Universiti Malaysia Perlis

1. Universiti Malaysia Perlis ENT356 INSTRUMENTATION SYSTEM Lecture 10: Force and Torque Measurement & Strain and Stress Measurement Sem 2, 2010/2011

2. PRESSURE

3. DEFINITION • Pressure is an effect which occurs when a force is applied on a surface (What kind of surface????). • Pressure is the amount of force acting on a unit area. • Example: • Consider a measurement of pressure of the wall of a vessel containing a perfect gas. As a molecule with some amount of kinetic energy collides with the solid boundary, it will rebound off in different direction. • From Newton’s second law, the change in linear momentum produces an equal but opposite force on the boundary. • The net effects of the collision yields the pressure sensed at boundary surface.

4. A pressure scale can be related to molecular activity, since a lack of any molecular activity must form the limit of absolute zero pressure. • A pure vacuum, which contains no molecules, would form a primary standard for absolute zero pressure. Relative pressure scales

5. The pressure under atmospheric condition is defined as 1.01320 × 105 Pa absolute, which equivalent to: • 101.32 kPa absolute • 1 atm absolute • 14.696 lb/in.2 absolute (psia) • 1.013 bar absolute • The pressure unit: • Pa • N/m2 • kgm-1s-1 • Psi • bar • any other units??

6. Observe: • The gauge pressure scale is measured relative to some absolute reference pressure. • where pois the reference pressure. • Hence, a differential pressure, such as p1 – p2 is a relative pressure, and cannot be written as absolute pressure. • A derivation of absolute pressure from hydrostatic fluid:

7. From hydrostatic, the pressure • at any depth: • Rearranged; • ,where  is the fluid • specific weight, • The standard is based on Mercury with density of 0.0135951 kg/cm3 at 0˚C and water at 0.000998207 kg/cm3 at 20˚C

8. PRESSURE REFERENCE INSTRUMENTS • Why is it required? • Basic reference instruments: • (a) McLeod Gauge • (b) Barometer • (c) Manometer • (d) Deadweight Testers

9. ~~ Question 1 of Assignment 2 leaked!! ~~

10. PRESSURE TRANSDUCERS/SENSORS Recall back lecture 5!

11. Pressure transducers either convert the pressure into mechanical movement or into an electrical output. •  This is actually a hybrid. • The primary sensor usually an elastic element that deforms/deflects under pressure.

12. A secondary sensing element could be employed to converts the elastic element deflection into measurable signal (electrical or mechanical pointer). • Factor that causes Pressure measurement errors: • Resolution • Zero shift error • Linearity error • Sensitivity error • Hysteresis • Drift caused by changes of temp.

13. Bourdon Tube • The Bourdon tube1 is a curve metal tube having an elliptical cross section that mechanically deforms under pressure. • One tube end is held fixed, and the input pressure applied internally. • A pressure different between the outside and inside of the tube will bring about the tube deformation and deflection of the tube free end. • The magnitude of deflection is proportional to the magnitude of pressure different. • Typical Bourdon tube design is shown next. 1Eugene Bourdon (1808-1884), French Inventor, patented the Bourdon tube on 1849

15. The mechanical dial gauge is commonly used pressure transducer. • Secondary element is the mechanical linkage that converts the tube displacement into a rotation of a pointer. • The range is normally specified by its manufacturer. • Various gauges exists typically within the range of 104 - 109 Pa (0.1 – 100,000 psi). • Instrument uncertainties as low as 0.1% is best, but 0.5% - 2% are more common.

16. Flash animation of Bourdon tube, courtesy of MATEC Online

17. Bellows and Capsule

18. A bellow sensing element is a thin-walled, flexible metal tube formed into deep convolutions and scaled at one end. • One end is held fixed and pressure is applied internally. • The difference between the internal and external pressures will cause the bellow to change length. • A capsule sensing element is similar to bellow but tending to have wider diameter and shorter length. • A mechanical linkage is normally used to convert the translational displacement of the bellows or capsules into a measurable form. • Following Figure shows secondary transducer, which is the sliding arm potentiometric.

