An Approach To Present Basic Design Of I C

Engine.
Major Components of IC Engine
Introduction.
Principal Parts of an I. C. Engine.

1. Cylinder, Cylinder Liner and Head

Construction of Cylinder & Cylinder
HeadDesign of a Cylinder.

2. Piston.
Construction of Piston
Design Considerations for a Piston.
Material for Pistons.
Piston Head or Crown .
Piston Rings.
Piston Barrel.
Piston skirt.
Piston Pin.
Piston Clearance

3. Connecting Rod.
Construction of Connecting Rod
Forces Acting on the Connecting Rod.
Design of Connecting Rod.
 Principal Parts of an I. C. Engine.

4. Crankshaft.
 Construction
 Types
 Material and Manufacture of Crankshafts.

 Design Of Crank Pin

 Bearing Pressures and
 St resses in Crankshaft s.

 Design of Crank Webs

 When gas Force is Maximum

 Design Procedure for Crankshaft.

 Design for Centre Crankshaft.
 Side or Overhung Crankshaft.

5. Valve Gear Mechanism.

 Valves.
 Rocker Arm.
 1. Introduction -


World needs transportation to fulfill most of the basic need either in the form of one or the other. Internal
combustion engine comes under the radar from this point.

It needs different kinds of fuels to work. From past to recent future, world is working in the field of I C
Engine, its systems and for its betterment.

“An Internal combustion engine is an engine in which the combustion of fuel such as petrol, diesel takes
place inside the engine cylinder. ”

Spark Ignition Engines Compression Ignition Engines

Or S.I Engines Or C.I Engines

 In petrol engines (S.I engines),  In diesel engines (C.I engines), only air is

the correct proportion of air and supplied to the engine cylinder during suction
petrol is mixed in the carburetor and stroke and it is compressed to a very high
fed to engine cylinder where it is pressure, thereby raising its temperature from

ignited by means of a spark 600°C to 1000°C.

produced at the spark plug.  The desired quantity of fuel (diesel) is now
injected into the engine cylinder in the form of a
very fine spray and gets ignited when comes in
contact with the hot air.
 The operating cycle of an I.C. engine may be completed either by the
two strokes or four strokes of the piston.

• I.C. engine two strokes of • I.C. engine four strokes of

piston. piston.

 An engine which requires two strokes of  An engine which requires four strokes
the piston or one complete revolution of of the piston or two complete
the crankshaft to complete the cycle, is revolutions of the crankshaft to
known as two stroke engine. complete the cycle, is known as four

 The 2 stroke petrol engines are stroke engine.

generally employed in very light vehicles  The 4 stroke petrol engines are
such as scooters, motor cycles and generally employed in light vehicles
three wheelers. such as cars, jeeps and also in aero

 The 2 stroke diesel engines are planes.

generally employed in marine  The 4 stroke diesel engines are

propulsion. generally employed in heavy duty
vehicles such as buses, trucks,
tractors, diesel locomotive and in the
earth moving machinery.
2. Principal Parts of An I C Engine

The principal parts of an I.C engine,

asshown in Fig. and are as follows :

1. Cylinder, cylinder liner and

Cylinder Head,

2. Piston, piston rings and piston

pin or gudgeon pin,

3. Connecting rod with small and

big end bearing,

4. Crank, crankshaft and crank pin,

and

5. Valve gear mechanism.

The design of the above

mentionedprincipal parts are
discussed, in detail in next slides
 1.Cylinder, Cylinder Liner & Cylinder Head
 Primary function of a cylinder is to retain the working fluid & secondary function to
guide the piston. The cylinders are usually made of cast iron or cast steel

Construction –
• Cylinder has to withstand high temperature due to the combustion of
fuel, therefore, some arrangement must be provided to cool the cylinder.

