Chapter 2 Transducers (Sensors) PDF

Chapter- 2 TRANSDUCERS When you have completed studying this chapter the student will be : Understands static and dynamic specifications of a transducer. To know position transducers and its application to measure displacement. To know how to measure force...

Chapter- 2 TRANSDUCERS When you have completed studying this chapter the student will be : Understands static and dynamic specifications of a transducer. To know position transducers and its application to measure displacement. To know how to measure force acting on using strain gages and load cells and how to increase their sensitivity. Knows methods for measuring angular as well as linear velocities. Knows how to measure pressure , level and flow rate of fluids. Knows temperature transducers, as metallic stripes, thermocouple, and RTD's. 60  Chapter- 2 : TRANSDUCERS 1. INTRODUCTION The purpose of a transducer is to convert a physical quantity into an electrical signal. The most common physical quantities measured by transducers are position, force, velocity pressure level, flow and temperature. The transducer output may be voltage current, resistance, capacitance, or frequency. Transducer performance is described by the manufacturer in two sets of specifications. Static specifications describe the steady state relation between the value of the output and the physical input. Accuracy, resolution, repeatability, hysteresis, and linearity are all static specifications. Dynamic specifications determines how quickly the output changes in response to changes in input. Parameters of dynamic specifications are rise time, time constant, dead time frequency response for first order element while if the transducer is described as a second order element parameters will be the damping ration, natural frequency beside the dead time and frequency response in the frequency domain. 2. STATIC SPECIFICATIONS This set of specifications determines the relation between the output and the input only when they reach their steady state ( i.e. become constant ) after a change. Accuracy Accuracy is specified in Terms of the percent error. Error is the difference between the true ( correct or ideal ) output should come from the transducer and the actual output. There are three different ways of expressing the accuracy : 1 - percent error of the full scale output ( i.e. the max. reading ), 2 - Percent error of the true reading, and 3 - Absolute error of the input quantity. Example-1 A load cell is a transducer used to measure weight. A calibration is given in table ( 1 ). It gives a full scale output of 20 mV at the full scale load 100 Kg. 61 (A) plot the curve load (KG) output ( mV ) increasing decreasing 0 0.08 0.06 10 1.o2 2.04 20 2.55 4.19 30 4.49 5.04 40 6.53 9.06 50 8.70 10.52 60 11.01 12.s4 70 13.32 14.92 80 15.4 16.94 90 17.66 l8.7 100 19.93 20.02 ( B ) Determine the accuracy in both % FSO and of reading V fullscale Vtrue = xLoad mV Load fullscale (c)For accuracy + 7.85 % FSO, what is the absolute error ?. So1ution (A) The plot is in Fig.( 1 ) (B) We shal1 calculate, the true reading , error ( mV ) and accuracy in % FSO and % of reading for one reading ( increasing ) and another one (decreasing ) i - Load = 20 KG increasing 20mV Vtrue = x 20 Kg = 4 mV 100 Kg error e = Vtrue - Vactual = 4 - 2.55 = 1.45 mV Accuracy 1.45 % FSO = x100 = 7.25 % 20 62 % reading = (1.45/4) x 100 = 36.25 % Therefore, it is important to determine whether accuracy calculated w.r.t. FSO or true reading. OUTPUT 100 FSO 90 80 70 60 50 40 30 20 10 INPUT 0 10 20 30 40 50 60 70 80 90 100 Fig.(1) A plot of data in table (1) Fig.(2) Simple optical encoder. ( C ) Absolute error is 7.85 % of 100 KG = 7.85 KG Thus the output will be in error with 7.85 % of. 20 mV i.e. + 1.57 mV. Resolution It is the smallest change in the input of the transducer that will result a change in the output. As an example consider the optical encoder shown in fig.(2).The shaft must rotate ‫ח‬/2 in order for a pulse is produced at the output. A rotation less than ‫ח‬/2 may not result any countable output. So this encoder has 90o resolution. Industrial encoders provide 100 and 1000 pulse per revolution i.e. resolution 2‫ח‬/100 to 2‫ח‬/1000 rad. Example 2 A 2.5 meter long vane rotates in a circle by a motor and gears attached to its center. It is required to know the position of the vane within 2 cm. What must be the resolution of the optical encoder attached to the shaft that positions the vane. Sol : The circumference of rotation circle is C = ‫ח‬d = ‫( ח‬2.5 ) =7.854 m 63 The resolution in degrees is 2 Re s. = x360 = 0.917 o 785.4 360 785.4 Number of pulses per revolution is = = = 392.7 pulses 0.917 2 Therefore, the optical encoder must produce at least 393 pulses per revolution. Repeatability It is a measure of how well the output returns to a given value when the same input is applied several times. Be careful not to confuse repeatability with accuracy. As an example consider a 3 transducers with same input applied to each several times the results are plotted in Fig. 3 a, b, c. In transducer A we fined all readings are scattered widely about the average of these readings which is very near to the correct value. Therefore Transducer A is accurate but not repeatable. The transducer B has all readings grouped about its average which is far from the true reading. Therefore, Transducer B is repeatable but not accurate. The transducer C has all readings grouped about its average which is the true readings, thus this transducer is accurate and repeatable. Repeatability is measured by one of the following measures : Maximum reading − Minimum reading Re beatability = x100 Full scale output L arg est deviation Re beatability = x100 Full scale output Hysteresis : Hysteresis is also an indication of the reproducibility of a transducer output. An input value when reached through increasing input values may produce an output that is produced by the same input through decreasing process. Fig.(4 ) shows the calibration curve of a transducer. A measure of the Hysteresis is : Maximum devation Hysteresis % = x100 Full scale output 64 Note that the calibration curve is produced by applying an input and measure the output after settling (i.e. becoming constant). x x x x x average x x x x x x average True output x x true output x x (a) Accurate but not repeatable (b) Not accurate but repeatable x x x x True output x x x x (c) Accurate and repeatable Fig.(3) Repeatability OUTPUT 100 FSO 90 80 70 60 50 Y 40 30 20 10 INPUT 0 10 20 30 40 50 60 70 80 90 100 fig.(4) Hysteresis Linearity : Ideally the transfer curve ( output - input ) of a transducer is a straight line. In practice the curve will be as shown in Fig. (1). Linearity measure how different the actual characteristic from the ideal one. Linearity is measured in three different ways: 65 1 - Endpoint Linearity : A straight line between the two endpoints of the calibration curve. Then the maximum deviation both above and below that line are determined these are reported as + % and - % of full scale. Output-(Electrical) 10 0 OUTPUT 90 100 80 90 70 80 70 60 Va 50 Vb 60 Va 50 Vb 40 40 30 30 20 20 10 Input-(Physical) 10 INPUT 0 0 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 (a) End points linearity (b)Independent straight line linearity Fig.(5) Linearity 2 - Independent straight line linearity : Two parallel lines are drawn to just enclose the calibration curve. An independent line is drawn halfway between these two boundaries, and the maximum deviations above and below that line are determined and reported as + % and - % of ful1 scale output. 3 - Least squares linearity : It is a statistical measure of linearity, the best straight line which fits the transducer characteristics is calculated as : If : Xi = input values Yi = output values m = slope of the straight line b = vertical intercept of straight line n = number of data points 66  n n n n ( X i Yi ) −  X i  Yi m= i =1 n 1 n 1 n X i2 − ( X i ) 2 1 1 n n  Yi X i b= 1 − 1 n n The equation of the line is then Y = mX + b Example 3 For the weight cel1 of the characteristics shown in Fig.(1), determine end point linearity, independent linearity and least square linearity. a - End-point line linearity : 12.0 − 12.94 x100 = −4.7 % FSO 20 5.0 − 3.43 x100 = 7.85 % FSO 20 b - Independent line linearity 11.9 − 12.94 x100 = −5.20 % FSO 20 5.65 − 4.48 x100 = 5.85 % FSO 20 c - Least Squares linearity n = 20 m= 0.2079 b =-0.6368 mV the line equation is Y=0.2079 X - 0.6368 mV. (X is in KG), Therefore : 11.84 − 12.94 x100 = −5.46 % FSO 20.15 6.53 − 7.68 x100 = 5.71 % FSO 20.15 67  Input 2 1 Time Output 3 1.0 0.9 0.632 Td 0.10 Tr Tc Time Fig.(6) Response of a first order Fig.