CH-2 Transducers (Sensors) PDF

Ch. 2 : TRANSDUCERS (Sensors) 1- INTRODUCTION STATIC SPECIFICATIONS DYNAMIC SPECIFICATIONS  2. STATIC SPECIFICATIONS Accuracy – Resolution – Repeatability – Hysteresis and Linearity Accuracy: Error is the difference between true output and actual output of transducer 1 -...

Ch. 2 : TRANSDUCERS (Sensors) 1- INTRODUCTION STATIC SPECIFICATIONS DYNAMIC SPECIFICATIONS  2. STATIC SPECIFICATIONS Accuracy – Resolution – Repeatability – Hysteresis and Linearity Accuracy: Error is the difference between true output and actual output of transducer 1 - Percent error of the full scale output ( i.e. the max. reading ). 2 - Percent error of the true reading. 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. (A) plot the calibration curve. (B) Determine the accuracy in both % of FSO and of true reading. )C) For accuracy + 7.85 % FSO, what is the absolute error.?  load (KG) output ( mV ) increasing decreasing 0 0.08 0.06 10 1.02 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  Solution (A) The plot is in Fig.( 1 ) OUTPUT 100 FSO 90 80 70 60 50 40 30 20 10 INPUT 0 10 20 30 40 50 60 70 80 90 100  (B) We shall 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 V fullscale Vtrue = xLoad mV Load fullscale 20mV Vtrue = x 20 Kg = 4 mV 100 Kg  increasing error e = Vtrue - Vactual = 4 - 2.55 = 1.45 mV Accuracy : percentage error of: true reading, or FSO: %True reading = (1.45/4) x 100 = 36.25% Percent error of full scale output : 𝟏. 𝟒𝟓 % 𝒆𝒓𝒓𝒐𝒆 𝒐𝒇 𝑭𝑺𝑶 = 𝒙𝟏𝟎𝟎 = 𝟕. 𝟐𝟓% 𝟐𝟎  Decreasing Error e = Vtrue – Vactual= 4- 4.19= -0.19 mV Percentage error: (of true reading) = (- 0.19/4)x100 = - 4.75% % of FSO =(- 0.19/20)x100= - 0.95 %  ( 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.  A rotation less than  / 2 may not result any countable output. So, this encoder has 90o resolution  Industrial encoders provide 100 and 1000 pulses per revolution i.e. resolution is: 𝟐𝝅/𝟏𝟎𝟎 𝒕𝒐 𝟐𝝅/𝟏𝟎𝟎𝟎 (i.e. 3.6 to 0.36 deg) 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. C = d =  (2.5) = 7.854 m 2 Re solutionin(deg) = x360 = 0.917 O 785.4 360 No.of − pulse / Re v = = 392.7 Pulses 0.917 Therefore, the optical encoder must produce at least a 393 pulses/rev to achieve the resolution required  Repeatability It is a measure of how well the output returns to a given value when the same input is applied several times. 𝑴𝒂𝒙𝒊𝒎𝒖𝒎 𝒓𝒆𝒂𝒅𝒊𝒏𝒈.. −.. 𝑴𝒊𝒏𝒊𝒎𝒖𝒎 𝒓𝒆𝒂𝒅𝒊𝒏𝒈 𝐑𝐞 𝒑 𝒆𝒂𝒕𝒂𝒃𝒊𝒍𝒊𝒕𝒚% = 𝒙𝟏𝟎𝟎 𝑭𝒖𝒍𝒍𝒔𝒄𝒂𝒍𝒆.𝒐𝒖𝒕𝒑𝒖𝒕 𝑳𝒂𝒓𝒈𝒆𝒔𝒕 𝒅𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝐑𝐞 𝒑 𝒆𝒂𝒕𝒂𝒃𝒊𝒍𝒊𝒕𝒚% = 𝒙𝟏𝟎𝟎 𝑭𝒖𝒍𝒍 𝒔𝒄𝒂𝒍𝒆 𝒐𝒖𝒕𝒑𝒖𝒕  ‫ش‬ x x x average x x x x x average x x x True output x true output x x x (a) Accurate but not repeatable (b) Not accurate but repeatable True x x x x x x output x x (c) Accurate and repeatable  Hysteresis : Maximum devation Hysteresis % = x100 Full scale output OUTPUT 100 FSO 90 80 70 Y 60 X 50 40 30 20 10 INPUT 0 10 20 30 40 50 60 70 80 90  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.  Endpoint Linearity Output-(Electrical) 10 0 90 80 70 60 Va 50 Vb 40 30 20 10 Input-(Physical) 0 10 20 30 40 50 60 70 80 90 100  2 - Independent straight line linearity : OUTPUT 100 90 80 70 60 Va 50 Vb 40 30 20 10 INPUT 0 10 20 30 40 50 60 70 80 90 100  3 - Least squares linearity : If : Xi = input values Yi = output values m = slope of the straight line b = vertical intercept of straight line n = number of data points Y = mX + b n n n n  ( X i Yi ) −  X Y i i m = i =1 n 1 n 1 n  X i2 − (  X i ) 2 1 1 n n Y i X i b= 1 − 1 n n  DYNAMIC SPECIFICATIONS First order element Time Constant - dead time Input Time Output 1.0 0.9 0.632 Td 0.10 Tr Tc Time  Second order element: Damping Ratio – Natural Frequency, DT 2 1 3  4. POSITION TRANSDUCERS Potentiometer as a displacement sensor Resistor element Resistor element i Linear displacement X i + + o E _ - _ eo ( xo ) + E  Wire wound 𝐹𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 Re 𝑠 𝑜𝑙𝑢𝑡𝑖𝑜𝑛 % = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑖𝑟𝑒 𝑡𝑢𝑟𝑛𝑠 Carbon resistors: advantages are: higher resolution smooth resistive surface increased speed  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 250o 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 ?.  