INSTRUCTION MANUAL
HTM.9
Flywheel Apparatus
SIMPLE FLYWHEELAPPARATUS
INTRODUCfION
Most machineryhas parts which revolve on their longitudinal axis~for example,wheels,shafts,
electric motors, centrifugalpumps,etc. This rotary motion is subjectto the samebasiclaws as
linear motion, but all the terms haveto be transformedto comply with the specialconditionsof
rotation.
For examplethe secondlaw of motion changesasfollows:-
--
Force
Forcex Radius
Couple
~
In symbols
F = ma -+ C - la
Massx Acceleration
RotationalMassx RotationalAcceleration
Moment of Inertia x Angular Acceleration
The coupleC is alsoreferredto asthe torque,beingthe turning force exerted. The applicationof
this alternativeform of the secondlaw is widespreadand most importantin underStanding
the
performanceof rotating machinery.
1n"M.9.Page J.
2. October, /997.
Whereit is necessary
to start rotating machineryquickly the momentof inertia mustbe assmallas
possibleto pem1itfast accelerationwith the maximumvalue of torque. On the other hand,whena
reciprocatingenginei.e. requiredto run at a unifonn speedregardlessof the fluctuationin driving
force aseachcylinderdeliverspower it is commonpracticeto increasethe overallmomentof
inertiaby addinga flywheelto the engineshaft. A further useof a flywheelis to storerotational
energywhich is recoverableas it slowsdown. therebymakinga largecoupleavailablefor a short
period.
The experimentsthat follow show how a flywheelcomplieswith the secondlaw of motion,and
how it actsasa storeof energy.
LIST OF PARTS
The apparatuscomprises the following:-
1-250mm old x 30 mm wide flywheel
1-Cord assembly
1- Wall bracketdw ball bearingsandpointer
1- HWH.3load hangerIN.
Additionalaccessories
required:1- HTM.9w set of weights
A stop watch is requiredto perfonn this experiment.
DESCRIPTION
The HTM.9 flywheelconsistsof a steeldisc 250 mm old x 30 mm wide which is integralwith a
shaftrunningin ball bearings.
A pegfixed in the shaftactsas an anchorfor the end of a pulling cord which is wound roundthe
shaft. On the peripheryof the disc is an engravedmark which passesa pointer asthe flywheel
revolves.
The bracketcarryingthe flywheelshouldbe boltedto a vertical surfaceat least 1 m abovethe
ground. This will allow the pulling cord and its load hangera sufficientfree fall to drive the
flywheelfor up to 10 revolutions.
EXPERIMENT 1
OBJECT
The object of this experimentis to detenninethe relationshipbetweenthe angularaccelerationof
a flywheelandthe torque producingthe acceleration.
tfUe
HTM.9. Pagel.
1. October. 1997.
THEORY
Consider
thefallingmass
Net Force
= mg- F
Acceleration= a
Hence ma = mg- F
F = m(g-a)
~
Providedthat a is muchsmallerthang
F=mg
For the wheel
Angulardisplacemente = 27tH [rad]
where
N = numberof revolutions
Averageangularvelocity = t<O +CI>N) [rad/s]
Time for N revolutions= t
Angular displacement 9 = tmN. t
Cl)N
~
.
at
1
e = ~2
from which
(1 =
41tH
(2
Accordingto secondlaw of motion
Torqueproducingacceleration = Fr
from which
k = ~ 1 . Ct2
The constantof proportionality k is calledthe momentof inertia and may be calculatedfrom the
dimensionsandmassof the flywheel.
k
(=1)
=p7tR2w.
R2
2
where R = radius of flywheel
w = width of flywheel
p = density of steel = 7850 kg/m3
PROCEDURE
Takethe load hangerand pulling cord, and hook the end loop over the peg on the flywheel shaft.
Wind up a definitenumberof turns, say8, from the position wherethe cord loop falls off the peg.
lm..l9.
Page 3.
. October,
/997.
This ensuresthat the driving torque due to a load on the hangerwill act for a set numberof
revolutions.
Wind up the pulling cord 8 turns and hold the flywheel with one hand and a stop watch in the
other. The engravedmark shouldbe by the pointer at this stage. Releasethe flywheel and start
the watch. Count the revolutionswith the aid of the mark, using this to judge when to stop the
watchasthe setnumberof revolutionsis turned. The load hangerwill fall onto the ground.
Repeatthe aboveprocedureaddingload by incrementsof IN. Keep on repeatingthe experiment
until at least six readingshave beenobtained. Try re-timing one or two of the readingsto see
what the probableaccuracyof the measurement
is.