(7) Response of second order element element with time delay 3. DYNAMIC SPECIFICATIONS : The dynamic specifications of a transducer describes its behavior during the changes of input, which produces a changes in the output. The output continuous to change until it reaches a constant value. The dynamic performance of a transducer may be described in two categories. A Step function is a standard test signal usually used for dynamic specification of systems. The first order transducer is specified mainly by the time constant parameter. Also rise time, and dead time are of interest. If the transducer is 2nd order, the damping coefficient (ξ), natural frequency (ωn) are the important parameters. The response of lst order and 2nd order elements are shown in Fig.(6) and Fig.(7). The main parameters are defined as follow : Time Constant : It is used to describe first order element, it is the time at which the output reaches 63.2 % of its final value. And after a time equal 5x time constant the output reach about 98% of this final value. Dead Time It is the length of time from the application of a step change at the input of a transducer until the output begins to change. Dead time ( some times known as time delay) adds difficulties to the overall system performance. 68 Damping coefficient ξ and natural frequency ωn. are the two important parameters used to describe second order elements. They are determined from the transfer function of the 2nd order transducer. Damping coefficient for most physical elements is positive. If its value is in the range 0 to 1 the system is said to be over daped. 4. POSITION TRANSDUCERS The location or the displacement made by an object is of primary concern in many measurement and servo-control systems. Robots, milling, shaping and drilling of machine parts as well as the movement of heads on computers disk drive or the pen on a plotter require the measurement and control of position. Three techniques will be described here : 1 - Potentiometers : Potentiometers are inexpensive and easy to use for position measurement. Linear potentiometer for straight line displacement and angular potentiometer for rotary displacement measurements are available. The basic forms are shown in Fig (8). Full- scale angular displacements ranges from 10o up to 357 are also available. Multi turn potentiometers may measure up to 3500o of rotation, this is done by the helical resistive potentiometers. Resistor element Resistor element i Linear displacement X i + + o E _ - _ eo ( xo ) + E (a) Linear (b) Angular Fig(8) Potentiometer as a displacement sensor. 69 The resistive body of potentiometers may be wire wound. A very thin (0.01 mm diameter ) wire of platinum or nickel alloy is carefully wound on a form made of an insulating material. As the wiper is moved from winding to winding the resistance between it and either end varies. The smallest change in position that can be detected (i.e. resolution) occurs when the wiper moves from one turn to another. So numerically the resolution is: Full scale displacement Re solution % = Number of wire turns Example 4 It is necessary to measure the position of a panel. It moves 0.8 meter. Its position must be known within 0.1 cm. part of the mechanism which moves the panel is a shaft that rotates 2500 when the panel is moved from one end to the other. A control potentiometer has been found which is rotated at 300o full scale movement. It has 1000 turns of wire. Can this potentiometer be used ?. So1ution : The shaft 250o/80 cm= 3.1250 / Cm = 0.31250 / mm This means the shaft rotates 3.125 degrees in order for the panel to make a linear movement of one cm. This is the required resolution for the potentiometer, but the available potentiometer has a resolution of: 300o /1000 = 0.3o The actual potentiometer resolution is less ( i.e. finer or better ) than the required, therefore the potentiometer will work. Continuous potentiometers have a body made of carbon film, metal film, conductive plastic or ceramic metal (cermets). These potentiometers have several advantages over those which are wire wound. These advantages are : higher resolution smooth resistive surface increased speed 70 An important parameters to be observed for potentiometers are the power rating, ambient temperature and self heating. Example 5 A control potentiometer is rated as : 150 Ω, 1 W ( derate at 10 mW/Co above 65 Co ), 30 Co/W thermal resistance θ. Can it be used with a 10 V supply at 80 Co ambient temperature ? Solution: The power dissipated by the potentiometer is: P=E2/R = (10)2/150 =667 mW The actual temperature of the potentiometer depends on the ambient temperature and the rise in temperature, caused by the power the potentiometer is dissipating ( Self- heating ). Tpot = Tamb. + Pθ = 80 Co + ( 667 mW ) ( 30 Co/W ) =80Co+20Co = 100 Co The allowable power dissipation must be derated ( decreased ) by 10 mW for each degree above 65 Co Pallowed = =Prated-(Tpot - 65 Co )x( l0 mW/Co ) =1 W - (100-65)X10 mW = 1000 mW - 350 mW = 650 mW Thus the dissipated power in the potentiometer must be less than 650 mW. The actual power dissipated is 667 mW, therefore, this potentiometer will fail. Therefore, it is not suitable for this application. Potentiometer Connections : There are several connections of potentiometers. The simplest is shown in Fig.(9a). This causes zero volts output when the wiper has been driven all the way down to the bottom and outputs the full supply voltage when the wiper at the top. In the configuration of fig.(9-b), the zero point will be at the potentiometer midposition. The 71 output voltage may take positive as well as negative values according to the wiper displacement from the mid point. When the actual displacement moves the wiper to the top position, the output voltage will be +E When the actual displacement moves the wiper to the bottom position, the output voltage will be -E. For the circuit in Fig.(9- c) Zero may be adjusted to any position on the potentiometer. The full -scale adjustment lets us calibrate the output voltage to some convenient value when the wiper has been driven as far up as it will be.. In connection of Fig.(9-d), the set point (reference input or required output) is adjusted by the set point potentiometer. The slider of the process variable potentiometer is driven by the process variable being measured. The error is defined as : Error(e) = SP- PV E f E f Rp i V E i V (a) (b) mechanical link to controlled R variable E CV SP E V (Error) (c) (d) Fig.(9) Potentiometers connections 72  V out V in 1 Rp Vin =0 R2 RL R1 R L Vout Rp 0 RL increasing 1 Xr (a) Connection (b) Effect of loading Fig.(10) Potentiometer loading Loading In reality each Potentiometer transducer must drive a load. This load can Produce a nonlinearity. Consider the connection in fig.(10). The desired output assuming no loading is: 𝑅1 𝑉𝑑𝑒𝑠𝑖𝑟𝑒𝑑 = 𝑉 𝑅1 + 𝑅2 𝑖𝑛 However, RL parallels R1 ,so its effect must be considered. [𝑅1 𝑅𝐿 /(𝑅1 + 𝑅𝐿 )] 𝑉𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑉 [𝑅1 𝑅𝐿 /(𝑅1 + 𝑅𝐿 )] + 𝑅2 𝑖𝑛 or 𝑅1 𝑅𝐿 𝑉𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑉 𝑅1 𝑅𝐿 + 𝑅1 𝑅2 + 𝑅2 𝑅𝐿 𝑖𝑛 If : Rp= R1+ R2 ,total petitioner resistance, Xa , the actual wiper displacement, and Xfs, the full scale potentiometer displacement, then: 𝑋𝑎 𝑅1 𝑋𝑟 = = 𝑋𝑓𝑠 𝑅𝑝 R1= Xr.Rp 𝑉𝑜𝑢𝑡 1 Then from above : = 1 𝑅𝑝 𝑉𝑖𝑛 +(1−𝑋𝑟 ) 𝑋𝑟 𝑅𝐿 A plot of the last equation is shown in fig.(10-b) 73 Example 6 Plot the transfer curve and determine the end point linearity of a 1 KΩ potentiometer driving a 5 KΩ load powered from a 10 V source. So1ution : The desired and actual values are presented in table (2) these are obtained at 100 Ω steps of the wiper R1. Even if the load is five times the resistance of the potentiometer, up to 2.8 % error is produced by the load. R1(Ω) R2(Ω) Vdesired(V) Vactual(V) % Dev. of FS Xr Vactual/Vin error % 0 l000 0 0 0 0 0 0 100 900 1 0.9823 0.18 0.1 0.098 0.2 200 800 2 1.9380 0.62 0.2 0.194 0.6 300 700 3 2.8791 1.21 0.3 0.288 1.2 400 600 4 3.8168 1.83 0.4 0.382 1.8 500 500 5 4.76L9 2.38 0.5 0.476 2.4 600 400 6 5.7252 2.75 0.6 0.573 2.7 700 300 7 6.7179 2.82 0.7 0.672 2.8 800 200 8 7.7519 2.48 0.8 0.775 2.5 900 100 9 8.8409 1.59 0.9 0.884 1.6 l00 0 10 10.0 0.0 1.0 1.0 0.0 table (2) Example 6 Example :7 A position measurement may have a nonlinearity of no more than 0.5% when driving a 10 KΩ load resistance. What size potentiometer should be used? So1ution : From table (2) for nonlinearity of O.5 % RL/Rp = 29.41 Rp=RL/29.41 =10 KΩ/29.41 = 340 Ω 74 We must use a potentiometer with resistance less than 340 Ω Voct 1.0 Vin 0.9 Actual 0.8 Desired 0.7 0.6 0.5 0.4 0.3 0.2 Nonlinearity error = 2.8% 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Xr Fig.