• The single cylinder engines (such as scooters and motorcycles) are generally
air cooled. They are provided with fins around the cylinder. These fins
increases surface area of cylinder wall and also improves overall heat
transfer coefficient ( For e.g. Scooters & Motorcycles)

• The multi-cylinder engines (such as of cars) are provided with water

jackets around the cylinders to cool it.
• In smaller engines. the cylinder, water jacket and the frame are made
as one piece, but for all the larger engines, these parts are manufactured
separately.
The cylinders are provided with cylinder liners so that in case of
wear, they can be easily replaced.
 1. Cylinder & Cylinder Liner

Advantages – of Use of Separate cylinder liner

1. More Economical , easily replaced against worn out (complete assembly of

cylinder, frame & jacket need not be replaced).

2. Only Cylinder Liner is Made up of Better Grade wear resistant CI ,while frame &
jacket made up of Low grade CI (This saves Cost of manufacturing)
3. Use of Cylinder liner allows Longitudinal expansion.

The cylinder liners are of the two types :, 1. Dry Liner and 2. Wet liner.

A cylinder liner which does not have any direct contact with
the engine
cooling water in jacket, is known as Dry liner, as in Fig. (a).

A cylinder liner which have its outer surface in direct contact

with the engine cooling water in jacket , is known as Wet liner,
as in Fig. (b).

Material – The cylinder liners are made from good quality close
grained cast iron, (i.e. pearlite CI), grey CI ,nickel CI, and nickel
chromium CI. In some cases, nickel chromium cast steel with
molybdenum may be used.

The inner surface of the liner should be properly heat-treated
in order to obtain a hard surface to reduce wear & then
finished by Honing
 • Cylinder flange and studs.
The cylinders are cast integral with the upper half of the crank-case or they are
attached to the crankcase by means of a flange with studs or bolts and nuts.

The cylinder flange is integral with the cylinder and should be made thicker than the cylinder
wall.

The flange thickness should be taken as 1.2 t to 1.4 t, where t is the thickness of
cylinder wall.

The diameter of the studs or bolts may be obtained by

Gas load due to the maximum pressure in the cylinder = Resisting force offered by all the
studs or bolts.

Mathematically,
where D = Cylinder bore in mm,

p = Maximum pressure in N/mm2,

ns = Number of studs. It may be taken as ( 0.01 D + 4 ) to ( 0.02 D + 4 )

dc = Core or minor diameter, i.e. diameter at the root of the thread in mm,

σt = Allowable tensile stress for material of studs or bolts in MPa or N/mm 2.

It may be taken as 35 to 70 MPa.

The nominal or major diameter of the stud or bolt (d ) usually lies between 0.75 tf to

tf, where tf is the thickness of flange. In any case Nominal diameter of a stud or bolt should
not be less than 16 mm.
Diameter of Bolt/Stud Pitch circle & Flange - The distance of the flange from the center of the hole
for the stud or bolt should not be less than d + 6 mm and not more than 1.5 d, where d is the
nominal diameter of the stud or bolt.

pitch of the studs or bolts - In order to make a leak proof joint, the pitch of the studs or
bolts should lie between 19 to 28.5 where d is in mm.
 • Cylinder Head –
Usually, a separate cylinder head or cover is provided with most of the engines.
 It is, usually, made of box type section of considerable depth to accommodate ports for
air and gas passages, inlet valve, exhaust valve and spark plug (in case of petrol engines) or
atomiser at the centre of the cover (in case of diesel engines).
 The cylinder head may be approximately taken as a flat circular plate whose thickness

(th) may be determined from the following relation :

where D = Cylinder bore in mm,

p = Maximum pressure inside t he cylinder in N/mm2,

σc = Allowable circumferential stress in MPa or N/mm2. It may be t aken as 30 t o 50 MPa &

C = ( or k) as Const ant whose value is t aken as 0.1. or 0.162.

Note- 1. Allowable circumferential stress σc in above equation as Allowable tensile stress σt i.e. σc =
σt = Sut/ f.o.s.

