SV SLA-PA201, Manual

Page: 65 / 88

65
ISO8041:1990
Annex D
D. 1 Nomenclature
a
: Instantaneous magnitude of signal
0
a
: Reference magnitude of signal(
2
1 / or 1 m s pW
μ
=
) if power is measured
τ
: Time constant for running averaging
t
: Time
o
t
: Time of observation
1
t
: Start time of integration
2
t
: Stop time of integration
or exp e
: Exponential Function
2 1
( ) T t t
= −
: Measurement period for linear averaging
D.2 Integration
The equivalent continuous vibration value or the equivalent continuous vibration level are based on
normal start-stop integration (linear integration) of the squared signal. The time weighting
characterizes a running integration of the squared signal. The result is the running r.m.s value.
1
2
2
,
0
1
( ) ( )
o
o
t t
t
rms o
a t a t e dt
τ
τ
τ
−
⎡ ⎤
= ⎢
⎥
⎣ ⎦
∫
It is a function of the instant time
o
t
. All recent parts of the signal
( )
a t
contribute to the value.
They are weighted by a factor decreasing exponentially with the time distance from
o
t
.
The corresponding time weighted vibration level, in decibels, is given by
2
,
2
0
1 ( )
( ) 10 log
o
o
t t
t
rms o
o
a t
L t e dt dB
a
τ
τ
τ
−
⎡ ⎤
=
⎢ ⎥
⎣ ⎦
∫
NOTE – These equations describe the behavior of a hot-wire ampere meter and can be realized by
relatively simple means or digital algorithms. The running r.m.s value responds to fluctuations of the
signal as slowly as the constant allows. A considerable reduction of data is achieved without losing
essential information about changes of amplitude or level.