(11) Nonlinearity caused by loading Linear variable differential transformers (LVDT ) The LVDT is an electromechanical device that produces an electrical output proportional to the displacement of a separate movable core. It consists of a primary coil and two secondary coils symmetrically spaced on a cylindrical form. When the primary coil energized by an external source, voltages are induced in the two secondary coils, fig.(12). The secondary coils are connected oppositely so that the two voltages are opposite in polarity. Therefore, the net output is the difference between These voltages, which is zero when the core is at the center or null position. When the core is moved from the null position the induced voltage in the coil toward which the core is moved increases while decreases in the other coil. This action produces a differential voltage output that varies approximately linear with changes in core position. Full scale ranges from 0.05 inch to 10 inch. The LVDT has many useful and wide variety of applications. There is no physical contact between the movable core and coil structure, which means that, LVDT is a frictionless device, therefore, there is nothing to wear out and has essentially infinite mechanical life. The infinite mechanical life is important in high reliability 75 mechanisms and systems found in aircrafts, missiles, space vehicles and critical industrial installations. Sec. coil 1 Sec. Primary coil Sec. coil 1 coil 2 Core e1 e = e − e Primary o 1 2 coil Core motion e2 Sec. coil 2 Core (a) (b) Fig(12) LVDT connection(a), and construction (b) Output (V) Displacement Linear displacement Fig(13) LVDT output versus displacement LVDT Carrier Rectifier & Demodulator DC amplifier generator filter AC Power supply Fig.(14) LVDT electronics 76 The fact that LVDT is a transformer means that there is a complete isolation between excitation input ( primary ) and output (secondaries). This make it an effective analog computing element without the need for buffer amplifies. Fig. (14) shows the block diagram for any measurement involving LVDT type transducer. Optical Encoder: Optical encoders are very reliable angular displacement transducer. It is suitable for computer applications, because data in digital form. There are two types : A - Incremental Encoder : Incremental encoder creates a series of equally spaced pulses corresponding to the mechanical increment occurred. The simplest type of incremental encoder is known as the tachometer encoder. The encoder is a disk with a track on it near to its outer edge this track is divided into dark and transparent parts with light source on one side and light sensor on the other. Therefore, a complete revolution produces a number of square pulse, equals to the number of transparent divisions. Single track incremental encoder has only one output and cannot detect direction. The output waveform and code track on the disk are shown in Fig. (15). Velocity information is available by looking at the time interval between pulses or at the number of pulses within a time period. 1 0 fig.(15) Incremental encoder (single track)  Most incremental encoders use two output channels shifted in phase by (quadrature) 2 for position sensing. The output waveforms and code tracks on disc are shown in fig.(16). This allows us to count the transitions and to view the state of the other channel during these transitions. Using this information we can determine if A leads B and thus determine the direction. Once the quadrature signal is decoded we can 77 generate pulse of fixed duration within a cycle. These pulses can be fed to up-down counters or programmable controller input port. Many programmable controller manufacturers include a quadrature detection signal (called anti-jitter) as part of their electronics. A B A B C reference pulse C Fig(16) Incremental encoder with two tracks shifted by  / 2 B - Absolute Encoder Absolute encoders provide a "Whole world" output with a unique code pattern representing each position. Absolute encoder is represented in fig.(17). The output code is derived from independent tracks on the encoder disk corresponding to individual photo detectors. The output from these detectors would then be high or low depending on the code disk pattern for that particular position. Absolute encoders are used in applications where a device is inactive for long periods of time or moves at slow rates such as flood control, telescopes cranes, etc. Absolute encoders are capable of using many different codes but the most common are Gray Code, natural binary, and binary coded decimal (BCD). Best accuracy is obtained with Gray code. (a) Natural binary code. Outer tack (b)Grey code , only one bit switch is the LSB and inner tack is the MSB at a time 78  (c) Digital encoder pattern (d) Light emitting diodes and photocells for linear position for reading digital encoder pattern Fig.(17) Arrangements of digital encoder. 5. FORCE TRANSDUCERS In servo and process control the measurement of force is very important. An entire engineering discipline (experimental stress analysis) has been established to evaluate the force applied to various parts of a machine or vehicle. Accurately measured forces allow the design of machinery (including cars and spacecrafts) that is lighter, more efficient, more reliable, less expensive, and which provides higher performance. Also being able to measure force allows us to obtain indirectly the value of parameters which are difficult to measure directly like mass, level, pressure, flow rate.... etc. Finally the force exerted by a spring is directly proportional to how much it has been expanded : F = KX where K is the spring constant. Measurement of force exerted on (or by) the spring is an indirect way to measure the displacement X in spring-mass-damper system. Stress and strain 79 The relationship between stress and strain is one of the most fundamental concepts. When a force is applied to a body, the body deforms. This deformation is called strain. We will define the term Strain to mean deformation per unit length or fractional change in length and give it the symbol ε. Strain may be either tensile (positive) or compressive (negative),Fig.(18). In equation the strain is: L = L For most metals the strain measured in experimental work is typically less than 0.005000 in / in. Since practical strain values are very small, they are often expressed in microstrain, which is ε X 106 , for example 0.00500 in/ in = 5000 microstrain ( με). Fig.(18). Strain with unilateral force (a), and cantilever in bending (b) Stress refers to force per unit area on a given plane within a body, in equation: F = A and has units of force per unit area. Young's modulus E (modulus for elasticity) for a material is defined as the ratio between the stress σ to the strain ε , i.e.  E=  Strain Gage: 80 Probably the most important electrical characteristic which varies in proportion to strain is that of electrical resistance. Devices whose output depends on this characteristic are the piezoresistive or semiconductor gage, the carbon resistor and the bonded metallic wire and foil resistance gages. Bonded Resistance Strain Gage : It is the most widely used strain measurement tool. It consists of a grid of very fine wire or of thin metallic foil bonded to a thin insulating sheet called a carrier matrix. The electrical resistance of this grid material varies linearly with strain. In use the carrier matrix is attached to the part under test with an adhesive. Then the part is loaded, the strain on its surface is transmitted to the grid material by the adhesive and the carrier system. The strain is found by measuring the change in the electrical resistance of the grid material. The bonded resistance strain gage is low in cost and has small physical size and low mass and has medium sensitivity to strain. The ratio between the relative resistance change ( ∆R/R ) and the strain (∆L /L) is the gage factor ( G ). G is dimensionless and the larger the value of G, the more sensitive the strain gage, in equation gage factor is expressed as R / R G=  Bonded wire Metal foil strain strain gauge gauge (A) Bonded-Wire Strain Gage (B) Metal Foil strain Gage fig. (19) Pictorial Representation of wire and foil Strain gages Example :8 A strain gage is bonded to a steel beam which is 10 cm long and has cross sectional area of 4 cm2. Young's modulus of elasticity for steel is 20.7 x l0l0 N/m2. The strain gage has a nominal (unstrained) resistance of 240 Ω and a gage factor Of 2.2. When 81 load is applied, the gage's resistance changes by 0.O13 Ω. Calculate the change in length of steel beam and the amount of force applied to the beam. So1ution : R / R G= , or L / L R L =G R L R L 0.013 0.1 L = x = x = 2.46 x10 −6 meter R G 240 2.2 = 2.46 x 