X20 system modules • Other functions • X20CM4810
2088
X20 system User's Manual 3.10
Oscillation parameters
Parameter
Explanation
Symbol
Formula
Rest position
The structure's undisplaced position
s
0
Amplitude
The greatest displacement from the rest position
A
Period duration
Minimal time span for a complete oscillation after which a structure has reached
its initial position and initial speed again
T
Frequency
Number of oscillations per unit of time
f
f = 1 / T
Angular velocity
Change of angle in the radian measure over time
ω
ω = 2 * π * f
Rest position (S
0
)
Am
pl
itu
de
(
A)
Cycle duration (T)
Time
Large mechanical oscillations
An oscillation consists path (s), velocity (v) and acceleration
(ɑ)
values.
These three values have a consistent relationship with one another and can be converted from one to the other
using simple calculations.
The B&R sensors measure oscillation acceleration. The unit is m/s
2
, although acceleration is often specified in the
unit g (1g = 9.81 m/s
2
) for the earth's acceleration.
For some diagnostics, however, the oscillation velocity or displacement is more significant. The acceleration can
then be passed converted to the oscillation velocity through integration. The path can be calculated from the ac-
celeration by using integration twice.
Displacement
s = ŝ · sin(ωt + φ)
Oscillation velocity
v = = ŝ · ω · cos(ωt + φ)
ds
dt
Oscillation acceleration
ɑ =
=
-ŝ · ω · sin(ωt + φ)
2
d s
2
dt
2
dv
dt =
C
on
ve
rti
ng
fr
om
o
ne
v
al
ue
to
th
e
ot
he
r t
hr
ou
gh
In
te
gr
at
io
n
or
d
iff
er
en
tia
tio
n
Table 729: Mathematical relationship
Information:
Displacement is not calculated by the X20CM4810.
s
=
m
ax
, v
=
0
, ɑ
=
m
ax
s
=
0,
v
=
m
ax
, ɑ
=
0
s
=
m
ax
, v
=
0
, ɑ
=
m
ax
s
=
0,
v
=
m
ax
, ɑ
=
0
Time
Am
pl
itu
de
Figure 653: The s-v-a relationship
