FLYWHEEL AND GOVERNOR CLASS NOTES FOR MECHANICAL ENGINEERING

FLYWHEEL & GOVERNOR

CLASS NOTES FOR

MECHANICAL ENGINEERING

 

Flywheel is an energy storage device

where more power is available in the

working stroke. It supplies back this

energy to the machine in the remaining

strokes of the cycle. Thus it maintains a

constant speed of the machine.

Operation of the flywheel is continuous

whereas the operation of governor is

intermittent. Flywheel controls the

variation of speed at the crankshaft.

It is used to store excess energy

available during working stroke.

Energy is supplied back n non

working strokes. It finds its

application in diesel engines. Its

design includes the design of rim

and arms.

The Governor controls the speed

variation due to load fluctuation on

the engine. Both stabilize speed during

fluctuations. There is a difference in their

working

FLYWHEEL

Flywheels store kinetic energy. Flywheel is just a rotating mass and its mass moment of inertia helps to achieve its purpose. Remember flywheel is not a source of generating power. It is a highly efficient, reliable durable non polluting device. Its maintenance is simple and less costly. However there are safety concerns because of high speed. Its makes the speed of the machine constant. Its own speed varies. Thus there is a fluctuation of speed & fluctuation of energy of a flywheel.

ENERGY STORAGE

Four stroke internal combustion engines develop power only during the working stroke. This power is much more than the power required for use. Thus the excess energy is stored in the flywheel. It will supply back this stored energy during  suction, compression and exhaust strokes. Energy is supplied back during compression stroke in case of a two stroke engine. Since it stores energy, it is a mechanical battery.

PERFORMANCE PARAMETERS OF A FLYWHEEL

  1. Coefficient of fluctuation of speed, Cs
Cs =(ωmax — ωmin)/ ωmean =(Nmax — Nmin)/ Nmean
Firstly ωmax is maximum angular speed
Secondly ωmin   is minimum angular speed               
Thirdly ωmean is mean angular speed =(ωmax+ ωmin)/2
Fourthly N max  is maximum RPM
Fifthly N min is minimum RPM
N mean is the mean RPM = (N max + N min)/2

Empirical data for coefficient of fluctuation of speed

Sr. No.

Type of machine

Value of Cs

1.
Reciprocating pumps and compressors
0.04
2.
Automobile (normal speed)
0.1
3.
Automobile (idling)
0.2
4.
Punching/pressing machine
0.2 to 0.07
 
Coefficient of Fluctuation of energy, Ce
Ce = ∆E/E
  1. E = (1/2) I ω2mean
  1. ∆E = Maximum Fluctuation of energy as speed changes from ωmax to ωmin .
here   ∆E =Maximum K.E. –Minimum K.E.
Maximum K.E. =(1/2)(I) ω2max
Minimum K.E.=(1/2)(I) ω2min
        ∆E   = (1/2)(I)(ω2max – ω2min)
On simplification
                = (1/2)(I)(ωmax + ωmin) ( ωmax — ωmin)
Further simplification gives
               = I ωmean ( ωmax — ωmin)
               = I ω2mean ( ωmax — ωmin)/ ωmean
           ∆E = 2ECs
Ce =∆E/E= 2ECs/E= 2Cs
Ce= 2Cs
Where
I = mass moment of inertia = mR2
m=2πR b t ρ
b = width of rim
t = thickness of rim
Generally     b/t = 2
Ρ = density of the flywheel material
=7260 kg/m3 for Cast iron
= 7800 kg/m3 for steel
Material of the flywheel = Cast iron
TYPES OF FLYWHEELS
  1. Solid Disc Type
  2. Rim type with number of arms
NOTE: Rim type is maximum in use and hence will be considered in detail.
MOI = Ir = k I
Where
k =0.9
I = MOI of entire flywheel
Ir = mrR2
mr = mass of rim
R = mean radius of rim < (30/ vmean)
TABLE: Empirical data on limiting rim velocity

Sr. No.

