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The angular velocity can be found either from the amplitude or the frequency of the output signal.
The voltage amplitude signal is susceptible to noise and loading errors. Thus, less error is introduced if
the frequency is used to determine the angular velocity; typically, some means of counting the pulses
electronically is employed. This frequency information can be transmitted digitally for recording,
which eliminates the noise and loading error problems associated with voltage signals.
Force Measurement
The measurement of force is most familiar as the process of weighing, ranging from weighing
micrograms of a medicine to weighing trucks on the highway. Force is a quantity derived from
the fundamental dimensions of mass, length, and time. Standards and units of measure for these
quantities are defined in Chapter 1. The most common techniques for force measurement are
described in this section.
Load Cells
‘‘Load cell’’ is a term used to describe a transducer that generates a voltage signal as a result of an
applied force, usually along a particular direction. Such force transducers often consist of an elastic
member and a deflection sensor. These deflection sensors may employ changes in capacitance,
resistance, or the piezoelectric effect to sense deflection. A technology overview for such devices is
provided elsewhere (5). Consider first load cells that are designed using a linearly elastic member
instrumented with strain gauges.
Strain Gauge Load Cells Strain gauge load cells are most often constructed of a metal, and have a
shape such that the range of forces to be measured results in a measurable output voltage over the
desired operating range. The shape of the linearly elastic member is designed to meet the following
goals: (1) provide an appropriate range of force-measuring capability with necessary accuracy, (2)
provide sensitivity to forces in a particular direction, and (3) have low sensitivity to force
components in other directions.
A variety of designs of linearly elastic load cells are shown in Figure 12.20. In general, load
cells may be characterized as beam-type load cells, proving rings, or columnar-type designs. Beamtype load cells may be characterized as bending beam load cells or shear beam load cells.
A bending beam load cell, as shown in Figure 12.21, is configured such that the sensing element
of the load cell functions as a cantilever beam. Strain gauges are mounted on the top and bottom of
the beam to measure normal or bending stresses. Figure 12.21 provides qualitative indication of the
shear and normal stress distributions in a cantilever beam. In the linear elastic range of the load cell,
the bending stresses are linearly related to the applied load.
In a shear beam load cell the beam cross section is that of an I-beam. The resulting shear stress in
the web is nearly constant, allowing placement of a strain gauge essentially anywhere in the web with
reasonable accuracy. Such a load cell is illustrated schematically in Figure 12.22, along with the shear
stress distribution in the beam. In general, bending beam load cells are less costly due to their
construction; however, the shear beam load cells have several advantages, including lower creep and
faster response times. Typical load cells for industrial applications are illustrated in Figure 12.23.
Piezoelectric Load Cells Piezoelectric materials are characterized by their ability to develop a charge
when subject to a mechanical strain. The most common piezoelectric material is single-crystal quartz. The
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The angular velocity can be found either from the amplitude or the frequency of the output signal.
The voltage amplitude signal is susceptible to noise and loading errors. Thus, less error is introduced if
the frequency is used to determine the angular velocity; typically, some means of counting the pulses
electronically is employed. This frequency information can be transmitted digitally for recording,
which eliminates the noise and loading error problems associated with voltage signals.
Force Measurement
The measurement of force is most familiar as the process of weighing, ranging from weighing
micrograms of a medicine to weighing trucks on the highway. Force is a quantity derived from
the fundamental dimensions of mass, length, and time. Standards and units of measure for these
quantities are defined in Chapter 1. The most common techniques for force measurement are
described in this section.
Load Cells
‘‘Load cell’’ is a term used to describe a transducer that generates a voltage signal as a result of an
applied force, usually along a particular direction. Such force transducers often consist of an elastic
member and a deflection sensor. These deflection sensors may employ changes in capacitance,
resistance, or the piezoelectric effect to sense deflection. A technology overview for such devices is
provided elsewhere (5). Consider first load cells that are designed using a linearly elastic member
instrumented with strain gauges.
Strain Gauge Load Cells Strain gauge load cells are most often constructed of a metal, and have a
shape such that the range of forces to be measured results in a measurable output voltage over the
desired operating range. The shape of the linearly elastic member is designed to meet the following
goals: (1) provide an appropriate range of force-measuring capability with necessary accuracy, (2)
provide sensitivity to forces in a particular direction, and (3) have low sensitivity to force
components in other directions.
A variety of designs of linearly elastic load cells are shown in Figure 12.20. In general, load
cells may be characterized as beam-type load cells, proving rings, or columnar-type designs. Beamtype load cells may be characterized as bending beam load cells or shear beam load cells.
A bending beam load cell, as shown in Figure 12.21, is configured such that the sensing element
of the load cell functions as a cantilever beam. Strain gauges are mounted on the top and bottom of
the beam to measure normal or bending stresses. Figure 12.21 provides qualitative indication of the
shear and normal stress distributions in a cantilever beam. In the linear elastic range of the load cell,
the bending stresses are linearly related to the applied load.
In a shear beam load cell the beam cross section is that of an I-beam. The resulting shear stress in
the web is nearly constant, allowing placement of a strain gauge essentially anywhere in the web with
reasonable accuracy. Such a load cell is illustrated schematically in Figure 12.22, along with the shear
stress distribution in the beam. In general, bending beam load cells are less costly due to their
construction; however, the shear beam load cells have several advantages, including lower creep and
faster response times. Typical load cells for industrial applications are illustrated in Figure 12.23.
Piezoelectric Load Cells Piezoelectric materials are characterized by their ability to develop a charge
when subject to a mechanical strain. The most common piezoelectric material is single-crystal quartz. The
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