Sol. The shaft Required res. = 250/800 = 0.3125o/mm Rotation of 0.3125 degrees is required to move the panel 1 mm. Available potentiometer has resolution of : 300/1000 = 0.3o/ turn Pot. resolution < required resolution. Potentiometer will work.  Potentiometer Connections : (a) (b) E E f f i R p i V V E )c( )d( mechanical link to controlled R variable E CV SP E V (Error)  Effect of Loading V out V in 1 Rp =0 RL Vin R2 R1 Rp 0 R L Vout RL increasing 1 Xr  𝑅1 𝑉𝑑𝑒𝑠𝑖𝑟𝑒𝑑 = 𝑉𝑖𝑛 𝑅1 + 𝑅2 [𝑅1 𝑅𝐿 /(𝑅1 +𝑅𝐿 )] RL parallels R1 then, 𝑉𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑉 [𝑅1 𝑅𝐿 /(𝑅1 +𝑅𝐿 )]+𝑅2 𝑖𝑛 𝑹𝟏 𝑹𝑳 𝑽𝒂𝒄𝒕𝒖𝒂𝒍 = 𝑽𝒊𝒏 𝑹𝟏 𝑹𝑳 + 𝑹𝟏 𝑹𝟐 + 𝑹𝟐 𝑹𝑳 If: Rp= R1+ R2 ,total petitioner resistance. Xa the actual wiper displacement, and Xfs the full scale potentiometer displacement, then: 𝑋𝑎 𝑅1 𝑋𝑟 = = R1= Xr.Rp 𝑋𝑓𝑠 𝑅𝑝 𝑽𝒐𝒖𝒕 𝟏 Then: = 𝟏 𝑹𝒑 𝒇𝒐𝒓 𝑹𝑳 = ∞, 𝑽𝒐𝒖𝒕 = 𝑿𝒓 𝑽𝒊𝒏 𝑽𝒊𝒏 +(𝟏−𝑿𝒓 )𝑹 𝑿𝒓 𝑳  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. Solution : 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 l000 0 10 10.0 0.0 1.0 1.0 0.0  Nonlinearity caused by loading 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  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, connected in opposite polarity. No physical contact between the movable core and coil structure, i.e., LVDT is a frictionless device  Sec. Sec. coil 1 coil 2 Primary coil Core motion Core  Sec. coil 1 Primary coil Core e1 e = e − e o 1 2 e2 Sec. coil 2  LVDT output versus displacement a Output (V) Displacement Linear displacement  LVDT electronics LVDT Carrier Rectifier & Demodulator DC amplifier generator filter AC Power supply  LVDT provides complete isolation between excitation input ( primary ) and output (secondaries). This makes it an effective analog computing element without the need for buffer amplifies Frictionless, infinity life. used in aircrafts, missiles, space vehicles and critical industrial equipment.  Optical Encoders: Incremental Encoder: The encoder is a disk with a track on it near to its outer edge this track is divided into equal dark and transparent parts with light source on one side and light sensor on the other. 1 0  Incremental encoder with two tracks shifted by  / 2 for direction detection A B A B C reference pulse C  B - Absolute Encoder: 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. It gives a different and full binary word for each position increment.  (a) Natural binary code. (b) Grey code, only outer track is the LSB, one bit switch at a inner track is the MSB time  A 4 bits Gray code absolute encoder:.  5. FORCE TRANSDUCERS An entire engineering discipline (experimental stress analysis) has been established to evaluate forces applied to various parts of a machine or vehicle. Accurately measured forces allow proper design of machinery (including cars and spacecrafts) that is lighter, more efficient, more reliable, less expensive, and which provides higher performance.  Measurement of force allows us to evaluate 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 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 Strain may be either tensile (positive) or compressive (negative), 𝜟𝑳 𝜺= 𝑳 Usually expressed in microstrain, which is ε X 10-6 , for example 0.00500 in/ in = 5000 micro strain ( με).  a 𝑭  𝑺𝒕𝒓𝒆𝒔𝒔 𝝈= E (Young ' s − mod) = 𝑨   Strain Gage: Probably the most important electrical characteristic which varies in proportion to strain is the electrical resistance : piezoresistive or semiconductor gage, carbon resistor. bonded metallic wire gage. foil resistance gages.  Bonded Resistance Strain Gage : Bonded wire Metal foil strain strain gauge gauge Δ𝑅/𝑅 𝐺= , 𝑔𝑎𝑔𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 𝜀  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 load is applied, the gage's resistance changes by 0.013 Ω. Calculate the change in length of steel beam and the amount of force applied to the beam.  Solution: Gage factor: 𝜟𝑹/𝑹 𝑮= 𝜟𝑳/𝑳 In above equation the only unknown is ∆L Young’s modulus E : 𝑭 𝜟𝑳 =𝑬 𝑨 𝑳 The only unknown is the force F  It would be preferred that the gage resistance changes only with strain, but practically the gage resistance varies also with temperature. 