• Lubrication is the science of reducing friction by application of a suitable substance called

lubricant, between the rubbing surfaces of bodies having relative motion.

• The lubricants are classified into following three groups:

(i) Liquid lubricants, like mineral or vegetable oils.

(ii) Semi-solid lubricants, like grease.

(iii) Solid lubricants, like graphite or molybdenum disulphide.

• The objectives of lubrication are as follows:

(i) To reduce friction;

(ii) To reduce or prevent wear

(iii) To carry away heat generated due to friction

(iv) To protect the journal and the bearing from corrosion.

• The basic modes of lubrication are thick and thin film lubrication.

Zero film bearing is a bearing that operates without any lubricant, i.e. with- out any film
of lubricating oil.

Thick film lubrication describes a condition of lubrication, where two surfaces of the
bearing in relative motion are completely separated by a film of fluid. Since there is no
contact between the surfaces, the properties of surface, like surface finish, have little or no
influence on the performance of the bearing.

The resistance to relative motion arises from the viscous resistance of the fluid. Therefore,
the viscosity of the lubricant affects the performance of the bearing.

• Thick film lubrication is further divided into two group’s hydrodynamic and hydrostatic
lubrication.

Hydrodynamic Lubrication :

Hydrodynamic lubrication is defined as a system of lubrication in which the load

supporting fluid film is created by the shape and relative motion of the sliding surfaces.

The principle of hydrodynamic lubrication in journal bearing is shown in Figure

 Initially, the shaft is at rest and it sinks to the bottom of the clearance space under the action
of load W. The surfaces of the journal and bearing touch during rest.

As the journal starts to rotate, it will climb the bearing surface and as the speed is further
increased, it will force the fluid into the wedge-shaped region.

As more and more fluid is forced into the wedge-shaped clearance space, pressure is
generated within the system.

The pressure distribution around the periphery of the journal is shown in Fig.

Since the pressure is created within the system due to rotation of the shaft, this type of bearing is
known as self-acting bearing.

The pressure generate in the clearance space supports the external load W.
• In this case, it is not necessary to supply the lubricant under pressure and the
only requirement is sufficient and continuous supply of the lubricant. This
mode of lubrication is seen in bearings mounted on engines and centrifugal
pumps. Frequently, a term journal bearing is used.

• A journal bearing is a sliding contact bearing working on hydrodynamic

lubrication and which supports the load in radial direction. The portion of the
shaft inside the bearing is called journal and hence the name journal bearing.

• There are two types of hydrodynamic journal bearings namely, full journal
bearing and partial bearing. The construction of full and partial bearings is as
shown in figure.

• In full journal bearing, the angle of contact of the bushing with journal is
360°. Full journal bearing will take load in any radial direction. Most of the
bearings used in industrial applications are full journal bearing.

• In partial bearings, the angle of contact between the bush and the journal is
always less than 180°. Most of the partial bearings in practice have 120° angle
of contact. Partial bearing can take load in only one radial direction.Partial
bearings are used for railroad- cars.

• The advantages of partial bearing compared with full journal bearing are as
follows:

• Partial bearing is simple in construction.

• It is easy to supply lubricating oil to the partial bearing.

• The frictional loss in partial bearing is less. Therefore, temperature rise is low.

• There are two terms with reference to full and partial bearings namely,
clearance bearing and fitted bearing.

• A clearance bearing is a bearing in which the radius of the journal is less

than the radius of the bearing. Therefore, there is a clearance space between
the journal and the bearing. Most of the journal bearings are of this type.
• A fitted bearing is a bearing in which the radius of the journal and the bearing
are equal. So fitted bearing must be partial bearing and the journal must run
eccentric with respect to bearing in order to provide space for lubricating oil.
• There are two types of thrust bearings that take axial load, namely footstep bearing, and
collar bearing, as shown in Fig.

• The footstep bearing or simply step bearing is a thrust bearing in which the end of the
shaft is in contact with the bearing surface.

• The collar bearing is a thrust bearing in which a collar integral with the shaft is in contact
with the bearing surface. In this case, the shaft continues through the bearing. The shaft
can be with single collar or can be with multiple collars.

• Hydrostatic lubrication is defined as a system of lubrication in which the load supporting

fluid film, separating the two surfaces is created by an external source, like a pump,
supplying sufficient fluid under pressure. Since the lubricant is supplied under pressure,
this type of bearing is called externally pressurised bearing.
• The principle of hydrostatic lubrication in journal bearing is illustrated in Fig. Initially, the
shaft rests on the bearing surface. As the pump starts, high pressure fluid is admitted in the
clearance space, forcing the surfaces of bearing and journal to separate out.

• Hydrostatic bearings are used on vertical turbo generators, centrifuges and ball mills.

• Compared with hydrostatic bearings, hydrodynamic bearings are simple in construction,

easy to maintain and lower in initial as well as maintenance cost.