20. Bellow-resistance pressure sensor • The pressure is proportionate to the resistivity. • The resistance change is detected by displacement of sliding contact in the resistance element. Bellows Calibrated spring Sliding contact Resistance Output Signal

21. Bellow-inductance pressure sensor • The pressure is proportionate to the inductance change which is detected from the displacement of the core in the wire coil. • The core movement will produce AC signal output which will give the value and direction of inductance. • LVDT (linear variable differential transformer) demodulator is used to convert the AC output to DC. Bellows Core Output Signal

22. Example • A field engineer finds a desirable potentiometric bellows gauge with a stated range of 0-700 kPa in a catalog. It uses a sliding contact potentiometer having a terminal resistance of 50 Ω – 10k Ω over full range. • What is the output voltage at pressure equal to 0 kPa, 350 kPa, and 700 kPa if the excitation voltage is 5 V? • What is the sensitivity of the bellow gauge?

23. Diaphragms • A yet so far effective primary sensing element. • It is a thin elastic circular plate supported by about its circumferences. • It’s action is somewhat similar to trampoline, and pressure differential across the surface acts to deform it. • The magnitude of the deformation is proportional to the pressure differences. • Two design of diaphragms (refer figure in slide #12): • Membrane • Corrugated

24. Membranes are made of metal or non-metallic materials, such as plastic or neoprene. • Corrugated diaphragm contains a number of corrugation that purposes to increase diaphragm stiffness and to increase diaphragm effective surface area. • Diaphragm sensing suitable for both static and dynamic pressure measurement. • They have good linearity and resolution over their useful range.

25. An advantage of diaphragm sensor compared to other pressure transducer •  Because of its low mass and relative stiffness of the thin diaphragm • thus, give the sensor a very high natural frequency • and small damping ratio. • Therefore, a wide frequency response is obtained with a very short 90% rise and settling time. • Estimated natural frequency of circular diaphragm:

26. , where Em = bulk modulus (psi or N/m2) • t = thickness (in. or m) • r = radius (in. or m) • ρ= material density (lb/in.3 or kg/m3) • vp = Poisson’s ratio for the diaphragm material with gc = 386 lbm in./lb s2 = 1 kg m/Ns2.

27. The maximum elastic deflection of a uniformly loaded, circular diaphragm supported about its circumference occurs at its center can be estimated by; • Provided that the deflection does not exceed one-third of the diaphragm thickness. • Selection of suitable diaphragm should consider as not to exceed this maximum deflection over the anticipated operating range.

28. Translating the primary displacement from the primary sensing element (diaphragm) into measurable signal requires special attention. • Some of the methods are: • (A) Strain gauge elements • (B) Capacitance elements • (C) Piezoelectric Crystal elements

29. (A) Strain gauge elements

30. (A) Strain gauge elements • Again, recall back from lecture 5, the strain gauge. • The strain gauge is patched onto the diaphragm surface. • As it is displaced, the strain is induced thus the resistance is measured from the Wheatstone bridge. • Strain gauge resistance is reasonably linear over a wide range of strain and can be directly related to the diaphragm sensed pressure.

31. (B) Capacitive elements

32. (B) Capacitive elements • When a fixed metal plates are places directly above/below a metallic diaphragm, a capacitor is formed. • The capacitance, C developed between the plates separated by a distance, t is determined by; • ,where c = proportionality constant, given by 0.225 (when A and t is in. unit), or 0.0885 (when A and t is in cm unit) • ε = dielectric constant of the material • A= overlapping area of the two plates • Deformation of diaphragm changes the average gap separation. • In the circuit shown, the measured voltage is linear with developed capacitance;

33. (B) Capacitive elements • The pressure is proportionate to the capacitance change at the output through dielectric change. • Pressure from the sensor element causes the diaphragm to move towards the plate and produces dielectric change.

34. (C) Piezo-electric elements

35. (C) Piezo-electric elements • Piezoelectric crystal form effective secondary elements for dynamic pressure measurement. • A preloaded crystal is mounted to the diagram sensor. • Under the action of compression, tension, shear, a piezoelectric will deform and develop a surface charge, q • A pressure acts to the crystal axis, and changes the crystal thickness, t by a small amount of Δt . Thus the charge is developed; • where p is the pressure acting over the electrode area A • and Kqis the crystal sensitivity, a material sensitivity.

36. (C) Piezo-electric elements • The voltage developed across the electrodes is given as; • where C is the capacitance of the crystal-electrode combination • The capacitance can be obtained from; • where KE is the voltage sensitivity of the transducer. • Quarts is commonly used materials, with properties as follow: • Kq = 2.2 x 10-9 C/N • KE = 0.055 V m/N • Advantages; • This sensor does not require any voltage supply. • This sensor is suitable for fast changing pressure measurement.

