Balancing of Reciprocating and Rotating Masses

The balancing of machines is an important design parameter. Failure of which will cause an unbalanced moment of inertia and the machine can fail. Ever noticed that our car’s engine is made up of pistons and cylinders. Where inside cylinder pistons reciprocated. But it never makes any vibrations on the car. This happens because during designing the piston and bellcrank assembly is well balanced such that the overall center of mass lies on the axis of rotation and the moment of inertia gets canceled out. Let us discuss this balancing in reciprocating and rotating masses in detail.

Balancing in Rotating Masses

Let us understand this phenomenon of balancing rotating masses with an experiment. Which is a very basic one.

Consider a thread and a stone tied at one end. And you’re holding another end of the rope and holding your hand up towards the sky. At this moment the thread and stone will be pointing towards the downside irrespective of your hand pointing upward. Now the moment you start rotating it keeps the axis of rotation in your hand. Stone will try to come perpendicular to your hand. You will experience that the stone wants to take your hand away. Now your hand is being pulled away because of centrifugal force created by the stone. And a moment of inertia not being on the axis of rotation. If we change the consideration a little bit. Instead of one thread and stone, there would have been two threads and stones of the same length and weight. And rotating both at 180 degrees apart as shown. Then, both would be trying to pull your hand towards opposite direction canceling out each other’s centrifugal force and your hand would be still at one position.

The same phenomenon is used in balancing a rotating mass. If there is a mass on one side of the axis. A counter mass is attached on the other side of the axis 180 degrees apart. 

The force due to which unbalancing is being caused is called a centrifugal force. Which is expressed as:

F=m2r

Where,

F = Centrifugal force

m = mass 

= angular velocity

r = distance of object from the axis

Balancing of single rotating mass 

Balancing of a single rotating mass about an axis can be done by completely nullifying the centrifugal force or disturbing force. For this, another mass has to be placed at a particular distance from the axis in a way such that the centrifugal force created by both the mass becomes equal. The new mass has to be placed exactly 180 degrees opposite the original mass. For this below equation can be used:

maa2ra=mbb2rb

Here, balancing of mass by another single balancing mass occurring in the same axis and the same plane is called internal balancing. 

An external balancing of mass is the balancing of mass by using two or more masses on the same axis and at a different plane of rotation parallel to the original plane of rotation. 

Balancing of more than one rotating masses

To balance more than one rotation mass on the same plane, we just have to take care that again the net resultant force produced by all the rotating masses should be equal to zero.

I.e., 

F1+F2+F3+F4+……….+Fn=0

Where,

Fn= Force generated by nth rotating mass.

And to balance different masses lying on the same axis but different planes as shown in the image. We need to add the same amount of force generated by those masses in that particular axis.

Balancing of Reciprocating Masses

One very common device or machine on which the mass reciprocates is the IC engine. The normal engine is used on cars and bikes. In a reciprocating device, there are primary and secondary unbalanced masses produced. Consider the case of a piston and a crank pin. The piston is accelerated on the line of reciprocation. And the crankpin is experiencing centrifugal force about the axis of rotation. 

The acceleration of piston or reciprocating parts can be given as:

Ar=2(cos+cos2n)

Where, 

= angular speed

n = ratio of rod connecting piston and crank pin to crank pin and shaft

 = angle between line of stroke and radius of mass (crank pin)

And inertial force generated is equals to 

FI=massacceleration

=mAr=m2(cos+cos2n)=m2cos+m2cos2n

Here, 

m2cos is called as primary unbalanced force and m2cos2n is a secondary unbalanced force. 

Now the primary force is acting along the line of stroke and thus this primary force is considered equal to balancing of mass of the crankpin in this case. So, the mass-produced by the crankpin can be called as primary unbalanced force Therefore, to balance the primary unbalanced force created by this crankpin we need to have another mass opposite to the crank pin. 

Forces will be balanced if below condition satisfies,

m12r1cos=m22r2cos          or           m1r1= m2r2

This balancing method is called partial balancing of reciprocating masses.

Conclusion

Unbalanced reciprocating masses or rotating masses both are harmful to any device, thus it needs to be balanced. For which another mass is attached at exactly opposite of the original mass either in the same plane of rotation or a different plane of rotation.