weighing-systems.com
weighing-systems.com
 |
1
= arm 2 = hinged joint (suspension point) 3 = pan carrier 4 = suspended weighing pan 5 = housing By placing an object on one pan it can be compared with a weight placed on the other pan. When the object or the weight is not placed in the center of the pan, the pan will move so that the center of gravity is below the suspension point. So there is no error caused by eccentric load. When the balance is in equilibrium the weight of object and comparison standard are the same. The mass may not be the same! Because of air buoyancy 1 kg lead on one side seems to have more weight than 1 kg of feathers on the other side. |
|
1
= arm 2 = hinged joint 3 = pan carrier 4 = weighing pan 5 = housing 6 = counterweight 7 = pan for compensation weights In this weighing system there is no error caused by difference in armlength: object and compensation weights are on the same arm. The weight of the object is compensated not by placing weights but by removing them. This usually has the form of a rack of weights with a lifting mechanism. The last digits of the weight are mostly read with a pointer which shows the off-balance position of the system. |
 |
1
= arm 2 = hinged joint 3 = pan carrier 4 = weighing pan 5 = housing 6 = counterweight 7 = rack with comparison weights 8 = (optional) pointer for last digits 9 = guide If an object is off-centered on the weighing pan, this causes torque, which generates a counterforce in the suspension guide and arm. If both are parallel the forces in them will not distort the weighing result. Therefore exact adjusting of the joints is important. |
 |
1 = weighing
pan 2 = pan carrier 3 = guides 4 = joints 5 = to the force transducer This works the same in relation to eccentric placing of an object on the pan as in the mechanical toploading scale: the counterforce in the guides will neutralize this, provided they are parallel. |
 |
1
= direction of the force being measured (and compensated) 2 = coil 3 = permanent magnet 4 = position sensor (null sensor), usually a photocell or capacitive sensor 5 = servo amplifier 6 = precision resistor (measuring resistor) 7 = digital display The force on the weighing pan is compensated by the permanent magnet and the magnetic field generated by the current in the coil. This current is regulated by the sensitive position sensor and the servo amplifier, and measured over the precision resistor by the analog-digital converter. For short: the balance measures the current needed to keep the pan in its position, the pan does not move! |
|
|
 |
1
= weighing pan 2 = pan carrier 3 = upper guide 4 = flexible coupling pin 5 = lower guide 6 = housing 7 = flexible joint 8 = lever 9 = coil Here the force is transferred to the coil by a lever with a large transmission ratio. The negative effect of the presence of extra joints is much smaller than the positive effect of a lower current in the coil and less possible vertical movement of the guides. |
 |
1
= weighing platform (pan) 2 = pan carriers 3 = levers 4 = coupling between levers 5 = to the force transducer If an object is placed on the left-hand side of the platform, a force is applied to the left lever, to the right lever if the object is placed on the right-hand side. If the transmission ratio of both levers is equal, then the force on the transducer is also equal. The same also applies to intermediate positions, in which the forces are transmitted partially by both levers. Thus the readout is independent of the objects position on the weighing pan. A platform scale like this can be over 2m wide and have a weighing range of over 1000kg |
 |
1 = pan carrier
(weighing pan removed) 2 = upper guide 3 = adjustment screws for parallel position of the guides 4 = lower guide just visible 5 = lever 6 = magnet, covered by a magnetic shield with in the center a photocell as position sensor 7 = housing block, made out of the same material as guides, lever, and pan carrier to minimize temperature effects. |
 |
1 = spring
body (side view and in perspective) 2 = weighing pan 3 = mounting plate (housing) 4 = placing and wiring of the strain gauges (R3 and R4 can also be placed on the under side of the beam) The strain gauges are wired as a Wheatstone-bridge to compensate for temperature changes. When the system is not loaded all four resistors are the same and the input of the amplifier is zero. When an object is placed on the pan R1 and R4 are compressed and their resistance decreases, R2 and R3 are strained and their resistance is increased. This causes a voltage difference at the input of the amplifier, proportional to the weight of the object. The shape if this spring body is comparable with the basic construction of the electronic balance with two guides. |
 |
< Cross section of a double-ring shaped spring body: When a force is applied in the centre the inner ring will tilt, the top being compressed and the under side stretched. |  |
< A cylindrical deforming body: When a force is applied the cylinder will get shorter an the diameter larger. For very heavy loads. Several of these can be placed under a large platform with their output signals being electronically added. |
The strain-gauge method of measurement has its limitations for high resolution weighing machines, which are primarily due to creep in the spring material and the adhesive between the spring body and the strain gauges. The moisture sensitivity of the adhesive and the low output signal also cause difficulties. The major advantages of this method are the compact design,cost and its easy adaptability to various maximum capacities.
