Inertia Forces_Ppt.pdf .

Department of Mechanical & Manufacturing Engineering, MIT, Manipal 1 of 38
CHAPTER 2
INERTIA FORCES
DYNAMICS OF MACHINERY

Crank Effort
The driving force acting on the piston is termed as
piston effort. In a vertical cylinder IC engine, following
three types of forces act:
a. Gas Force. The force due to variation of working
fluid pressure is known as gas force, or Gas force
Fg =
πD2
4
× p ……..(1)
where
D = diameter of the piston and
p = gas pressure

b. Inertia force. In an IC engine, during the first half
of the stroke, the reciprocating mass accelerates and
the inertia force tends to resist the motion. Thus the
net force on the piston is decreased.
However, during the second half of the stroke, the
reciprocating mass decelerate and inertia force
opposes this deceleration. Thus it increases the
effective force on the piston.
The inertia force of the piston is given as
………………(2)

c. Weight of the reciprocating mass.
The weight of reciprocating mass assists the piston
during its movement towards bottom dead centre
(BDC). Therefore, piston effort is increased by an
amount equal to the weight of the piston. However,
when the piston moves towards top dead centre
(TDC), the piston effort is decreased by the same
amount.
Net piston effort: P = Fg + Fi  W ………….(3)

Forces acting on a slider crank mechanism
(Analytical Method)
To determine crank effort:

Graphical Method to determine crank effort or torque
T = P x distance OY
Where OY is the distance measured between centre
of crank and a point of intersection of Y axis and
extension of connecting rod P2B

Note:
The crank effort is a function of piston effort P and
crank rotation angle. Further, the piston effort is also
a function of crank angle .
The diagram showing the crank effort or torque as a
function of crank rotation angle  for any reciprocating
engine is called crank-effort diagram or turning
moment diagram.

The turning moment diagram of any engine can be
plotted if the gas pressure p is known for all positions
of the crank. The value of gas pressure can be found
from a given pressure-volume (P-V) diagram
(Figure 3).
Figure 3. P-V diagram of petrol engine

Using these pressure values, gas forces can be
computed and plotted as shown in Figure 4.
Figure 4. Variation of Gas force and Inertia force

Further, the variation of inertia force due to mass of
reciprocating parts can be plotted as shown in Figure
5 with dashed line.
Figure 5. Variation of piston effort

T= piston effort x OY
Where OY is the crank effort arm length. The
variation in crank effort arm length for different crank
position is shown in figure 6.
Figure 6. Variation of crank effort arm length

Finally the turning moment diagram is shown in figure 7. A close
look at the turning moment diagram (Figure 7) shows that
torque T is entirely positive in expansion stroke of engine
whereas in suction, compression and exhaust strokes, it is
negative. This indicates that in these strokes, power is
consumed. Thus there is large variation of torque which may
cause fluctuation of speed.
Figure 7. Turning moment diagram

Figure 8. Turning moment diagram for a
multi-cylinder engine.
In multi-cylinder engine,
the turning moment
diagram of each cylinder is
obtained separately and
they are superimposed
over each other with
starting point shifted to
phase difference of angle
between respective crank
positions. A typical turning
moment diagram of multi-
cylinder engine is shown in
figure 8.

Flywheel
A flywheel is an inertial energy storage device. It
absorbs mechanical energy and serves as a
reservoir, storing energy during the period when the
supply of energy is more than the requirement and
releases it during the period when the requirement of
energy is more than the supply.
Internal combustion engines with one or two
cylinders are a typical example. Piston compressors,
punch presses, rock crushers etc. are the other
systems that have flywheel.

Types of Flywheel
Generally, three types of flywheel – disc type, web type and
arm type are most commonly used (Figure 11).

Types of Flywheel

A plot of torque vs. crank angle or turning moment
diagram of a multi cylinder engine is shown in the
figure 12.
Figure 12. Turning moment diagram of a multi cylinder engine

Fluctuation of energy (Ef):
The difference between maximum and minimum kinetic
energies of flywheel is known as maximum fluctuation of
energy, Ef.
A flywheel is used to control the variations in speed during
each cycle of an engine. A flywheel of suitable dimensions
attached to the crankshaft, makes the moment of inertia of
rotating parts quite large and thereby it acts as a reservoir of
energy. During the periods when the supply of energy is more
than required, it stores energy and during the period when the
supply is less than required, it releases the energy.

Coefficient of Fluctuation of energy (Ke):
Ratio of maximum fluctuation of energy and work done per
cycle is known as coefficient of fluctuation of energy.
Ke = Max. fluctuation of energy / work done per cycle.
Therefore Ke =
Ef
E
Work done / cycle = Tmean x 
where Tmean = Mean torque and  = angle turned by the crank
in radians.
Also Work done per cycle is given: = P x 60,000/N
where P = Power in KW and N is in rpm.

Coefficient of Fluctuation of speed (Ks):
The difference between the greatest and the least angular
speeds of the flywheel is called the maximum fluctuation of
speed and the ratio of greater fluctuation of speed per cycle
to the mean speed is called Coefficient of fluctuation of
speed.

Flywheel of a Punching Press:

Flywheel of a Punching Press:
Formula’s Used:

KINEMATICS OF MACHINERY
Numericals from
Chapter : Inertia Forces
End of Chapter

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