B&R X90, Руководство пользователя

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X90 mobile modules
X90 mobile system User's manual V 1.20 - Translation of the original manual 241
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
)
Amplitude
(A)
Period duration (T)
Time
Large mechanical oscillations
The amplitude of an oscillation can be defined by its path (s), velocity (v) and acceleration (ɑ) values.
These 3 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
, often the acceleration is also indicated with
the unit g (1g = 9.81 m/s
2
) for the acceleration due to gravity.
For some diagnoses, however, the oscillation velocity or oscillation path is more meaningful. The acceleration
can then be passed converted to the oscillation velocity through integration. The path can be calculated from the
acceleration 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 =
Converting from one value to
another
by integration or differentiation
Table 27: Mathematical relationship
Information:
Displacement is not calculated by the module.
s = max, v = 0, ɑ = max
s = 0, v = max, ɑ = 0
s = max, v = 0, ɑ = max
s = 0, v = max, ɑ = 0
Time
Amplitude
Figure 71: The s-v-a relationship