Page 23 - Rotating Machinery Pratical Solutions to Unbalance and Misalignment

Rotating Machinery: Practical Solutions

(a) V max = 13.1 ft./sec.

The maximum acceleration occurs when x = x , using Equa-
0
tion 1.11:

(b) a max = (2/0.1863)(4) = 42.9 ft./sec. 2

When the displacement equals 2 feet, using Equation 1.9

2
2
(c) V = k(x 2 - x )/m = (2)(16 – 4)/(0.1863)
0
Therefore V = 11.35 ft./sec.
Using Equation 1.11
(d) a = (k/m) × = (2/0.1863)(2) = 21.47 ft./sec. 2

VIBRATION AS A DIAGNOSTIC TOOL

In the following chapters, there will be a more detailed look
at vibration as a diagnostic tool for determining unbalance and
misalignment in rotating machinery. In addition, beat frequencies
and natural or harmonic frequencies will be discussed in detail.
The mode shape for objects vibrating in their first, second, and
third harmonic frequencies will also be presented. A great deal of
emphasis is placed on determining what is taking place even if
you do not have access to a vibration analyzer.
The characteristic of a machine’s vibration(s) can be used to
identify specific problems. There are numerous causes of vibration
in machines, but about 90% of all problems are due to unbalance
or misalignment. Some of the other sources of vibration are:

• Mechanical looseness • Bad drive belts or chains
• Bad bearings (anti-friction type) • Hydraulic forces
• Bent shafts • Electromagnetic forces
• Aerodynamic forces • Resonance
• Worn, damaged or eccentric gears • Rubbing