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Sensors and Measurements Penderia & Pengukuran ENT 164 Piezoelectric Sensors

Sensors and Measurements Penderia & Pengukuran ENT 164 Piezoelectric Sensors. Hema C.R . School of Mechatronics Engineering Northern Malaysia University College of Engineering Perlis , Malaysia Contact no: 04 9798442 Email: hema@kukum.edu.my. General Structure of Measurement System.

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Sensors and Measurements Penderia & Pengukuran ENT 164 Piezoelectric Sensors

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  1. Sensors and MeasurementsPenderia & PengukuranENT 164Piezoelectric Sensors Hema C.R. School of Mechatronics Engineering Northern Malaysia University College of Engineering Perlis , Malaysia Contact no: 04 9798442 Email: hema@kukum.edu.my

  2. General Structure of Measurement System SIGNAL CONDITIONING ELEMENT SIGNAL PROCESSING ELEMENT SENSING ELEMENT INPUT TRUE VALUE DATA PRESENTATION ELEMENT Piezo-electric Hall effect OUTPUT MEASURED VALUE

  3. Sensing Elements silicon • Resistive • temperature & strain • Capacitive • Pressure, level ,strain & humidity • Inductive • strain • Thermo Electric • temperature • Piezoelectric • vibration , force & acceleration • Electro Chemical • gas composition & ionic concentration • Hall Effect Sensor • Magnetic field pressure temperature O2 Flow

  4. Piezoelectric Sensing Elements

  5. Further Reading : Crystal classes & Piezoelectric crystal classes • The word piezo is derived from the Greek piezein, which means to squeeze or press. • The effect known as piezoelectricity was discovered by brothers Pierre and Jacques Curie in 1880. • Crystals which acquire a charge when compressed, twisted or distorted are said to be piezoelectric. • Piezoelectric materials also show the opposite effect, called converse piezoelectricity, where the application of an electrical field creates mechanical deformation in the crystal.

  6. Isotropic materials have same physical properties in all directions Crystals • Crystals are naturally occurring material that can be induced to resonate or vibrate at an exact frequency. • Crystals are anisotropic materials • physical properties depend on the direction • Quartz, a piezoelectric crystal that provides excellent mechanical and electrical stability, acquires a charge when compressed, twisted, or distorted. • Quartz crystals are used as active elements in oscillators A Quartz "Crystal"

  7. Piezoelectric Materials • Quartz (SiO2) • Barium Titanate (BaTiO3) • Gallium Orthophosphate (GaPO4), • Polymer materials like rubber, wool, wood and silk exhibit piezoelectricity to some extent Applications • Microphones, guitars, sonar, motors microbalances, clocks and vibration sensors.

  8. Piezoelectric Effect

  9. When force is applied to a crystal , the crystal atoms are displaced from their normal positions • Displacement x is proportional to applied force F (1) where k is the stiffness in the order of • The displacement can be summarised using a transfer function

  10. Transfer Function of an Element When input signal of an element is changed suddenly the output signal will not change instantaneously. The way in which an element responds to sudden input changes are termed its dynamic characteristics, which can be conveniently summarised using a transfer function Element Transfer Function: Transfer function of an output signal is the product of element transfer function and transfer function of the input signal

  11. kx Spring F Mass m Damper x x=0 Transfer Function Of Second Order Elements Sensor converts force into displacement , diagram shows the conceptual model which has a mass m kg, a spring ofstiffness k N/m and a damper constant Ns/m. The system is initially at rest at time t =0- so that the initial velocity and the initial acceleration . The initial input force F(0-) is balanced by the spring force at the initial displacement x(0-) Model of an Elastic force sensor an analogous system to a piezo force sensor

  12. (i) If input force is suddenly increased at t = 0, then element is no longer in a steady state and its dynamic behavior is described by Newton ‘s second law resultant force = mass x acceleration and Defining and to be deviations in F and x (ii)

  13. (iii) The differential equation now becomes Which using equation (i) reduces to (iv) Second-order Linear Differential Equation

  14. If we define Undamped natural frequency (xi ) rad /s and Damping ratio (v) then Eqn.(iv) can be expressed in standard form (vi) Second-order Linear Differential Equation

  15. Laplace Transform of Time functions f(t) To find transfer function of the element we use Laplace transform of equation (vi) (vii) Since and Equation (vii) reduces to

  16. (viii) Thus Where 1/k =steady-state sensitivity K (ix) Transfer Function for a second–order element

  17. Transfer Function of a Piezoelectric Element Further Reading : Page 56 - Bentley • Using transfer function for a second order element • xand F can be represented by the second order transfer function • Where natural frequency is large = 10 to 100 kHz and damping ratio = 0.01 (2)

