Balancing of rotating and reciprocating masses

1. Mechanism of machinery
Chapter 11
BALANCING OF ROTATING AND RECIPROCATING MASSES
Pr.by. Mr. TESFAYE MENGESHA
3/15/2023 1

2. Introduction
In many moving parts of machines which have rotary or reciprocating motion, inertia
forces cause shaking of machine members. These forces may induce unwanted
vibrations. If such vibrations occur at frequencies near the natural frequencies of
flexible members, amplitudes of vibration may become excessive causing discomfort
and failure of parts. Even if the amplitudes of vibration are not so large as to cause
failure of parts, they may cause fatigue which eventually leads to failure. It is,
therefore, very essential that all rotating and reciprocating parts be completely
balanced as far as possible.
Balancing is a technique of correcting or eliminating unwanted inertia forces, thereby
neutralizing or minimizing unpleasant and injurious vibratory effects.
Balancing of inertia forces is effected by introducing additional masses or by removing
some mass to counteract the unbalanced forces.

3. 11.1 Balancing of Rotating Masses
Static balance and dynamic balance
Static balance is a balance of forces due to the action of gravity.
The shaft which is assumed to be perfectly straight, rests on hard and rigid rails and
rolls without friction. A reference system, x-y-z, is attached to the disc. Roll the disc
gently by hand and allow it to come to rest. Then, mark the lowest point of the
periphery of the disc. Repeat this four or five times and observe the location of the
marks. If the marks are placed randomly, the disc is balanced. On the other hand, if
the marks are concentrated in the same area, then the disc is statically unbalanced;

4. For a rotor with different masses shown in Fig. below, the requirement for static
balance is that the center of gravity of the system be at the axis 0-0 of rotation. From
this we conclude that moments about the x- and y-axes must be zero, for which
condition we the relations

5. 11.2 Balancing of Different Masses Lying In The Same Transverse Plane
Consider the rotor carrying masses m1 , m2 and m3 at radial distances r1, r20, and r3,
respectively, as shown in Fig. below

6. For balance of the rotor, the vector sum of all forces, including the balancing mass,
must be equal to zero. i.e.
For balance of the rotor, equation above
must be satisfied.

9. where 𝑊
𝑒𝑟𝑒 is due to the balancing mass 𝑚𝑒 and
𝑟𝑒 is the radial distance of the balancing mass from
the axis of the rotor.
𝑚𝑒 = (𝑊
𝑒/𝑔) = 𝑊
𝑒𝑟𝑒/ 𝑟𝑒𝑔 = 𝟎. 𝟖𝟗 𝒌𝒈

10. 11.3 Balancing of Different Masses Rotating In Different Planes
If the rotating masses lie in different transverse planes as shown in Fig.
(a), to achieve balance of the rotor, first, the equation must
be satisfied. In addition, balance of moments due to the inertia forces
is also required.