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 ∆T change in temperature only is: ΔR = αo ΔT RTo  Example: 9 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 : ∆R = 0.003925 x 1 x 240 = 0.942 Ω 𝑹𝒕𝒆𝒎𝒑 𝟎. 𝟗𝟒𝟐 = = 𝟕𝟐. 𝟓 𝑹𝒔𝒕𝒓𝒆𝒔𝒔 𝟎. 𝟎𝟏𝟑  Wheatstone Bridge Circuit : Because of its sensitivity, Wheatstone bridge is the most used circuit for strain measurements Rg = Ro + R Ra + Vo E - Rc Rb  𝒄𝒐𝒏𝒔𝒊𝒅𝒆𝒓: 𝑹𝒐 = 𝑹𝒂 = 𝑹𝒃 = 𝑹𝒄 = 𝑹 when stress is applied, the strain gage changes its resistance by ΔR : R R Vout = E− E R+R R + R + R 1 R R = E− E= E 2 2 R + R 4 R + 2R but as R >> ΔR , 4R >> 2ΔR R Vout = E 4R  Use of active and dummy gages to compensate temperature Ro active Ra gauge + V Rc E Rb - dummy gauge  acting force active guage dummy guage Rg Rc  Beside the temperature effect will be eliminated, the bridge sensitivity can be increases if we make both gages active, by having one gage in tension ( its resistance increase with load ) and the other in compression ( its resistance decrease with Load). The output voltage for a given load doubles the single active gage output : R Vout = E 2R  Two active gages ,one placed on surface under tension, other on compressed surface Gage place in tension Force Tension Copmression R + R Ro + R Ro − R + Vout R − R Gage placed in E compression - R c Rb  Four active gages to increase sensitivity and temperature compensation R Vout = E R Tension Compression R + R R − R + E Vout - R − R R + R Compression Tension  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 It 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. A set of specifications, but the important one is the output at rated capacity i.e. sensitivity, 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 load ( rated capacity=max. or rated load) 500 Ib is 2 mV/V Nonlinearity ± 0.050 %FS Bridge resistance 300 ohms Compensated temp. 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 ?  (a) Vout. max = output at rated capacity x Vsupply = 2 mV/V x 10 V = 20 mV Vout/Ib = 20 mV/500 Ib = 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 * (c) Zero shift=(0.002/100)(100F)(500 Ib)=1 Ib must be adjusted  6. Velocity Transducers Linear velocity sensors Electromagnetic linear transducer d emf = − N dt  Laser-Doppler System The Doppler effect relies on a shift in frequency Frec= Fo + Fv Frec is the frequency of the echo Fo the frequency of the transmitted signal Fv the shift in echo frequency which is a function of the target velocity. Radar speeders detector, missile targeting, tracing & navigation of spacecrafts Angular Velocity Measurements : DC Tacho-generator: Stator Field: permanent magnet or separately excited Rotor has a series of coils + Commutator Induced emf in the coil is directly proportional to the rotor speed The output is pure DC (commutation + brushes) PM: Output 3V to 7V per 1000 r/min or Electromagnet : 10 V to 20 V per 1000 r/min. Accuracies of 0.1 % to 0.25 % FSO  AC Induction Tachogenerator: Called the AC permanent magnet tachometer. It has no brushes. Primary and secondary windings placed at right angles on the stator. Rotor is squirrel cage made of high conductance metal. When the rotor is stationary the magnetic field of the rotor induced emf does not link the secondary, then output equals zero,  At ω=0, no flux linkages between primary and secondary, (right angle) the output voltage = 0 When the rotor is rotated, the field links the secondary, inducing an output voltage. The more faster the rotor, the larger output in the secondary. The output is AC, rectified, smoothed to be used as a measure for the rotational velocity. It overcomes the problems (sparks and electromagnetic interference to other control circuits) resulted by the brushes of the DC tachometer.  Counter-type Velocity Sensors Outputs a signal its frequency depends on the speed of rotation. Conditioned in order to be a series of countable pulses. AC permanent magnet tachometer the incremental optical encoder Gears, belts and shafts all introduce errors. Also, the inertia of the transducer may load down the system.  