SV SLA-PA201, Руководство пользователя

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21
IV. Real Time Measurement in Vibration Level Meter/Sound Level Meter
1. Basic Theory of Vibration Level Meter / Sound Level Meter
1. 1 Understanding of Integration Time and Time Constant
The RMS(Root-Mean-Square) calculation routine is based on “IEC60804:2000-Integrated
Averaging Sound Level Meter” and “ISO8041:1990-Human response to vibration-Measuring
instrumentation”.
Generally, RMS is calculated by the equation below :
2
0
1
( )
T
rms
a a t dt
T
=
∫
<Eq. IV-1-1>
where
( ) a t
is instantaneous acceleration and
T
is measuring time.
rms
a
is calculated for
T
second. The calculation method in real-time is named Running RMS Acceleration which is described
at ISO(International Standard Organization) standard.
The RMS calculation equation in real-time can be arranged as below :
0
0
2
0
1
( ) ( )
t
rms
t T
a t a t dt
T
−
=
∫
<Eq. IV-1-2>
where
0
t
is current time,
T
is measurement period(time) for calculation. Sometimes, this period
is called by integral time. This calculation for RMS is linear Averaging RMS.
0
t
0
t T
−
t
T
[Fig. IV-1-1] The Calculation Method with Linear Averaging RMS
The linear averaging RMS Method is used for RMS, but is inferior to the exponential averaging
RMS in real-time calculation. The equation below represents the exponential averaging RMS.
2
,
1
( ) ( )
o
o
t t
t
rms o
a t a t e dt
τ
τ
τ
−
−∞
=
∫
<Eq. IV-1-3>
where
τ
is the time constant and we can read it with ‘tau’ pronunciation. As [Fig. IV-1-2] is
shown, the exponential averaging RMS equation is different to the linear averaging RMS, but the
results are similar and the former emphasizes recent data of signal as [Fig. IV-1-2].