Sensors and Transducers--Summary

Sensors are required to monitor the performance of machines and processes and to compensate for the uncertainties and irregularities of the work environment. Using a collection of sensors, we can monitor a particular situation in an assembly line, in a way that can substitute a human being.

Sensors can be used to evaluate operations, conditions of machines, inspection of the work in progress, and identification of parts and tools. Sensors are also used for pre-process, post-process inspection and on-line measurements. Some of the more common measurement variables in mechatronic systems are temperature, speed, position, force, torque, and acceleration. When measuring these variables, several characteristics become important. These include the dynamics of the sensor, stability, resolution, precision, robustness, size, and signal processing. Progress in semiconductor manufacturing technology has made it possible to integrate various sensory functions. Intelligent sensors are available that not only sense information but process it as well. These sensors facilitate operations normally performed by the control algorithm, which include automatic noise filtering, linearization sensitivity, and self-calibration. The ability to combine these mechanical structures and electronic circuitry on the same piece of silicon is an important breakthrough. Many micro-sensors, including biosensors and chemical sensors, have the potential to be mass produced.

+++++++++

PROBLEMS

Errors and Sensitivity Analysis:

1. A torque transducer is used to measure the power of a rotating shaft. During the mode of measurement, the following parameters are monitored.

Speed of rotation of the shaft during the time t, (R) Force at the end of the torque arm, (F) Length of the torque arm, (L) Time (t) The errors in each of the measurements are Shaft speed, R 2502 1 revolutions Force on the arm, F 55.02 0.18 N Length of the arm, L 0.0397 0.0013 m Time in seconds, t 30 0.50 s The power is computed using the equation

Determine the absolute error in the measurement of torque.

2. The discharge coefficient, Cq, of an orifice can be found by collecting water that flows during a timed interval when it's under constant head, h. The following formula is used to measure the discharge coefficient.

where W 200 0.23 kg t 500 2 s 1000 kg/m3 d 1.25 0.0025 cm g 9.81 0.11 m/s^2 h 66 0.003 m Find Cq and its component error.

The resistance of certain length of wire R is given by R = 4 l_d2 where

_ resistivity of the wire in O-cm l = length of the wire in cm d = diameter of the wire in cm Determine the nominal resistance and the uncertainty in resistance of the wire with the following data.

_ 45.6 _ 10_6 0.15 _ 10_60-cm l _ 528 0.2 cm d = 0.062 1.2 _ 10_3 cm 4. Calculate the power consumption in an electric circuit. The voltage and current are measured to be, , . What is the maximum possible error? 5. This example is about an explosive detonation manufacturer. The shell is filled with explosives. A pres sure of 35,000 kPa (absolute) is exerted as shown. The formula for hoop stress is given as I = 5 ; 0.2 A V = 50 ; 1 V

Find the hoop stress on the wall of the shell and component error if Shell Thickness = 0.028 ; 0.0001 cm Shell Radius = 0.287 ; 0.007 cm Pressure exerted is = 35,000 ; 70 kPa (absolute)

6. The mass moment of inertia for a sphere is given by

where m = mass of the sphere in kg r = radius of the sphere in mm m _5 0.04 kg; r = 100 0.2 mm Calculate the absolute error in the measurement of the mass.

7. Choose the appropriate definitions from the following list for the sentences.

a. null-type device

b. amplifier

c. drift

d. transducer

e. precision

f. accuracy

g. calibration

h. resolution

i. linearity

j. backlash

k. relative error

l. noise ( )

Device whose output is an enlarged reproduction of the essential features of the input wave and which draws power from a source other than the input signal ( ) Measure and generates an opposing effect to maintain zero deflection ( ) A device that converts input energy into a form of an output with different form of energy ( ) Ratio of difference between measured value and true value of the measurand ( ) .Smallest increment in measurand that can be detected with certainty by the instrument ( ) Ability of the instrument to give identical output measurements when repeat measurements are made with the same input signal ( ) Gradual departure of the instrument output from the calibrated value ( ) Maximum distance or an angle, any part of the mechanical system can be moved in one direction without causing the motion of the next part ( ) Characteristic of the instrument whose output is a liner function of the input 8. The voltmeter scale has 100 divisions. The scale can be read to 1/5 of a division. Calculate the resolution of the instrument in mm.