Reflective optical sensor  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 degradation in performance.  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. Thus, we must get 1720 counts during the counting period (0.1 s), i.e., 1720 = 2.867 x Number of pulses per revolution No. of pulses/revolution = l720/2.867 = 600 pulse/ revolution. That is to get a measure for the speed in r/min every 0.1 sec.  Simply how many revs occur in 0.1 sec., 1720 𝑥 0.1 Revs in 0.1 sec = = 2.867 𝑅𝑒𝑣𝑠 60 In 2.867 revs we must get 1720 counts (pulses), 1720 How many pulses/one rev= = 600 pulses 2.867  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, we obtain a measure for the speed in r/min every 10 Sec. which is too long for most control applications. 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. This also may be shown as follow:  With 6 pulse/rev, the number of revolutions required to obtain 1720 counts = 𝟏𝟕𝟐𝟎 = = 𝟐𝟖𝟔. 𝟕 𝒓𝒆𝒗𝒔 𝟔 Time required to obtain 286.6 revs 𝟐𝟖𝟔.𝟕 = = 𝟏𝟎 𝑺𝒆𝒄. 𝟐𝟖.𝟔𝟕 Therefore, we obtain a measure for the speed in revs/min every 10 seconds instead of 0.1 S which is too long for most control systems. Also, we my use an F/V converter then multiply by a gain of 100, then use V/F converter.  7. FLUID TRANSDUCERS Fluid transducers are used extensively throughout the industry. Applications : food processing industry, drug and chemical industries, and along the entire line of oil production, from exploration, drilling, pumping, transportation, refining to sales. Pressure, level and flow  Pressure Transducers : Normally pressure measured in comparison to a reference : a - Absolute pressure : (Vacuum) The unit is :psia (a=absolute) b - Gage pressure : (ambient) The unit is :psig. c - Differential pressure : The unit is :psid.  A common industrial unit for the pressure is pounds per square inch (psi) In metric system pressure units is Newton/meter2 which is called Pascal (Pa) 1 psi = 6.8948 x 103 Pa Pascal is a small unit, 1 KPa = 103 Pascal 1 psi = 6.8948 KPa  The height of a column of mercury that yield a certain pressure is also used as a unit of pressure measurement: 1 inch of mercury (Hg) = 3.386 KPa 1 mm Hg = 133.32 Pa (also called torr) 1 torr = 1 mm Hg = 133.32 Pa Atmospheric pressure at sea level is defined as: 1 atm = 76 Cm Hg = 760 mm Hg = 1.01325 x 105 Pa Barometric pressure, in weather reporting is measured in bar or millibar 1 bar = 105 Pa = 100 KPa  Manometric means for pressure measurements: P2 P2 P1 Tube cross A1 sectional area P1 h h Well cross sectional area A2 Well-type manometer  - Vacuum h 0 Barometer  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 h: the differential height between the two Liquid surfaces. P2 = P1 + ρ g h  1 h= ( P2 − P1 ) g The accuracy 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  Elastic Pressure Transducers All elastic deformation pressure transducers use the same principle. Pressure causes a deformation of the transducer material usually a metal. This deformation results in a deflection or displacement, i.e. these transducers are pressure to position transducers We will consider three types: Bourdon tube, the bellows , and the diaphragms.  Bourdon Tubes Bourdon tube is one of the oldest and most popular pressure transducers. It was invented in 1851 by E. Bourdon Made of brass, bronze, or steel The tube deforms nonlinearly Bourdon tube is simple to manufacture, inexpressive and accurate and it measures pressures up to 100,000 psi (700,000 KPa) Motion of the free end Pressure Helical tube C type  C - type Bourdon tube with LVDT  Diaphragms Flexible plate usually made of metal or rubber. For greater sensitivity, these plates are corrugated. Increase in pressure causes deformation in the diaphragm, measured using strain gage giving electric signal represents the applied pressure (a) Flat Diaphragm (b) Corrugated Diaphragm  Pressure Pressure P2 P1 Diaphragm  Vacuum Pressure Diaphragm  Bellows Pressure bellow is a cylindrical shaped device, corrugated along its edges. As pressure increases the bellows expands, moving the shaft upwards. The shaft may be attached to a pointer or an electric displacement transducer like an LVDT 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 measurements.  