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Note 7

Sensors and Data Acquisition (2)

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2. Wheatstone Bridge Circuit The Wheatstone bridge circuit, as shown in Figure 4, is used to convert the change in resistance into voltage output. It is a standard circuit used as port of sensor signal conditioners. The Wheatstone bridge has a power supply voltage, Vi, and four resistances arranged in the bridge branches, R1, R2, R3, and R4. Usually, one of the branches is the resistance of the sensor. The sensor resistance change as a function of the measured variable. For example, the resistance of a Resistance Temperature Detector (RTD) changes as a function of temperature, and the stain-gauge resistance changes as a function of strain.

Figure 4: Wheatstone bridge Analysis of the Wheatstone bridge will be discussed in class.

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Example 2 Consider that an RTD type temperature sensor is used to measure the temperature of a location. The two terminals of the sensor are connected to the R1 position of a Wheatstone bridge circuit (Figure 4). The sensor temperature-resistance relationship is as follows

( ))(1 00 TTRR −+= α where from the sensor calibration data it is know that α = 0.004 oC-1, T0 = 0 oC reference temperature, and R0 = 200 Ω at temperature T0, Assume that Vi = 10 V, and R2 = R3 = R4

= 200 Ω. What is the temperature when Vo = 0.5 V?

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3. Sensors 3.1 Position sensors Potentiometer is one of the common sensors for position measurements. It relates the change in position (linear or rotary) into the change in resistance, as shown in Figure 5 and 6. The resistance change is then converted to a proportional voltage change in the electrical circuit of the sensor. Hence, the relationship between the measured physical variable, translational displacement x or rotary displacement θ, and the output voltage for a ideal potentiometer is ( ) xVkV rout ⋅⋅= or ( ) θ⋅⋅= rout VkV where the sensitivity, ( )rVk ⋅ , of the potentiometer is a function of the winding resistance and physical shape of the winding. The range and resolution of the potentiometer are designed into the sensor as a balanced compromise – the higher the resolution, the smaller the range of the potentiometer.

Figure 5: Linear and rotary potentiometer for position measurement In addition to the potentiometer, there are other position sensors introduced in our textbook. In these sensors, the change in position is translated into the change in other sensor properties, such as capacitance and magnetic coupling.

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Figure 6: Pictures of linear and rotary potentiometers 3.2 Velocity sensors Tachometer is one of the common sensors for velocity measurements. The construction of tachometer is identical to the construction of a brush type DC motor, except that it is smaller because the tachometer is used for measurement purposes, not for the purpose of the converting electrical power to mechanical power like an electric motor actuator. A tachometer involves a rotor winding, a permanent magnet stator, and commutator-brush assembly. Figure 7 shows the operating principle of a tachometer. In the steady state, the output voltage, Vo, is proportional to the shaft speed, i.e.,

θ&⋅= KVo where K is the gain constant, determined by the tachometer structure; and )(tθ& is the shaft speed.

Figure 7: Operating principle of a tachometer

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Due to the finite number of commutators, the output voltage has a periodic ripple as function of rotor position. The frequency of the ripple depends on the number of commutators. The ripple due to commutations is generally less than 0.1% of the maximum output voltage. Example 3 Consider a tachometer with a gain, Kvw = 2 V/1000 rpm. It is interfaced to a data-acquisition system though an A/D converter, which has 12 bit resolution and ± 10 V input range. The sensor specifications state that the ripple voltage due to commutators on the tachometer is 0.25% of the maximum voltage output. (1) Determine the maximum speed that the sensor and data-acquisition system can

measure. (2) What are the measurement errors due to the ripple voltage and due to the ADC

resolution, respectively? (3) If the ADC is 8 bit, which error source is more significant – ripple or ADC

resolution? 3.3 Acceleration Sensors There are different types of acceleration sensors (also called accelerometers), which are based on different transduction principle. One of them is the inertial-motion-based accelerometers. The transduction principle and the dynamic behavior are discussed in Example 1. Besides, there are other two accelerometers: piezoelectric-based and strain-gauge based (see textbook for details).

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3.4 Strain, Force, and Torque Sensors Strain gauges are used to measure the strain (or small displacement) that occur in a material or object that is subject to a mechanical load. The strain gauge transduction principle is based on the relationship between the change in length and its resulting change in the resistance of a conductor. Typical strain gauge material used is constantan (55% copper and 45% nickel). A fine wire of strain gauge material is given a directional shape and bounded to the part surface by using adhesive bonding materials. The resistance and the strain relationship is

LLG

RR Δ=

Δ

where G is the gauge factor of the sensor and ΔL/L is the strain in the strain direction (Figure 8). In order to increase the resulting resistance change under a given strain conditions, we need to pack more length, L, into a sensor size. This is the reason for the many rounds of conductor wire in one direction in the construction of a strain gauge, as shown in Figure 8. The change in the strain gauge resistance is converted to a proportional voltage using a Wheatstone bridge.

