Tribology is the study of friction, lubrication, and wear between interacting surfaces in relative motion. It helps improve machine reliability and reduce failures. Reynolds' equation, derived in 1886, quantifies fluid film lubrication and allows prediction of hydrodynamic, hydrostatic, and squeeze film mechanisms by modeling pressure as a function of coordinates and time. The equation assumes laminar flow of an incompressible Newtonian fluid with negligible inertia and pressure gradients in the film thickness direction.

1. Introduction to tribology
By- Kumar Ankur
Mechanical Engineering Department

2. What is Tribology ?
• Tribology is derived from the Greek word “Tribos”. Meaning of
Tribos is Rubbing.
• Tribology is a science that deals with friction, lubrication and
wear in all contacting pairs.
• Tribological knowledge helps to improve service life, safety and
reliability of interacting machine components; and yields
substantial economic benefits.

3. Consider few failed machine components, failure of which could had been avoided using
tribological knowledge.
Example 1 CAM
Example 1 is related to pitting wear on the cam surface. Cams are used to transmit rotary
motion in reciprocating motion. These components are subjected to jerks in sliding
distance, which leads to form some pits on the cam surface. Creation of pits on cam surface
increases noise pollution and reduces mechanical performance. Understanding the
mechanism of pit formation helps to estimate the life of component and find methods to
reduce such pitting failures.

4. Example 2 JOURNAL BEARING
In these examples of journal bearing, wear increases the clearance between shaft and
bearing and leads to reduction in load support capacity of the bearing. Often such
failures occur in absence of sufficient lubricant hydrodynamic film thickness due to
relatively low speed. Learning tribology cultivates an understanding that at low
speeds, the main purpose of oil is the lubrication and high viscosity oil will be
preferred to low viscosity oil, while at high speeds the major purpose of oil is to act as
a coolant and low viscosity lubricants are preferred to carry away frictional heat of
operation. Here lubrication is a secondary consideration.

5. Example 3 Multi-row Roller Bearing
Here cracking means deep cracks which breaks outer ring in number of pieces. Such
failure occurs due to faulty manufacturing and wrong assembly of roller bearing.
Tribological relations help estimating increase in contact stresses due to misalignment
of shaft and improper mounting of bearing surfaces. Hence an approximation on
reduction in service life can be estimated.

6. Example 4 Gear
The pit generally occurs due to excessive contact stress. Understanding the effect of contact
stress helps in developing an equation for estimation of perspective gear life.

7. Need of Tribology as subject
• Most tribological phenomenon are inherently complicated and interconnected, making it
necessary to understand the concepts of TRIBOLOGY in details.
• Integration of knowledge from multifaceted disciplines(solid mechanics, fluid mechanics,
material science, chemistry etc) is essential and therefore a separate subject is required.
• Solid Mechanics: Focus is on expressions of contact stresses/deformations and surface
temperatures due to rolling/sliding.
• Fluid Mechanics: Study of lubricant film formed between various geometric shapes of
rolling/sliding surfaces.
• Material Science: Focus is on atomic and micro scales mechanisms whereby solid surface
degradation or alteration occurs during relative motion.
• Chemistry: Deals with reactivity between lubricants and solid surfaces.
• Thermodynamics: Heat and mass transfer in fluids and bounding solids.

8. Fluid Film Lubrication
Fluid Mechanics Concepts : Fluid is defined as a substance that easily moves and
changes its relative position without a separation from the bulk mass.
• Lubrication makes relative motion between two surfaces very smooth. It reduces
the friction and minimizes the wear.
• In general, real area of contact between tribo-pair is hardly ten percent of
apparent area.
• Here, stress-state always exceeds the elastic/fracture point of all known solids. It
results in high plastic deformation in ductile materials, while generates cracks in
brittle materials, which causes excessive wear.
• Therefore, it is essential to reduce the normal stresses imposed by applied load
and to reduce the shear stresses induced due to relative motion.
There are some ways to reduce the normal and shear stresses shown on
next slide.

10. In hydrostatic lubrication that separates two surfaces by an external pressure source.
It is suitable for extremely high load carrying capacity at low speed or at highly
controlled precision works.
• As pressure is generated and supplied by external sources, it is one of the
expensive approaches to separate two surfaces.
• If applied load is reduced, the film thickness (separation between tribo-pair) will
increase. Similarly if more load is added to the moving surface, the film thickness
will decrease.
• To compensate cost, often a hybrid concept of hydrodynamic + hydrostatic is used
to achieve best of both the mechanisms of fluid film lubrications.

11. In a hydrodynamic lubrication mechanism, a fluid is drawn into the region between
the relatively-moving surface by the virtue of its viscosity and adhesion to the
surfaces.
Due to the converging geometry of the surfaces, a pressure is generated within the
fluid that separates the tribo-surfaces. The separating film is only generated when the
there is relative motion.

12. • Reynolds’ Equation :
Fluid film lubrication between two plates.

13. In 1886, Reynolds derived an equation for estimation of
pressure distribution for “Fluid Film Lubrication”.
• Quantification of fluid film lubrication can be made by
solving Reynolds’ Equation, which provides fluid film
pressure as a function of coordinates and time. Reynolds
equation helps to predict hydrodynamic, squeeze, and
hydrostatic film mechanisms.

14. Derivation of Reynolds’ Equation :
To model the pressure as a function of angle of inclination, let us consider a fluid
element subjected to pressure and viscous forces, assuming gravity and inertia forces
acting on fluid element can be neglected.
Fig: Fluid element subjected to pressure & viscous forces.
On balancing forces shown in figure-

15. For laminar flow of Newtonian fluid,
On substitution
Equation is based on following assumptions :
1. Negligible inertia terms
2. Negligible pressure gradient in the direction of film thickness
3. Newtonian fluid

16. Asaas

17. Assuming no slip at liquid-solid boundary;
y = 0, u = U2
y = h, u = U1
Utilizing these boundary conditions, values of integration constants can be evaluated.

18. This equation is applicable for following assumptions :
1. Negligible inertia terms.
2. Negligible pressure gradient in the direction of film thickness.
3. Newtonian fluid.
4. Constant value of viscosity.
5. No slip at liquid solid boundary.
In that equation, on right hand side there are three terms, two velocity terms and one
pressure term. Velocity terms represent “shear flow” also known as “Couette flow”.
Flow due to pressure gradient is termed as “Poiseuille flow”. similarly flow velocity in z
direction.