10-4 cm The stress σ = E Є = F/A or F L =E A L = 20.7 x 10l0 x 4 x 10-4 x 2.46 x 10-6/0.1 = 2.037 x 103 N Ideally it would be preferred that the gage resistance changes only with strain, but practically the gage resistance varies also with temperature. In fact when the temperature changes both gage resistance and gage factor will change. In simple terms, the resistance of a conductor at a given temperature T is: RT = RTo(1+αoΔT) where : RT = resistance at T RTo = resistance at a reference temperature To αo = temperature coefficient ΔT = change in temperature from To. i.e. the change in resistance due to temperature only is ΔR = αo ΔT RTo Example: 9 82 Calculate the change in resistance caused by a 1 Co change in temperature for the strain gage in the last example. The temperature coefficient αo for most materials αo = 0.003925 / Co Solution : ∆Rtemp =0.003925 x 1 x 240 = 0.942 Ω But the stress applied by the load in last example caused only 0.013 Ω change in the strain gage resistance. So 1 Co change in the temperature of the strain gage caused a change in resistance : Rtemp 0.942 = = 72.5 Rstress 0.013 or 72.5 times larger than the 2037 N force produced. From this example you should see that it is absolutely necessary to compensate for temperature effects on the strain gage. Wheatstone Bridge Circuit : Because of its sensitivity, Wheatstone bridge is the most used circuit for strain measurements. The circuit is shown in Fig.(20). Rg = Ro + R Ra + Vo E - Rc Rb Fig.(20) The Wheatstone bridge With no stress ΔR = 0, and all four resistors are equal. So V out = 0 , when stress is applied, the strain gage changes its resistance by ΔR : 83  R R Vout = E− E R+R R + R + R 1 R R = E− E= E 2 2 R + R 4 R + R but as R >> ΔR , 4R >> 2ΔR R then : Vout = E 4R This signal will be very small and must be amplified by a circuit with a very large input impedance. So what is the advantage of using Wheatstone bridge ? acting force Ro active Ra active guage dummy guage gauge + V Rc E Rb - Rg Rc dummy gauge Fig.(21) Use of active and dummy gages to compensate temperature. The answer is that the effect of temperature can be eliminated by replacing both resistors on one side of the bridge with strain gages. As shown in Fig.(21) one strain gage is mounted so that the applied force will change its resistance. This is the active gage. The other is placed transverse to the stress so that the force has no effect on its resistance. This is the inactive ( dummy ) gage. The applied force will affect only the active gage, unbalancing the bridge. However, any change in temperature will affect both gages in the same way. Identical changes in resistance of both resistors on one side of the bridge will not affect the balance condition of the bridge, therefore, the effects of temperature are eliminated. It may be useful if we make both gages active, Fig. (22), by having one gage in tension ( its resistance increase with load ) and the other in compression ( its resistance decrease with Load). Beside the temperature effect will be eliminated, the bridge sensitivity increases. The output voltage for a given load doubles when compared to the circuit with single active gage i.e. the output is : 84  R Vout = E 2R Gage place in Tension Copmression tension Force Ro + R Ro − R + R + R Vout E - R c R − R Rb Gage placed in compression Fig.(22) Two active gages ,one place on surface under tension, other on compressed surface One of the problems is that the resistors in bridge arms other than those contain strain gages must be exactly equal. The solution may be by connecting strain gages in the four arms of the bridge, two gages in the tension side and the other two in the compression side, as shown in Fig.(23). the output of the bridge in this case is : R Vout = E R Tension Compression R + R R − R + E Vout - R − R R + R Compression Tension Fig.(23) Four active gages to increase sensitivity and temperature compensation Example 10 Determine Vout in figure (20) given that R0 = 240 Ω, E = 10 V, and Ra=Rb=240 Ω. (a) stress causes the upper resistor (active gage) on the left to increase by 0.013 Ω. 85 (b) temperature causes both resistors on the left, fig.(21) ( both active and passive ) to increase by 9.4Ω. (c) stress causes the active gage to increase by 0.013 Ω and temperature causes both resistors to increase by 9.4 Ω. Solution : (a) Use equation R Vout = E 4R 0.013x10 = = 0.13 mV 4 x 240 The stress produces a rather small signal. (b) Using the voltage-divider law gives us 249.4 x10 240 x10 Vout = − 249.4 + 249.4 240 + 240 =5V–5V=0V The use of dummy gage eliminates the effect of temperature. (c) With both a temperature and a stress-induced resistance change, 240 x10 249.4 x10 Vout = − 240 + 240 249.4 + (249.4 + 0.013) = 5 V - 4.99987 V = 0.13 mV So even in the presence of both stress and temperature resistance change, the use of a dummy gage eliminates the effects of the temperature change. Accurate measurements using strain gages are only obtained if the following conditions are satisfied. - Gage must be perfectly aligned with the force. - Adhesive material must transmit faithfully the force between gage and the beam. - The beam must provide equal tension and compression to opposite legs of the bridge. - Negligible solder connections to the gage. LOAD Cells 86 A load cell is a transducer specially designed to measure force. It consists of a beam with properly mounted four strain gages. Excitation voltage source, amplification and display electronics are needed. Associated with load cell like any other transducer a set of specifications, but the important one is the output at rated capacity ( called sensitivity ). It is expressed in mV/V i.e. the output voltage in (mV) at the full load applied for each volt of the supply voltage. Example 11 A load cell type GS5353 has the following specifications: Output at rated capacity ( 500 Ib ) 2 mV/V Nonlinearity error ± 0.050 %FS bridge resistance 300 ohms compensated temperature range + 25 Fo to 125 Fo Temperature effect on zero ± 0.002 % FS/Fo Recommended excitation 10 V DC a - What is the output voltage per pound ? b - What is the nonlinearity error in pounds ? c - What is the zero shift in pounds if the temperature varies across its rated range ? Solution : (a) Vout. max = output at rated capacity x Vsupply = 2 mV/V x 10 V = 20 mV Vout/Ib = 20 mV/500 = 40 µV/Ib This means that our electronic circuits associated with the cell must be able to clearly and accurately amplify signals of 40 µV or less if we expect to resolve and display 1 Ib increments. (b) Nonlinearity is ± 0.05 % FS = ± 0.05 x (1/100) x 500 = ± 0.25 Ib So no matter how good our electronics, there will be a ± 0.25 Ib error in the results. So trying to display results with accuracy more than 1/4 Ib is pointless. 87  (c) The temperature range is + 25 Fo to 125 Fo , i.e. 100 Fo. Thus the zero shift is : zero shift = ( + 0.002 % / Fo ) x ( 100 Fo ) x ( 500 Ib ) = +1 Ib This means that if the temperature become 100 Fo the zero point will be shifted To +1 Ib. This shift is four times that caused by the nonlinearity and it must be adjusted. 6. Velocity Transducers There are types of velocity transducers according to if the velocity is linear or angular. Linear velocity transducers If the movement is along an axis (linear), velocity may be measured in several ways. For motion that, will have a limited range of displacement, the electromagnetic linear transducer works wel1, This transducer is illustrated in fig.(24). All electromagnetic velocity transducers operate on the fact that the voltage (i.e. electromotive force emf) induced into a coil by a magnetic field is directly proportional to rate of change of magnetic field: d emf = − N dt Fig.(24) Linear velocity sensor. 