Displacement methods: Instead of strain-gauge measurement at the bending points, a weighing system with a flexural component can determine the load-dependent displacement of the load receptor by any given method of displacement measurement. For low accuracy requirements, for instance, inductive transducers are available in which the displacement of coils or ferrite cores is used to generate the weighing signal. For medium accuracy, the change in distance of capacitor electrodes is used. Optical measurement is also possible.
Magnetic induction: Under the influence of an external force, some materials
alter their magnetic properties; e.g., the permeability drops in the direction
of the force. This can be used by bringing two coils, perpendicular to each
other, in a block of such material: In unloaded condition, the primary coil
induces zero voltage in the secondary coil. Under load, the magnetic-flux lines
become asymmetrical and a voltage proportional to the load is induced in the
secondary coil. This method is used in scales that weigh in the ton range, particularly
under rough conditions.
Vibrating cord systems: The resonance frequency of a string is dependent
on its length, mass per unit of length, and the tension on it. The tension on
the string can also be the weight of an object. As the output signal of such
a system is a frequency change, it can be digitized very easily, no analog-digital
convertor needed. There is one problem however: The relation between tension
force an frequency is not linear. This can be solved digitally by calculating
the result, or mechanically by using two vibrating cords. In this case, the
quotient of the two cord frequencies is evaluated.
A variation on this is a system that can even be used under weightless conditions:
Of a vibrating rod the frequency is also dependent on its length and mass. By
placing the sample on a pan at the top of the rod the mass can be evaluated
by measuring the change in resonance frequency. Of course the sample has to
be attached tightly to the pan!
Systematic
errors : The cause of the error is known, perhaps even the value of this
error, or at least an upper limit of error.
Examples:
There is no hard-set difference between systematic and random errors. By means of additional measurements or information, many random errors can be transformed into correctable systematic errors.
Example 1: The influence of air pressure on the determination
of mass.
The density of air is dependent on air pressure, therefore the buoyancy is dependent
on air pressure. If during an extended measuring cycle the momentary air pressure
is unknown, this will lead to apparently random fluctuations in results. If
the air pressure is measured, the systematic influence can be calculated and
corrected accordingly. This means less fluctuation in the weighing results.
Example 2: Incorrectly adjusted balance: When the same
balance is always used this is a systematic error in all measurements.
When several balances are available, one of which is incorrectly adjusted, the
error will depend on the lab records: without proper statement of the balance
being used there is a random error. When the balance used for each measurement
was recorded, the error can be calculated and corrected fo accordingly; a known
systematic error.
When all balances were adjusted with the same incorrect weight, all measurements
will have the same systematic error.
 |
|
((1mg)2;
+ (1mg)2;) = 1.4mg Rule
3 (error propagation for products and quotients): In products or quotients
the squares of the relative individual errors are added and the square
root of this sum is taken.
Example: Density determination in accordance with the equation 
= mass / volume.
measured mass m = 150.27g 
0.01g,
measured volume V = 173.4cm3; 0.1cm3;.
calculated density =
m / V = 150.27 / 173.4 = 0.866609g/cm3;.
Error calculation: The relative error of the mass is 0.01g / 150.27g = 0.666
.
The relative error of the volume is 0.1cm3; / 173.4cm3;
= 5.77.
