Campbell Scientific CDM-VW300 Series Dynamic Vibrating-Wire Analyzer System - Manual (Page 85)

Appendix E. Calculating Measurement
Error
When using a CDM-VW300 analyzer, the basic output of a measurement is
frequency (Hz) or frequency squared (Hz
2 ). Vibrating-wire sensors are usually
designed with a linear relationship between wire tension and the phenomenon
being measured. Further, wire tension usually has a linear relationship to the
square of the resonant frequency (f
2 ). Manufacturers typically provide a
formula for converting frequency to an engineering unit (U
E
) in the form,
U
E
= Kf 2 , Eq. 1
where K is a constant determined from sensor specifications.
So, for a very small change in frequency, ∆f, change in output, ∆U
E
, is given
by,
∆U
E
= 2Kf∆f Eq. 2
where Eq. 2 is obtained by taking the first derivative of Eq.1 with respect to f,
and f is the present frequency on the wire.
Use Eq. 2 together with noise levels, N (Hz RMS), found in TABLE 5-3,
CDM-VW300/305 Effective Frequency Measurement Resolution, to calculate
the effective resolution (R
e
) of a measurement. For a specific sample rate in
TABLE 5-3, use the corresponding value of N in place of ∆f. Eq. 2 can then be
expressed as,
R
e
= 2KfN Eq. 3
E.1 Example Error Calculation: Geokon Strain Gage
When using a Geokon strain gage, constant K is given by,
K = GB / 1000
Where G is the gage factor 4.062 or 0.391, dependent on gage type, and B is a
batch factor (a number usually near 1, such as 0.97), given on the sensor
calibration sheet.
Substituting into Eq. 1 using engineering units of microstrain (µε):
µε = GBf 2 / 1000,
The effective resolution, R
e
, of the output, or ∆µε, is:
∆µε = 2GBfN / 1000
or
∆µε = GBfN / 500,
E-1