free fixed motion pressure  FLOW TRANSDUCERS 1 - Volumetric flow Q : Units are m3/sec. litre/s or gallon/min. 2 - Mass flow Qm : Units are KG/Sec. or pounds/Sec Velocity of flow Qv : Unit is m/sec. Qm = mass flow = Q.ρ volumetric flowrate Q Qv ( flow velocity ) = = pipe cross sec tional area A  Laminar Flow : fluid moves parallel to the walls of the pipe, sliding smoothly. Turbulent Flow: fluid tumbles and swirls. The degree of turbulence Q v d N = U N: Reynolds number , QV: Velocity of flow, d: diameter of the pipe ρ: density of the fluid , U: Viscosity For N > 4000 the flow is turbulent, For N < 2000 the flow is laminar  The material may vary from powder, solid, gas or liquid We will consider only fluid (liquid or gases) transducers Flow transducers are divided into two groups Obstruction: uses the energy in the flow to produce a measurable effect. Two effects: First, it causes a pressure drop across the obstruction. Second, the flow will be lowered. Non intrusive:  Orifice Plate : Sharp edges Orifice Plate Q = K P1 − P2 Q = flow rate K = Constant depends on the geometry of the orifice and the units used. P1, P2 = high side and low side pressures  advantages. simple to design, build and install. It can be used for most fluids which are free of particles. disadvantages : poor accuracy, limited range and inability to be used with slurries  Venturi Tube diameter of the tube is gently narrowed, and then widened lower tendency to plug up. P1 is very near to P2, so flow measurement error due to pressure loading is much lower. 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.  Venturi Tube  Dall Tube. least insertion loss. Two cones, the shorter one upstream of the restriction, the longer cone downstream. cheaper to purchase and install than the Venturi tube. However, it cannot be used with solids and slurries. Flow P1 P2  Elbow tube. P2 > P1. Installation of elbows poses no problems. No pressure loss as there is no restriction. However, the elbow flowmeter has only ±5% accuracy at best  Rotameter Produces a noticeable pressure drop and may be nonlinear. Leads from the potentiometer or LVDT Glass Tube Scale Float X Flow  Cantilever Flow Meter Flow causes a force on the target producing a deflection, sensed by strain gages bonded to the beam To compensate for temperature variation of the fluid, four active strain gages should be used. Target Strain gages Flow  Disadvantages: As with other obstruction-type flow sensors: There is a pressure drop across the beam, although not as severe as with orifice plate. The target encourages clogging and may be damaged by particles. In addition, the strain gage leads must be brought out through the wall of the tube. This requires extra effort in sealing the transducer  Turbine flowmeter: Electromagnetic assembly Output signal Turbine Flow e Low rate High rate E High rate Frequency to Voltage Converter Low rate t t  Rotary speed depends on the flow rate of the fluid. By reducing bearing and other losses to a minimum, one can design a turbine whose speed varies linearly with flow rate. turbine blades produce voltage pulses when pass near a magnet. Counting these pulses one can measure flow rate, accumulating the total number of pulses during a timed interval the total flow is obtained.  If an analog voltage signal is desired to represent the flow, the pulses can be fed to a frequency-to-voltage converter Electromagnetic Flowmeter magnetic field Applied voltag (ac) to produce the magnetic field b Flow a Electrodes Nonconductive pipe (a) Basic components E b + 2 E a − 2 0 V line (b) Tube cross section Conductor Magnetic field Direction of motion (a) E + 2 E − 2 0 V (b) R E E R 2 2 2 2 0V - + - + - E + (c)  If a liquid is mildly conductive the electromagnetic flow meter may be used. A nonconductive section of pipe is required or lining a metal pipe with a nonconductive material. A magnetic field is placed at right angles to the flow. The generator rule will apply to both the electromagnetic field and the liquid in motion. Electrodes are placed so as to sense this induced emf, which is linearly proportional to the flow velocity, strength of the magnetic field, and the diameter of the pipes.  