Type of machine

Rim velocity, v, m/min

1.
Cast iron flywheel below 100 kg
1500
2.
Cast iron flywheel for auto mobiles
3100
3.
Cast steel flywheel for auto mobiles
6200

FLYWHEEL DESIGN

(a) DESIGN OF RIM

Stresses in a rim

  • Tensile stress due to centrifugal force

σt = ρv2

  • Tensile stresses due to bending of arms

σb = M/Z

BENDING MOMENT

M = wL2/12

w = UDL

Equals centrifugal force between two arms per unit length

w = mRω2 =ρbtLR ω2/L

     =ρbtR ω2

L = length between two arms

= Behaves as a fixed beam

L =2πR/n

NUMBER OF ARMS

n = number of arms (normally 4,6 and 8)

M = wL2/12= ρbtLR ω2L2/12

    = (ρbtLR ω2/12)( 2πR/n)2

    = π2ρbt v2R/3n2

Z = bt2/6

σb = M/Z =2 π2ρv2R/n2 t

NOTE: Arms stretch by ¾ of free expansion due to the centrifugal force

Total stress in the rim

σtotal = (3/4) σt + σb/4

          = (3/4) ρv2 +  π2ρv2R/2n2 t

           = ρv2(0.75 + 4.935R/n2 t )

For a safe design for a cast iron flywheel

Total stress should be less than the allowable stress of 38 MPa.

CHECK  σtotal <38 MPa.

  • Shrinkage stresses are due to uneven rate of of cooling of the casting. It is difficult to calculate but is accounted for a certain factor say 10 %.

(b) DESIGN OF ARMS

Stresses in arms

  • Tensile stress due to centrifugal force acting on the rim

  • Bending stresses due to torque transmitted from the rim to the shaft

  • Shrinkage stresses—Cannot be determined. To account for this, 10% stress is added.

Tensile stress due to centrifugal force       σt = 0.75 ρv2

BENDING MOMENT

M is due to the torque  ‘T’ transmitted, M = = T(R-r)/nR

Where n is the number of arms

Firstly σbt1 =Due to torque( hence due to M)

σbt1 =M/Z

Secondly σbt2=Due to belt tensions  =(F1—F2)(R–r)/(n/2)Z

Only half the arms are considered for transmitting power.

Finally σtotal = σtbt1 +  σbt2

CHECK       σtotal < 38 MPa

The cross section of the arms is normally elliptical.

Let a = Major axis near the hub

B= Minor axis near the hub

Zy = section modulus = πba2/32

Taking b = a/2

a= (64Z/π)1/3

Dimension near the rim are taken 2/3rd of dimension near the hub.

 

 

DIFFERENCES BETWEEN FLYWHEEL AND GOVERNOR

Sr. No.

Flywheel

Governor

1.
Maintains constant speed but
the means is different from that of Governor. Stores excess of rotational energy from the power stroke.  Supply back during non- power strokes of the cycle
Maintains constant speed but the
means is different from that of
Flywheel. Controls mean speed
of the engine under
full/half/varying load conditions
by regulating the supply of
working fluid to the engine
2.
 In this, there are energy variations but runs the crankshaft at constant speed in each stroke of the cycle
  When load on the engine
increases, speed decreases.
It increases the flow of fuel to
keep the constant mean speed
3.
 Flywheel controls the speed for one cycle only
 Governor maintains constant
mean speed over a period of time.
4.
 Flywheel is not essential in all the prime movers (engines)
  Governor is essential in all
prime movers (engines)
5.
It is a  heavy machine part
It is a relatively light machine
part
6.
Has large moment of inertia
Relatively small moment of
inertia
7.
 Rotating part
Non- Rotating part
8.
 Running charges are less
 Running charges are high
9.
 Angular speed increases while storing energy and decreases during supply back of energy
 Runs at mean speed under all
loads on the engine
10.
Crankshaft runs at constant speed
Load increases speed decreases
and vice -varsa. But it controls
the MEAN speed by controlling
the flow of fuel in the engine
11.
There are no valves with the flywheel
 Valves are there.  There
opening is controlled by the
centrifugal force on the balls
attached
 12.
Flywheel does not need any extra mechanism to supply back energy
 Governor needs a piston /plunger mechanism
 13.
 It absorbs energy from the high momentum generated in power stroke.  Engine is running smooth in non power strokes
  It controls the air supply to the carburetor and fuel supply to the engine
 14.
  Connected to the crank shaft and runs it at a constant speed
  It has no connection with the crankshaft
 15.
 It is an energy storing device and prevents the fluctuations of energy during each cycle of operation of the engine.
 It is not an energy storing device.
 16.
 It is a wheel and only its size may differ from one machine to another
 There is a large variety of governors used in different prime movers
 17.
Flywheel is a fairly rigid structure and undergoes no changes while in operation
 A governor undergoes changes while in operation
 18.
 Short term energy storage
 A long term speed controller as per load on the prime mover
 19.
 Used in reciprocating steam and IC engines
 Used in riveting machines to store energy from the motor. It releases energy during the riveting operation. Used in SI and CI engines
 20.
 It cannot change the speed of the crankshaft
  It limits the speed.
21.
Flywheel supply back energy as when required
Engine supply power to the governor
22.
Energy stored in a flywheel is directly proportional to the square of its rotational speed
There is no such relation

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