The relative error of
is ((0.666)2;
+ (5.77)2;)
= 5.80.
The absolute error of
is 5.80 . 0.866609g/cm3;
= 0.5.10-3g/cm3;.
Thus, the final result is:
= (0.8666 0.0005)g/cm3;.
 |
The
characteristic curve can be shifted by a constant amount, the zero error ZP
(the blue line). This error is eliminated by correctly setting the balance
to zero before weighing. Therefore, the zero error plays a role only during
prolonged measurements, during which the object being weighed cannot be
removed from the pan. If the slope of the curve deviates from the ideal characteristic curve (red line), this is known as sensitivity error S.
A sensitivity error has a negligible effect for small weights or weight
differences, but greater for heavier weights. As a result, the sensitivity
error is always specified as a relative figure; e.g. 2mg/100g, 20ppm or
20 /K. A sensitivity error
can be caused by temperature drift, aging, adjusting with an incorrect calibration
weight, or by incorrect adjustment for compensation of an off-center load
error (S will then be
dependent of the position of the sample on the weighing pan). The curve can also be arched: This is known as linearity error (or linearity). The maximum linearity is usually listed in the specifications of a balance. |
All
of these deviations from the ideal can depend on the temperature; this is denoted
as the temperature coefficient (abbreviated TC). If a data sheet indicates
a "sensitivity TC of 
2/K",
this means, for example, that when the sensitivity of the balance is adjusted
at 18°C and the balance is subsequently used at 21°C, it can show a
sensitivity deviation of (21-18).2
= 6 maximum, which is the
equivalent to 0.6mg/100g.
The effect of aging is known as long-term drift of the zero point or
sensitivity.
If you repeat a weighing procedure under the same ambient conditions, the individual
results may deviate slightly from one another. This is known as the reproducibility
of a weighing instrument. Expressed as a quantity, this is indicated by the
standard deviation "s",
Other errors: the effects of moving the balance to a different location.
Non- horizontal position of the weighing instrument: Accurate balances are fitted with a spirit level (this is even mandatory on legally verified weighing instruments) for always being able to find back the reference position after moving the instrument: this is the position in which the instrument was correctly adjusted. In the reference position the direction in which the force (the weight) is measured is the same as the direction of gravity. If, for instance, the weighing instrument is moved to a table that is not level, but is tilted 5mm on a length of 1m, and it is not set level again, the direction of measurement deviates 0.2865° from the reference position. The measured weight value W will then be cos0.2865 smaller (W1 = cos0.2865.W = 0.9999875.W), that means on a weight of 200g a 2.5mg lower readout. The zero setting also changes: the zero point is also a weight value, it is the weight of the empty weighing pan.
When in the reference position the direction of measurement exactly coincides
with the direction of gravity, the result will always decrease when the instrument
is tilted, when this is not the case, the error can be plus or minus. On weighing
instruments with a small number of measuring steps (up to about 10000 digits)
the influence of a not horizontal position under normal circumstances
is negligible, therefore these often don't have a spirit level: "level on the
face of it" will then be good enough. On a classical two-armed balance the effect
is again different: on the comparison of two weights there will be no influence,
both scales will always hang straight below the measuring point (suspension
point). But if the last digits of the difference between the weights are read
by a pointer on the arm an error will occur in the sensitivity of this pointing
device.
Moving the weighing instrument in height: As the force of attraction
(= gravity) between two objects (the earth and the object being weighed) depends
on their distance, the measured value will change when the weighing instrument
is moved to a different height. By every meter elevation (at moderate heights)
the field of gravity changes from sea level -0.3086
N/(mkg). Or as a more practical figure: when the weighing instrument is placed
one floor higher (about 4m), a weight of 200g will weigh 0.26mg less.
Moving over a larger distance: The acceleration of gravity g is
not the same everywhere on earth: As a consequence of centrifugal forces caused
by the earth's rotation it is less at the equator than at the poles. Also the
earth is not a perfect sphere: the distance from the surface to the earth's
center of gravity is larger at the equator than at the poles.
