ASTM E1270-88(2003)
(Test Method)Standard Test Method for Equal Arm Balances
Standard Test Method for Equal Arm Balances
SIGNIFICANCE AND USE
This test method should enable the user of the balance to interpret data determined thereon in terms of accuracy and precision. It should be helpful in using a particular instrument to best advantage. Weaknesses as well as strengths should become apparent. It is not the intention of this test method to compare similar instruments of different manufacture but rather to assist in choosing an instrument which will meet the needs of the user.
SCOPE
1.1 This test method can be used for testing equal-arm balances of any capacity and sensitivity. The testing procedure should enable the user to characterize his instrument sufficiently to determine whether or not it is suitable for the purpose for which it is to be used.
1.2 The characteristics to be examined include:
1.2.1 Sensitivity at all loads,
1.2.2 Lever arm ratio,
1.2.3 Damping ratio (for instruments without accessory dampers),
1.2.4 Period of oscillation,
1.2.5 Precision, and
1.2.6 Linearity and calibration of accessory devices that provide on-scale indication of weight.
1.3 This standard does not purport to address all of the safety concerns associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation:E1270–88(Reapproved2003)
Standard Test Method for
Equal Arm Balances
This standard is issued under the fixed designation E1270; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
This test method is designed to test balances whose lever-arm ratio is substantially equal to unity.
Although largely superseded by new technologies, equal-arm balances retain a special niche for very
high precision weighing of larger samples (usually greater than 1 kg) as well as objects with large
buoyancy (such as gas bottles). Balances of this type can range from simple instruments of moderate
precision (1:10000) to extremely high precision devices with precision of 1:10000000 or better. A
number of accessory devices may be included for assisting in the weighing process. These devices
may contribute to errors as well as can the basic lever mechanism.This method is designed to test the
entire instrument including the accessories.
1. Scope 3.1.1 capacity—maximumloadrecommendedbythemanu-
facturer. Usually, the capacity refers to the maximum load on
1.1 This test method can be used for testing equal-arm
each pan simultaneously.
balances of any capacity and sensitivity. The testing procedure
3.1.2 readability—value of the smallest unit of weight
should enable the user to characterize his instrument suffi-
which can be read. This may include the estimation of some
cientlytodeterminewhetherornotitissuitableforthepurpose
fraction of a scale division or, in the case of a digital display,
for which it is to be used.
will represent the minimum value of the least significant digit.
1.2 The characteristics to be examined include:
3.1.3 sensitivity—smallest value of weight which will cause
1.2.1 Sensitivity at all loads,
a change of indication which can be determined by the user.
1.2.2 Lever arm ratio,
This may be independent of the readability because of the
1.2.3 Damping ratio (for instruments without accessory
choice of the reading device used. For example, a magnifying
dampers),
glass may be used in conjunction with a reading scale to
1.2.4 Period of oscillation,
observe a sensitivity not readily determined without the mag-
1.2.5 Precision, and
nifying glass.
1.2.6 Linearity and calibration of accessory devices that
3.1.4 precision—repeatabilityofthebalanceindicationwith
provide on-scale indication of weight.
the same load under essentially the same conditions.The more
1.3 This standard does not purport to address all of the
closelythemeasurementsaregrouped,thesmallertheindexof
safety concerns associated with its use. It is the responsibility
precision will be. The precision should be measured under
of the user of this standard to establish appropriate safety and
environmental conditions that represent the conditions under
health practices and determine the applicability of regulatory
which the balance is normally used.
limitations prior to use.
3.1.5 accuracy—degree of agreement of the measurement
2. Referenced Documents
with the true value of the magnitude of the quantity measured.
3.1.6 linearity—characteristic of a direct reading device. If
2.1 ASTM Standards:
a device is linear, calibration at 2 points (for example, 0 and
E617 Specification for Laboratory Weights and Precision
full-scale) calibrates the device (for example, 2 points deter-
Mass Standards
mine a straight line); if a device is nonlinear, additional points
3. Terminology
are needed (perhaps a great many).
3.1.7 standard weight—any weight whose mass is given.
3.1 Definitions of Terms Specific to This Standard:
Since weights are not always available with documented
corrections, weights defined by class (see Specification E617)
This test method is under the jurisdiction of ASTM Committee E41 on
may be used if the class has sufficiently small tolerance limits
Laboratory Apparatus and is the direct responsibility of Subcommittee E41.06 on
and there is an understanding that errors perceived as being
Weighing Devices.
instrumental could be attributed to incorrectly adjusted
Current edition approved Sept. 30, 1988. Published November 1988.
