + k

k is obtained from the diagram below but can be approximated as 0.002 over an L/D ration 0 0.75 - 2.6

The Sommerfeld Number is a dimensionless parameter used in lubrication analysis.

S = ( m .n / p ). ( D /C) ²

This parameter has been used as the abscissa for a number of design curves.  The ordinate can be selected to allow the friction value, film thickness, oil leakage, temperature rise etc to be determined.   Design curves have been produced of various variables against the Sommerfeld using computer techniques by A.A Raimondi and J.Boyd of Westinghouse Research Labs(ASLE Transactions Vol 1 No 1 April 1958).    These graphs include compensation for end leakage and eccentricity.

The illustrative design curve has been included below.   Detailed journal and thrust bearing designs should be completed using the relevant specialist sources of information or software..

In comparing the value of f(D/C) resulting from the Petroff, McKee and the Raimondi-Boyd data the values are in close agreement for the higher values of the Sommerfeld number (above 0.5) i.e the lightly loaded bearings..

Journal clearances -
The table below provides some typical diametrical clearances for journal bearings under steady loads and for hydrodynamic lubrication.   These are very crude values.   Serious journal bearing design should include a detailed analysis.   The diametric clearance is the journal diameter - the shaft diameter