• Hydrostatic bearings, although costly, offer the following advantages:

• high load carrying capacity even at low speeds;

• no starting friction; and

• no rubbing action at any operating speed or load.

• Thin Film Lubrication:

• Thin film lubrication, which is also called boundary lubrication, is defined as a condition
of lubrication where the lubricant film is relatively thin and there is partial metal to metal
contact.

• This mode of lubrication is seen in door hinges and machine tool slides.

• The conditions resulting in boundary lubrication are excessive load, insufficient surface
area or oil supply, low speed and misalignment.

The mechanism of boundary lubrication is shown in Fig.

• Certain fatty acids, contain polar molecules, in which there is a permanent separation of
positive and negative charges.

• Their polarity has a tendency to orient and stick to the surface in a particular fashion.
 • The clusters of polar molecules, cohering to one another and adhering to the surface, form
a compact film that prevents metal to metal contact as is seen in region B. This results in
partial lubrication.

• There is also a zone (region A) where metal to metal contact takes place, junctions are
formed at high spots and shearing takes place due to relative motion.

• The performance of bearing under boundary lubrication depends upon two factors, namely
the chemical composition of the lubricating oil, such as polar molecules (at region B), and
surface roughness (at region A).

• The hydrodynamic bearing also operates under the boundary lubrication when the speed is
very low or when the load is excessive.

• Elasto-hydrodynamic lubrication:

• There is a particular mode of lubrication known as elastohydrodynamic lubrication.

• When the fluid film pressure is high and the surfaces to be separated are not sufficiently
rigid, there is elastic deformation of the contacting surfaces.

• This elastic deflection is useful in the formation of the fluid film in certain cases.

• Since hydrodynamic film is developed due to elastic deflection of the parts, this mode of
lubrication is called elastohydrodynamic lubrication.

• This type of lubrication occurs in gears, cams and rolling contact bearings.

VISCOSITY:

• Viscosity is defined as the internal frictional resistance offered by a fluid to change its
shape or relative motion of its parts.

An oil film placed between two parallel plates is shown in Fig.

 The lower plate is stationary while the upper plate is moved with a velocity U by means of
a force P.

The molecules of oil are visualised as small balls, which roll in layers between two plates.

The oil will stick to both the surfaces, and therefore the layer of molecules in contact with
the stationary plate has zero velocity.

Similarly, the layer of molecules in contact with the upper plate will move with a velocity
U.

The intermediate layers will move with velocities, which are proportional to their distance
from the stationary plate.

This type of orderly movement-is called streamline, laminar or viscous flow.

According to Newton's law of viscosity, the shear stress is proportional to the rate of
shear at any point in the fluid.

U 
p = Z ' A 
 h

 dU 
p = Z ' A 
When the velocity distribution is non-linear withrespect to h,  dh 

The constant of proportionality in the above equations is called absolute viscosity. The unit

N − sec
2
of absolute viscosity is given by, m or .

dyne − sec
The popular unit of viscosity is Poise, which gives absolute viscosity in m2

dyne − sec N − sec

1cP = 10 − 2 Poise = 10 − 2 2
= 10 −9
m mm 2 .

N − sec Kgf − sec cP

10 9 cP = =
mm 2 cm 2
9.81  10 7

Poise is a large unit and viscosities of most of the lubricating oils are given in terms of centi-Poise
(cP), which is one-hundredth of Poise. Therefore, following two separate notations are used for
viscosity,

Z ' = Absolute viscosity in units of (N-s/mm2) or (MPa-s)

Z = Absolute viscosity in units of (cP)

• Viscosity is determined by measuring the time required for the given volume of oil to pass
through a capillary tube of standard dimensions.

• The oil is kept in a reservoir, which is immersed in the constant temperature bath. Based
on this principle, there are three commercial viscometers named after Saybolt, Redwood
and Engler.

• The Saybolt universal viscometer is widely used in USA, the Redwood viscometer in UK
and Engler viscometer in the continent.

• In the Saybolt universal viscometer, (60 cm3) of lubricating oil is passed through a capillary
tube of standard dimensions and the time is measured in seconds. The unit of viscosity is
called Saybolt Universal Seconds (SUS), which is related to kinematic viscosity by the
 180 
following relationship: Z k = 0.22t − where, t is viscosity in Saybolt Universal
 t 
Seconds (SUS) and Zk is kinematic viscosity in centistokes (cSt).

• The kinematic viscosity is defined as the ratio of absolute viscosity to the density of
Z (centiPoise )
lubricant. Therefore, Z k (centiStokes ) =
 ( gm / cm 3 )

• In the Redwood viscometer lubricating oil is passed through a capillary tube of specific
dimensions and the time is measured in terms of Redwood Seconds.

• In Engler viscometer, the viscosity is measured in terms of Engler degrees ( oE), which is
the ratio of time taken by the oil to the time taken by water at the same temperature.