Advantages: Producing no pressure drop to load down the flow. Flow reversal 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 Nonintrusive flow uses the propagation of ultrasonic waves through the fluid Detection and encoding Ultrasound transciever Flow f2 f1 Ultrasound transciever  The transducers are piezoelectric crystals capable of both receiving and transmitting ultrasonic signal. 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  Level Transducers Discrete Level Transducers Float switch Photoelectric level sensors high level low level Inferared indication indication light emitting Photo-sensitive diod transistor retainer Reed relay permanent contacts magnet Optical transmitter Float reflector reed relay contacts Reciever (b) retainer nonferrous tube  Continuous Level Transducer Level measurement by pressure sensing Offset transducer h to be measured Pressure transducer offset to be corrected by electronics  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 P = head (pressure) ρ = density of the liquid h = height of the column  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 = gh + Ptop Pbottom − Ptop h= g Sealed tank  Float Level Sensors A float and valve arrangement installed inside the tank. The valve can be replaced with the slider arm of a linear potentiometer  The force applied by the float to the valve is amplified by a factor of ℓ1/ℓ2. Scale l2 Pointer open float l1 Float pivot close valve  Capacitive Level Sensors When the material or the liquid in the tank is an insulating material, it can serve as a dielectric in a capacitor. The capacitor behaves as two capacitors in parallel 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.  a AC bridge - RF oscillator  Ultrasonic radiation (ultrasonic range detector) Ultrasonic Transceiver Level readout  d = 0.5 V.t where: d = distance to the surface V = velocity of sound = 331.5 m/s sea level and 0 Co t = total time to the surface and back.  TEMPERATURE TRANSDUCERS Early 1700s, when Gabriel Fahrenheit a Dutch instrument maker, produced an accurate and repeatable mercury thermometers 1742, Anders Celsius proposed that the melting point of ice and the boiling point of water be used for the two benchmarks Co = 5/9(Fo - 32) Fo = 9/5Co + 32 Ko = Co + 273.15 A) Mercury thermometer (b) Thermometer with an electrical output using Bourdon tube and an LVDT Capillary Bourdon Tube Bulb Tcap T LVDT eout ein  Bimetallic thermometers: Two metallic stripes bonded 1 >  2 At T1 (normal) the two stipes are r in normal position (flat). At T2 one stripe will expand T1 more the the other, thus, deforms into a circular arc 1 2 T2  T1 T2  T2  T1 Temperature change from T1 to T2  Details of materials and bonding processes are in some cases considered trade secrets. Invar, a nickel steel with a nearly zero [l.7 x 10-6 in./(in. Co)] expansion coefficient. Brass was originally employed, also a variety of alloys are now used for the high-expansion strip. Bimetallic devices are used for temp. measurement and also used widely as combined sensing and control elements in temp.-control systems, mainly of the ON-OFF type.  2r = 3( a −  b )(T2 − T1 ) ρ : radius of curvature r : total strip thickness, 0.0005 inch < r < 0.125 inch in practice. T2 – T1 : temperature rise The working temp. ranges from -100 to 1000 Fo. Inaccuracy of the order of 0.5 % to 1 % of scale range may be expected in bimetal thermometers of high quality.  Thermocouples: Thomas Seebeck made the discovery in 1821 “ Seebeck Effect ” any 2 diff metals Copper – constantan (Cu57+Ni43) (type-T) thermocouple, to connect a voltmeter, two more metallic junctions : J2 is a constantan-copper junction which will add an emf (V2) in opposition to V1 The other junction will have no effect as it is copper-copper junction.  