88 The core of the electromagnetic linear velocity transducer is a permanent magnet. The voltage induced into the coil depends on how fast the core is pulled. Reversing the direction of the motion reverses the polarity of the induced voltage. Of course the magnet must, not be pulled out completely of the core so this limits the total travel of the part whose velocity is measured. Laser-Doppler System The Doppler effect relies on a shift in frequency, which is proportional to the velocity. In Doppler radar or laser unit, a continuous wave of a series of pulses is projected toward the moving object whose velocity is to be measured. The beam is reflected back from the target and its frequency is shifted from the transmitted beam according to the relative velocity. This echo is received and its timing and frequency is compared with the transmitted signal. The length of time it takes for the signal to reach the target and return is a measure of the distance to the target. The frequency of the echo is compared with the transmitted frequency, the shift Fv indicates the velocity of the target. Frec=Fo + Fv Frec is the frequency of the echo Fo the frequency of the transmitted signal Fv the shift in echo frequency whish is a function of the target velocity. Of course a most familiar example of this form of velocity transducer is the radar used by police to detect speeders. However, systems working on same principles are used in missile targeting and in tracking and navigation of spacecrafts. Angular Velocity Measurements : DC Tacho-generator: The most common angular velocity transducer is the DC electromagnetic tachogenerator. The field is produced by a permanent magnet or separately excited electromagnetic winding on the stator. The rotor is made of a series of coils. When rotated through the magnetic field , voltage is induced into the coils. The magnitude of the induced emf in the coil is directly proportional to the rotor speed. By connecting several coils in series and rotating these through the magnetic field, a large, ripple free 89 output is obtained. This signal is coupled from the rotating coils to the outside world through commutator and brushes. This also assures that the output is pure DC. If the direction of speed is reversed, the output will change its polarity. There are several reasons that DC tachometers are so common. They are easy to use, and output is relatively high. Therefore, it requires little or no additional signal conditioning. Tachometers, using permanent magnets typically output 3V to 7V per 1000 r/min while those with electromagnet windings on the stator output 10 V to 20 V per 1000 r/min. Direction of rotation is indicated by the polarity of the output voltage. Accuracies of 0.1 % to 0.25 % FSO can obtained. However the commutator and brushes needed to connect the output from the rotor cause significant problems. Good routine (preventive) maintenance is necessary. Any sparks at the brushes produce radio frequency interference (RFI) from which the rest of the control system must be protected. For applications where brushes related problems are unacceptable, ac induction tachometer must be considered instead. AC Induction Tachogenerator: It also called the AC permanent magnet tachometer. This rotational velocity transducer has no brushes. It consists of primary and secondary windings placed at right angles on the stator. The rotor is squirrel cage and made of high conductance metal. When a 50 HZ signal is connected to the primary, an eddy current at right angle is induced in the rotor. When the rotor is stationary the magnetic field produced by the eddy current will not link the secondary and thus no emf in the secondary is induced. When the rotor is rotated, the field links the secondary, inducing an output voltage. The more faster the rotor, the faster the field cuts the secondary, producing larger output in the secondary. The output is AC, so it must be rectified and smoothed in order to be used as a measure for the rotational velocity. As the primary and secondary are making an angle of 90 o, the secondary voltage will be 90o, out of phase with primary voltage. The phase difference between secondary and primary voltages is lead or 1ag according to the direction of rotation. The ac tachometer overcomes the problems resulted by the brushes of the DC tachometer. 90 However, you must provide phase sensitive rectification and filtering to obtain a useful signal. Counter-type Velocity Sensors Another group of velocity transducers output a signal whose frequency depends on the speed of rotation. This signal may be conditioned in order to be a series of countable pulses. The amplitude of this signal may or may not vary. One type of these transducers may be an AC permanent magnet tachometer which uses a rotor with several permanent magnet poles. A single coil on the stator is cut repeatedly as the rotors magnets passed the coi1. A pulse of one polarity is produced when a north pole passes the coil, while a pulse of apposite polarity is produced when a south pole passes the coil. The amplitude of these pulses and their rise time vary with the speed of the shaft. So, signal conditioning is necessary to convert these pulses into TTL compatible levels for counting or timing. Another type is the incremental optical encoder explained before. It produces a fixed number of pulses per revolution. So the frequency of these pulses is a measure of the angular velocity of the shaft. Most of rotational speed transducers explained so far require attachment of transducer shaft to the shaft to be measured. This may present significant mechanical problems. Fig.(25) Angular speed measuring system Gears, belts and shafts all flex and introduce errors. Also the inertia of the transducer may load down the system you are trying to measure. 91 All of these problem are overcome by the reflective optical sensor. A narrow strips of reflective tape (usually six) are carefully placed on a nonreflective shaft or coupling. An optical source and sensor are placed on a convenient location where an infrared beam from the transmitter can fall on the rotating shaft. When the reflective strips rotates with the shaft, the light is reflected back to the sensor which outputs a pulse. This sensor arrangement is shown in Fig.(25). Example 12: A dc motor that drives a conveyor belt has a maximum speed of 1720 r/min. It is necessary to monitor the speed with a resolution of 1 r/min and provide new number every 100 ms. - How many pulses per revolution are required ? - If it were necessary to use a 6-pulse/revolution reflective optical sensor, describe the degradation in performance. Solution a- The revolutions per second are: speed = 1720 x (1/60)= 28.67 r/sec. In 100 ms (the allowed counting time) the number of revolutions = = 28.67 x 0.1 = 2.867 revolutions Note that 0.1 sec. is the counting period, thus we must get 1720 counts during the counting period (0.1 Sec. i.e. from 2.867 revs), or: 1720 = 2.867 x Number of pulses per revolution Number of pulses / revolution = l720/2.867 = 600 counts/ revolution. b - If we must use a 6-pulse / revolution reflective optical sensor, the number of pulses will be less with a factor 1/100. Thus to obtain the same counts (i.e. 1720), 10 second period is required instead of 0.1 sec. But 10 sec. is a very long time for most control systems, 0.1 sec. is about as long as most control applications can tolerate. With 6 pulse/rev, the number of revolutions required to obtain 1720 counts = 1720 = = 286.7 𝑟𝑒𝑣𝑠 6 92  286.7 Time required to obtain 286.6 revs = = 10 𝑆𝑒𝑐. 28.67 Therefore, we obtain a measure for the speed in revs/min every 10 seconds instead of 0.1 seconds which is too long for most control systems. The solution may to use a frequency multiplier with a factor of 100, or to use a frequency/ voltage F/V converter and then amplify the voltage by a gain of 100, then use V/F converter. 7. FLUID TRANSDUCERS Fluid transducers are divided into three groups according to the variable being measured: pressure, level or flow. Fluid transducers as used in many applications as food processing industry, drug and chemical industries, and along the entire line of oil production, from exploration, drilling, pumping, transportation, refining to sales. Monitoring and control of all types of engines rely on fluid transducers. Hydraulic systems employed in automated production (such as industrial robots) require accurate control of pressure f1ow, and level. Fluid transducers are used extensively throughout the industry. Pressure Transducers : Pressure is not a primitive quantity but it describes the relation between force and the area exerted on. So it is expressed in terms of force per unit area. A common industrial unit for the pressure is pounds per square inch(psi). Normally pressure measured in comparison to a reference. According to that reference there are three types of pressure measurement : a - Absolute pressure : When the pressure of a container is measured referenced to perfect vacuum (pressure of perfect vacuum is zero), unit used psia (a=absolute): b - Gage pressure : When the pressure is measured and the reference was the ambient pressure, the unit is psig. 93 c - Differential pressure : When the pressure of a container is measured w.r.t. the pressure of another container so that the measurement is for the differential pressure between the two containers, the unit is psid. In metric system pressured units is Newton/meter2 which is called Pascal (Pa) 1 psi = 6.8948 X 1O3 Pa Thus Pascal is a small unit, therefore, the practical metric unit for pressure is KPa 1 KPa = 103 Pascal The height of a column of mercury that yield a certain pressure is also used as a unit of pressure measurement: l inch of mercury (Hg) = 3.386 KPa l mm Hg = 133.32 Pa 1mm Hg is also called torr which is used in measuring vacuums 1 torr = 1 mm Hg = 133.32 Pa Standard atmospheric pressure at sea level is defined as: 1 atm. = 76 Cm Hg = 76O mm Hg = 1.01325 x 10s Pa Barometric pressure, in weather reporting is measured in bar or millibar 1 bar = 105 Pa = 100 KPa Manometric means for pressure measurements: There are different forms of the manometer, but the most common is the U-tube manometer, fig.