9. A rotary variable differential transformer (RVDT) has a specification on ranges and sensitivities.

Range 30°, linearity error 0.5% full range Range 90°, linearity error 1.0% full range. Sensitivity 1mV/V input per degree What is the error reading in 50° due to non linearity if the RVDT is used in 90° range? 10. What will be the change in resistance of a strain gauge, with a gauge factor of 4 and resistance of 50 _ if the gauge is subjected to a strain of 0.002? 11. A pressure gauge uses four strain gauges to monitor the displacement of a diaphragm. Four active gauges are used in a bridge circuit (Figure 11) The gauge factor is 2.5 and resistance of gauges 100

_. Because of the differential pressure on the diaphragm, gauges R1 and R3 are subjected to tensile strain of (2)(10)_4 and gauges R2 and R4 are subjected to compressive strain of (2)(10)_4.

The supply voltage to the bridge is 12 V. What will be the offset voltage? 12. A force of 5400 N is exerted on an aluminum rod, whose diameter is 6.2 cm and length 30 cm. Calculate the stress and strain in the beam if the Young's modulus of aluminum is 70 GN/m2. A strain gauge with a gauge factor of 4 and resistance of 350 _ is attached to the rod. Calculate the change in resistance. If the strain gauge is used in a bridge circuit and all other resistances are 350 _, find the offset voltage of the bridge. Supply voltage of the bridge is 10 V.

Ill. 11 BRIDGE CIRCUIT

1 A Resistance-wire strain gauge uses soft iron wire of small diameter. Gauge factor is 4.2. Neglect piezo-resistive effect. Calculate Poisson's ratio.

14. A compressive force is applied to a structure, the strain _ 5 microstrains. Two separate stain gauges are attached to the structures, one is a nickel wire stain gauge of gauge factor __12.1 and another is a nicrome wire stain gauge of gauge factor _ 2. Calculate the value of resistance of the gauges after they are strained. The resistance of strain gauge _120 _.

15. A resistance wire strain gauge with a gauge factor _ 2 is bonded to a steel structure member subjected to a stress of 100 MN/m2. Modulus of elasticity of steel is 200 GN/m2. Calculate the percentage change in value of the gauge resistance due to the applied stress.

16. A strain gage has a resistance of 250 _ and a gage factor of 2.2. it's bonded to an object to detect movement. Determine the change in resistance of the strain gage if it experiences a tensile strain of 450 _ 10_6 due to the change in size of the object. Also, if the relationship between change in resistance and displacement is 0.05 _.mm_1, determine the change in the size of the object.

17. A steel bar with modulus of elasticity 200 GPa and diameter 10mm is loaded with an axial load of 50 kN.

If a strain gage of gage factor 2.5 and resistance 120 _ is mounted on the bar in an axial direction., first find the change in resistance. Assuming this change in resistance is in positive direction, let us connect the strain gage to one branch of a wheatstone bridge (R1) with the other three legs having the same base resistance (R2 _ R3 _ R4 _ 120 _). Input voltage to the bridge is 12 V. What is the output voltage of the bridge in the strained state? 18. This is an example of a sensing operation during the process of work-handling in a robot manipulator. Strain gauges can be used to measure the force acting on the object while the object is gripped. Strain gauges are mounted on the fingers of a gripper. Strain gauges 2 and 3 are attached inside of the finger. Strain gauges 1 and 4 are attached to the outside of the finger. When the object is grasped, gripping force causes strain gauges 2 and 3 to stretch and 1 and 4 to compress. The resistance of the gauges 2 and 3 increase, while the resistance of gauges 1 and 4 decrease. Suppose the strain gauges are used as force-sensors, what is the bridge output when there is no gripping force? What is the output voltage for a gripping force that causes a strain of 3000 _m. (Let us assume the supply voltage to be 12V; strain gauges have unstrained resistance of 1000 _. Use the formula, .)

19. (a) What will be the change in resistance of a strain gauge, with a gauge factor of 2 and resistance of 100 _, if the gauge is subjected to a strain of 0.005 ? (b) An angular incremental encoder is used with a 80 mm radius tracking wheel. This is used to monitor linear displacement. The angular

¢R = 2Rnom

• strain encoder provides 128 pulses per one rotation. What will be the number of pulses for a linear movement of 250 mm

20. Strain is monitored in a cantilever beam using strain gauges of resistance 1 K_ , GF _ 2 and temperature Coefficient _ 10_5/°C at room temperature. it's mounted on beam and connected to the bridge circuit.