37. Self Exercise • Find the natural frequency of a 1mm thick, 6-mm-diameter steel diaphragm to be used for high-frequency pressure measurements. What would be the maximum operating pressure difference that could be applied? What is the effect of a larger diameter for this application? • A diaphragm pressure transducer has a water-cooled sensor for high-temperature environments. Its manufacturer claims it to have a rise time of 10ms, a ringing frequency of 200 Hz, and damping ratio of 0.8. • Describe a test plan to verify the manufacturer’s specification. • Would this transducer have a suitable frequency response to measure the pressure variations in a sensitive industry i.e semiconductor industry? Justify your answer.

38. STRAIN & STRESS

39. Quiz #1 Remember back lecture 5 on Introduction to Sensors and Transducer. Answer the following in 10 min: Draw the shape of a strain gauge. How many strain gauge can be applied for a measurement at one time? A strain gauge is glued to a structure. It has a gauge factor of 2.1 and a resistance of 120.2 Ω. The structure is stressed and the resistance changes to 120.25 Ω. Calculate the strain and convert this into stress. Take E = 205 Gpa

40. Recall back Lecture 5!!

41. Example: Strain Gauge Pressure Sensor

42. Resistance Strain Gauges • The resistance of a strain gauge changes when it deformed. • The amount that the resistance changes depends on how the gauge is deformed, the materials it is made of, and the design of the gauge. • Gauges can be made small for good resolution, and with a low mass to provide a high-frequency response. • With some ingenuity, ambient effects can be minimized, or eliminated. • The resistance strain gauge also forms the basis for variety other transducers, such as load cells, pressure transducers, and torque maters.

43. Resistance Strain Gauges • The measurement of the small displacements that occur in a material or object under mechanical load, determines the strain. • Strain can be measured in two ways: • Observing the change of distance (resistance) of marks on the material surface • Advance using optical holography • The ideal strain transducers characteristics: • Have good spatial resolution • Be unaffected by changes in ambient condition • Have high-frequency response for dynamic strain measurement. • Strain sensors that closely meets these characteristic, is the bonded resistance strain gauge!

44. Resistance Strain Gauges • Let us appraise the derivation of the strain gauges. • Consider a conductor having a uniform cross-sectional area, Ac and a length, L, made of a material having a resistivity ρe. • For this electrical conductor, the resistance, R is given as • If the conductor is subjected to normal stress, Ac and L will change, resulting a change in the R, which total differential are;

45. Resistance Strain Gauges • The earlier derivation could be expressed in Poisson’s ratio, which is; • Hence, we have proved that the changes in resistance is causes by: • change of geometries • change of value of resistivity

46. Example: Determine the total resistance of a copper wire having a diameter of 1 mm and a length of 5 cm. The resistivity of copper is 1.7 x 10-8Ωm (answ: 1.08 x 10-3Ω) A very common material for the construction of strain gauges is the alloy constantan (55% copper with 45% nickel), having resistivity of 49 x 10-8Ωm. A typical strain gauge might have a resistance of 120 Ω. What length of constantan wire of diameter 0.025 mm would yield a resistance of 120 Ω? (answ: 0.12 m)  what is the effect of single strip conductor????

47. Resistance Strain Gauges • Single straight conductor is definitely not practical. Imagine 12cm long????? What if the materials to be strain-measured only have 10cm long???? • Thus, a simple solution is made, to bend the wire conductor so that several lengths of wire are oriented along the axis of the strain gauge as Figure below;

48. Resistance Strain Gauges • A typical metallic-foil bonded strain gauge   • Consists of a metallic foil pattern that is formed similarly to Printed Circuit Board (PCB) • The photoetched metallic foil pattern is mounted on a plastic backing material. • The gauge lengthis an important specification for a particular application. • Adhesive is used in the bonding process.

49. Resistance Strain Gauges • Fundamental aspects common to all bonded resistance gauge; • Strain gauge backing function: electrically isolates the metallic gauge from the test specimen, and transmit ideally the applied strain to the sensor. • Adhesive serves as a mechanical and thermal coupling between the metallic gauge and the test specimen • Example of industrial adhesives uses with strain gauge: • epoxies • cellulose nitrate cement • ceramic-based cement

50. Resistance Strain Gauges – Gauge Factor • Gauge factor is empirically determined parameter, to express the change of resistance of a strain gauge. • For a particular strain gauge, it is normally supplied by the manufacturer. • It is expressed by; • From the equation, it is somewhat related to Poisson’s ratio earlier. • For metallic strain gauge, Poisson Ratio is normally ~ 0.3, thus the resulting Gauge Factor is typically ~ 2