The absolute deviation caused by moving the instrument can be considerable larger
than the error of the weights used for adjustment (and larger than the maximum
permissible errors for verified weighing instruments). Therefore after moving
to a different location readjustment is necessary. Many weighing instruments
are fitted with a built-in adjustment weight for this purpose: with this the
sensitivity deviation caused by relocating the instrument is easily corrected.
Other errors: forces working on an object being weighed.
Air
currents / drafts: These are often the cause of large random errors, as
the effect of air currents depends on unpredictable circumstances like the shape
and size of the object being weighed, posture and movements of the operator,
or opening doors. Sometimes the metrological demand for the least possible air
currents collides with safety requirements: Poisonous substances must be weighed
in a fume cupboard. To minimize the effect of ambient air flow, draft shields
are used. For balances with a readability of 1mg, an open draft shield, e.g.,
in the shape of a glass cylinder, will suffice under normal conditions. Balances
with a readability of 0.1mg or less require a closed draft shield. Contrary
to practical considerations, a draft shield should be as small as possible from
a metrological viewpoint, because internal drafts can be generated within a
large draft shield chamber.
A special case of air-current effect is what happens when the object being weighed
does not have the same temperature as the balance an the surrounding air: Convection
currents will make objects that are hotter appear to be lighter and those that
are colder, heavier. Only when the shape, surface, and temperature of the object
is exactly known, this will be a quantifiable error (see under the chapter "tables"
the one about the temperature effects on weights). It is always important to
condition an object being weighed to the ambient temperature!
Adsorptive layer of moisture on the surface: Allowing an object sufficient
time to reach the same temperature as that of the weighing instrument is also
necessary in order for the adsorptive layer of moisture on the surface of the
object to equilibrate. Particularly when small objects are weighed on a high-resolution
balance, this is essential to obtain reproducible weighing results. To minimize
adsorption of humidity, users must avoid soiling or otherwise touching the objects
with their hands, for example, as this leaves fingerprints, which can affect
the weighing results (a fingerprint does not only have a weight of its own of
0.1 - 1mg, but is also very hygroscopic).
Electrostatic forces: These are generated when nonconductive objects
or containers (glass or plastic) are electrically charged, for example, by pouring
from one container to another or by air currents. Static electricity can be
prevented by maintaining sufficient air humidity (at least 60%), or by using
an electrically conductive enclosure that is connected to the weighing pan.
Other solutions: Let the sample condition on a metal plate that is connected
to the same electrical ground as the balance, ionize the air in and around the
balance with an ionizing blower, don't use a plastic draft shield or sample
container: plastics are more easily electrically charged than glass.
Electrostatic forces usually show up as a drift in the weighing results (the
balances readout seems to stand still after placing the sample on the pan, but
than slowly starts to drift in one direction), or in poor reproducibility
in repeated weighing procedures.
Magnetic forces that act on an object being weighed can be counteracted
only by carefully demagnetizing the object, by shielding the magnetically active
object using soft magnetic materials such as mumetal, or by keeping the object
at sufficient distance from all magnetic or magnetizable parts. Weighing instruments
with electromagnetic force compensation contain magnetic parts (which are usually
well shielded), but even on a mechanical balance the earths magnetic field can
have a considerable effect on a magnetized sample. Magnetic forces generally
manifest themselves in poor reproducibility of the results and, particularly,
in a strong dependency of the position of the object on the weighing pan. An
often made mistake is weighing a liquid sample with a magnetic stirrer still
in it: This can only be done on a specially prepared scale that always keeps
bottle and stirrer in the same position and compensates for the error, or a
scale that weighs while stirring; the error than becomes an alternating effect
which can be filtered out.
