5. GFS TOOLS SOFTWARE
Page 151
© 2007 DH Instruments, a Fluke Company
the initial measured mass and all ambient conditions are again stored. If the balance has not
drifted and ambient conditions have not changed (and the AutoZero system repeated
perfectly), the balance output would be 0. However, this is never the case. The bulk of the
resultant mass change is the result of the change in buoyancy and the drift of the balance.
Any error associated with the AutoZero system cannot be compensated for. In general, this
error can be experimentally proven to be small relative to drift and buoyancy change.
Therefore, neglecting its effect is valid.
Since the cylinder is buoyancy corrected real time when taking measurements, the buoyancy
correction of the reference mass should not be part of the AutoZero correction used to
determine the instantaneous cylinder mass. To remove the
buoyancy
mass
from the
AutoZero correction, the difference in the calculated true mass is used. The actual true mass
of the reference mass is not used because any error in the balance will result in an offset that
is normally “tared” out. Span error of the balance is not an issue since only a small portion of
the balance span is used. Using the true mass of the reference mass would complicate the
issue by requiring a correction factor for the balance.
d
m
T
m
T
m
m
m
m
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
−
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
=
Δ
ρ
ρ
ρ
ρ
2
1
1
1
re-arrange and simplify…
m
T
d
m
m
m
ρ
ρ
ρ
2
1
−
−
=
Δ
Note that if the balance did not drift, an increase in density should result in a negative mass
change relative to the original reference mass measurement and a decrease should result in
a positive mass change. The above equation holds true.
VARIABLE
DEFINITION
m
d
The calculated mass drift of the balance in grams. This is the AutoZero correction
value used to determine the instantaneous mass measured by the balance. The
value will change only when an AutoZero occurs. Between AutoZeros, the value
remains constant. When the balance is first zeroed, the value is 0.
m
T
The true mass value for the reference mass stored in GFS Tools in grams. This
should equal the calibrated value of the reference mass within the uncertainty of the
balance.
m
Δ
The averaged output of the balance when the reference mass is lowered for
AutoZero. The balance must have been originally checked with the reference mass
lowered.
ρ
2
Air density at the time of the AutoZero (kg/m
3
).
ρ
1
Air density at the time of the original reference mass check (kg/m
3
).
ρ
m
Reference mass density at the time of the original check (kg/m
3
).
5.7.5
REFERENCE CYLINDER BUOYANCY
If a cylinder is activated in the configuration, the cylinder pressure and buoyancy mass are
determined based on the instantaneous mass, AutoZero correction, cylinder parameters and
ambient conditions. The cylinder buoyancy mass is used to correct the instantaneous mass
of the balance by removing the buoyancy changes of the cylinder.
GFS Tools
calculates the
total buoyancy mass of the cylinder with each new mass update. This total buoyancy is
added back to the instantaneous mass to determine the final corrected mass.
The cylinder pressure is calculated using the indicated mass of the cylinder and ambient
conditions in an iteration. The balance output is not the cylinder mass when the cylinder is
on the scale. In general use, the mass output on the balance must be added to the AutoZero