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of 3/15/2011
Variation torque of an engine crankshaft
The torque on an engine crankshaft varies considerably throughout
the working cycle, due to variations in the crank position, the pressure
in the cylinder and the inertia of the moving parts.
Crank Effort Diagrams
Crank Effort Diagram
Mean Torque
If the crankshaft torque is plotted against the crank angle, a turning
The net area of the diagram, shown shad ed, represents the wor k d one
during the cycle and the ave rage h eight represents the m ean torque
moment or crank effort diagram is obtained.
exerted (line AE).
Crank effort
diagram for a
single-cylinder
four-stroke
e ngine .
Mean Torque
Mean Torque
If the resisting torque is uniform, this is equal to the mean engine torque if
the mean speed is to remain constant.
Engine torque > resisting torque (AB)
Engine torque < resisting torque (BC)
Engine speeds up;
Engine slows down;
At points of intersection (A, B C etc), Engine torque = resisting torque no
acceleration or deceleration:
speed is max. or min. at these points
1
3/15/2011
A turning moment diagram for a four stroke cycle internal combustion
engine: In a four stroke cycle internal combustion engin e, there is one
working stroke after the crank has turned through two revolutions, i.e.
720 (or 4 radians).
Note:
Since the pressure inside the engine cylinder is less than the
atmospheric pressure during the suction stroke, therefore a
negative loop is formed;
During the compression stroke, the work is done on the gases,
therefore a higher negative loop is obtained;
Turning Moment Diagram for a Multi-cylinder Engine
Note:
During the expansion or working stroke, the fuel burns and the
gases expand, therefore a large positive loop is obtained. In this
stroke, the work is done by the gases.
Turning moment diagram for a compound steam engine having three
cylinders and the resultant turning moment diagram:
During exhaust stroke, the work is done on the gases, therefore a
negative loop is resultant formed.
The turning moment diagram is the sum of the turning moment
diagrams for the three cylinders.
Fluctuation of speed and energy
Fluctuation of speed and energy
The horizontal line AG represents the mean torque line. Let a1, a3,
a5 be the areas above the mean torque line and a2, a4 and a6 be
the areas below the mean torque line.
To keep the fluctuation of speed due to the variation of net
torque within acceptable limits, a flywheel is fitted to the engine
or machine shaft; its function is to act as a reservoir, absorbing
energy as speed increases and releasing energy as speed falls.
These areas represent some quantity of energy which is either added or
subtracted from the energy of the moving parts of the engine.
2
3/15/2011
Fluctuation of speed and energy
Fluctuation of speed and energy
Fluctuation of speed and energy
Fluctuation of speed and energy
The excess e nergy available between the points of minimum and
maximum speeds is called the fluctuation of energy and this represents
the difference between the kinetic energies of the system at these
points.
If the maximum fluctuation of energy is U and 1 and 2 are the
maximum and minimum speeds respectively between the cycle, then
U
1
21
I 1 - I 2
2
2
2
where I is the moment of Inertia of the rotating parts.
Coefficient of fluctuation of energy, CE
The work done per cycle is represented by the area of the rectangle
below the mean torque line and the ratio of fluctuation of energy to
work done per cycle is called the coefficient of fluctuation of energy.
U
U
1
2
I ( 1 - 2 )
2
2
1
I (1 - 2 ) (1 2 )
2
Coefficient of fluctuation of energy
The fluctuation of speeds, 1 - 2, is small in comparison with the mean
speed and, assuming that the variations above and below the mean
speed are equal,
1 2 2
U
1
I x 2 (1 2 )
2
U I ( 1 2 )
3
3/15/2011
Coefficient of fluctuation of speed
The ratio (1 - 2)/, is called the coefficient of fluctuation of speed .
Hence
(1 2 )
U
2
I
4

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