(26). This manometer is used to measure the differential pressure applied to the liquid surfaced of the two manometer arms. This differential pressure equals to the weight of liquid between the two surfaces. If Pl = P2, then h = 0, where P1, P2 are pressures applied to the two arms and h is difference between the levels of the two surfaces, i.e. if P2 > P1 P2 - P1 = g h ρ where ρ: is liquid density g: gravity constant 94  h: the differential height between the two Liquid surfaces. P2 = P1 + ρ g h or 1 h= ( P2 − P1 ) g As we see, the relation between h and ΔP=P2–P1 is linear, a regular scale can be arranged to reed directly the differential pressure. The accuracy of this instrument depends mainly on : the effect of temperature on ρ , the deviations in g according to the place, the instrument also must be exactly in vertical position. P2 P2 P1 Vacuum Tube cross A1 sectional area h P1 h h Well cross sectional area 0 A2 Well-type manometer Barometer (a) U – tube manometer (b) (c) (d) Fig.(26) Manometric means for pressure measurement 95 Also a major disadvantage of this arrangement is that they are strictly mechanical. However, they can be converted to electrical systems (i.e. the output signal for pressure is electric) with a float device attached to a displacement transducer such as the LVDT on both arms of the tube. Elastic Pressure Transducers All elastic deformation pressure transducers use the same transduction principle. Pressure causes a bending or deformation of the transducer material usually a metal. This deformation results in a deflection or displacement, i.e. we might say that. these transducers are pressure to position transducers. As we will see the indicators can be purely mechanical or they can use electric transducers to convert the displacement to an electric signal. We will discuss three types of elastic deformation transducers, all based on the same principle but each different in physical shape and size. The transducers we will consider are the Bourdon tube, the bellows , and the diaphragms. Motion of the free end Pressure Helical tube (a) (b) (c) Fig.(27) Burdon tubes Bourdon Tubes The Bourdon tube is one of the oldest and most popular pressure transducers. It was invented in 1851 by Eugene Bourdon and has been used in industry ever since. Bourdon tubes come in three basic shapes: C tube, spiral tube and helical tube as illustrated in Fig.(27) a, b and c. 96 All three devices work in essentially the same way. They are all composed of a flattened metal tube, usually made of, brass, phosphor bronze, or steel, fig.(27). The pressure at the input is communicated to the inside of the device. The tube deforms nonlinearly. Therefore, mechanical pointers fastened to the moving tips have displacement applied through a gearing system. This gearing system compensates for the nonlinearity of movement. Nonlinearity may also be compensated for by using a nonlinear scale. The Bourdon tube is simple to manufacture inexpressive and accurate and it measures pressures up to 100,000 psi (700,000 KPa). The C-shaped Bourdon tube is the least sensitive to pressure changes and the helical tube is the highest in sensitivity. These devices don't work with pressures under 50 psi (750 KPa). Bourdon tubes are converted simply into an electric transducers by using LVDT, fig.(28). Fig.(28) C type Bourdon tube with LVDT. Diaphragms The diaphragm is a flexible plate as illustrated in fig.(29). This plates are usually made of metal or rubber. For greater sensitivity these plates are corrugated. Increase in pressure will cause deformation in the diaphragm, measurement of this deformation using strain gages gives electric signal represents the applied pressure. Also diaphragm deformation may produce displacement which is measured using LVDT. Sometime 97 the deformation occurred to the diaphragm may be used to affect the capacitance of a capacitor. Fig.(29) shows different forms of diaphragm pressure sensors. Vacuum (a) Flat Diaphragm Pressure Pressure P2 Pressure P1 (b) Corrugated Diaphragm Diaphragm Diaphragm (c) (d) Fig.(29) Diaphragms for pressure measurement. (a) flat, (b) corrugated, (c) Differential pressure sensor ,(d) Absolute pressure sensor Bellows The pressure bellows is a cylindrical shaped device with corrugation along its edges as shown in fig.(30-a). As pressure increases the bellows expands, moving the shaft right. The shaft may be attached to a pointer or an electric displacement transducer like an LVDT. In fig.(30-b) bellows are connected to indicate the differential pressure. If Pl > P2 the pointer moves left. The amount of displacement is proportional to the difference in pressure. Bellows are more sensitive to pressures in the range 0-30 psi (0-210 KPa) than Bourdon tubes. Thus they are useful at lower pressures. (a) (b) fig(30)Bellows 98  (c)Capsules FLOW TRANSDUCERS Flow tells you how fast material is moving. Flow is expressed in three ways : 1 - Volumetric flow Q : The volume of the fluid moving past a point per unit time, units are m3/sec.or gallon/min. 2 - Mass flow Qm : The mass flow per unit time. Units are KG/Sec. or pounds/Sec. 3 - Velocity of flow Qv : The flow velocity defines the amount of flow rate passing a point, units is m/sec. The relation between the three types of flow is Qm = mass flow = Q ρ ρ: is the density of the fluid volumetric flowrate Q Qv ( flow velocity ) = = pipe cross sec tional area A A : is the cross sectional area of the pipe. Movement of the fluid in a pipe takes one of two forms: Laminar Flow : If the fluid moves parallel to the walls of the pipe, sliding smoothly in single and uniform direction, the flow is laminar flow. Turbulent Flow: If the fluid tumbles and swirls, it turbulent flow. The degree of turbulence is indicated by the Reynolds number: Q v d N = U N: Reynolds number , QV: Velocity of flow, d: diameter of the pipe ρ: density of the fluid , U: Viscosity of the fluid For N > 4000 the flow is turbulent, for N < 2OOO the flow is laminar 99 The material may vary from powder, solid, gas or liquid. In our discussion we will explain only fluid (liquid or gases) transducers. In general flow transducers are divided into two groups. One group introduces an obstruction and uses the energy in the flow to produce a measurable effect. The other group is non intrusive. We will explain a few in each group. Placing an obstruction in the line of flow will have two effects. It will cause a pressure drop across the obstruction. The pressure on the upstream side will go up, while the pressure on the down stream side will drop. Second, the flow will be lowered. Orifice Plate : It is the simplest differential pressure obstruction. It is a p1ate with a hole in it. The pressure drop across the plate is measured using a differential-pressure transducer. The relation between the amount of flow and the pressure drop across the orifice is : Q = K P1 − P2 Q = flow rate K = Constant depends on the geometry of the orifice and the units P1 , P2 = high side and low side pressures Notice that the flow is proportional to the square root of the pressure drop. The orifice plate has several advantages. It is simple to design, build and install. It can be used for most fluids which are free of particles. The disadvantages are poor accuracy, limited range and inability to be used with slurries (liquid with suspended solid particles). Pressure P1 P2 Sharp edges Flow Orifice Plate P P2 1 Deferential pressure sensor Orifice Plate (a) Orifice plate. 100  Flow P1 P2 (b) (c) Fig.(31) Venturi Tube The Venturi tube is shown in fig.(31-b). Instead of an abrupt barrier in the line of flow, the diameter of the tube is gently narrowed, and then widened. The relationship between flow and pressure difference is the same as with the orifice plate equation. However, since there is no sudden stop, there is a much lower tendency to plug up. Also, the pressure on the outlet side of the tube is very near the inlet pressure (P1). So flow measurement error due to pressure loading is much lower for a Venturi than for an orifice plate. Look at the physical construction of both the orifice plate and the Venturi in fig.