Air buoyancy: An effect which is often underestimated, is air buoyancy:
Every object is subject to an upward force, which is equal to the weight
of the displaced air. Therefore, this force will be larger on an object with
a large volume (low density), and smaller on an object with high density. A
weighing instrument compares two forces; the force exerted on the pan by the
object being weighed, and the force exerted by the standard weight that was
used to adjust the instrument (or the compensation weights in the case of a
mechanical balance). The effect is a difference in display dependent on the
density of the object, as depicted in the following graph:
= 1.2mg/cm&3;)  |
As
shown by the green dotted line: When 10g of water (density 1.0) is weighed
at an average air density, the real mass of the water in the container is
10.5mg higher than the displayed value; a considerable difference.
When air pressure and temperature change, the air density will also change. In the example above this can increase the difference up to 11.5mg or decrease down to 9.5mg. If the sample has a density of 8.0g/cm3;, which is the same as the weight used for adjustment, the displayed mass will be the same as the real mass (the flat line in the graph). |
 |
In which: g = local gravitational acceleration m = mass of the object mA = mass of the displaced air |
= density
of the object  = air
density Vm = volume of the object |
 |
mw = displayed
value m = real mass of the object = air
density |
 = density
of the object  = density
of the calibration weight used to adjust the instrument
|
",
both by calculation and measurement: | In accordance
with the equation recommended by the "Comité International des Poids
et Mesures", for the air density ,
the equation between numerical values yields the following: |
 |
| Where:
= air density in kg/m&3;
p = barometric pressure in Pa T = air temperature in Kelvin Z = real gas factor (Z = 0.9996....0.9997 between 15°C and 25°C and p = 0.1MPa Xco2 = content of CO2 in % by volume Xv =molar fraction of water vapor |
|
Where:
= air density in kg/m3;
p = barometric pressure in mbar T = temperature in Kelvin (T = 273.15 + t, t = temperature in °C) Q= relative humidity in % |
| Ps = saturation
vapor pressure of water in mbar, according to the following table: |
| Temperature t in °C |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Ps in mbar |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
is equal to the air density in g/cm3;. |
|
|
|
| Nanogram | ng | 1 ng = 1 kg |
| Microgram | µg | 1 µg = 1 kg |
| Milligram | mg | 1 mg = 1 kg |
| Gram | g | 1 g = 1/1000 kg |
| Kilogram | kg | base unit |
| Ton | t | 1 t = 1000 kg |
| Carat | ct | 1 ct = 20 mg = 20 kg |
Anglo-American and other weight units:
|
|
|
|
|
| Pound | lb | 2.2046 LB | 453.595 g |
| Ounce | oz | 35.274 oz | 28.349 g |
| Troy ounce | oztr | 32.1505 oztr | 31.104 g |
| Grain | gn ( gr ) | 15432 gn | 0.06480 g |
| Pennyweights | dwt | 643.02 dwt | 1.55517 g |
| Mesghal | m | 217.00 m | 4.6083 g |
| Momne | m | 266.70 m | 3.7495 g |
| Tola | t | 85.733 t | 11.664 g |
| Baht | b | 65.790 b | 15.200 g |