 The studs or bolts are screwed up tightly along with a metal gasket or asbestos packing to
provide a leak proof joint between the cylinder and cylinder head.

 The tightness of the joint also depends upon the pitch of the bolts or studs,
which should lie
between 19 to 28.5 .
 The pitch circle diameter (Dp) is usually taken as D + 3d.

The studs or bolts are designed in the same way as discussed above.
 2.Piston - Introduction & Constructional Details –

The piston is a disc which reciprocates within a cylinder. It is either moved by the fluid or it
moves the fluid which enters the cylinder.

The main function of the piston of an internal combustion engine is to receive the
impulse from the expanding gas and to transmit the energy to the crankshaft
through the connecting rod.

The piston must also disperse a large amount of heat from the combustion chamber to the
cylinder walls.

The piston of IC Engines of trunk type ( open at one end ) & of following parts as shown in
Fig.

1. Head or crown. The piston head or crown may be flat, convex or concave depending

upon the design of combustion chamber. It withstands the pressure of gas in the cylinder.

2.Piston rings. The piston rings are used to seal the cylinder in order to prevent leakage of the
gas

past the piston.

3.Skirt. The skirt acts as a bearing for the side thrust of the connecting rod on the walls of
cylinder.
4.Piston pin. It is also called gudgeon pin or wrist pin. It is used to connect the piston to
the

connecting rod.
2. Piston - Introduction & Constructional Details –
2.Piston
Design Considerations for a Piston
In designing a piston for I.C. engine, the following points should be taken into
consideration :

1. It should have enormous strength to withstand the high gas pressure and inertia
forces.

2. It should have minimum mass to minimize the inertia forces.

3. It should form an effective gas and oil sealing of the cylinder.

4. It should provide sufficient bearing area to prevent undue wear.

5. It should disperse the heat of combustion quickly to the cylinder walls.

6. It should have high speed reciprocation without noise.

7. It should be of sufficient rigid construction to withstand thermal and mechanical

distortion.

8. It should have sufficient support for the piston pin.

Material for Pistons

The most commonly used materials for pistons of I.C. engines are cast iron, cast
aluminium, forged aluminium, cast steel and forged steel. The cast iron pistons are used
for moderately rated engines with piston speeds below 6 m / s and aluminium alloy
pistons are used for highly rated engines running at higher piston speeds.
It may be noted that 2. Piston - Material for Pistons
1.Since the *coefficient of thermal expansion for aluminium is about 2.5 times that of cast iron,

therefore, a greater clearance must be provided between the piston and the cylinder wall (than
with cast iron piston) in order to prevent seizing of the piston when engine runs continuously
under heavy loads. But if excessive clearance is allowed, then the piston will develop ‘piston
slap’ while it is cold and this tendency increases with wear. The less clearance between the piston
and the cylinder wall will lead to seizing of piston.

2.Since the aluminium alloys used for pistons have high **heat conductivity (nearly four times
that of cast iron), therefore, these pistons ensure high rate of heat transfer and thus keeps
down the maximum temperature difference between the center and edges of the piston head
or crown.
Notes: (a) For a cast iron piston, the temperature at the center of the piston head (TC) is about 425°C
to 450°C under full
load conditions and the temperature at the edges of the piston head (TE) is about 200°C to 225°C.

(b) For aluminium alloy pistons, TC is about 260°C to 290°C and TE is about 185°C to 215°C.

3.Since the aluminium alloys are about ***three times lighter than cast iron, therefore, its

mechanical strength is good at low temperatures, but they lose their strength (about 50%) at
temperatures above 325°C. Sometimes, the pistons of aluminium alloys are coated with
aluminium oxide by an electrical method.

* The coefficient of thermal expansion for aluminium is 0.24 × 10–6 m / °C and for
cast iron it is 0.1 × 10– 6 m / °C.
* The heat conductivity for aluminium is 174.75 W/m/°C and for cast iron it is 46.6
W/m /°C.
* The density of aluminium is 2700 kg / m3 and for cast iron it is 7200 kg / m3.
2. Piston - Material for Pistons
The piston head or crown is designed keeping in view the following two main
considerations, i.e.

