ME3112-2 Dynamic Balancing

& Gyroscopic Effects

by

LIN SHAODUN A0066078X

Group 1A

Date 06-Sept-2012

TABLE OF CONTENTS

RAW DATA 1

SAMPLE CALCULATION 3

DISCUSSION 5

F.A.Q 8

CONCLUSION 10

1

RAW DATA

Table 1 Unbalanced Dynamic Force - Two-Plane Balancing

Weight: 2.690g Angular position: 87

Trial Mass Added Deflections of the spring Resultants Counter balance

mass required

M(g) b

(mm)

c

(mm)

d

(mm)

a

(mm) Mb(g)

2.690 0.20 - -

0.24 93 2.07 5.181 - 0.32 -

7.672 - - 0.52

mu = 2.690g mt = 2.491g

Table 2 Gyroscopic Effects

Spin Rate Precession Rate

S/No. Ni (rpm) i

rad/sec

1=

sec/rad t i sec (=

2

t )

i

rad/sec

1 2817 295.0 3.390X10-3 4.51 1.390

2 3859 404.1 2.475X10-3 6.53 0.962

3 4928 516.1 1.938X10-3 9.43 0.666

4 6008 629.2 1.589 X10-3 11.59 0.542

5 7074 740.8 1.350 X10-3 12.68 0.496

RESULTS

Texpl (Nm) (T / I)expt (= a) theoI/T Difference (T / I)expt - theoI/T

0.052 408.8 282 126.8

Note: Above data was from G4 group

2

Table 3 Regression analysis for results of gyroscopic effects experiment

S/No. i' i i'2 i i'

1 3.390X10-3 1.390 1.149 X10

-5 4.712 X10

-3

2 2.475X10-3 0.962 6.126 X10

-6 2.381 X10

-3

3 1.938X10-3 0.666 3.756 X10

-6 1.291 X10

-3

4 1.589 X10-3 0.542 2.525 X10

-6 8.612 X10

-4

5 1.350 X10-3 0.496 1.823 X10

-6 6.696 X10

-4

n =5 'i 1.074X10-2 i 4.056 2'i i i'

2

'i 1.154X10-4 2.572 X10

-5 9.915 X10-3

Equations for Least Square Method:

8.408

10154.110572.26

056.4100742.110915.96

''1

''145

23

22

ii

iiii

n

na

056.010154.110572.26

10915.910074.1056.410572.2

''1

'''45

325

22

2

ii

iiiii

nb

056.0'8.408''1 baITIT

Note: Theoretically 'a' should correspond to (T/I)expl and 'b' should be zero.

y = 454.31x - 0.16

R² = 0.99

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.E+00 1.E-03 2.E-03 3.E-03 4.E-03

Ω

ω'

Using Excel to find 'a' and 'b'

3

SAMPLE CALCULATION

1. Dynamic Balancing

√

√

(

) (

)

2. Gyroscopic Effects

[(

) ]

[(

) ]

∑

∑ ∑

(

)

4

Table 4 Group 4 setup dimensions

Knob

Position

Rotor Spin

Speed(rpm)

Set-up Dimensions

(mm)

Moment of

Inertia

Set-up G4 Dimension G4 Mass (kg) Kg.m2

30 2817 L1 100.5 0.05556 4.6768 X10-5

40 3859 L2 89.5 0.03509 2.3424 X10-5

50 4928 L3 50.3 -

60 6008 D1 9.5 -

70 7074 D2 8.0 -

Density of Steel : 7800 kg/m3 D3 68.7 0.20420 6.2268 X10-5

Density of Gear : 1190 kg/m3 D4 20.0 0.01518 5.4610 X10-7

C1 16.8 -

Dimensions of Gear (mm) C2 7.6 -

A = 10 C = 28 T1 7.2 -

B = 15 P.C.D = 35.5 T2 8.0 -

X 5.0 -

5

DISCUSSION

1. Explain why it is necessary to have 2 trail masses added to determine the

counter-balance mass and the location.

Because there are two unknowns: the location and orientation of the balancing mass (a and ), so

we need two equations to solve these two unknowns.

Let a be the amplitude of vibration due to the trial mass m alone. The following relations are

obtained between the various variables by using equation in the form of a moment diagram as

shown in below figure. From the vibration amplitude caused by different mass added on disk,

balancing mass a and the phase angle can be determined easily.

2a

a

b

cd

The equations to calculate a , and are as follow base on trigonometry:

√

(

)

2. Compare the two values of (T/I) and comment on the errors involved in the

experiments as well as the model setup.

Base the calculation, the (T/I) expr is much larger than (T/I) theo , the error in involved in the

experiment as follows:

A. Human error

a. When using stop watch to measure the Precession Rate, human error will be

introduced when judge the rotation time of one turn.

b. The way we disengaged the motor gear and pulled out the disk support may not be

consistent which will directly affect the measurement result. And after disengage the

gear the disk may not in horizontal position, which will introduce additional variable

to the system.

c. When engage the motor gear to disk gear, the force is controlled by hand, so the motor

speed and the disk initial speed may be affected.

6

B. Equipment error

a. The RPM of the motor may not be consistent when engage the gear pair as the load is

partially controlled by hand.

b. The bearing of the disk unit has friction, which will affect the Precession Rate

significantly.

c. The dimension provided to calculate the mass and moment inertia of each component

may not be very accurate.

d. The experiment setup may not be well calibrated in level position.

3. Name two application of balancing machine, describe briefly the apparatus,

apply the knowledge you learnt in the experiment.