  18. Direct Piezoelectric Effect This deformation of crystal lattice results in crystal acquiring a charge q,proportional tox q = Kx(3) From equation (1) and (3) we get (4) where is the charge sensitivity to force

  19. Inverse Piezoelectric Effect • A piezoelectric crystal gives a direct electrical output, proportional to applied force, so that a secondary displacement sensor is not required. • Piezoelectric crystals also produce an inverse effect where an voltage applied to the crystal causes a mechanical displacement. (5) inverse effect is used in ultrasonic transmitters is identical with

  20. t Piezoelectric crystal Metal Plate Permittivity of free space (vacuum) Relative permittivity or dielectric constant of the insulating material (here the piezo ) A Area of plate Further Reading : Page 160 - Bentley Measuring ‘q’ • Metal electrodes are deposited on opposite faces of the crystal to form a capacitor to measure the charge q • Capacitance of the parallel plate capacitor formed (6)

  21. Further Reading : Page 82 - Bentley The crystal can be represented as charge generator q in parallel with a capacitance or a Norton equivalent circuit consisting of current source in parallel with . Magnitude of is (7)

  22. Further Reading: http://en.wikipedia.org/wiki/Laplace_transform#Formal_definition transfer function form of (8) whered/dtis replaced by the Laplaceoperators For steady forceF, Fandxare constant with time Such that dx/dtandare zero.

  23. Piezoelectric Force Measurement System

  24. Capacitive Cable Piezoelectric Crystal Recorder Circuit of a force measurement system Consider a piezoelectric crystal connected to a recorder where is a pure resistive load is pure capacitance of the cable is the recorder voltage Figure 1. Piezoelectric Force measurement system

  25. Further Reading : Page 84 - Bentley Transfer function relating to and is (9) Overall system transfer function relating recorder voltage to input force is (10)

  26. Transfer Function for basic Piezoelectric force measurement system From equation (2),(8) and (9) we get where (11) (Tau )

  27. Disadvantages of the basic piezoelectric system 1.Steady state sensitivity is equal to . Thus the system sensitivity depends on the cable capacitance i.e. length and type of cable. 2.The dynamic part of the system transfer function is (ignoring recorder dynamics) (12) Thesecond term is characteristic of all elastic elements and cannot be avoided , however it causes no problem if the highest signal frequency is well below (Tau )

  28. Capacitive Cable Piezoelectric Crystal Recorder The first term indicates that system cannot be used for measuring d.c. and slow varying forces. Illustration Consider a frequency response characteristics plot for and arg of a typical measurement system Figure 1. Piezoelectric Force measurement system

  29. (13) Amplitude Ratio Phase difference arg Figure 2: Approximate Frequency Response Characteristics Piezoelectric Measurement System with charge amplifier

  30. The term causes a low frequency roll-off so that at and system cannot be used for frequencies much below These disadvantages can be overcome by introducing a charge amplifier into the system as shown in Figure 2

  31. This system gives an output proportional to i.e. an output proportional to charge q . Since the system gives a non zero output for steady force input. From Figure 3 we Have and charge on feedback capacitor is For an ideal operational amplifier we have and In this case we have and so that (14) (15) (16)

  32. (17) Since the potential drop across and is zero From equation and we have From equation , and the overall transfer function for force measurement system is (16) (17) (18) Transfer Characteristic Of Ideal Charge Amplifier (18) (3) (2) (19) Transfer Function for Piezoelectric system with Ideal Charge Amplifier

  33. The steady state sensitivity is now i.e. it depends only on the capacitance of the charge amplifier and is independent of transducer and cable capacitance Common Piezoelectric materials Quartz Lead zirconium titanate (PZT) Barium titanate (BaTi2O3) PolyVinylidine DiFluoride (PVDT)

  34. Piezoresistive Sensing Elements

  35. Gauge factor of Strain gauge v is Poisson’s Ratio Further Reading : Page 158 - Bentley Piezoresistivity is defined as the change in resistivity of a material with applied mechanical strain and is represented by the term in the equation (20) Silicon doped with small amounts of n type or p type materials exhibits a large piezoresistive effect and is used to manufacture strain gauges. (20)

  36. Poisson’s Ratio When a sample of material is stretched in one direction, it tends to get thinner in the other two directions. Poisson's ratio (v) is a measure of this tendency. It is defined as the ratio of the strain in the direction of the applied load to the strain normal to the load. For a perfectly incompressible material, the Poisson's ratio would be exactly 0.5. Most practical engineering materials have v between 0.0 and 0.5..

  37. Reference • ‘Principles of Measurement Systems’ by John P Bentley. [Text book] • http://www.resonancepub.com/piezoele.htm • http://hyperphysics.phy-astr.gsu.edu/hbase/solids/piezo.html • ‘Piezoelectric Transducers and Applications’ by Antonio Arnau

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