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EducationalPRODUCTS

KEEP FOR FUTURE REFHKBNCE

Safety and Operation Information

PRODUCT: TMI04 GYROSCOPE APPARATUS

In compliance with the EC directive on Safety of Machinery, the followinginformation should be noted:

This equipment is only to be used in accordance with instructions in themanual. Students using the equipment must be adequately supervised. Localregulations regarding the use of electricity, gasoline, diesel oil, kerosene,mercury must be observed in using this apparatus.

Foreseen use of apparatusDemonstration of gyroscopic effects

Installation and assembly instructionsThe apparatus is supplied fully assembled. Before use, remove the perspexcover and take off the red transit bracket which holds the torque arm in place.Replace the cover.

The apparatus is designed to operate with the following TecQuipmentsupplied units:

2xE67 Speed Control UnitslxE64 Tachometer UnitRefer to separate literature for safety and operation information about theseunits.

Operating Ins tru cti 0 osThe perspex cover of the apparatus is fitted with an interlock so that neitherof the two motors will operate unless the cover is fitted securely. Connect thetwo E67 units and the EM to the electrical supply. Connect the outputterminals on the E67s to the input terminals on the TMI04 using 4mmconnectors. Connect the tachometer output on the TMI04 to the input on theEM using the single lead provided. Switch on the electrical supply. The twoE67s control the speed of rotor rotation and the precession speed. Thetachometer measures rotor rotation speed. A stopwatch is necessary to timethe speed of precession of the apparatus.

The equipment must be used within its operating limits (see operatingconditions).

Maintenance and inspectionPeriodically inspect elecbical leads and connections for wear. Periodicallycheck that all warning labels are in position and legible.

Handling instructionsNet weight 22kg.Ensure the correct procedures for handling the above weight are used whenmoving this apparatus.

Operating Conditions

~hoDi1cr TMI04- See serial number plate

+SOC to +4OOC~ to 9s-.!o (In\~ens~)

~

~ Safe opera~ relative humidity ran~

Noise LevelThe measured sound pressure level of this apparatus is less than 70 dB(A).

SparesRefer to Packing Contents List for any consumables to cover the warrantyperiod supplied with the apparatus. Refer to manufacturer or importer forany other spares required.

-~~

1. INTRmUCTION

Gyroscopic action occurs whenever the axis of a rotating body is made to

change its direction. The angular momentum of a rotating body causes the

axis of rotation to remain in the same direction so long as no external

couple acts on the system. However, if a turning couple is applied to

the axis, a torque reaction is produced which tends to turn the axis in

a plane at right angles to the plane in which the applied couple acts.

This torque reaction, or "gyroscopic couple" as it is called, results

from attempting to alter the direction of angular momentum of the body.

The study of gyroscopic action is particularly important in the field of

vehicle engineering. The gyroscopic couple produced by rotating com-

ponents can often lead to undesirable effects which affect the stability

of vehicles. for example, when a road vehicle travels round a bend, the

gyroscopic couple produced by turning the axes of the wheels tends to

overturn the vehicle. In the case of an aircraft changing direction,

the gyroscopic couple due to the rotating components of the engine

causes the aircraft to pitch up or down. In a similar way, the couple

produced by a turbine rotor in a pitching ship tends to make the ship

swing sideways. A knowlege of gyroscopic action can enable the designer

to calculate the torque reactions and thus allow for any undesirable

effects.

Gyroscopic effects can also be used to advantage as in the case of gyro-

stabilisers and gyroscopic instruments. If mounted in a suitable

position, a gyroscope consisting of a rotating disc can be used to re-

sist undesirable motion and so provide a means of stabilisation.

Successful use of gyroscopic stabilisation has been achieved in ships

where significant reductions in rolling amplitudes have been obtained.

In the gyro-compass, the effect of gravity is used to produce rotation

of the axis of a gyroscope in the horizontal plane such that the axis is

always aligned in a north-south direction, irrespective of its position

on the earth's surface.