Application 1: Grinding wheel balancing,

this device consist two bearing supports,

the grinding wheel with center shaft

inserted is placed on the bearing support,

balancing weights are added onto grinding

wheel flange and adjust them in different

orientation until the grinding wheel can

stop at any position without further rotate,

then the balancing is consider done.

This balancing method is not considered as

dynamic balancing; hence the accuracy of

balancing is not as good as dynamic

balancing.

Grinding wheel also can be balanced

dynamically by accelerometer and optical

sensor to determine the balancing mass and

the orientation of unbalance. Below is a

picture of dynamic grinding wheel

balancing device.

7

Application 2: Tyre balancing machine, when

the wheel rotates, asymmetries of mass may

cause it to hop or wobble, which can cause ride

disturbances, usually vertical and lateral

vibrations. It can also result in a wobbling of the

steering wheel or of the entire vehicle. The ride

disturbance due to unbalance usually increases

with speed. Vehicle suspensions can become

excited by unbalance forces when the speed of

the wheel reaches a point that its rotating

frequency equals the suspension’s resonant

frequency. Wheels are balanced on a wheel

balancing machine. The machine rotates the tire

and wheel assembly and automatically calculates

the weight and location of the balance counter weight.

Application 3: Propeller balancing, Propeller

for ship and aircraft needs to be dynamically

balanced to reduce the component wear, the

internal stress, the risk of fatigue failure, as well

as improve the performance as lesser energy is

wasted in the form of vibration.

4. Describe some applications of gyroscopic effect which is used as sensors.

Application 1: Attitude Indicator, An attitude indicator (AI),

also known as gyro horizon or artificial horizon or attitude

director indicator (ADI), is an instrument used in an aircraft

to inform the pilot of the orientation of the aircraft relative to

earth. It indicates pitch (fore and aft tilt) and bank or roll

(side to side tilt) and is a primary instrument for flight in

instrument meteorological conditions.

8

Application 2: Anti-rolling gyro, Ship stabilizing

gyroscopes are a technology developed in the 19th

century and early 20th century and used to stabilize

roll motions in ocean-going ships. The gyroscope

does not rely on the forward speed of the ship to

generate a roll stabilizing moment and therefore has

shown to be attractive to motor yacht owners for

use whilst at an anchorage. The ship gyroscopic

stabilizer typically operates by constraining the

gyroscope's roll axis and allowing it to "precess"

either in the pitch or the yaw axes, allowing it to precess as the ship rolls causes its spinning rotor

to generate a counteracting roll stabilizing moment to that generated by the waves on the ship's

hull.

In addition to being used in compasses, aircraft, computer pointing devices, etc., gyroscopes have

been introduced into consumer electronics. Since the gyroscope allows the calculation of

orientation and rotation, designers have incorporated them into modern technology. The

integration of the gyroscope has allowed for more accurate recognition of movement within a 3D

space than the previous lone accelerometer within a number of smartphones.

Examples of Gyroscope in consumer electronics include Nexus S, iPhone 4, PlayStation 3

controller, Wii Remote(Nintendo has integrated a gyroscope into the Wii console's Wii Remote

controller by an additional piece of hardware called "Wii MotionPlus". ), etc.

FAQS

PART A: DYNAMIC BALANCING

1. Is it possible to place mass (es) on the other disk? Why?

If place the masses on the other disk, the experiment will result in large error. The setup of this

experiment is designed to measure the two-plane balancing, if the mass was placed in other disk,

which will become a more complex balancing problem.

And in this experiment setup, the LVDT used to measure the vibration level is located at one side

of disk, so the change of vibration level will be less sensitive if the mass was placed on another

disk. In summary, it is better to place the masses on same side of disk for better accuracy.

9

2. What is the relation between angular position recorded in the table and

calculated θ?

The relation between angular position recorded in the table and calculated θ is :

Angular position ϕ = 180° - θ

3. What is the relation between mu and mb ?

If mu and mb are on the same plane, based on equation 0~ii rm , we have:

If mu and mb are on the different plane, based on equation 0~~ iii rzm , we have:

PART B: GYROSCOPIC EFFECT

1. Can we engage the rotor gear the other way, compared to demonstration? Why?

If engage the rotor gear the other way, the direction of precession will be different base on below

table, the reason is the torque produced will be in different direction.

S (spin) P (precession) T (torque)

CW CW CW

CW ACW ACW

ACW ACW CW

Base on below figure,

Idt

dAOT

, so if is in different direction, the direction of T

will be changed accordingly.

O

A

B

H

H'

S

TP

H

10

2. How many precession rounds are used to obtain experimental precession rate?

Why?

Only ONE precession round is used to obtain experimental precession rate.

Because the precession rate is affected by bearing friction and become slower over time, in order

to obtain an accurate precession rate, it is advisable to only use the timing of the first round of

precession.

CONCLUSION

After this experiment, I had learnt how to perform dynamic balancing for rotary object, and the

significance of achieve dynamic balance in industrial applications. I understand that the

unbalanced forces induce further mechanical vibrations in the machinery and connected parts

thereby creating environmental noise problem through radiation of sound, and it is desirable to

balance all such uncompensated masses and thus reduce the effect of unbalance forces in a

dynamics balancing machine.

I also learnt the gyroscopic effects based on principles of angular momentum and its applications

in applications like inertial guidance, gyrostabilizers, navigation.

In summary, with this experiment, I had gain more physical experience in dynamic balancing and

gyroscopic effects .