1. It should have adequate strength to withstand the straining action due to pressure of
explosion inside the engine cylinder, and
2.It should dissipate the heat of combustion to the cylinder walls as quickly as possible.

On the basis of first consideration of straining action, the thickness of the piston head is
determined by treating it as a flat circular plate of uniform thickness, fixed at the outer
edges and subjected to a uniformly distributed load due to the gas pressure over the
entire cross-section.
……eqn (1)

The thickness of the piston head (t H ), according to Grashoff’s formula is given by

where p = Maximum gas pressure or explosion pressure in N/mm2,

D = Cylinder bore or outside diameter of the piston in mm, and

σt = Permissible bending (tensile) stress for the material of the piston in MPa or
N/mm2.
It may be taken as 35 to 40 MPa for grey cast iron,50 to 90 MPa for nickel cast iron
and aluminium alloy and 60 to 100 MPa for forged steel.
 2. Piston - Material for Pistons

On the basis of second consideration of heat transfer, the thickness of the piston head should be such that the
heat absorbed by the piston due combustion of fuel is quickly transferred to the cylinder walls. Treating the
piston head as a flat circular plate, its thickness is given by

….. (2)

Where, H = Heat flowing through t he piston head in kJ/s or watts,

k =Heat conductivit y fact or in W/m/°C. Its value is 46.6 W/m/°C for grey cast iron, 51.25
W/m/°C for
st eel and 174.75 W/m/°C for aluminium alloys.

TC = Temperat ure at the cent er of t he piston head in °C, and

TE = Temperat ure at t he edges of t he piston head in °C.

 The temperature difference (TC – TE) may be taken as 220°C for cast iron and 75°C for aluminium.
 The heat flowing through the position head (H) may be determined by the following expression, i.e.,

H = C x HCV x m x B.P. (in kW)

Where C = Const ant representing that portion of t he heat supplied t o t he engine which is absorbed by t he
pist on. Its value is usually t aken as 0.05.

HCV = Higher calorific value of t he fuel in kJ/kg. It may be t aken as 45 × 103 kJ/kg for diesel and 47 ×
103 kJ/ kg for pet rol,

m = Mass of t he fuel used in kg per brake power per second, and

B.P. = Brake power of t he engine per cylinder

 2. Piston - Material for Pistons

Notes :

1. The thickness of the piston head (tH) is calculated by using equations (i) and (ii) and
larger of the two values obtained should be adopted.

2. When tH is 6 mm or less, then no ribs are required to strengthen the piston head
against gas loads. But when tH is greater then 6 mm, then a suitable number of ribs
at the center line of the boss extending around the skirt should be provided to distribute
the side thrust from the connecting rod and thus to prevent distortion of the skirt.
The thickness of the ribs may be takes as tH / 3 to tH / 2.

3. For engines having length of stroke to cylinder bore (L / D) ratio up to 1.5, a cup is
provided in the top of the piston head with a radius equal to 0.7 D. This is done to provide a
space for combustion chamber.
 2. Piston Rings
The piston rings are used to impart the necessary radial pressure to maintain the seal between
the piston and the cylinder bore. These are usually made of grey cast iron or alloy cast iron because
of their good wearing properties and also they retain spring characteristics even at high
temperatures.

The piston rings are of the following two types :

1. Compression rings or pressure rings, and 2. Oil control rings or oil scraper.

The compression rings or pressure rings are inserted in the grooves at the top portion of the
piston and may be three to seven in number. These rings also transfer heat from the piston to the
cylinder liner and absorb some part of the piston fluctuation due to the side thrust.