a A J2 J1 i T2 (a) T1 B Ammeter A A J2 J1 (b) i T2 T1 B A thermojunction Voltmeter J1 (c) et i T2 B Copper Heat source (measured Teperature)  Copper – Constantan (type T) thermocouple Connecting a voltmeter will form another junction 𝐽2 Copper A Copper J1 E T2 Copper Constantan B T1 J2  J1 temp. is measured wrt J2 Voltmeter reading V will be proportional to the temp. difference between J1 and J2. This says that we can't find the temp. of J1 unless we first find the temp. of J2 One way to determine the temp. of J1 is to physically put the Junction J2 into an ice bath (i.e. at zero Co), forcing its temp. to be 0 Co and establishing J2 as the reference junction. V = V1 – V2 = TJ1 - TJ2= TJ1 – 0 = TJ1  Temp. measurement with a thermocouple and an external reference Copper Copper J1 E T2 Copper Constantan J2 J2 at zero temp.  We may use a different arrangement without ice box by using a thermistor to measure the reference junction temperature. Then calculations has to be made in order to find the temp. of the junction J1. This is called “ software compensation” as it require computation to compensate for the effect of the reference junction.  According to thermoelectric law-3 (follows) & measure the ref. jun. temp. Isothermal block of temperature T ref iron J2 copper T + J1 _ V J3 copper Constantan Thermistor.  Electronic ice point reference: We could insert a battery to cancel the offset voltage of the reference junction The combination of this hardware compensation voltage and the reference junction voltage is equal to that of a 0 Co junction. The major drawback is that a unique ice point reference circuit is usually needed for each individual thermocouple type.  The AD594/AD595 is a complete instrumentation amplifier and thermocouple cold junction compensator on a chip. It combines an ice point reference with a pre-calibrated amplifier to produce a high level 10 (mV/Co) output directly from a thermocouple signal. A given thermocouple material must be calibrated over the complete range of temperature in which it is to be used.  Thermoelectric Laws: These laws, are used for analysis of most practical thermocouple circuits. 1-The thermal emf of a thermocouple with junctions at T1 and T2 is totally unaffected by temp. elsewhere in the circuit if the two metals used are each homogeneous T3 T5 J2 J1 T2 T1 emf( )= emf( ) J2 J1 T2 T1 T4 T6  2-If a third homogeneous metal C is inserted into either A or B , as long as the two new thermojunctions are at same temps., the net emf of the circuit is unchanged irrespective of the temp. of conductor C away from the junctions. A A J2 J1 J2 J1 emf( )= emf( J3 J4 ) T1 T2 T1 T2 B B B C  3. If a metal C is inserted between A and B at one of the junctions, the temp. of C at any point away from the AC and, BC junctions is immaterial. So long as the junctions AC and BC are both at the temp. T1, the net emf is the same as if C were not there. A T1 C A J2 J2 J1 emf( T3 ) = emf( ) T2 T1 T2 T1 B B Fig.(47  4. If the thermal emf of metals A and, C is EAC and that of metals A and B is EAB and that of metals B and C is EBC, the thermal emf of metals A and C is EAB + EBC. i.e. EAC=EAB+EBC A A B T2 T1 T2 T1 T2 T1 emf( ) = emf( )+ emf( ) C B C  5. If a thermocouple produces emf E1 when its junctions are at T1 and T2, and E2 when at T2 and T3, it will produce E1 + E2 when the junctions are at Tl and T3. A A A T3 T1 T3 T2 T2 emf( T1 ) = emf( ) + emf( ) B B B ET3 −T1 = ET3 −T2 + ET2 −T1  Common types of thermocouples: Thermojunctions formed by welding, soldering, or by pressing the two materials together give identical voltages. If current is allowed to flow, the currents may be different since the contact resistance differs for the various joining methods. Welding (gas or electric) is most widely used although silver solder is used in copper/constantan couples.  Resistance Temperature Detector RTD Pure metals such as platinum, nickel, tungsten, and copper, have positive temperature coefficients. RT= Ro( 1+αT) Ω RT = resistance at temperature T Ro = resistance at 0 Co α = temperature coefficient of resistance. RTD is the most accurate and stable temperature sensor.  