Download FORCE AND PRESSURE MEASURING TRANSDUCERS 1. Scope

Institute of Measurement Science, Electronics and Control, Laboratory of “Fundamentals in Metrology”
FORCE AND PRESSURE MEASURING TRANSDUCERS
1. Scope of the experiments
The aim of the exercise is to:
- learning of principles of operation and construction of force and pressure transducers popular in
industrial practice, ,
- getting knowledge of the issues associated with the calibration of measurement transducers and
meters.
2. Introduction 1)
The measurement of forces, tensions and pressures are performed both in industrial
installations and in other situations (e.g. weighing). They are carried out for objects of different
states of aggregation (solids, liquids, gases, vapors and suspension), under static conditions
(measurement object doesn't move) and kinetic (moving measurement object). Since the force,
tension and pressure values are closely related, and their effects are similar, issues relating to the
measurement are considered together. The effect of the force on a rigid body is its deformation
and usually the accompanying changes in physical properties of the body, such as magnetic
permeability, electrical conductivity, natural frequency, etc. In case of force measurement usually
the effect of focused forces (i.e. applied to the test object at a specific point) is examined. In the
case of measurement of mechanical tension and pressure the effect of force distributed over a
specified area is examined. The term mechanical tension to be understood distributed intensity of
the force acting in a direction tangential to the surface in question and the pressure may be treated
as distributed intensity of the force acting in the direction normal to the surface in question. In the
International System of Units (SI) unit of force is 1 N, and the unit of stress and pressure is 1
N/m2 (1 Pa). Also derivative units and so-called technical units are used in practice.
The measurement of force can be done by measuring the effects of the force acting on the
sensor of gauge-meter. Force causes a deformation of the elastic element of the sensor, which in
turn can be converted into an electrical signal. Was developed a variety of structures of
transducers to measure forces and pressures. The aim of the exercise is to know and laboratory
testing of selected types of industrial measuring transducers of pressure and force, in which the
output signal is of electric nature. Today, such transducers are the most used in practice because
of the convenience of electrical signals for further analog (amplification, filtering), and digital
processing. These transducers are composed of three basic elements:
• Resilient element - a suitable mechanical structure in which as a result of the force (pressure)
arise stresses and deformation of the selected elements. These elements are designed in such a
1) More detailed information on this topics can be find in:
Zakrzewski J., Kampik M.: Sensory i przetworniki pomiarowe. Wyd. Polit. Śląskiej, Gliwice 2013, part 7.
Institute of Measurement Science, Electronics and Control, Laboratory of “Fundamentals in Metrology”
way that when the force (pressure) is within the measuring range, the resulting deformations are
as high as possible (due to desired high sensitivity of transducer), but within the elastic range of
materials.
• The sensor mounted permanently to the mechanical part of the transmitter, whose task is to
convert the strain onto the convenient electrical parameter (i.e. resistance, capacitance) or an
electrical signal (electric voltage, electric charge).
• The signal conditioning circuit that additionally converts the electrical signal (or parameter) to
obtain an output signal with a range convenient for transmission to other devices and / or further
processing, e.g. analog-to-digital converter (ADC). In industrial applications, are often used
voltage 0..5 V, 0-10 V, or current 0..20 mA, 4..20 mA.
3. Force measuring converters (force transducers)
The deformation of the elastic element of a force transducer depends on the method of
application of the measured force. Typical methods of force application are shown in Figure 1. On
the surface of the elastic element stress sensor is glued. This sensor (called strain gauge) is
stretched (marked T+) or compressed (T-) according to how this surface deforms under stress.
a)
c)
b)
F
+T M
+T
σ
σ
T
−σ
-T
F
-T
F
Fx
Fig. 1. Typical methods of application of the measured force F to the elastic element of the force
transducer: stretching (a), bending (b), torsion (c).
Strain gauge sensor (pol. czujnik tensometryczny, tensometr) is a converter of the object
strain, due to the existing stress, into other quantity, usually of electrical nature. A consequence of
the strain effect is to change the selected parameter, such as resistance, permeability, piezoelectric
effect, the index of refraction or reflection of light, etc. The most popular are resistive strain
gauges which usually work in the electrical bridge circuit (see Fig. 3b) supplied from an external
stabilized power source. The voltage in unbalance of the bridge is the output signal of transducer.
Resistive strain gauges have a special design to enable attachment them on the surface of the
object in order to deform thereby along this surface. The sensitivity of the strain gauge
(deformation sensitivity) depends on the direction of strain and the strain gauge construction.