The oil control rings or oil scrapers are provided below the compression rings. These rings
provide proper lubrication to the liner by allowing sufficient oil to move up during upward stroke
and at the same time scraps the lubricating oil from the surface of the liner in order to minimize
the flow of the oil to the combustion chamber.
 2.Piston Rings

 The compression rings are usually made of rectangular cross-section and the diameter
of the ring is slightly larger than the cylinder bore.
 A part of the ring is cut- off in order to permit it to go into the cylinder against the liner
wall.
 The diagonal cut or step cut ends, as shown in Fig. (a) and (b) respectively, may be
used.
 The gap between the ends should be sufficiently large when the ring is put cold so that
even at the highest temperature, the ends do not touch each other when the ring
expands, otherwise there might be buckling of the ring.
 2.Piston Rings
 The radial thickness (t1) of the ring may be obtained by considering the radial
pressure between the cylinder wall and the ring. From bending stress
consideration in the ring, the radial thickness is given by

where D = Cylinder bore in mm,

pw = Pressure of gas on the cylinder wall. Its value is limited from 0.025 N/mm2 to 0.042
N/mm2, and σt = Allowable bending (tensile) stress in MPa.
Its value may be taken from 85 MPa to 110 MPa for cast iron rings.

The axial thickness (t2 ) of the rings may be taken as 0.7 t1 to t1.
The minimum axial thickness (t2 ) by empirical relation:

where nR = Number of rings.

The width of the top land (i.e. the distance from the top of the piston to the first
ring groove) is made larger than other ring lands to protect the top ring from high
temperature conditions existing at the top of the piston,
∴ Width of top land, b1 = tH to 1.2 tH

The width of other ring lands (i.e. the distance between the ring grooves) in the
piston may be made equal to or slightly less than the axial thickness of the ring (t2).
∴ Width of other ring lands, b2 = 0.75 t2 to t2
 2. Piston Rings

The depth of the ring grooves should be more than the depth of the ring so that the ring
does not take any piston side thrust.
The gap between the free ends of the ring is given by 3.5 t1 to 4 t1.
The gap, when the ring is in the cylinder, should be 0.002 D to 0.004 D.

3.Piston Barrel

 It is a cylindrical portion of the piston.

 The maximum thickness (t3) of the piston barrel by empirical relation :

t3 = 0.03 D + b + 4.5 mm

where b = Radial depth of piston ring groove which is taken as 0.4 mm larger
than the radial thickness of the piston ring (t1)
b = t1 + 0.4 mm

Thus, the above relation may be written as t3 = 0.03 D + t1 + 4.9 mm

 The piston wall thickness (t4) towards the open end is decreased and should be
taken as
0.25 t3 to 0.35 t3.
 5.Piston Pin

 The piston pin (also called gudgeon pin or wrist pin) It is used to connect the
piston and the connecting rod.

 It is usually made hollow and tapered on the inside, the smallest inside diameter
being at the centre of the pin, as shown in Fig. 2

 The piston pin passes through the bosses provided on the inside of the piston
skirt and the bush of the small end of the connecting rod.

 The centre of piston pin should be 0.02 D to 0.04 D above the centre of the
skirt, in order to off-set the turning effect of the friction and to obtain uniform distribution
of pressure between the piston and the cylinder liner.
 5.Piston Pin

 The connection between the piston pin and the small end of the connecting rod may be
made either full floating type or semi-floating type.

 In the full floating type, the piston pin is free to turn both in the *piston bosses and the
bush of the small end of the connecting rod. The end movements of the piston pin should
be secured by means of spring circlips, as shown in Fig. 32.6, in order to prevent the pin
from touching and scoring the cylinder liner.

 In the semi-floating type, the piston pin is either free to turn in the piston bosses and
rigidly secured to the small end of the connecting rod, or it is free to turn in the bush of the
small end of the connecting rod and is rigidly secured in the piston bosses by means of a
screw, as shown in Fig.

 The piston pin should be designed for the maximum gas load or the inertia
force of the piston, whichever is larger. The bearing area of the piston pin should be
about equally divided between the piston pin bosses and the connecting rod bushing. Thus,
the length of the pin in the connecting rod bushing will be about 0.45 of the cylinder bore or
piston diameter (D), allowing for the end clearance of the pin etc.