It is linear and covers high temperature range. Disadvantages include slowness of response, small resistance change, and high cost. Common resistance values for RTD's range from 10 Ω to several thousand ohms. The most common value of resistance is 100 Ω  Thermistor Like the RTD the thermistor is also a temperature-sensitive resistor. Thermistor exhibits the largest parameter change with temp. i.e. higher sensitivity. The price is loss of linearity. Thermistors are made of semiconductor material. Most thermistors have a negative temperature coefficient (NTC) The NTC can be as large as several percent per Co, allowing the thermistor circuit to detect minute changes in temp. which could not be observed with an RTD or thermocouple circuit. So it is the most sensitive temp. sensor  Thermistor–temperature characteristics: (Nonlinear) Resistance: Ohms 5 10 Rt 4 10 10 3 2 10 max. continuous 10 temperature 1 100 200 300 o Temperature: C  The price we pay for this increased sensitivity is loss of linearity. The thermistor is an extremely nonlinear device.  Thermistor curve can be approximated through use of the equation : 1 = A + B ln( R) + C{ln( R)}2 T T = degrees Kelvin R = resistance of the thermistor A,B,C = curve-fitting constants Thermistor RT R To - Ei + Eo  Circuits used for sensing temperature with thermistor E V Termistor or ist m o o T RT er T Th E Eo R1  Connecting a resistor Rs in parallel to improve thermistor linearity Resistance (Ohm) T Resistor Thermistor Rt Linear Thermistor-resistor R s o (a) (b) Temperature C  Semiconductor Temperature Sensors: Germanium can be used to sense temp. near absolute zero. It has a negative temp. coefficient (NTC) and is very nonlinear. Silicon is also employed as temp. sensors. Silicon crystals have a positive linear temp. coefficient (PTC) in this range Their useful range extends from - 67 to 275 FO  Recall that a reverse-biased PN junction conducts a small amount of leakage, or minority carrier, current flow. As temp. increases, leakage current increases exponentially. A reverse biased diode with a CDA (Current Differencing Amplifier) is used as a temp. sensor.  CDA is a linear amplifier circuit in which the reverse current in the diode 𝑰𝑫 is mirrored in the feedback resistor 𝑹𝑭 producing an output voltage: 𝑽𝒐 = 𝑹𝑭 𝑰𝑫 This effect is used to measure temp. with transistors and reverse-biased diodes. Normally, germanium semiconductors are used, because their leakage is much greater than that of silicon.  Suppose we have a feedback resistance RF of 1 MΩ and a diode current ID at room temperature of 10 μA. For the circuit shown above ,the output voltage is Vo = ID RF = (10 μA))1MΩ) = 10 V The temp. sensitivity (S) of the germanium diode is about 0.0333 μA/Co Let us suppose that the temp. goes from 25 Co to 75 Co. Then the change in current (∆ID) equals the change in temp. (∆T) times the sensitivity:  ∆ID = (∆T)(S) = (50 Co x 0.033 μA/Co) = 1.67 μA The total diode current at 75 Co equals the change in current plus the current at 25 Co ID(75Co) = ∆ID + ID(25Co) = 1.67 μA + 10 μA = 11.67 μA The output voltage at 75 Co is then Vo = ID RF = (11.67 μA) x )l MΩ) = 11.67 V  The transistor VBE depends on temp., varying -2.25 mV/Co. For every Co increase in temp., VBE will decrease by 2.25 mV.  IC temperature sensors: One of the most recent innovations in thermometry is the IC temp. sensor. The output of the IC (either voltage or current) is directly proportional to temp. Linearity exceeds that of the RTD. Typical sensitivity value is 1 μA,/Co or 10 mV/Co (i.e. current mode or voltage mode) Vo = S x temperature.  AD590 manufactured by Analog Devices sensitivity value is 1 μA,/Co or 10 mV/Co LM335, which has an output equal to 10 mV/Ko. National Semiconductor LM34 and LM35. LM34 have an output voltage that is linearly proportional to the Fahrenheit temperature scale. Its output voltage sensitivity is + 10 mV/Fo  LM34 Temperature sensor  The LM35 is similar to the LM34, but it has a sensitivity of 10 mV/Co (i.e. works with Celsius scale). Both devices have a low output impedance and a linear output voltage, and both can be used with single or dual power supply voltages. Generally speaking, semiconductor temperature sensors produce good linearity, small in size and low in cost.