| Hongkong Teals | TL | 26.717 TL | 37.429 g |
| Singapore Teals | TL | 26.461 TL | 37.792 g |
| Taiwanese Teals | TL | 26.667 TL | 37.500 g |
| Chinese Teals | TL | 26.455 TL | 37.799 g |
| Carat ( Karat ) | CT ( k ) | 50000.0 CT | 0.02000 g |
VISIT
OUR COMPREHENSIVE UNIT CONVERSION CENTRE
A brief history of balances
Refer to the section on terms and definitions
Error limits for calibration weights (OIML R111):
| Nominal mass value | Class E1 | Class E2 | Class F1 | Class F2 | Class M1 |
| 50 kg | 25 | 75 | 250 | 750 | 2500 |
| 20 kg | 10 | 30 | 100 | 300 | 1000 |
| 10 kg | 5 | 15 | 50 | 150 | 500 |
| 5 kg | 2.5 | 7.5 | 25 | 75 | 250 |
| 2 kg | 1.0 | 3.0 | 10 | 30 | 100 |
| 1 kg | 0.5 | 1.5 | 5 | 15 | 50 |
| 500 g | 0.25 | 0.75 | 2.5 | 7.5 | 25 |
| 200 g | 0.10 | 0.30 | 1.0 | 3.0 | 10 |
| 100 g | 0.05 | 0.15 | 0.5 | 1.5 | 5 |
| 50 g | 0.030 | 0.10 | 0.30 | 1.0 | 3.0 |
| 20 g | 0.025 | 0.080 | 0.25 | 0.8 | 2.5 |
| 10 g | 0.020 | 0.060 | 0.20 | 0.6 | 2.0 |
| 5 g | 0.015 | 0.050 | 0.15 | 0.5 | 1.5 |
| 2 g | 0.012 | 0.040 | 0.12 | 0.4 | 1.2 |
| 1 g | 0.010 | 0.030 | 0.10 | 0.3 | 1.0 |
| 500 mg | 0.008 | 0.025 | 0.08 | 0.25 | 0.8 |
| 200 mg | 0.006 | 0.020 | 0.06 | 0.20 | 0.6 |
| 100 mg | 0.005 | 0.015 | 0.05 | 0.15 | 0.5 |
| 50 mg | 0.004 | 0.012 | 0.04 | 0.12 | 0.4 |
| 20 mg | 0.003 | 0.010 | 0.03 | 0.10 | 0.3 |
| 10 mg | 0.002 | 0.008 | 0.025 | 0.08 | 0.25 |
| 5 mg | 0.002 | 0.006 | 0.020 | 0.06 | 0.20 |
| 2 mg | 0.002 | 0.006 | 0.020 | 0.06 | 0.20 |
| 1 mg | 0.002 | 0.006 | 0.020 | 0.06 | 0.20 |
Influence of non temperature- acclimatized weights:
| Weight value > |
|
|
|
|
|
| Maximum deviation of the weight for class E1 | 0.030 mg | 0.05 mg | 0.10 mg | 0.25 mg | 0.50 mg |
| Maximum deviation of the weight for class E2 | 0.10 mg | 0.15 mg | 0.30 mg | 0.75 mg | 1.5 mg |
| Maximum deviation of the weight for class F1 | 0.30 mg | 0.5 mg | 1.0 mg | 2.5 mg | 5 mg |
| Displayed error at 10 K temperature difference | 0.3 mg | 0.6 mg | 0.8 mg | 1.6 mg | 2.5 mg |
| Displayed error at 5 K temperature difference | 0.15 mg | 0.3 mg | 0.4 mg | 0.8 mg | 1.2 mg |
| Half-life time of the error | 9 min. | 12 min. | 20 min. | 35 min. | 60 min. |
|
|
scale intervals e |
scale intervals e |
||
|
|
e |
|
|
|
|
|
e
|
|
|
|
|
|
e
0.05g 0.1g e
|
50 e |
5 000 |
100 000 |
|
|
e
2g 5g e
|
20 e |
500 |
10 000 |
|
|
scale intervals e |
scale intervals e |
||
|
|
e |
|
|
|
|
|
ei
|
|
|
|
|
|
ei 0.05g
0.1g ei
|
50 e1 |
5 000 |
100 000 |
|
|
ei
|
|
|
|
maximum permissible errors:
|
|
|
|
|
|
m 50 000 e
|
m 5 000 e
|
m 500 e
|
0.5 e
|
|
200
000 e
|
20 000
e
|
2 000
e
|
1.0 e
|
|
|
10 000
e
|
10 000
e
|
1.5 e
|
These
are maximum permissible errors on initial verification. The maximum permissible
errors "in use" are twice these errors.
|
|
|
| Groningen | 9,81331 |
| Den Helder | 9,81324 |
| Zwolle | 9,81290 |
| Amsterdam | 9,81273 |
| Utrecht | 9,81251 |
| Delft | 9,81241 |
| Dordrecht | 9,81226 |
| 's Hertogenbosch | 9,81199 |
| Middelburg | 9,81205 |
| Maastricht | 9,81127 |
relative. Data taken from
report of Technical University Delft. 
= mean value of the individual
results measured: 