 The outside diameter of the piston pin (d0 ) is determined by equating the load on the
piston due to gas pressure (p) and the load on the piston pin due to bearing pressure
( pb1 ) at the small end of the connecting rod bushing.
 5.Piston Pin

* The mean diameter of the piston bosses is made 1.4 d0 for cast iron pistons and
1.5 d0 for aluminum pistons, where d0 is the outside diameter of the piston pin. The
piston bosses are usually tapered, increasing the diameter towards the piston wall.
 5. Piston Pin

Let d0 = Outside diameter of the piston pin in mm

l1 = Length of the piston pin in the bush of the small end of the connecting rod in
mm.

Its value is usually taken as 0.45 D.

pb1 = Bearing pressure at the small end of the connecting rod bushing in
N/mm2.

Its value for the bronze bushing may be taken as 25 N/mm2.

We know that

Load on the piston due to gas pressure or gas ...

load (i)

And

Load on the piston pin due to bearing pressure or bearing load

= Bearing pressure × Bearing area = pb1 × d0 × l 1 ...(ii)

From equations (i) and (ii), the outside diameter of the piston pin (d0) may be
obtained.
 5.Piston Pin

 The piston pin checked in bending by assuming the gas load to be uniformly
distributed over the length l1 with supports at the centre of the bosses at the two ends.
From Fig.

we find that the length between the supports,

Now maximum bending moment at

the centre of the pin,
 5.Piston Pin

 We have already discussed that the piston pin is made hollow. Let d0 and di be the
outside and inside diameters of the piston pin.
 We know that the section modulus,

 We know that maximum bending moment,

 where σb = Allowable bending stress for the material of the piston pin.

It is usually taken as 84 MPa for case hardened carbon steel and 140 MPa for
heat treated alloy steel.
Assuming di = 0.6 d0, the induced bending stress in the piston pin may be checked.
5. Connecting Rod
 5.Connecting Rod

The connecting rod is the intermediate member between the piston and the crankshaft.

Its primary function is to transmit the push and pull from the piston pin to the crankpin
and thus convert the reciprocating motion of the piston into the rotary motion of the
crank.

The usual form of the connecting rod in internal combustion engines is shown in Fig.

It consists of a long shank, a small end and a big end.

The cross-section of the shank may be circular, rectangular, tubular, I-section or H-
section. Generally circular section is used for low speed engines while I-section is
preferred for high speed engines.

The *length of the connecting rod ( l ) depends upon the ratio of l / r, where r is the radius
of crank.

It may be noted that the smaller length will decrease the ratio l / r. This increases the
angularity of the connecting rod which increases the side thrust of the piston against the
cylinder liner which in turn increases the wear of the liner.
 5.Connecting Rod


The larger length of the connecting rod will increase the ratio l / r. This decreases
the angularity of the connecting rod and thus decreases the side thrust and the
resulting wear of the cylinder. But the larger length of the connecting rod increases
the overall height of the engine.

Hence, a compromise is made and the ratio l / r is generally kept as 4 to 5.

The small end of the connecting rod is usually made in the form of an eye and is
provided with a bush of phosphor bronze. It is connected to the piston by means of a
piston pin.

The big end of the connecting rod is usually made split (in two **halves) so that it
can be mounted easily on the crankpin bearing shells. The split cap is fastened to the
big end with two cap bolts.

The bearing shells of the big end are made of steel, brass or bronze with a thin lining
(about 0.75 mm) of white metal or babbit metal.
 5.Connecting Rod


The wear of the big end bearing is allowed for by inserting thin metallic strips (known as
shims) about 0.04 mm thick between the cap and the fixed half of the connecting rod. As
the wear takes place, one or more strips are removed and the bearing is trued up.