• Calculate the change in resistance of the gauge if the gauge is strained 0.1% (Use strain 5 .0011;

• Calculate the change in effective strain indicated when the room temperature increases by 10°C;

• Suggest a way of reducing this temperature effect.

21. A resistance transducer has a resistance of 250 _ and a gauge factor of 2.2. it's bonded to an object to detect movement. Determine the change in resistance of the strain gauge if it experiences a strain of due to the change in the size of the object. Also if the relationship between the change in the resistance and displacement is 0.05 _ per mm, determine the size of the object.

22. A strain gage bridge has a strain gage of resistance R = 200 _ and gage factor G = 1.9. R2, R3, and R4 are fixed resistors also rated at 200 _. The strain gage experiences a tensile strain of 400 microstrain due to the displacement of an object. Determine the change in resistance _R of the strain gage. If the input voltage is Vi volts then determine the change in output voltage _Vo UNITS 1Picofarad (pF) _ 10_12 f, 1 Nanofarad (nF) _ 10_9 f 2 A capacitance transducer consists of two plates of diameter 2 cm each, separated by an air gap of 0.25 mm. Find the displacement sensitivity 24. A capacitance transducer has two plates, with 12 cm^2 area and are apart by 0.12 cm. The plates are in vacuum. Given the permittivity of vacuum is , calculate the capacitance. What would happen to the capacitance if one of the plates were moved 0.12 cm further away from the other plate? 25. A transducer using the capacitance principle consists of two concentric cylindrical electrodes. The outer diameter of inner cylinder is 4 mm. The inner diameter of the outer electrode is 4.2 mm. The length of the electrode is 0.03 m. Calculate the change in capacitance if the inner electrode is moved through a distance of 1.5 mm.

26. A parallel plate Capacitance transducer uses plates of area 500 mm which are separated by a distance of 0.2 mm. (a) calculate the value of capacitance when the dielectric is air having a permitivity of 8.85 _ 10 F/m. (b) A linear displacement reduces the gap length to 0.18 mm. Calculate the change in capacitance. (c) Calculate the ratio of per unit change of capacitance to per unit change in displacement. (d) Suppose a mica sheet of .01 mm thick is inserted in the gap, Calculate the value of original capacitance and change in capacitance for the same displacement. The dielectric constant of mica is 8[C _ A/d].

27. A quartz PZT crystal having a thickness of 2 mm and voltage sensitivity of 0.055 Vm/N is subjected to a stress of 1.5 MN/sq.m. Calculate voltage output and charge sensitivity.

28. A ceramic pickup has a dimension of 5 mm _ 5 mm _ 1.25 mm. The force acting on it's 5 N. The charge sensitivity of the crystal is 150 PC/N, its permitivity 12.5 _ 10_9 F/m. If the modulus of elasticity of the crystal is 12 _ 106 N/m2, calculate the strain, the charge, and the capacitance.

29. A piezoelectric crystal has a dimension of 100 mm2. Its thickness is 1.25 mm. it's held between two electrodes for measuring the change of force across the crystal. Young's modulus of the crystal is 90 GN/m^2.

Charge sensitivity is 110 pC/N. Permittivity is (or) 1200. The connecting cable has a capacitance of 250 pF, while the oscilloscope for display has a capacitance of 40 pF. What is the resultant capacitance? 8.85 * 10-12 F/m 450 * 10-6

30. Piezoelectric crystal of 1 cm2area, 0.1 cm thick has been subjected to a force. Two metal electrodes measure the changes in the crystal. Young's modulus of the material _ 9 _ 1010 Pa. Charge sensitivity 2pC/N, Relative permitivity is 5; the applied force is 0.01 N

• Find the voltage across the electrodes.

• Find the change in crystal thickness

31. The output of an inductance type transducer (such as LVDT) is connected to a 5 V voltmeter. An out put of 2 mV appears across the terminals of the transducer when the core of the LVDT moves through a distance of 0.1 mm. Calculate the sensitivity of LVDT.

32. In a resistance temperature detector (RTD) using platinum and nickel, the temperature coefficient at 20°C is 0.004/°C and resistance R _ 106 _. Find the resistance at 25°C.