VISCOSITY INDEX

• The approximate relationship between viscosity and temperature is as follows:

B
log(Z ' ) = A + , where A and B are constants and T is the absolute temperature.
T

• The rate of change of viscosity with respect to Temperature is indicated by a number

called viscosity index (VI.).

• The viscosity index is d¢fined as an arbitrary number used to characterize the variation of
the kinematic viscosity of lubricating oil with temperature.

• In order to find out viscosity index of the oil, two groups of reference oils are considered.
One group consists of oils having VI= 100 and these oils have very small change of
viscosity with temperature.
 • The other group consists of oils having VI = 0 and these oils have very large change of
viscosity with temperature.

• The given oil is compared with these two reference oils, one with a viscosity index of 100
and the other of 0.

• Measure the viscosities of the given sample of oil at 1000F and 2120F. Suppose the
viscosities of the given sample of oil at 1000F and 2120Fare y and x respectively. They
are plotted in the figure at points B and A respectively. The line BA shows the variation
of viscosity for the given sample of oil.

Viscosity index indicates the rate of change of viscosity with temperature, as compared to
oils with very small or very large rates of change of viscosity with temperature.

An oil with VI = 70 has less rate of change of viscosity with temperature compared with
oil with VI = 60.

PETROFF'S EQUATION

The Petroffs equation is used to determine the coefficient of friction  in journal bearings.

It is based on following assumptions:

(i) The shaft is concentric with the bearing.

(ii) The bearing is subjected to light load.

  Zn  D 
 = 2 2    Petroff's equation indicates that there are two important dimensionless
 P  C 
Zn D
parameters namely & that govern the coefficient of friction and other frictional properties
p C
like frictional torque, frictional power loss and temperature rise in the bearing.

MCKEE’s EQUATION:

• In hydrodynamic bearings, initially the journal is at rest. There is no relative motion and
no hydrodynamic film. Therefore, there is metal to metal contact between the surfaces of
the journal and the bearing.

• As the journal starts to rotate, it takes some time for the hydrodynamic film to build
sufficient pressure in the clearance space. During this period, there is partial metal to
metal contact and partial lubricant film. This is thin film lubrication.

• As the speed is increased, more and more lubricant is forced into wedge shaped clearance
space and sufficient pressure is built up, separating the surfaces of the journal and the
bearing. This is thick film lubrication.

• Therefore, there is a transition from thin film lubrication to thick film lubrication as the
speed increases.

• The transition from thin film lubrication to thick film hydrodynamic lubrication can be
Zn
better visualized by means of a curve called curve. This curve is shown below.
P

Zn
• P curve is an experimental curve developed by McKee brothers. A bearing
characteristic number is a dimensionless group of parameters given by, Bearing
Zn
characteristic number = where,
P

Z = absolute viscosity of the lubricant

n = speed of the journal

P = unit bearing pressure (load per unit of projected area of bearing)

• The bearing characteristic number is plotted on abscissa. The coefficient of friction  is

plotted on ordinate. The coefficient of friction  is the ratio of tangential frictional force
to the radial load acting on the bearing.
 As seen in Fig., there are two distinct parts of the curve -BC and CD.

(i) In region BC, there is partial metal to metal contact and partial patches of lubricant.
This is the condition of thin film or boundary lubrication.

(ii) In region CD, there is relatively thick film of lubricant and hydrodynamic lubrication
takes place

(iii) AC is the dividing line between these two modes of lubrication. The region to the left
of line AC is thin film zone while the region to the right of line AC is thick film zone.

(iv) It is observed that the coefficient of friction is-minimum at C or at the transition

between these two modes. The value of bearing characteristic number corresponding
to this minimum coefficient is called bearing modulus.It is denoted by K in the figure.

(v) The bearing should not be operated near the critical value K at point C. Slight drop in
Zn
speed N or slight increase in load P will reduce the value of resulting in boundary
P
lubrication.

The guidelines for hydrodynamic lubrication are as follows:

Zn
• In order to avoid seizure, the operating value of bearing characteristic number should
P
be at least 5 to 6 times the value when the coefficient of friction is minimum.

• If the bearing is subjected to fluctuating loads or impact conditions, the operating value
Zn
of bearing characteristic number ( ) should be at least 15 times that when the
P
coefficient of friction is minimum. (15 K or 15 times bearing modulus).
 Zn
• It is observed from the ( ) curve, that when viscosity of lubricant is very low, the value
P
Zn
of ( ) parameter will be low and boundary lubrication will result.
P

• If the viscosity of lubricant is very low, then the lubricant will not separate the surfaces of
the journal and the bearing and metal to metal contact will occur resulting in excessive
wear at the contacting surface.

Zn
• The ( ) curve is important because it defines the stability of hydrodynamic journal
P
bearings and helps to visualize the transition from boundary lubrication to thick film
lubrication.