TecQuipmentscopic effects

couple and the

TMl04 Gyroscope is designed to demonstrate the gyro-

and to enable the relationship between the gyroscopic

direction of rotation or "precession" of the gyroscope

axis to be determined

-2-

y

x

Fig 2.1 Principle of Gyroscopic Action

-3-

2. THEORY

Gyroscopic Couple

If we have a stationary flywheel, of moment of inertia I, on a shaft

mounted in a trunion frame such that it is supported but free to rotate

about an axis, then any couple applied to the system will cause the

shaft to move in the plane of application of the couple.

Now case shown in rig 2.1, where the flywheel disc is

spinn J angular velocity w, and the axis of spin simultaneouslyrotating in the horizontal plane lOX with angluar velocity w. The

pangular momentum of the disc can be represented by the vector Oa at one

instant, and Ob after a short interval of time ct. The momentum vector

lies along the axis of rotation, in a direction such that the rotation

is clockwise when viewed in the direction of the vector (right hand

screw rule). rrom rig 2.1 it is clear that there is a change in angular

momentum, as represented by the vector ab. This change in momentum must

be produced by the action of a couple in the disc. The applied couple

is equal to the rate of change of angular momentum, so the torque is

given by:

consider

ina with

the

tS(lw)~ t

or =

The change of angular momentum is represented by the vector ab, so we

can write 6 (100) = ab = Oa.60 where 66 is the angle through which the

axis of spin rotates in time 6t.

cSe"&

6e~

Os Ioo,. = =

In the limit when o~~t:'..+

deIw "dt"T !(A)-.OOP

= . . . . 2.1=

where: w is the "precession" velocity in rad/spw is the angular velocity of the disc in rad/s

I is the moment of inertia of the disc in kgm

-4-

Mg

Fig 2.2 B1f11ar Suspension

-5-

From Fig 2.1 the vector ab lies in the XOZ plane and in the limit when

06 is very small, its direction is perpendicular to Oa, that is to say,

perpendicular to the XOV plane. The direction of the vector lies along

the axis about which the couple acts, so the applied couple must there-

fore act in the XOV plane. To conform with the right hand screw rule,

its sense must be clockwise when viewed in the direction abn, that is

when viewed in the direction OZ.

The applied couple represents the couple required to keep the axis of

the disc rotating in the XOZ plane. By rotating the axis of the disc,

the disc therefore produces a couple which acts in the opposite direct-

ion to the applied couple, that is to say, anti-clockwise about the OZ

axis. This is termed the gyroscopic couple. Thus, if no restoring

couple were applied, any attempt to rotate the axis of the disc in the

XOZ plane would result in the axis tipping in the anti-clockwise direct-

ion about the OZ axis.

2.2 Moment of Inertia

In order to investigate the validity of equation 2.1 it is necessary to

determine the moment of inertia of the gyroscope rotor. In the experi-

ment, this is done by suspending the rotor on two wires as shown in rig

2.2. If the rotor is of mass M and the wires are of length L and dis-

tance d apart, then the tension in each wire is Mg/2. If the rotor is

rotated through a small angleeabout its vertical axis, then an angular

displacement ~ is produced at the wires. If both angles are small, we

may write L~ = del2. The restoring force due to the tension in each wire

is:

Mg sin ~/2 Mg #2 (for small ~ )=

Substituting for ~ = dti/2L we obtain the restoring force as,

~4L

The restoring couple is thus:

Mgde.d- 4l

-6-

The equation of motion is therefore:

~~- 4LI~ =

Re-arranging thia equation we have:

e+~ e4IL

0=

This represents

gi ven by,fijF;T 2 4IL

= 1fMg"'dT

simple harmonic motion in which the periodic time T is

The moment of inertia I is therefore:

~g~16'"' LI . . . . 2.2

-7-

APPARATUS3.

The apparatus (see fig 3.1 consiats of a rotor disc (A) mounted on the

shaft of a small variable speed motor (B) which is carried in a gimbal

frame (C). This assembly can be rotated about the vertical axis by a

variable speed geared motor housed inside the base of the app-

Attached to one end of the rotor motor is a torque arm which

a mass (0) at its end to balance the motor and rotor disc. A

! balance weight (H) is also fitted to the torque srm to balsnce

the assembly in its static unloaded condition. The motor pivots in the

gimbal frame such that it csn rotate in the vertical plsne. A retsining

plate (E) is fitted over the torque arm to limit the angular movement of

the motor assembly. Additional masses (f) can be attached to the end of

the torque arm to bslance the gyroscopic couple produced when the rotor

disc is spinning and the gyroscope is being rotated (precessed) about

the vertical axis. A removable, but electrically interlocked trans-

parant safety cover is fitted over the complete rotating assembly. Re-

moving this cover automatically stops both motors.

second

aratus.

carries

movable

The rotor motor assembly is fitted with an opt{cal pick up (G) which

picks up from the four strips of reflective tape on the rotor disc (A).

