BALANCING

BALANCING

Static

Dynamic

1. Mass

2. Radius

3. Angle

Same plane

Different plane

mr

mrl

EXERCISE 1

Four masses m1, m2, m3 and m4 are 200kg, 300kg, 240kg, and 260kg respectively. The corresponding radius of rotation are 0.2m, 0.15m, 0.25m and 0.3m respectively. The angle between mass 1 and 2 = 45 °, 1 and 3 =120° also mass 1 and 4 = 255 °. Find the position and magnitude of the balance mass required if its radius of rotation is 0.2m.

1ST STEP

Table of Polygon

Angle

Plane Mass,m(kg)

Radius,r(m)

Centrifugal Force

m X r (kgm)

0° 1 200 0.2 40

45° 2 300 0.15 45

120° 3 240 0.25 60

255° 4 260 0.3 78

Space Diagram

2nd STEP

0°

90°

180°

270°

1

23

4 mb

45°120°

225°

Scale1cm : 10kgm

Polygon mr

2nd STEP

1 2

3

4

ResultantForce, R

45°

120°

255°

201°

4cm

4.5cm

6cm

7.8cm

From polygon mr Resultant Force, R =2.4cm = 2.4 X 10 =

24kgm The balancing force is equal to the resultant

forcem X r = R

m X 0.2 =24m = 120kg

Angle of inclination of balancing mass, θ =201°

A, B, C and D are four masses carried by a rotating shaft at radius 100,125, 200 and 150 mm respectively. The planes in which the masses revolve are spaced 600mm apart and the mass of B, C and D are 10 kg, 5 kg, and 4 kg respectively. Find the required mass A and the relative angular settings of the four masses so that the shaft shall be in complete balance.

EXERCISE 2

1ST STEP

Table of Polygon

Angle

Plane Mass, m

(kg)

Radius, r

(m)

Cent. Force (mXr)[kgm]

A mA 0.1 0.1mA

B 10 0.125 1.25

C 5 0.2 1

D 4 0.15 0.6

A B C D

0.6m 0.6m 0.6m

R.P+ve

Distance from

plane, l(m)

Couple(m X r X

l)kgm²

0 0

0.6 0.75

1.2 1.2

1.8 1.08

From table of polygon,Column mr have 1 unknown, ma

Skip to draw polygon mr and draw polygon mrl

2nd STEP

Scale1cm : 0.2kgm²

BO 3.75cm

6 cm5.4 cm

C

118 °

260°

1ST STEP

Table of Polygon

Angle

Plane Mass, m

(kg)

Radius, r

(m)

Cent. Force (mXr)[kgm]

A mA 0.1 0.1mA

0 ° B 10 0.125 1.25

118 °

C 5 0.2 1

260 °

D 4 0.15 0.6

A B C D

0.6m 0.6m 0.6m

R.P+ve

Distance from

plane, l(m)

Couple(m X r X

l)kgm²

0 0

0.6 0.75

1.2 1.2

1.8 1.08

Polygon mrScale1cm : 0.1kgm

BO 12.5cm

118 °

C260 °

6cm 10cm

213 °Resultant Force, R

Resultant Force, R =5.3cm = 5.3 X 0.1 = 0.53kgm

0.1mA = 0.53 mA = 0.53/0.1 = 5.3kg

Three masses A, B and C are placed on a balanced disc as shown at radius of 120mm, 100mm and 80mm respectively. The masses are 1kg, 0.5kg and 0.7kg respectively. Find the 4th mass which should be added at a radius of 60mm in order to statically balance the system.

EXERCISE 3

B

A

C

30 °

100 °

1ST STEP

Table of Polygon

Angle

Plane Mass,m(kg)

Radius,r(m)

Centrifugal Force

m X r (kgm)

0° A 1 0.12 0.12

30° B 0.5 0.1 0.05

100° C 0.7 0.08 0.056

D mD 0.06 0.06mD

Polygon mrScale1cm :

0.01kgm

2nd STEP Angle Plane

Mass,m

(kg)

Radius,r

(m)

Centrifugal Force

m X r (kgm)

0° A 1 0.12 0.12

30° B 0.5 0.1 0.05

100° C 0.7 0.08 0.056

D mD 0.06 0.06mD

O A12cm

B

30 °

5cm

C

5.6cm17.4cm

, D

208°

100 °

The resultant is 17.4cm = 17.4 X 0.01 = 0.174kgm

The mass required is 0.174 / 0.06 = 2.9kg

Find the mass and the angle at which it should be positioned in planes A and D at radius of 60mm in order to produce complete balance of the system shown.

EXERCISE 4

1ST STEP

Table of Polygon

Angle

Plane

Mass,m

(kg)

Radius,r

(m)

Centrifugal Force

m X r (kgm)

Distance, l(m)

Couplem X r X l

A 0.06 0.06 0 0

90° B 5 0.075 0.375 0.2 0.075

30° C 2 0.05 0.1 0.3 0.03

D 0.06 0.06 0.375 0.0225

R.P

Polygon mrl

2nd STEP

Scale1cm :

0.01kgm²

O

B

7.5cm

9.35cm

30 °

C3cm

254 °

9.35cm = 9.35 x 0.01 = 0.0935kgm²

0.0225 x mD = 0.0935

mD = 4.156kg

, D

Angle

Plane

Mass,m

(kg)

Radius,r

(m)

Centrifugal Force

m X r (kgm)

Distance, l(m)

Couplem X r X l

A 0.06 0.06 0 0

90° B 5 0.075 0.375 0.2 0.075

30° C 2 0.05 0.1 0.3 0.03

254° D 4.156 0.06 0.249 0.375 0.0225

Polygon mr

Scale1cm : 0.1kgm

Polygon mr

Scale1cm : 0.1kgm

O

B

C

D

30 °

254°

262 °

, A

3.75cm

1cm2.49cm

1.9cm

The resultant is 1.9cm = 1.9 x 0.1 = 0.19kgm

Figure shows THREE (3) masses attached to a shaft. The shaft is supported by bearings at both ends. The system is in static equilibrium.

EXERCISE 5

2 m

2.5 m

3 m

4.5 m

A B C YX

Mass MA = 7 kg , Radius rA = 0.2 m

MB = 12 kg , rB = 0.18 m

MC = 15 kg , rC = 0.15 m

By using the data given:

i. complete the mr and mrl table, draw the space diagram, the mr and mrlii. Determine the unbalance couple for the shaft when the shaft

rotates at 180 rpm

Soulutions:

Table of Polygon

Angle

Plane Mass, m

(kg)

Radius, r

(m)

Cent. Force (mXr)[kgm]

X - - Rx

A 7 0.2 1.4

B 12 0.18 2.16

C 15 0.15 2.25

Y - - Ry

Distance from

plane, l(m)

Couple(m X r X

l)kgm²

0 0

2 2.8

2.5 5.4

3 6.75

4.5 4.5Ry

1st draw polygon mr(abaikan Rx dan Ry)Scale1cm:1kgm

105°

246°

O, C A

B

Table of Polygon

Angle

Plane Mass, m

(kg)

Radius, r

(m)

Cent. Force (mXr)[kgm]

X - - Rx

0 ° A 7 0.2 1.4

105 °

B 12 0.18 2.16

246 °

C 15 0.15 2.25

Y - - Ry

Distance from

plane, l(m)

Couple(m X r X

l)kgm²

0 0

2 2.8

2.5 5.4

3 6.75

4.5 4.5Ry

2nd draw polygon mrl

Scale1cm:1kgm²

105°

O A

B

246°

C