Page 46 - Rotating Machinery Pratical Solutions to Unbalance and Misalignment

Rotating Machinery: Practical Solutions

a frequency other than the natural frequency.
If the applied force is exactly in phase with the natural fre-
quency, the amplitude will increase dramatically. This is true even
if the force is relatively small.

Figure 3-2. Vibrating at Natural Frequency

Two factors influence the natural or resonant frequency of an
object, its mass and its stiffness. For a given object, adding mass
lowers its natural frequency, and increasing the stiffness of an
object increases its natural frequency.

Example 3.1
A 20-pound object vibrates at its natural frequency of 25 Hz.
It is decided to add 5 pounds to the object to change its natural
frequency. What will be the resulting new natural frequency?
The object originally has a mass of 20/32.2 or .62111 pounds.
Its new mass will be 225/32.2 or .77639 pounds. The original fre-
quency can be described by:

f = 1/(2π(m/k) .5 (3.1)

Rearranging to solve for the constant k:

k = m (2πf) 2 (3.2)

Since the original frequency was 25 Hz and the original mass
was .62111 pounds, using Equation (3.2) yields k = 15,325 lb./ft.
Now, using the constant k and the new mass, and substituting into