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= m饾潕2r
m: mass (kg)
饾潕 : 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掳, 75掳 and 135掳.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掳, 135掳 and 270掳 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掳, B
to C 70掳 and C to D 120掳. 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 胃(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 胃y
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掳. B and C
make angles of 210掳 and 120掳 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