The distance between thia disc and the optical pick up is pre-set at the

factory and must not be adjuated. Power is supplied to the rotor motor

via a slip ring unit (J) mounted at the base of the gimbal frame, which

also provides a signal path from the optical sensor to the E64

Electronic Tachometer. -

The apparatua is designed to operate from two E67 units, which allow

independant control over the rotor motor and the geared precession motor

mQunted in the base.,' When in operstion; the rotor speed, vsrisble

between 0 and 3000 rpm, is measured on the E64 Electronic Tachometer,

whilst the precession rate, vsriable between 0 and 40 rpm, is measured

using a stop-watch.

An additional gyroscope rotor and armature assembly is provided together

with a aimple fold-out bifilar suspension arm mounted on the base of the

apparatus. The moment of inertia of the rotor assembly can be deter-

mined by suspending it from the arm and timing the torsional

oscillations

~ o. 5 M~ ~ 2.0~M

8. View of Main Gyroscope Components

b. View of Gyroscope with Trsnsit Brscket in Position -rig 3.1 Gyroscope Assembly

-9-

4. EXPERIMENTAL PROCEDURE AND RESULTS

Installation

Remove the safety cover by pushing the cover sideways until the rim is

free of one of the retaining blocks and lift the cover away. Remove

the red transit bracket (Fig 3.lb, item K), which holds the torque arm

rigidly to the frame. The apparatus requires two 12 V d.c. variable

voltage supplies which are provided by the TQ [67 Speed Control Units.

These operate from a mains input and two 4mm terminals are provided for

connection to the respective inputs on the TM104 unit. .

Make the following connections:

1. The mains input supply to the [64 Tachometer and the [67 Speed

Control ~its.

The output terminals of the [67 units to the input terminals on the

TMlO4 unit.

The tachometer output on the TMl04 to the [64 Tachometer using the

signal lead provided.

2.

J.

is now wired up and ready for operation.

Switch on all the units.

Re-fit theThe apparatus

safety cover.

Investigstion of Gyroscopic Couple Direction

Ensure that the power supplies to the unit are switched OFF. Remove the

safety cover and check that the rotor assembly is balanced, so that with

no weights added to the mass at the end of the torque arm, the torque

arm lies between the marks on the retaining plate. If necessary, slack-

en the knurled retaining screw on the torque arm balance weight and

position the balance weight to obtain the balanced condition. When the

rotor assembly is satisfactorily balanced, re-tighten the knurled re-

taining screw and re-fit the safety cover.

Check that the cover is correctly in position, then set the rotor and

precession motors running. Note the direction of rotation of the rotor,

the direction of precession of the gyroscope and whether the torque arm

-11-

rises or falls. By interchanging the motor input connections on the

front panel, determine the direction of the gyroscope couple for each

combination of rotor and precession directions.

The results should be ss shown in rig 4.1. It will be seen that the

gyroscopic couple produced by precessing the gyroscope slways acts about

an axis which is perpendicular to both the gyroscope rotor and precess-

ion axes. The couple direction depends on the directions of precession

and rotor rotation. Notice that the couple always acts to tip the gyro-

scope in the same direction as the leading edge of the rotor. ror

exsmple, in disgram (s) the leading edge is moving downwsrds and the

gyroscopic couple scts to tip the rotor downwards.

petermination of Moment on I~tia

Lift the spare armature and rotor aasembly from its clips and fold out

the bifilar support arm. Hang the assembly from the arm as shown in Fig

4.2, then twist it about the vertical axis by about loa and release it.

Use a stop-watch to time, say, 50 oscillations of the rotor assembly.

Measure the length L of the wires and the distance d between them. The

mass of the rotor assembly is nominally 1.09 kg. You can check this

value by weighing the assembly on suitable scales if you wish to do so.