Annual Book of ASTM Standards, Vol 14.02. weights.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E1270–88 (2003)
3.1.8 off-center errors—differences in indicated weight instrument in a controlled environment, it may be necessary to
when a sample is shifted to various positions on the weighing allow 24 h for such equilibrium.
area of the weighing pan. No separate test is described. 7.6 Read the manufacturers instructions carefully. During
3.1.9 full-scale calibration of an accessory device— each step of the test procedure, the instrument should be used
indicatedreadingatequilibriumofanaccessorydevicewhena in the manner recommended by the manufacturer.
standard weight equal to the full-scale range of the device
8. Procedure
isplaced on the sample pan. Usually, some means is provided
bythemanufacturertoadjustthefull-scaletomatchtheweight
8.1 Sensitivity—The sensitivity can be measured at a num-
of the standard.
ber of different loads from zero to the capacity to provide a
sensitivity versus load curve, or, it can be measured at the load
4. Summary of Test Method
of particular interest. This test applies to balances which have
a null position indicator. Balances which are direct reading in
4.1 Throughout this test method, the instrument is to be
used in the manner for which it is intended by the manufac- the on-scale range must be calibrated according to 8.8.4, 8.8.5,
8.8.6 or 8.8.7.
turer. All measurements are made with weights whose values
are sufficiently well known for the purpose of the user. The 8.1.1 Place nominally equal weights on each pan for the
selected load.
nominal value of the weights used will be determined by the
capacity and rated sensitivity of the balance as well as by the 8.1.2 Observe the indication. If necessary, place small
weights on the appropriate sample pan to obtain an indication
resolution and range of the accessory reading devices.
near zero.
5. Significance and Use 8.1.3 Place a small weight on the left pan sufficient to
change the indication about ⁄2 scale of the on-scale range.
5.1 Thistestmethodshouldenabletheuserofthebalanceto
Record the indication as d .
interpret data determined thereon in terms of accuracy and
8.1.4 Remove the small weight and place it on the right pan
precision. It should be helpful in using a particular instrument
and record the new indication as d (remember that for
to best advantage. Weaknesses as well as strengths should
indicatorscalesgraduatedeithersideofcenterzero,indications
become apparent. It is not the intention of this test method to
to the left are recorded as negative values).
compare similar instruments of different manufacture but
8.1.5 Compute the sensitivity as follows:
rather to assist in choosing an instrument which will meet the
needs of the user. S 52 3 W/~d 2 d ! (1)
1 2
6. Apparatus
where:
6.1 Standard Weights—Individual or summations of
S = sensitivity in mass units/scale division, and
1 1 3
weights equal to approximately ⁄4 , ⁄2 , ⁄4 and the total
W = mass of small test weight.
capacity.
Example: d =5.5 div.
6.2 Tare Weights—Weights of the same denominations as
d =−5.3 div.
the standard weights but not necessarily calibrated.
W =10mg
6.3 Calibrating Weights—Balances equipped with acces-
S =2 310/(5.5−(−5.3))=1.85 mg/div.
sory devices such as sliding beam weights, chainweights,
8.2 Sensitivity as a Function of Load—Balancedesignsvary
optical scales or electrical transducers require small standard
but in the case of high precision balances, the manufacturer
weights equal to the full-scale reading as well as smaller
usually tries to provide a nearly level sensitivity at all loads.
weightssuitableforcalibratingintermediatepointsbetweenthe
This is accomplished by the position of the plane determined
zero and full-scale points of the devices. Summations of small
by the terminal pivots in relation to the central pivot. If this
standards can be used for this purpose.
plane is lower than the central pivot, the sensitivity will
6.4 Stop Watch:
decrease with increasing load. Conversely, if the plane is
6.5 Aroom-temperaturethermometerwitharesolutionofat
higher than the central pivot, the sensitivity will increase with
least 1°C.
increasing load and can reach a state of instability if the center
of gravity goes above the center pivot. Placing all of the pivots
7. Preparation of Apparatus
in the same plane provides a nearly level sensitivity limited by
7.1 Place the instrument in the location at which it is to be the elastic properties of the weighbeam. To measure the
tested. If electrically operated, plug in the line cord to the type relationship of sensitivity to load, repeat 8.1 at various loads
of socket recommended by the manufacturer. from zero to the capacity and plot sensitivity as a function of
7.2 Place the standard weights near (or within) the instru- load.
ment. 8.3 Lever Arm Ratio—Equal arm balances are not usually
7.3 Placethethermometeronthebenchinpositionsothatit used as direct-reading instruments. Rather, they are used as
may be read without being touched. comparators using standard weights for reference. For preci-
7.4 Makesurethattheinstrumentandtestweightsareclean. sion measurements such as weight calibration, the measuring
7.5 Allow the instrument and weights to sit undisturbed technique eliminates errors due to the inequality of arm-
sufficiently long to reach temperature equilibrium with the lengths. For relative measurements such as quantitative chemi-
surrounding area. In the case of a large, high precision cal analysis, if the inequality is considered to be in a constant
E1270–88 (2003)
r 5 d /d (4)
ratio,theresultsofanumberofweighingsonthesamebalance
D 1 2
will have a common multiplier (L /L ) and the resulting
1 2
computationsrepresenting,perhaps,fractionalcomponentsofa
where:
compound will be mathematically correct. If there is a need to
d = first turning point, and
determine an absolute mass value from a single direct mea-
d = second turning point in the same direction.
surement, the lever ratio must be determined.
