18.1.4 Mass-balance (weighing)
instruments
Mass-balance instruments are based on
comparing the gravitational force on the measured mass with the gravitational
force on another body of known mass. This principle of mass measurement is
commonly known as weighing, and is used in instruments like the beam balance,
weigh beam, pendulum scale and electromagnetic balance.
Beam balance (equal-arm balance)
In the beam balance, shown in Figure
18.5, standard masses are added to a pan on one side of a pivoted beam until
the magnitude of the gravity force on them balances the magnitude of the gravitational
force on the unknown mass acting at the other end of the beam. This equilibrium
position is indicated by a pointer that moves against a calibrated scale.
Instruments of this type are capable
of measuring a wide span of masses. Those at the top of the range can typically
measure masses up to 1000 grams whereas those at the bottom end of the range
can measure masses of less than 0.01 gram. Measurement resolution can be as
good as 1 part in 107 of the full-scale reading if the instrument is
designed and manufactured very carefully. The lowest measurement inaccuracy
figure attainable is ±0.002%.
One serious disadvantage of this type
of instrument is its lack of ruggedness. Continuous use and the inevitable
shock loading that will occur from time to time both cause
damage to the knife edges, leading to
problems in measurement accuracy and resolution. A further problem in
industrial use is the relatively long time needed to make each measurement. For
these reasons, the beam balance is normally reserved as a calibration standard
and is not used in day-to-day production environments.
Weigh beam
The weigh beam, sketched in two
alternative forms in Figure 18.6, operates on similar principles to the beam
balance but is much more rugged. In the first form, standard masses are added
to balance the unknown mass and fine adjustment is provided by a known mass
that is moved along a notched, graduated bar until the pointer is brought to
the null, balance point. The alternative form has two or more graduated bars
(three bars shown in Figure 18.6). Each bar carries a different standard mass
and these are moved to appropriate positions on the notched bar to balance the
unknown mass. Versions of these instruments are used to measure masses up to 50
tonnes.
Pendulum scale
The pendulum scale, sketched in
Figure 18.7, is another instrument that works on the mass-balance principle.
The unknown mass is put on a platform that is attached by steel tapes to a pair
of cams. Downward motion of the platform, and hence rotation of the cams, under
the influence of the gravitational force on the mass, is opposed by the
gravitational force acting on two pendulum type masses attached to the cams.
The amount of rotation of the cams when the equilibrium position is reached is
determined by the deflection of a pointer against a scale. The shape of the
cams is such that this output deflection is linearly proportional to the
applied mass.
This instrument is particularly useful
in some applications because it is a relatively simple matter to replace the
pointer and scale system by a rotational displacement transducer that gives an
electrical output. Various versions of the instrument can measure masses in the
range between 1 kg and 500 tonnes, with a typical measurement inaccuracy of ±0.1%.
One potential source of difficulty
with the instrument is oscillation of the weigh platform when the mass is
applied. Where necessary, in instruments measuring larger masses, dashpots are
incorporated into the cam system to damp out such oscillations. A further
possible problem can arise, mainly when measuring large masses, if the mass is
not placed centrally on the platform. This can be avoided by designing a second
platform to hold the mass, which is hung from the first platform by knife
edges. This lessens the criticality of mass placement.
Electromagnetic balance
The electromagnetic balance uses the
torque developed by a current-carrying coil suspended in a permanent magnetic
field to balance the unknown mass against the known gravitational force
produced on a standard mass, as shown in Figure 18.8. A light source and
detector system is used to determine the null balance point. The voltage output
from the light detector is amplified and applied to the coil, thus creating a
servosystem where the deflection of the coil in equilibrium is proportional to
the applied force. Its advantages over beam balances, weigh beams and pendulum
scales include its smaller size, its insensitivity to environmental changes
(modifying inputs) and its electrical form of output.
18.1.5 Spring balance
Spring balances provide a method of
mass measurement that is both simple and cheap. The mass is hung on the end of
a spring and the deflection of the spring due to the downwards gravitational
force on the mass is measured against a scale. Because the characteristics of
the spring are very susceptible to environmental changes, measurement accuracy
is usually relatively poor. However, if compensation is made for the changes in
spring characteristics, then a measurement inaccuracy less than ±0.2% is
achievable. According to the design of the instrument, masses between 0.5 kg
and 10 tonnes can be measured.
18.2 Force measurement
If a force of magnitude, F, is applied
to a body of mass, M, the body will accelerate at a rate, A, according to the
equation:
F = MA
The standard unit of force is the
Newton, this being the force that will produce an acceleration of one metre per
second squared in the direction of the force when it is applied to a mass of
one kilogram. One way of measuring an unknown force is therefore to measure the
acceleration when it is applied to a body of known mass. An alternative
technique is to measure the variation in the resonant frequency of a vibrating
wire as it is tensioned by an applied force.
18.2.1 Use of accelerometers
The technique of applying a force to
a known mass and measuring the acceleration produced can be carried out using
any type of accelerometer. Unfortunately, the method is of very limited
practical value because, in most cases, forces are not free entities but are
part of a system (from which they cannot be decoupled) in which they are acting
on somebody that is not free to accelerate. However, the technique can be of
use in measuring some transient forces, and also for calibrating the forces
produced by thrust motors in space vehicles.
18.2.2 Vibrating wire sensor
This instrument, illustrated in Figure
18.9, consists of a wire that is kept vibrating at its resonant frequency by a
variable-frequency oscillator. The resonant frequency of a wire under tension
is given by:
where M is the mass per unit length
of the wire, L is the length of the wire, and T is the tension due to the
applied force, F. Thus, measurement of the output frequency of the oscillator
allows the force applied to the wire to be calculated.
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