Theory of Machines: Unit V: Balancing and Vibration

Balancing of single rotating mass

Balancing and Vibration - Theory of Machines

Consider a mass of m attached to shaft rotating at o rad/s, as shown in Fig.12.1(a).

BALANCING OF SINGLE ROTATING MASS

Consider a mass of m attached to shaft rotating at o rad/s, as shown in Fig.12.1(a). Let r be the radius of rotation (i.e., distance between the axis of rotation of the shaft and the C.G. of the mass m) of the mass 'm'.

We know that the centrifugal force (i.e., disturbing force) FC = m ω2 r, producing out-of- balance effect acting radially outwards on the shaft. This out-of-balance force can be balanced in any one of the following two ways.

1. By Introducing Single Revolving Mass in the Same Plane

The disturbing mass m is balanced by introducing a counter mass or balancing mass mB at radius of rotation rB diametrically opposite to m in the same plane, rotating with same angular velocity ω rad/s, as shown in Fig.12.1(b).


We know that, Disturbing force, FC1 = m ω2 r

and Balancing force, FC2 = mB ω2 rB

But for balancing, FC1 = FC2 or m ω2 r = mB ω2 rB


The value of rB may be kept larger to reduce the value of balancing mass mB.

Note 

The product mB rB or m r is very often called as the mass moment.

2. By Introducing Two Revolving Masses in Different Planes

Sometimes it is not possible to introduce balancing mass in the same plane in which disturbing mass m is placed. In that case two masses can be placed in different planes.

If the balancing mass and disturbing mass lie in different planes, disturbing mass cannot be balanced by a single mass as there will be a couple left unbalanced. In such cases, at least two balancing masses are required for complete balancing and the three masses are arranged in such a way that the resultant force and couple on the shaft are zero, as shown in Fig.12.2.


Let m = Mass of the disturbing body acting in plane A,

mB1 and mB2 = Masses of the two balancing bodies acting in plane B and C respectively,

r, rB1 and rB2 = Distance of C.G of m, mB1 and mB2 from the axis of rotation respectively,

l1 = Distance between the planes A and B,

l2 = Distance between the planes A and C, and

l = l1 + l2 = Distance between the planes B and C.

We know that the masses m, mB1 and mB2 experience the centrifugal forces as FC, FC1, and FC2 which are given as


(i) For balancing of the system, the centrifugal force of the disturbing mass must be equal to the sum of centrifugal forces of the balancing masses.


(ii) We also know that, for complete balance of the system, the sum of moments must be zero.

Taking moments about C, we get


Using equations (i) and (ii), we can find the balancing masses mB1 and mB2.


Theory of Machines: Unit V: Balancing and Vibration : Tag: : Balancing and Vibration - Theory of Machines - Balancing of single rotating mass


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Theory of Machines

ME3491 4th semester Mechanical Dept | 2021 Regulation | 4th Semester Mechanical Dept 2021 Regulation