8.5 Period of Oscillation—The time required to make one
8.3.1 Observe the rest point with empty weigh pans.
full oscillation is an indicator of the time required to make a
8.3.2 Placeapproximatelyequalweightsoneachpanwhose measurement either for a damped or undamped balance. The
value is near the capacity of the balance. period is a function of the magnitude of the moving mass and
of the sensitivity of the balance. For a given arm length,
8.3.3 Observe the new rest point.
balances of high sensitivity have longer periods.
8.3.4 Transpose the weights to the opposite pans and ob-
8.5.1 For the convenience of the user, high sensitivity
serve the rest point.
balances may have means for magnifying the indication thus
8.3.5 Measure the sensitivity at this load from 8.1.
allowingthesensitivitytobeloweredandtheperiodshortened.
8.3.6 Compute the lever ratio as follows:
However, such an approach must be used with care since such
M
magnification means smaller angles of deflection are measured
r 5 (2)
L
M 1 S ~d 2 ~d 1 d !/2!
and the balance becomes more sensitive to the tilting which
1 1 2
might occur on a bench or floor of insufficient rigidity.
where:
8.5.2 Placeweightsofequalvalueonthepansatornearthe
r = lever ratio,
L
load of interest. Release the beam and start the stop watch as
S = sensitivity in (mass units)/(scale division),
the direction of the indicator changes. Count several turning
d = rest point of empty pans in 8.3.1 (scale divi-
points and stop the watch after n periods of oscillation.
sions),
Calculate the period, p:
d = rest point from 8.3.3,
d = rest point from 8.3.4, and
p 5 t/n (5)
M = mass of test weights (the value on each pan).
Example: =
where:
M = 100 g (on each pan)
t = total elapsed time, and
S = 1.85 mg/div.=0.00185 g/div.
n = number of turning points.
d = +1.5 div.
8.6 Precision—The term 8precision’ in weighing usually
d = +8.5 div.
means repeatability. In quantitative terms, it refers to expected
d = −2.5 div.
r =
uncertainty of a single reading. The usual method for deter-
L
100 10.00185~1.5 2 ~8.5 22.5!/2! mining the precision is to compare the results of a series of
r = 1.0000278.
L
measurements by some statistical treatment and to compute
8.3.7 A ratio greater than 1 indicates that the left lever is
some value which gives the user an estimate of the potential
longer and if a sample is placed on the left pan and standard
uncertainty of a single reading. A common technique is to
weights on the right, the “true’’ weight is:
compute the standard deviation (s) of a series of observations.
W 5 W/r (3)
The larger the number of observations the better; but 10 is
T I L
usuallyenough.Assuminganormaldistributionofdata,3swill
represent with a high degree of certainty the maximum
where:
anticipated error of a single measurement. One convenient
W = indicated weight.
I
measurement model is a series of double substitutions.
8.4 Damping Ratio—An undamped balance will oscillate
8.6.1 Place a weight, 8A’, considered to be the standard, on
aroundarestpointwithdecreasingamplitudeofoscillationdue
the left pan and a tare weight of the same nominal value on the
toairdampingontheweightpansandtofrictioninthebearing
right pan. Observe the balance indication (A ).
system. The ratio of the amplitude of one oscillation to that of
8.6.2 Removethestandardfromtheleftpanandplaceatest
the next may be a measure of several characteristics of the
weight 8B’ontheleftpan.Thetareweightremainsontheright
balance. Since these cannot easily be separated, this measure-
pan. Observe the balance indication (B ).
ment is not especially useful since pivot conditions can be
8.6.3 Add a small weight (S) to the left pan chosen so that
better measured as part of a measurement of precision. In the
the change in indication will be approximately equal to the
case of a damped balance, this measurement may be useful
difference between the indications A and B . Observe the
1 1
insofarasitmaybeusedtocharacterizetheeffectivenessofthe
indication with this weight on the left pan B .
damping mechanism. Useful damping is that which produces a
8.6.4 Leaving the weight S in place, remove the weight 8B’
steady reading in one or two oscillations. Since the damping
from the pan and replace weight 8A’. Observe the indication
ratio is usually
...
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