Strain gauges may be of different shapes and constructions. The most common are built to
respond to the deformation only in one direction, however, there are special structures, such as
Institute of Measurement Science, Electronics and Control, Laboratory of “Fundamentals in Metrology”
spiral strain gauges, rosette strain gauges etc., sensitive to deformation in many directions. Such
structures are particularly suitable for measurement of the torque, the stresses in the membranes of
the pressure transducers etc. Figure 2 shows the constructions of selected types of strain gauges.
The active element of the strain gauge (resistor) is made of a shaped metallic conductor or a
semiconductor wafer. This element is placed between layers of insulating paper or film. Strain
gauge is mounted on the surface the tested object using a special adhesive that is selected
according to the material of the strain gauge and the test object. The mechanical properties of the
adhesive (stiffness, temperature coefficient of linear expansion, heterogeneity, the effect of creep)
significantly affect the characteristics of the sensitivity of the strain gauge.
a)
b)
c)
3
2
1
Fig. 2. Simplified construction sketches of selected types of resistive strain gauge;
a) - serpentine wire, b) - a foil meander, c) - the so-called. rosette strain gauge
1 - gage rod (wire, foil), 2 - pad (paper or insulation foil), 3 – pin, connector
Considering wire strain gauge, there is tension σ in the rods, the relative deformation ε can be
determined based on Hooke's law:
ε=
where l is the length of the rod, σ =
∆l
l
=
σ
E
(1)
F
the tension, A is the cross-sectional area of the rod, E –
A
Young’s modulus.
The electrical resistance of the metallic rod describes the general relationship:
l
R=ρ
A
where ρ is the resistivity of the rod material.
The change of resistance of the deformed rode can be determined by calculating the total
differential of equation (2):
∂R
∂R
∂R
l
ρ
ρl
dR =
dρ +
dl +
dA = dρ + dl − 2 dA
∂l
A
A
∂ρ
∂A
A
(2)
(3)
Each of the parameters (ρ, l, A) is changing due to the stress in the rod. The relative change of the
dA
dr
round rod is equal to
≈ 2 , the cross-section changing of the rod associated with the change
A
r
dA
dl
of its length is
= −2 µ = −2 µ ε , where µ ≈ 0,3 is the Poisson ratio. After taking into
A
l
account these formulas the relative change of resistance of the strain gauge is:
dR
dρ
= ε (1 + 2µ ) +
(4)
R
ρ
Institute of Measurement Science, Electronics and Control, Laboratory of “Fundamentals in Metrology”
The characteristic parameter of strain gauge is the so called deformation sensitivity, which is
calculated by dividing the equation (4) by the relative elongation of the rod ε.
dR
dR 1
dρ 1
K=
⋅ = R = (1 + 2µ ) +
⋅
(5)
dl
R ε
ρ ε
l
The sensitivity of deformation is dependent on the material constants of the strain gauge and
design parameters, whose precise values are not known. In practice, the exact value of this
parameter is determined from measurements of resistance increases ∆R induced by uniaxial
tension increments. Assuming parameters ε=0,2%, µ≈0,3 and ignoring small metal
piezoresistivity (a change of ρ under stress), can be estimated the deformation sensitivity K≈2,6.
This means that if the stress generated under the influence of the relative elongation of 0,1% will
be e.g., the relative change in resistance is then equal to approx. 0,26%. This value is very small
and thus difficult to directly measure. It is necessary to use a bridge circuit for converting the
resistance into output voltage (Fig. 3b). Such small changes in resistance strain gauges are also
inconvenient due to the dependence of the resistance of metals with temperature. Changes are on
the same level. Bridge circuit allows minimizing this effect, as explained below.
Force transducer metrological characteristics depend not only on the properties of the strain
gauges, but primarily on the parameters of the elastic element of the sensor. Elastic elements of
load cells are usually made of spring steel and have different shapes, e.g., hollow or solid cylinder
or a frame. In Figure 3a is shown sketch of the construction of a sensor with an elastic element in
the shape of a rectangular frame. There are marked the forces acting on the frame under the
assumption them non-axial (oblique) touchdowns. Also shown arrangement of strain gauges glued
to the side walls. Strain T1 and T3 are active elements (respond to the stresses because they are
glued longitudinally), and T2 and T4 are passive (not subject to stress, are glued transversely).