3 RTD of Problem 32 is used in a bridge circuit. If R1 _ R2 _ R3 _ 100 _, Supply voltage is 10 V.

Calculate the voltage the detector must resolve to define 1°C change in temperature.

System:

34. A steel mill has a production set up where metal sheets are rolled for desired thickness as they emerge from the production sequence. it's a continuous, real-time production and measurements have to be made on-line. Suggest a sensor that can do the job. The final output should be electrical.

35. Figure 35 shows a block diagram of an automotive cruise control system. This helps the driver in monitoring and controlling the speed.

Ill. 35 AUTOMOTIVE SPEED CONTROL SYSTEM:

Draw similar diagrams for the following applications by showing the modules of instrumentation system

• Automatic coffee maker for home use

• Motion of axes in a machine tool

36. A hospital is interested in developing an instrument to measure the force exerted by the human finger.

This instrument will be useful in the rehabilitation department. How will you approach the design of such an instrument? Identify the type of sensor; explain its principle with a possible sketch. How will you proceed with the data acquisition and display concept? 37. The automatic control system for the temperature of a bath of liquid consists of a reference voltage fed into a differential amplifier. This is connected to a relay, which then switches on or off the electrical power to a heater in the liquid. Negative feedback is provided by a measurement system, which feeds a voltage into the differential amplifier. Sketch a block diagram of the system and explain how the error signal is produced.

System:

38. Indicate True or False or the correct answer.

a. Condition monitoring means monitoring the condition of a machine when it's not running (T or F).

b. Eddy-current type of transducer produces an output proportional to velocity (T or F).

c. A common LVDT is

• A differential transformer

• A mechanical position-to-electrical transducer sensor

• Inductive electromechanical transducer

• All the above

d. A capacitance transducer has two plates of area 5 cm2 each, separated by an air gap of 1 mm thickness. Value of capacitance is 442 pF. (T or F).

e. Mechatronic Supervisory control system requires:

• A digital computer monitoring the system performance

• Individual controllers actually controlling each of the processes

• The controllers get the set point from the computer

• All of the above

• A supervisor in the loop

f. Which parameter the bonded strain gauge measures?

• Deformation

• Torque

• Force

• Pressure

• Stress

g. Which of the following parameters can a proximity sensor be used to measure?

• Speed of rotation of a shaft

• Closeness of an object

• Deformation of a metal piece

• Relative position of two linear motion surfaces

• Instantaneous position of a rotating shaft

h. Which of the following phenomenon is commonly used in industry to sense very small changes in the physical dimensions of a load (force) column?

• The proportionality between liquid level and pressure.

• The attenuation of nuclear radiation by solid materials.

• The variation of resistance of a wire as it's deformed.

• The sensitivity of hair to moisture.

• The principle that, if hydraulic flow-velocity is high, the corresponding pressure will be low, and vice versa.

i. Select the right answer: Rotameter is a

• Drag-force flow meter

• Variable-area flow meter

• Variable-head flow meter

• Rotating propeller-type flow meter

• Rotating speed indicator

j. Turbine flow meters are primarily used to measure the flow of fluids which are

• Corrosive

• Chunky

• Viscous

• Petrochemical

• For all liquids mentioned above

k. The type of electrical output should be expected from a digital shaft angle encoder?

• A series of digital pulses over a single pair of output wires.

• Several parallel wires, each one with a digital voltage level, which must be interpreted together to get the shaft angle.

• A variable resistance analog signal.

• A bipolar dc voltage.

l. Which of the following statements describe properties inherent in an open loop control system?

• Output has no effect on input.

• Inherently stable.

• Controller has no way of knowing if its command was executed.

• Controller does not care whether its command was executed.

• All of the statements above describe an open loop control system.

39. Make a table listing in one vertical column each of the following sensors: Pneumatic, LVDT, Eddy Current, Hall Effect. Then make four adjacent vertical columns, labeling them: Variable Measured, Principle of Operation, Advantages/ Disadvantages. Attempt to fill every blank space in the table.

40. Identify the sensor, signal conditioner, and display elements of a measurement system such as a mercury in-glass thermometer. Identify the input and output parameters

[omitted math content]

NEXT:

PREV: Fiber Optic Devices in Mechatronics

All related articles   Top of Page   Home