These measurements provide the information required to calculate the

moment of inertia I from equation 2.2. Check that you have recorded the

correct readings, then fold the arm away and replace the rotor assembly

in its clips.

Typical resulta are a8 follows

0.53 m0.073 m1.09 kg

47.5 8

0.95 8

l

d

M

t

T

=Length of wires

Distance between wires

~ss of rotor

Time for 50 oscillations

Periodic time =

Substituting valuea in equation 2.2 givea the moment of inertiathese

8S:1.09 x 9.81 x 0.0731 X 0.952I 16 x-"- xO.53

6.14 x 10-" kg m2Therefore I =

-12-

Fig 4.2 Bifilar Suspension

-

-l~-

Magnitude of Gyroscopic Couple

The object of this psrt of the experiment is to investigate the

relationship between the gyroscopic couple, the angulsr velocity of the

rotor and the precession velocity. The results provide the dsta

necessary to check the validity of equation 2.1, that is

Gyroscopic couple, T Iw w=p

Ideally the tests would involve measuring the gyroscopic couple for two

sets of conditions:- (i) varying rotor veocity at a constant precession

velocity, and (ii) varying precession at a constant rotor velocity.

However, the gyroscopic couple can only be set at a limited number of

discrete values (as determined by the balance mass on the torque ar~),

so a slightly different procedure has to be used. This involves measur-

ing the precession velocity for a range of rotor speeds and values of

balance mass. The procedure is as follows:

1. Screw a g mass onto the end of the torque arm and replace the

safety dome. Connect the rotor and precession motor supplies so

that the gyroscopic couple will raise the torque arm. Use the

results obtained under section 4.2 to determine the correct

electrical connections to achieve this.

50

2. Vary the precession velocity until the torque arm rises

to a level at which the scribed line on the arm lines

up with the indicating strips on the bracket (shown by

'E' in Figure 3.1 page 8). This is the point of balance

at which the gyroscopic couple is equal to the moment

produced by the mass on the torque arm.

.J. At this condition, measure the precession speed by

timing a suitable number of revolutions of the assembly

using a stop-watch. The number of revolutions you will

need to time depends on the test condition. To obtain

good accuracy, always use a timed period of at least 30seconds. Record the exact value of rotor speed.

-15-

4. Decreaae the rotor speed in steps of 500 rev/min and determine the

precession speed at the balance point for each different rotor

speed down to 500 rev/min.

5. Add additional masses to the torque arm and obtain similar sets of

results for each value of mass. It is best to obtain results for

50g increments in mass, so giving a total of 7 sets of results up

to a value of 350g. However, if time is limited it is sufficient

to use values of 50,150,250 and 350g.

A typical set of results is given in Table 4.1 for four different values

of balance mass. The gyroscopic couple is calculated from the mass and

the length of the torque arm (O.l4m). for example, for the firat

result, the couple is:

0.05 x 9.81 x 0.14

0.0687 ~

T =

The equation for gyroscopic couple suggests that graphs of the recip-

rocal of precession velocity (l/w ) against rotor velocity (w) should bep

straight lines. The results are plotted in this way in Fig 4.3, from

which it can be seen that the results do indeed lie on straight lines

which pass through the origin.

Two further graphs can be constructed from the reaults shown in Fig 4.3,

which demonstrates the independent influence of preceasion velocity and

rotor velocity. Fig 4.4 shows values of gyroscopic couple plotted

against precession velocity for a constant rotor velocity of 300 rad/s-

As expected, the results lie on a straight line through the origin.

Theoretical values of the couple can be calculated uaing the moment of

inertial found in the previous section. For example, at a precession

velocity of 2.5 rad/a:-

6.14 x 10~"

0.4608 ~

T x 300 x 2.5

The experimental

to within about 3~.

values are shown to agree with the theoretical values

-19-

REFERENCES

1. Morrison, J. L. M. and Crossland, B.

"~chanics of Machines" p. 30 - 32. Longmans

2. J. M. Prentis. "Dynamics of Mechanical Systems11. Longmans

3. Inglis, Sir Charles.

"Applied Mechanics for Engineers" Chapter XX p.380-404. Dover.

4. Swanson, S. A. V. "Engineering Dynamics".