Figure 8: Typical strain gauge for strain measurement Force and torque sensors operate on the same principle. There are three main types of force and torques sensor:

(a) Spring displacement based force/torque sensors (b) Strain gauge based force/torques sensors (c) Piezoelectric based force sensors

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The strain gauge based force/torque sensors measure the force/torque based on the measured strain. Now, there are various strain gauge based force/torque sensors (or called load cells) available in markets (Figure 9). A load cell has build-in elastic mechanical components on which strain gauges are mounted. As the load cell experiences the force/torque, a small amount of deformation or strain occurs on the elastic element. The strain is measured by the strain gauges. As a result, since the force/torque to strain relationship is linear by the design of the load cell, the measurement is proportional to the force/torque.

Figure 9: Various strain gauge based load cells The other alternative strain gauge based force/torque sensor is to mount the strain gauges directly over the shaft on which we want to measure the force/torque. In some applications, it is not possible to install a load cell. Force or torque on a shaft must be measured without significantly changing the mechanical design. Figure 10 shows such force and torque sensing by using several strain gauge pairs on a shaft. Notice that most force and torque sensors use symmetrically bonded strain gauges to reduce the effect of temperature variation and drift of the strain-gauge output.

Figure 10: Force and torque measurement on a shaft or beam by means of strain gauges

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Example 4 Consider the force measurement by using a strain gauge on a steel shaft under compression (Figure 10 (b)). Given that the steel elastic Young’s modulus E = 2×108 kN/m2, and the cross-sectional area of the shaft is A = 10.0 cm2. We have a stain gauge bonded on the shaft in the direction of the compression. The nominal resistance of the strain gauge is R0 = 600 Ω, and the gauge factor is G = 2.0. The other three branches of the Wheatstone bridge (as shown in the following figure) have constant resistances, i.e., R2 = R3 = R4 = 600 Ω. The reference voltage of the Wheatstone bridge is Vi = 10.0 V. Assume that the input impedance of the measurement device is infinity. If the output voltage measured Vo = 2.0 mV, find (1) the force applied to the shaft, (2) the change in the strain gauge resistance, and (3) the stain that the shaft experiences.

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3.5 Temperature Sensors There classes of temperature sensors are discussed below, RTD (i.e., resistance temperature detector) and Thermocouples. RTD Temperature Sensors operate on the transduction principle that the resistance of RTD material changes with the temperature. Then, the resistance change can be converted to a proportional voltage using a Wheatstone bridge circuit. The relationship between the resistance and temperature for most RTD material is

( ))(1 00 TTRR −+= α where α is the sensitivity of the material resistance to temperature variable. The following table lists the values of α for several common materials.

Thermocouples are perhaps the most popular, easy to use, and inexpensive temperature sensors. A thermocouple has two electrical conductors made of different metals. The two conductors are connected as shown in Figure 11. The key requirement is that the connections between the two conductors at both ends must form a good electrical connection. The fundamental thermoelectric phenomenon is that there is a voltage differential developed between the open circuit end of the conductor proportional to the temperature difference between both junctions. The thermoelectric phenomenon is a result of the flow of both heat and electricity over a conductor. This is called Seebeck effect, named after Thomas J. Seeback who first observed this phenomenon in 1821. The voltage differential measured at the output of the thermocouple is approximately proportional to the temperature difference between the two junctions, i.e.,

)( 21 TTKVout −= where K is a constant, depending the thermocouple materials of conductors A and B (see Figure 11). The voltage output of the thermocouple is in millivolts (mV) range and must

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be amplified by, for example, an op-amp circuit, before feeding it to a data-acquisition system. Thermocouple measures the temperature difference between its two junctions. In order to measure the temperature of one of the junctions, the temperature of the other junction must be known. Therefore, a reference temperature is required for the operation of the thermocouple. This reference can be provided by either ice-water or by built-in electronic reference temperature. The measurement error in most thermocouples is around ± 1 to 2 oC.

Figure 11: Thermocouple temperature sensor and its operating principle Different thermocouple materials pairs are designated with a standard letter to simplify the references to them, as shown in the following table.

4. Data Acquisition The transducer senses the physical quantity being measured and produces an analog signal (usually voltage). The raw output signal from a transducer requires conditioning and must be converted to digital signal before the computer processing. The data-acquisition system (DAS) enables the computer to gather, monitor, display, and analyze data. Figure 12 shows the signal flow scheme for a typical DAS.

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Figure 12: Signal flow scheme for a typical DAS

Signal Conditioning: Filters and Amplifiers. Analog signals usually require some type of signal conditioning for the proper interface with a digital system. Filters and amplifiers are the most common components used for the control of frequency content and amplifications of singles. Multiplexer. When multiple input signal lines are connected by a common throughput line to a single A/D converter, a multiplexer is used to switch between connections, one at a time.

A/D Converters. A/D converters are used to convert analog signals to digital signals.

Figure 13 shows a commercially available data-acquisition card for PCs. The board has 12-bit resolution, 32-channel differential ended or 64-channel single-ended, multiplexed A/D converter, 12-bit 2-channel D/A converter, four-channel digital input, and eight-channel digital lines. Maximum sampling rate that is supported by the board is 333 kHz.

Figure 13: Model-KPCI-1810HC data-acquisition card (Keithley)