Passive strain gauges are only used to compensate for the changes in temperature, since, as
mentioned earlier, the resistance of the strain gauge depends not only on stress but also on the
temperature. Compensation is possible by means of an electrical bridge circuit, as shown in Figure
3b. The output voltage Um depends on the change in resistance of strain gauges. Temperature
affects the resistance of all the strain gauges in the same way, without changing the output
voltage. Stress causes the resistance changes only of the active strain gauges T1 and T3, placed in
opposite branches of the electrical bridge, which makes the output voltage Um depends on the
stress in the elastic element.
An important factor in deteriorating accuracy of force is its non-axial touchdown. If the
transmitter is loaded with axial force (in the direction of the x axis), the side walls of frame
deform equally. In the case of oblique application of force to the sensor, the axial component Fx
and the orthogonal component Fz act on the frame. The orthogonal component acting in the zdirection generates an additional bending moment in the columns of the frame. As a result,
extension of strain gauges consist of deformation caused by the axial component Fx, which are the
same for both columns, and deformations caused by the action of the component Fz, equal in
value but of opposite signs. The resulting output voltage is not adequate to the applied force F there is an additional measurement error.
Institute of Measurement Science, Electronics and Control, Laboratory of “Fundamentals in Metrology”
a)
α
F
b)
x
Fx
RT1
Fz
T3
RT2
z
y
Uz
RT3
RT4
T4
Um
T2
T1
Fig. 3. Sketch of the load cell construction (a) and the system of electrical connections of strain gauges (b).
4. Pressure measuring transducers
The pressure transducers are frequently of constructions, which are schematically shown in
Fig. 4. Due to the difference of the measured pressure p and the reference pressure po occurs a
deformation of a particular element. This deformation is converted into an electrical parameter in
a different manners, for example by the use of strain gauges glued to the membrane (Fig. 4c, 6a),
by the displacement transducer (LVDT, as shown in Fig. 5 or capacitive - Fig. 6c).
b)
c)
po
po
elongation
elongation
a)
po
deflection
membrane
strain gauges
p
p
p
Fig. 4. The most common constructions of mechanical parts of pressure transducers: Bourdon tube (s),
bellows (b) and an elastic membrane (c).
A sketch showing the details of construction of transducer with Bourdon tube is shown in
Figure 5. The pressure p, greater than atmospheric pressure, is applied to the inside of a closed
chamber in the shape of a curved tube. This deforms (straightens) of the tube. Shifting of the tube
end is converted to a voltage by means of a LVDT transducer. The output voltage is proportional
to the measured pressure. The figure shows also a scale and pointer, which allows direct reading
of the measured pressure. The advantage of Bourdon tube transducers the linear characteristic,
high sensitivity, wide measuring range and high mechanical strength. The disadvantage is not
Institute of Measurement Science, Electronics and Control, Laboratory of “Fundamentals in Metrology”
very high accuracy (uncertainty 1% ÷ 5% of measuring range) resulting from the dependence of
properties of the material on the temperature and mechanical backlash.
Bourdon tube
A-A
spring
and gear
Scale
Uout
~p
connector
LVDT
p
Fig. 5. Sketch of construction of the pressure gauge with Bourdon tube
Uout - output voltage
Considerable increase in accuracy is achieved in the constructions without the indicating
mechanism shown schematically in Figure 6. Prevalent today can-type sensors in which the
mechanical part is made in monolithic form. The resilient element in these sensors is a substrate
of silicon dioxide; the piezoresistors are the diffused semiconductors having piezoelectric
coefficients with different signs. These are typically connected in the resistance bridge circuit,
similarly as in Fig. 3b. Monolithic sensors are characterized by small size, compact and robust
design, high sensitivity, relatively low temperature sensitivity, very low inertia and low hysteresis.
a)
p
T- T+
1
p
po
p
2
b)
1
5
3
po
T- T+
2
4
Fig. 6. Selected structures of can-type pressure sensors with pressure chamber and membrane with
strain gauges (a) and with diaphragm and differential capacitive sensor (b)
1 – pressure chamber, 2 – membrane, diaphragm, 3 – strain gauges, 4 – electrical connectors, 5 – insulating
bushing
Institute of Measurement Science, Electronics and Control, Laboratory of “Fundamentals in Metrology”
The deformation of the pressure chamber is converted into a resistance change by means of
strain gauges T + and T- (Fig. 6a), or changes in the differential capacitance (Fig. 6b). Strain
gauges typically operate in the bridge circuit and the capacitive sensor operates in the transformer
differential circuit of high frequency.
