Page 41 - Rotating Machinery Pratical Solutions to Unbalance and Misalignment

Developing the Vibration Equations

V= D*°F (2.14)
60,000

60,000
D= (2.15)
°F

Acceleration is the second derivative of displacement with
respect to time, which is expressed as:

2
2
2
A = dx /dy = X ω Sin (ωt) (2.16)
o
A occurs @ Sin (ω t) = 1; Sin (ωt) = 1 @ π/2, 3π/2, 5π/2,…
max
(2n–1) π/2
Letting the capital letter “G” stand for acceleration in terms
of G’s, then:

G = A/[32.2 * 12] (inches per second per second) (2.17)

G = A/386.4 (2.18)

2
G = [X ω ]/386.4 (2.19)
o
X = D/2 = [.001 * D]/2 (2.20)
o
2
ω = [2*π*f] 2 (2.21)
Substituting from Equation (2.8)

2
ω = [(2πF/60)] 2 (2.21)
Substituting from Equations (2.20) & (2.21)

2
.001 * D 2* °F
G= × /386.4 (2.22)
2 60 2

2
G = .014190252 * DF /1,000,000 (2.23)
G = .014190252 * D * [F/1000] 2 (2.24)