If thereis the opportunity,repeatthe experimentusinga lessernumberof turns of the pulling cord
on the shaft.
RESULTS
Tabulatethe timesfor the differentvaluesof massplus hangerandcalculateIlf
Table 1
Acceleration of a Flywheel
Plot the experimentalresultson a graphof total load againstIff, and draw the bestfit straightline
throughthe points.
The gradient of the line provides an average value for the relationship between the driving force
and the angular acceleration, and should be multiplied by the appropriate factor to obtain the value
of k (that is, the moment of inertia). The intercept on the total load axis gives the initial load for
which there is zero acceleration; this must be the load required to overcome the friction in the
bearings of the flywheel shaft. Deduct this from the total load for each result and hence calculate
the effective couple, which should be entered in the table.
If therewas time to repeatthe experimentwith a lessernumberof turns of the pulling cord, make
up a secondtable of resultsbut use the samegraph. One would expectthere to be a common
intercepton the massaxis.
OBSERVAllONS
Compare the experimentaland theoretical values of the moment of inertia obtained in the
experiment.Note the variability of any re-measuredresultsof time, and of the deducedfriction if
the experimentwasrepeated.Commenton the accuracyof the experiment.
The theory which was being verified assumedthe angular accelerationwas uniform Can the
experimenttest this assumption?
In"M.9. Page 4.
2. October. /997.
EXPERIMENT 2
OBJECT
The perfonnanceof a flywheelas a store of energyis studiedin this experiment. In particularthe
objectis to:(1)
(2)
Comparethe theoreticalandexperimentalvaluesof the momentof inertiaof a
flywheeland
studythe transformationsof energythroughoutthe experiment.
THEORY
The work output of the falling massis givenby its lossof potentialenergylessits kinetic energyat
the point of separationfrom the flywheel.
Potentialenergy= mgh
= mg. 27tr. No
whereNois the setnumberof revolutions
Final velocity of mass = CON
Kinetic energy = ! m (CI>Nr)2
Work doneon flywheel = mg. 27r.rNo - tm {roNr)2
The flywheel startsfrom rest and, left to revolve when the falling massseparates,will eventually
completeN1 revolutions and stop. Looked at this way. all the work is consumedin bearing
friction, which will be assumedconstant.
At the point of separationof the falling massthe flywheel will reachits maximumangularvelocity
(J)N
andhenceits maximumkinetic energyby ! I(J)~
Let the bearing frictional couple be Cr Thenequatingwork consumedin friction
mg. 21trNo-
t
m (mNrY = Cf . 21tH I
The energybalanceat the end of Norevolutionsis
Hence if No NI and CON
are measured,C( can be derived from (1) and Substituted in (2) to evaluate
I.
Fromthepreceding
experiment1 it is knownthat mN= ~
fmJ.9. Page 5.
2. October, 1997.
PROCEDURE
Part 1
Add 4N to the load hangerandwind up the pulling cord to 8 turns. Hold the flywheelin one hand
andthe stop watch in the other. Releasethe flywheel. start the watch,and start countingthe total
revolutionsby using the engravedline and the pointer. The watch must be stoppedon the count
of eight turns.but the revolutionsshouldbe countedtill the wheelstops. Repeatthe test two or
threetimes.
Part 2
Repeatthe wholeof Part 1 usinga differentload and/or a differentnumberof turns for the pulling
cord. Finallytakethe dimensionsof the flywheeland shaft.
RESULTS
Tabulatethe experimentalresultsandtake the averagevaluesof t andN. for eachPart. Calculate
OON
and substitutein expression(1) of the theory to detenninethe bearingfriction couple Cf .
Thensubstitutein expression(2) to obtainthe experimentalvaluesof I.
From the dimensionsof the flywheel and shaft, and using a density for steel of 7850 kg/m3,
calculatethe theoreticalvalue of I. Comparethis with the experimentalvalue. If the result of
Experiment1 is availableincludethis in the comparison.Also if the resultsof Experiment1 areto
handcomparethe friction coupleCf with the intercepton the graph.
OBSERVAllONS
Commenton the various comparisonsof momentsof inertia and bearingfriction obtainedin the
different ways. Use the effect of the variability where individual tests were repeatedto assess
which methodwas most accurate.
How would you provide a valuefor the momentof inertia of a toothedgearwheel?
Whatfractionof the energygivenup by the falling massis storedin the flywheel?
Couldthe efficiencybe improved?
HTM.9. Page 6.
'. October. /997.