The connecting rods are usually manufactured by drop forging process and it should have
adequate strength, stiffness and minimum weight. The material mostly used for connecting
rods varies from mild carbon steels (having 0.35 to 0.45 percent carbon) to alloy steels
(chrome-nickel or chrome molybdenum steels).

The carbon steel having 0.35 percent carbon has an ultimate tensile strength of about
650MPa when properly heat treated and a carbon steel with 0.45 percent carbon has a
ultimate tensile strength of 750 MPa.

These steels are used for connecting rods of industrial engines. The alloy steels have an
ultimate tensile strength of about 1050 MPa and are used for connecting rods of aero
engines and automobile engines.
 5. Connecting Rod

Splash Lubrication System Pressure Lubricating System

 The bearings at the two ends of the connecting rod In thepressure lubricating system,the lubricating oil

are either splash lubricated or pressure lubricated. is fed under pressure to the big end bearing through the
 The big end bearing is usually splash lubricated holes drilled in crankshaft, crank webs and crank pin.

while the small end bearing is pressure lubricated. From the big end bearing, the oil is fed to small end
 In the splash lubrication system, the cap at the big bearing through a fine hole drilled in the shank of the

end is provided with a dipper or spout and set at an connecting rod.


angle in such a way that when the connecting rod In some cases, the small end bearing is lubricated by the
moves downward, the spout will dip into the oil scrapped from the walls of the cylinder liner by the
lubricating oil contained in the sump. The oil is oil scraper rings.
forced up the spout and then to the big end bearing.

Now when the connecting rod moves upward, a
splash of oil is produced by the spout.

This splashed up lubricant find its way into the
small end bearing through the widely chamfered
holes provided on the upper surface of the small end.
Forces Acting on the Connecting Rod
The various forces acting on the connecting rod are as follows :
1. Force on the piston due to gas pressure and inertia of the reciprocating parts,
2. Force due to inertia of the connecting rod or inertia bending forces,
3. Force due to friction of the piston rings and of the piston, and
4. Force due to friction of the piston pin bearing and the crankpin bearing.
We shall now derive the expressions for the forces acting on a vertical engine, as
discussed below.
1. Force on the piston due to gas pressure and inertia of reciprocating
parts Consider a connecting rod PC as shown in Fig.
Let p = Maximum pressure of gas,
D = Diameter of piston,
A = Cross-section area of piston
mR = Mass of reciprocating parts
= Mass of piston, gudgeon pin etc. + 1/3 rd mass of connecting rod,
ω = Angular speed of crank,
φ = Angle of inclination of the connecting rod with the line of stroke,
θ = Angle of inclination of the crank from top dead centre,
r = Radius of crank,
l = Length of connecting rod, and
n = Ratio of length of connecting rod to radius of crank = l / r.
We know that,
Force on the piston due to pressure of gas,

and inertia force of reciprocating parts,

• It may be noted that the inertia force of reciprocating parts opposes the force on the
piston when it moves during its downward stroke (i. e. when the piston moves from the top
dead centre to bottom dead centre).
• On the other hand, the inertia force of the reciprocating parts helps the force on the
piston when it moves from the bottom dead centre to top dead centre.
∴ Net force acting on the piston or piston pin (or gudgeon pin or wrist pin),

The –ve sign is used when piston moves from TDC to BDC and +ve sign is used when piston
moves from BDC to TDC.
When weight of the reciprocating parts (WR = mR . g) is to be taken into consideration, then
The force FP gives rise to a force FC in the connecting rod and a thrust FN on the sides of
the cylinder walls. From Fig., we see that force in the connecting rod at any instant,

The force in the connecting rod will be maximum when the crank and the connecting rod are
perpendicular to each other (i.e. when θ = 90°). But at this position, the gas pressure would
be decreased considerably.
Thus, for all practical purposes, the force in the connecting rod (FC ) is taken equal to the
maximum force on the piston due to pressure of gas (FL), neglecting piston inertia
effects.