Mechanic of Machine

KJS 2233

Mohd Shukri bin Yob

Balancing of Rotating

Masses

INTRODUCTION

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INTRODUCTION

Rotating components are widely used in modern

machine

Example of rotating part/component/machine;

a. Wheel for vehicle

b. Fan

c. Quad copter

d. Engine

e. Turbine

ROTATING MASSES &BALANCING

For a machine rotating at high speed, balancing

is very important

Definition- resultant force acting for component

equal to zero

Types of rotating condition

I. Single plane

II. Multi plane

SINGLE PLANE Wheel for train

MULTI PLANE Crankshaft

EFFECTS OF NON BALANCED

PART

1. Part or component expose to higher load

2. Shaft expose higher load

3. Increase load to bearing

4. Vibration effect to component and system-

fatigue failure

THEORY OF ROTATING MASS

Rotating part/component- expose to centrifugal

force

Equation

Fc= m𝝎2r

m: mass (kg)

𝝎 : angular velocity (rad/s)

r : radius (m)

Balanced part- resultant force equal to zero

Unbalanced part- resultant force- not zero

SOLVING BALANCING PROBLEM

2 approaches

1. Analytical method

2. Graphical method

EXAMPLE 1 Four masses m1, m2, m3and m4 are 200 kg, 300 kg, 240 kg

and 260 kg respectively. The corresponding radii of rotation are

0.2 m, 0.15 m, 0.25 m and 0.3 m respectively and the angles

between successive masses are 45°, 75° and 135°.Find the

position and magnitude of the balance mass required, if its

radius of rotation is 0.2 m.

EXAMPLE 2 Four masses A, B, C and D are attached to a shaft and revolve in

the same plane. The masses are 12 kg, 10 kg, 18 kg and 15 kg

respectively and their radii of rotations are 40 mm, 50 mm, 60

mm and 30 mm. The angular position of the masses B, C and D

are 60°, 135° and 270° from the mass A. Find the magnitude

and position of the balancing mass at a radius of 100 mm.

EXAMPLE 3

Table below shows an unbalance rotating masses system, as an

engineer you are asked to propose the solution to correct this

unbalanced system.

Mass mass (kg) r (m) Angle(deg)

1 50 1.2 0

2 75 2 20

3 55 3 115

4 45 2.5 255

EXAMPLE 4

Table below shows the balanced rotating system, for this

system, find the mass of m1, m2 ,m3 and m4 if all the masses

have same weight.

m mass (kg) r (m) Angle(deg)

1 A 0.04 0

2 B 0.05 60

3 C 0.06 135

4 D 0.03 270

5 2 0.3 248

Multi Plane

Method

Choose reference plane

- and +

Table- mrl for x and y axis

Example 5

A shaft carries four masses A, B, C and D of magnitude 200

kg, 300 kg,400 kg and 200 kg respectively and revolving at

radii 80 mm, 70 mm, 60 mm and 80 mm in planes measured

from A at 300 mm, 400 mm and 700 mm. The angles

between the cranks measured anticlockwise are A to B 45°, B

to C 70° and C to D 120°. The balancing masses are to be

placed in planes X and Y. The distance between the planes A

and X is 100 mm, between X and Y is 400 mm and between Y

and D is 200 mm. If the balancing masses revolve at a radius

of 100 mm, find their magnitudes and angular positions.

Solution

Plane Mass (kg) Radius

(m) mr

Distance (m)

mrl θ(deg)

A 200 0.08 16 -0.1 -1.6 0

X(RP) Mx 0.1 0.1Mx 0 0 0

B 300 0.07 21 0.2 4.2 45

C 400 0.06 24 0.3 7.2 115

Y my 0.1 0.1my 0.4 0.04my θy

D 200 0.08 16 0.6 9.6 235

Example 6

Four masses A, B, C and D as shown below are to be

completely balanced.

The planes containing masses B and C are 300 mm apart. The

angle between planes containing B and C is 90°. B and C

make angles of 210° and 120° respectively with D in the

same sense. Find :

The magnitude and the angular position of mass A ; and

The position of planes A and D.

Solution

Example 7

A, B, C and D are four masses carried by a rotating shaft at

radii 100,125, 200 and 150 mm respectively. The planes in

which the masses revolve are spaced 600 mm 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.

Solution