Today are prevalent the can-type sensors in which the mechanical part is made in monolithic
form. The resilient element is made of silicon dioxide with diffused semiconductor piezoresistors
which have the piezoelectric coefficients with different signs. These are typically connected to the
resistance bridge circuit, similarly as in Fig. 3b. Monolithic sensors are characterized by small
size, compact and robust design, high sensitivity, relatively low temperature sensitivity, very low
inertia and low hysteresis. Small dimensions of integrated pressure sensors, high rigidity of the
elastic element and very small deformation allows to get sensors for measuring in ranges less
than 0.01 MPa and over of 100 MPa. Figure 7 shows an example of construction of a monolithic
integrated piezoresistive pressure sensor and the measuring circuit.
a)
p
b)
case
UZ
c)
R S1
resilient element
R+
Podłoże
base
R-
R+
R+
RP2
R-
Podłoże
UZ
R-
R+
RZ
insulating bushing
Um
R S2
electirc connector.
vent hoole
RP1
R-
Um
Fig. 7. Construction of the piezoresistive pressure sensor (a), basic electrical bridge circuit of the sensor
(b) and a modified circuit with the possibility of linearization and calibration of characteristics through
the choice of auxiliary resistorsRP1, RP2, RS1, RS2, RZ (c).
Increasingly being used semiconductor piezoresistive sensors integrated structurally (a "chip")
with the electronics and connected to the microprocessor system. This allows not only process the
measured pressure into an electrical signal, but also, if correspondingly programmed,
automatically set many other parameters and perform additional functions, e.g. sending the results
via the built-in interfaces. Such structures are called "smart transmitters" (pol. przetworniki
inteligentne 1)).
5. Laboratory stands
5.1. Investigation of force transducers
Figure 8 shows a sketch of stand for testing the force transducers. Two industrial strain gauge
force transducers are examined: No 1 in Fig. 8, with a measuring range of 5 kN and the 7, with the
1)
e.g.: Kwaśniewski J.: Wprowadzenie do inteligentnych przetworników pomiarowych, WNT, Warszawa, 1993.
Institute of Measurement Science, Electronics and Control, Laboratory of “Fundamentals in Metrology”
range of 4 kN. The transmitters are adapted to measure the tensile forces. The transducer 1 is
mounted on a base beam with a row of equally-spaced holes and its pin is connected via a pushbar 3 to the transducer 7 mounted in the saddle 4 of the testing machine. Use the dial 5, through
worm gears, moves the slide setting the required value of tension force F. The angle α of
application of force to the transducer 1 is determined by selecting an appropriate mounting hole in
the beam 2. The values of force for transmitters 1 and 7 are read at the readout devices 6 and 8,
respectively. Before the measurements by dial 5 should be set a minimum initial tension, at which
there is no backlash at joints. After that a zero adjustment should be perform for measuring
instruments 6 and 8.
8
F
1998
7
4
α
Electronic
circuit
3
Digital
voltmeter
1
h
6
2
5
b
F
Fig. 8. Sketch of a device for testing of force transducers.
Research is performed in two stages.
In the first stage the transducer 1 acts as a reference (standard). It is mounted in such a way that
the force F acts axially. The aim is designation of errors of the transducer 7 (the inspection of it).
Errors should be determined for different values of force - approx. 20 values in the whole range.
In the second stage the transducer 7 takes a role of standard (to be reported corrections for
previously designated errors). This time the aim is designation of an additional error of the
Institute of Measurement Science, Electronics and Control, Laboratory of “Fundamentals in Metrology”
transducer 1 as a result of non-axial application of force F. The measurements are repeated at
different angles of the applied force.
5.1. Investigation of pressure transducers
The measuring system for calibration of pressure transmitters and gauges used hydraulic oil
system, as shown in Figure 9. The reference pressure is generated by means of a piston-weight
device using calibrated weights aggravating the piston. Operation of the system is based on the
principle of a hydraulic press.
Measurements rely on standard pressure setting and reading indications of the tested devices.
The study of results should include a plot of the calculated corrections and the accuracy class of
the tested instrument should be determined.
indicator of piston position
standard weight
sensor under test
manometer under test
piston
expantion tank
valve
Zawór
oil
pump
oil
Fig. 9. A hydraulic piston-weight device for calibration of pressure transducer.
Edited by: H. Urzędniczok, J. Leks,
ver.: 02-2015