MEE 351

Mechanics of Machinery

Saad Been Mosharof

Lecturer
Department of Mechanical Engineering
Shahjalal University of Science and Technology (SUST), Sylhet-3114

Lecture-09
Balancing of Rotating Mass
 Introduction
 The vibratory force or motion is imparted to
its bearings as a result of centrifugal forces is
called unbalance

 The uneven distribution of mass about a

rotor’s rotating centerline.

• Balancing is the technique of correcting or

eliminating unwanted inertia forces or
moments in rotating or reciprocating masses.

• It is achieved by changing the location of the

mass centers
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Need for Balancing

Rotating a rotor which has unbalance causes the following problems.

 The whole machine vibrates.

 Noise occurs due to vibration of the whole machine.

 Abrasion of bearings may shorten the life of the machine.

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Benefits of balancing

 Increase quality of operation.

 Minimize vibration.

 Minimize audible and signal noises.

 Minimize structural fatigue stresses.

 Minimize operator annoyance and fatigue.

 Increase bearing life.

 Minimize power loss.

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 BALANCING OF ROTATING MASSES

 When a mass moves along a circular path, it experiences a centripetal acceleration

and a force is required to produce it.

 An equal and opposite force called centrifugal force acts radially outwards and is a
disturbing force on the axis of rotation.

 The magnitude of this remains constant but the direction changes with the rotation of
the mass.

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Types of balancing

• Static Balancing
A rotating mass is said to be statically balanced if the rotating mass can rest,
without turning, at any angular position in its bearings. This condition is attained
when the sum of the centrifugal forces on the rotating mass due to unbalanced
masses is zero in any radial direction.
Or
i) Static balancing is a balance of forces due to action of gravity.
ii)A body is said to be in static balance when its center of gravity is in the axis of
rotation.

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 Types of balancing

● Some examples of common devices which meet this criterion, and thus can
successfully be statically balanced, are:

● a single gear or pulley on a shaft,

● a bicycle or motorcycle tire and wheel,
● a thin flywheel,
● an airplane propeller,
● an individual turbine blade-wheel (but not the entire turbine)

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Types of balancing

• Dynamic Balancing
A rotating mass is said to be dynamically balanced when it does not
vibrate in its running state. To make a rotating mass dynamically
balanced, it must first be statically balanced.

● Dynamic balance is sometimes called two plane balance

● It require that two criteria to be met

● The sum of forces must be zero

● And the sum of moments must also be zero

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Dynamic or "Dual-Plane" balancing

Statically balanced
but dynamically unbalanced
m r 2

r
r
Brg A Brg B
l
m r 2
Load on each support Brg
= (m r 2 l)/ L
due to unbalance
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 Dynamic or "Dual-Plane" balancing

Some examples of devices which require dynamic balancing are:

•rollers

•crank-shafts

•camshafts

•axles

•clusters of multiple gears, motor rotors, turbines, propeller shafts.

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 Rotating Balancing

Rotating Unbalance occurs due to the following reasons.

●The shape of the rotor is unsymmetrical.

●Un symmetrical exists due to a machining error.

●The material is not uniform, especially in Castings.

●A deformation exists due to a distortion.

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 Rotating Balancing

 In a revolving rotor, the centrifugal force remains balanced as long as the centre of the
mass of rotor lies on the axis of rotation of the shaft.

 When this does not happen, there is an eccentricity and an unbalance force is produced.

 This type of unbalance is common in steam turbine rotors, engine crankshafts, rotors of
compressors, centrifugal pumps etc.
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 Rotating Balancing
• The unbalance forces exerted on machine members are time varying, impart vibratory motion
and noise,
• There are human discomfort, performance of the machine deteriorate and detrimental effect
on the structural integrity of the machine foundation.
• Balancing involves redistributing the mass which may be carried out by addition or removal of
mass from various machine members.

 Balancing of rotating masses can be of

1.Balancing of a single rotating mass by a single mass rotating in the same plane.
2.Balancing of a single rotating mass by two masses rotating in different planes.
3. Balancing of several masses rotating in the same plane
4. Balancing of several masses rotating in different planes

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 Balancing of a Single Rotating Mass By a Single Mass Rotating in the Same Plane

• Consider a disturbing mass m1 attached to a shaft rotating

at ω rad/s
• Let r1 be the radius of rotation of the mass m1

• This centrifugal force acts radially outwards and thus

produces bending moment on the shaft.
• In order to counteract the effect of this force,
a balancing mass (m2) may be attached in the same
plane of rotation.

𝑆𝑜, 𝐹𝐶1 = 𝐹𝐶2

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Balancing of a Single Rotating Mass By Two Masses Rotating in Different Planes

• The following two possibilities may arise while attaching the two
balancing masses :

1. The plane of the disturbing mass may be in between the planes of the two
balancing masses, and
2. The plane of the disturbing mass may lie on the left or right of the two planes
containing the balancing masses.

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 Balancing of a Single Rotating Mass By Two Masses Rotating in Different Planes

1. When the plane of the disturbing mass lies in between the planes of the two balancing masses
• Consider a disturbing mass m lying in a plane A to be
balanced by two rotating masses m1 and m2 lying in two
different planes L and M
• Let r, r1 and r2 be the radii of rotation of the masses in
planes A, L and M respectively.

(i)

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 Balancing of a Single Rotating Mass By Two Masses Rotating in Different Planes

1. When the plane of the disturbing mass lies in between the planes of the two balancing masses

Taking moment about P

(ii)

Taking moment about Q

(iii)

• It may be noted that equation (i) represents the condition for static balance, but in
order to achieve dynamic balance, equations (ii) or (iii) must also be satisfied.
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 Balancing of a Single Rotating Mass By Two Masses Rotating in Different Planes

When the plane of the disturbing mass lies on one end of the planes of the balancing
masses

• In this case, the mass m lies in the

plane A and the balancing masses
lie in the planes L and M.

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 Balancing of a Single Rotating Mass By Two Masses Rotating in Different Planes
2. When the plane of the disturbing mass lies on one end of the planes of the balancing
masses
Taking moment about P

(ii)

Taking moment about Q

(iii)

• It may be noted that equation (i) represents the condition for static balance, but in
order to achieve dynamic balance, equations (ii) or (iii) must also be satisfied.
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 Balancing of Several Masses Rotating in the Same Plane

The magnitude and position of the balancing

mass may be found out analytically or graphically

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 Analytical method
1. First of all, find out the centrifugal force exerted by each mass on the rotating shaft.

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Graphical method

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Graphical method

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Reference Links:
https://youtu.be/1t0eJzMgWBA
https://www.youtube.com/watch?v=7nJ0mnHXfxw
https://youtu.be/a8r1d5lX5M0

THANK YOU

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