(31-b). The orifice is simply a plate or p1ug, with a hole, bolted between two flanges. The Venturi is much more complex in shape and therefore more expensive and requires some extension the length of the flow line. Its main advantage is it can be used for slurries because there is no sharp edges. Its major disadvantage is cost, it is expensive to buy and install. Dall Tube. Of all the differential pressure flow-meters, the Dall tube has the least insertion loss. The Dall tube, shown in fig.(31-c), consists of two cones, the shorter one upstream of the restriction, the longer cone downstream. It is generally cheaper to purchase and install than the Venturi tube. However, it cannot be used with solids and slurries, as the Venturi can. Elbow tube. The elbow tube flowmeter is a differential pressure flowmeter that does not use the Bernoulli effect. It is shown in fig.(32-a). The differential pressure is developed by the 101 centrifugal force exerted by the fluid flowing around the corner. In this case, P 2 is greater than Pl. Since elbows (corners) usually already exist in pipes, installation of elbows poses no problems. There is no additional pressure loss because there is no restriction. However, the elbow flowmeter has only ±5% accuracy at best. Rotameter In the variable-area rotameter, shown in Fig(32-b), the flow pushes on a target, compressing a spring. The target comes to rest at a position where the force from the spring balances the force from the fluid flow. Since the compression force of a spring is proportional to its displacement, measuring how far the target has been pushed tells about the flow. If placed vertically, the force of gravity can replace the spring. This type of transducer produces a noticeable pressure drop (therefore, lowering flow and introducing error) and may be nonlinear. Also, you must bring out the leads from the potentiometer or LVDT used to measure displacement. Glass Tube Scale Float X Flow (a) Elbow (b) Rotameter Fig.(32) Cantilever Flow Meter The cantilever beam flow meter is shown in fig.(33-a). Flow causes a force on the target producing a deflection. This small deflection is sensed by strain gages bonded to the beam and can be measured and displayed with traditional strain gage electronics. To compensate for temperature variation of the fluid, four active strain gages should be used. Flow in either direction can be sensed and the direction is indicated by the 102 polarity of the dc voltage out. (The ability to measure flow in either direction is unusual among flow transducers.) Disadvantages associated with other obstruction-type flow sensors also plague the cantilever beam transducer. There is a pressure drop across the beam, although not as severe as with an orifice. The target encourages clogging and may be damaged by particles. In addition. the strain gage leads must be brought out through the wa1l of the tube. This requires extra effort in sealing the transducer. Electromagnetic assembly Output signal Target Strain gages Flow Turbine Flow e Low rate High rate E High rate Frequency to Voltage Converter Low rate t t Fig.(33-a) Cantilever flowmeter Fig.(33-b) Turbine flow meter Turbine flowmeters: If a turbine wheel is placed in a pipe containing a flowing fluid, its rotary speed depends on the flow rate of the fluid. By reducing bearing friction and other losses to a minimum, one can design a turbine whose speed varies linearly with flow rate; thus a speed measurement allows a flow-rate measurement. The speed can be measured simply and with great accuracy by counting the rate at which turbine blades pass a given point, using a magnetic proximity pickup to produce voltage pulses. By feeding these pulses to an electronic pulse-rate meter one can measure flow rate, and by 103 accumulating the total number of pulses during a timed interval the total flow is obtained. These measurements can be made very accurately because of their digital nature. If an analog voltage signal is desired, the pulses can be fed to a frequency-to- voltage converter with, however, some loss in accuracy. Fig.(33-b) shows a flow metering system of this type. Electromagnetic Flowmeter Nonintrusive measurement techniques do not load the system, then not lowering the flow. If you are measuring the flow of a liquid that is mildly conductive (even water will work), the electromagnetic flow meter may be used. The principle is illustrated in fig.(34). A nonconductive section of pipe is required. Lining a metal pipe with a nonconductive material will work. Which material to use is determined largely by the temperature and corrosives of the liquid. An electromagnetic field is placed at right angles to the flow. The generator rule states that a conductor cutting a magnetic field will induce a voltage that is at right angles to both the electromagnetic field and the direction of motion. Electrodes are placed so as to sense this induced electromotive force emf. This induced voltage is linearly proportional to the velocity of flow, the strength of the magnetic field, and the diameter of the pipes. Conductor Magnetic field magnetic field Applied voltag (ac) Direction to produce the of motion magnetic field b (a) Flow a E + 2 Electrodes Nonconductive pipe (a) Basic components E − 2 0V (b) E b + 2 R E E R E a 2 2 2 2 − 0V 2 - + - + 0 V line - E + (b) Tube cross section (c) Fig.(34) Electromagnetic flowmeter. 104 This type of transducer has the obvious advantage of producing no pressure drop to load down the f1ow. Flow reversals can easily be detected. Also there is nothing to clog up or break off. However, the fluid must be consistently conducive, a special section of pipe is required, and the output is in the microvolt range. Ultrasonic Flowmeter The other nonintrusive flow uses the propagation of ultrasonic waves through the fluid. One configuration is shown in fig.(35). The transducers are piezoelectric crystals capable of both receiving and transmitting ultrasonic signals. They may be operated into the megahertz range. These transducers are placed at 45o to the flow. Each transmits a different frequency. The signal traveling with the flow will arrive at a higher frequency than that at which it was transmitted. The signal traveling against the flow will have its frequency lowered. This difference in arrival frequencies is directly proportional to the velocity of the fluid. Ultrasonic flow transducers may be used on nonconductive fluids or on gages. It provides absolutely no obstruction or loading to the f1ow. In fact, there are flow transducers that may be clamped onto the outside of a pipe for occasional temporary measurement of the flow within. The disadvantage to ultrasonic flow measurement is the cost of the associated electronics. Detection and encoding Ultrasound transciever Flow f2 f1 Ultrasound transciever Fig.(35) Ultrasonic flow transducer. 105 LEVEL TRANSDUCERS : Knowing how much material there is in a tank is important in many manufacturing processes. Overflowing the tank can cause an expensive, perhaps very dangerous accident. Conversely, pumping a tank dry may spoil the process that was scheduled to receive the material from the now dry tank. Or it may damage the empty vessel if the process requires a certain amount of material to absorb heat. Accurate measurement of the quantity of material is critical. The material whose 1evel you are measuring is not necessarily a homogeneous liquid. Depending on the process, it may be a powder, beads, or flakes. Discrete Level Transducers Level transducers are divided into two major classes, continuous and discrete. Continuous transducers indicate the precise level, proportionally along the entire height of the tank. They will be discussed in more detail later in this section. On the other hand, it may only be necessary to have an indication (or alarm) when the tank reaches a prescribed level or if the tank is in danger of overflowing or being emptied. For these applications, a simple switch closure or voltage step is adequate. In fact, such discrete transducer outputs are much simpler for the controller to handle than is the output from a continuous transducer. high level low level Inferared indication indication light emitting Photo-sensitive diod transistor retainer Reed relay permanent contacts magnet Float Optical transmitter reflector reed relay contacts Reciever (b) retainer nonferrous tube (a) Float switch, (b) Photoelectric level sensors Fig.(36) Discrete level transducers. 106 Float Switch: The float switch is shown in Fig.