Liquid lubrication uses a fluid, normally an oil, to reduce friction and wear between surfaces in relative motion. The lubricant can also remove heat, protect surfaces against corrosion and contamination, and transmit or distribute load within fluid-film bearings.
Liquid-film bearings may operate under hydrodynamic or hydrostatic conditions. In a hydrodynamic bearing, relative motion and bearing geometry generate pressure within the lubricant film. In a hydrostatic bearing, pressurised lubricant is supplied from an external source.
Under full-film hydrodynamic lubrication the opposing surfaces are separated by a continuous lubricant film. During starting, stopping, low-speed operation or overloading, adequate film thickness may not be maintained and the bearing can enter mixed or boundary lubrication, where some surface contact can occur.
Viscosity is one of the most important lubricant properties because it affects film formation, frictional losses and bearing performance. See the Viscosity page for further engineering data.
The design and operation of a liquid lubrication system should consider:
These factors interact and should be considered together when selecting a lubricant and designing the lubrication system. The specialist references at the end of this page provide further information for detailed bearing and lubrication design.
Petroff's equation provides an approximate friction coefficient for an unloaded, concentric journal bearing. It assumes the journal is concentric with the bearing, neglects end leakage and represents a simplified full-film condition.
The bearing friction coefficient is:
The torque required to rotate the shaft is:
Substituting the Petroff relationship and gives:
With angular speed , the power loss is:
For the simplified rotating thrust-bearing case given in the original RoyMech reference, the corresponding power expression is:
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 wear
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
| Equipment | Bearing | Max Pressure | m | m n /p |
| MPa | Pa. s | |||
| Automobile /Aircraft Engines | Main | 5 - 12 | 0,007 | 3,67 x 10-8 |
| Crankpin | 10-23 | 0,008 | 2,50 x 10-8 | |
| Wrist pin | 14 -35 | 0,008 | ||
| Gas and Oil Engines | Main | 3.5 - 8 | 0,02 | 5,00 x 10-8 |
| Crankpin | 7 -12 | 0,04 | 2,50 x 10-8 | |
| Wrist pin | 8-14 | 0,065 | ||
| Marine Engines | Main | 3.5 | 0,03 | 5,00 x 10-8 |
| Crankpin | 4 | 0,04 | 3,67 x 10-8 | |
| Wristpin | 10 | 0,05 | ||
| Stationary steam engines | Main | 1,5 - 3 | 0,015 -0,06 | 5,00 x 10-8 |
| Crankpin | 4 -10 | 0,03 -0,08 | 1,50 x 10-8 | |
| Wristpin | 12 | 0,025 -0,06 | ||
| Reciprocating pumps and compressors | Main | 2 | 0,03 | 7,33 x 10-8 |
| Crankpin | 4 | 0,05 | 3,67 x 10-8 | |
| Wristpin | 7 | 0,08 | 3,67 x 10-8 | |
| Steam Turbines | Main | 0,5 - 2 | 0,002-0,016 | 25,0 x 10-8 |
| Rotary Pumps and Motors | Shaft | 0,5 -1.5 | 0,025 | 50,0 x 10-8 |
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
k is obtained from the diagram below but can be approximated as 0.002 over an L/D ratio 0 0.75 - 2.6
The Sommerfeld Number is a dimensionless parameter used in lubrication analysis.
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..
| Speed Range | Shaft Diameter | Diametrical Clearance |
| mm | mm | |
| Below 600 RPM | 25 | 0.025 - 0.05 |
| Above 600 RPM | 25 | 0.03 - 0.10 |
| Below 600 RPM | 40 | 0.03 - 0.08 |
| Above 600 RPM | 40 | 0.05 - 0.12 |
| Below 600 RPM | 50 | 0.04 - 0.09 |
| Above 600 RPM | 50 | 0.06 - 0.14 |
| Below 600 RPM | 80 | 0.05 - 0.11 |
| Above 600 RPM | 80 | 0.08 - 0.17 |
| Below 600 RPM | 100 | 0.06 - 0.13 |
| Above 600 RPM | 100 | 0.09 - 0.20 |
| Below 600 RPM | 125 | 0.07 - 0.14 |
| Above 600 RPM | 125 | 0.10 - 0.22 |
| Below 600 RPM | 150 | 0.08 - 0.15 |
| Above 600 RPM | 150 | 0.12 - 0.24 |
| Below 600 RPM | 200 | 0.09 - 0.17 |
| Above 600 RPM | 200 | 0.14 - 0.27 |