(36.a). It comes in either normally open or normally closed configuration. The contacts are similar to those used in relays. They are spring loaded open and are made of a ferromagnetic material. When a magnet moves above them the magnetic field pulls the contacts. These contacts are sealed inside a nonferrous tube. A permanent magnet (s) is embedded inside the float. This travels up and down the tube in response to the level you are measuring. Retainer rings restrict the range of motion of the float. These contacts will handle either dc or ac voltages. So you can easily configure switch to input to some logic circuitry, to drive a programmable controller, or to directly power an alarm or other actuator. Photo-Detectors: Photo detection can be used to sense leve1 if the optical properties of the material will reliably block the transmission of light. Several possible configurations are illustrated in Fig.(36). The transmitter is usually an infrared light- emitting diode with appropriate lenses and beam collimation. The receiver is a photo sensitive transistor with optical filters to pass only the wavelength of the light being transmitted. When the 1evel is below the sensor, light reaches the receiver, and the phototransistor saturates, giving you a logic low. When the Level in the tank blocks the light, the phototransistor goes off. There are also receivers available that use a light- sensitive thyristor rather than a phototransistor. These receivers output 22O V ac when hit by the beam. The reflective transmitter and receiver is easier to install than the units with separate transmitter and receiver. Only one set of wires is required and as long as the target is large enough, alignment is not, critical. The integrated transmitter and receiver provide added flexibility. By mounting it on a rod, it can be raised or lowered, allowing you easily to select the alarm level. Photodetectors are more durable than float switches since there are no mechanical parts to fail. However, the photodetector requires that the material block the transmission of light. This somewhat limits their application. 107 Continuous Level Transducer However, much of process control systems require a precise, linear indication of the amount of material in the tank. This demands a continuous level transducer. There are a wide variety of ways to produce a signal that tracks the amount of material in a tank. Some will be presented. Use of Pressure Sensors: The pressure at the bottom of the tank depends linearly on the level of the liquid in the tank. Whether liquid or solid, the weight of the tank is a measure of the amount it contains. Floats and levers can be used to track the top of the liquid and move a potentiometer or valve. For electrically insulating liquids or solids, the tank and an electrode can be turned into a giant capacitor. Ultrasonic detectors, like those used in the automatic range finder and focus of some cameras, will easily find the distance to the surface of the liquid. h to be measured Pressure transducer offset to be corrected by electronics (a) Offset transducer, (b) Sealed tank Fig.(37) Level measurement by pressure sensing 1- You saw that the pressure at the bottom of a column of liquid is defined as the head and is proportional to the height of the column. P=ρgh Where: P = head (pressure) ρ = density of the liquid h = height of the column. You can measure the 1evel of liquid in a tank by measuring the pressure at the bottom of the tank. However, this technique makes several assumptions of which you should 108 be aware. First, for the results to be consistent, the liquid must be uniform. Really all this says is that the density must be constant. Second, the height resulting from the pressure reading transducer up. So if you cannot mount the pressure transducer at the bottom of the tank, your signal-conditioning electronics must add or subtract some offset to get the zero point right. This is shown in fig.(37-a). The final consideration when using pressure to indicate level is the pressure at the top of the tank. If the tank is open to atmospheric pressure, the basic head equation works, and you can use a transducer that measures (pressure with respect to atmospheric pressure). However, if the tank is sealed, the pressure at the bottom of the tank depends not only on the head, but also on the pressure at the top : 𝑃𝑏𝑜𝑡𝑡𝑡𝑜𝑚 = 𝜌𝑔ℎ + 𝑃𝑡𝑜𝑝 , 𝑃𝑏𝑜𝑡𝑡𝑜𝑚 − 𝑃𝑡𝑜𝑝 ℎ= 𝜌𝑔 To perform this calculation automatically you can use a differential pressure transducer with the reference port plumbed into the top of the tank. This is shown in fig.(37-b). 2- A true measure of how much is in a tank is its weight. This works whether the rank is holding liquid, solid, or something in between. The tank should be fully supported by load cells. If it is necessary to use more than one, you must either assure that the weight is evenly distributed, or you most provide some form of circuitry that will add the loads indicated by each ce1l. Finally the signal-conditioning electronics must be adjusted to give a zero output when the load cells are supporting an empty tank. Use of Float Arrangement: Perhaps the most widely used level transducer and control system is the float and valve arrangement inside the tank. Its principle of operation is illustrated in fig.(38). A float moves up and down on the top of the liquid in the tank. Through a pivot arrangement (simplified in the drawing), a valve is positioned. The valve location is proportional to level. When the leve1 is low, the float falls, opening the valve. As the level rises, the float comes up, pushing down on the valve to close. The lever arm and pivot also mechanically amplify the force applied by the float to the valve by a factor of ℓ1/ℓ2. 109 For more sophisticated controls applications, the valve can be replaced with the slider arm of a linear potentiometer. As the level varies, the float goes up and down, moving the arm on the potentiometer. Gearing can be added to convert the vertical motion of the lever arm, ℓ2 to a circular motion, to turn the shaft of rotary potentiometer. Scale l2 Pointer open float l1 Float pivot close valve Fig.(38) Float arrangement to measure liquid level. AC bridge Ultrasonic - RF Transceiver oscillator Level readout (a) (b) Fig.(39) Level measurement , (a) Capacitive means, (b) Ultrasonic radiation Float potentiometer for measuring leve1 has several advantages over the other transducers. The output signal may be a high-level DC voltage. This needs no further signal conditioning and is easy for the controller and display electronics to use. Second, the system is simple. Also both relatively inexpensive and reliable. However, there are some disadvantages. The float has a rather limited range of motion. The mechanism must be inserted inside the tank, and properly positioned and supported. In many applications, placing something inside the tank is impossible. Also the potentiometer may have to be carefully sealed and protected from being submerged in the liquid. 110 Use of Capacitor Arrangement: When the material or the liquid in the tank is an insulating material, it can serve as a dielectric in a capacitor. In Fig.(39-a) the capacitance changes as the liquid level changes. The capacitor behaves as two capacitors in parallel one has the air as a dielectric while the other has the liquid as a dielectric, the total capacitance is the sum of the two capacitors. As liquid level changes the two capacitors plates areas will change. The change in capacitance is caused by the changing dielectric constant between liquid and air. This change in capacitance usually sensed by an oscillator in an AC bridge. Ultra-Sonic Sensors: With the advent of automatic focusing on consumer cameras has come an accurate, inexpensive, easy-to-use, modular, ultrasonic range detector. To measure level with an ultrasonic range detector you mount the module above the tank, looking down at the surface. A pulse must be applied to the module to initiate a measurement. When the ultrasonic signal is transmitted, the module outputs a pulse. When the echo is received, another pulse is outputted from the module. Using an external counter you must measure the time between the transmit pulse and the echo- received pulse. Since the ultrasonic signal is traveling at the speed of sound, the time between transmission and echo received is a measure of the distance to the surface. Distances to be measured should be between 0.5 and 10 m. d = 0.5 V T where: d = distance to the surface V = velocity of sound = 331.5 m/s sea 1evel and 0 Co T = total time to the surface and back. Mounting the ultrasonic range detector above the tank looking down is convenient. It is easy to get and installation is simple, and the unit does not to be sealed against the effects of the material in the tank. However, as the tank fills up, the distance from the sensor to the surface becomes smaller. This produces a smaller transit time and a lower count on the external timer. That is as, the level goes up, th