1. Types Of Transducers Resistive Position Transducer: The principle of the resistive position transducer is that the physical variable under measurement causes a resistance change in the sensing element.

2. Resistive Position Transducer(cont’d) A common requirement in industrial measurement and control work is to be able to sense the position of an object, or the distance it has moved. fig.(1) Resistive positive transducer, or displacement transducer.

3. Resistive Position Transducer(cont’d) One type of displacement transducer uses a resistance element with a sliding contact or wiper linked to the object being monitored. Thus, the resistance between the slider and one end of the resistance element depends on the position of the object. Figure (1-a) shows the construction of this type of transducer. Figure b shows a typical method of use. The output voltage depends on the wiper position and therefore is a function of the shaft position. This voltage may be applied to a voltmeter calibrated in inches for visual display.

4. Resistive Position Transducer(cont’d) Typical commercial units provide a choice of maximum shaft strokes from an inch or less to 5 feet or more. Deviation from linearity of the resistance versus-distance specification can be as low as 0.1% to 1.0%. Consider Fig. (1-b). If the circuit is unloaded, the output voltage V 0 is a certain fraction of V T, depending on the position of the wiper:

5. Resistive Position Transducer(cont’d) In its application to resistive position sensors, this equation shows that the output voltage is directly proportional to the position of the wiper, if the resistance of the transducer is distributed uniformly along the length of travel of the wiper, that is, if the element is perfectly linear.

6. EXAMPLE 1 A displacement transducer with a shaft stroke of 3.0 in. is applied in the circuit of Fig. The total resistance of the potentiometer is 5 k, and the applied voltage V T =5.0V. When the wiper is 0.9 in. from B, what is the value of the output voltage V 0 ?

7. Solution

8. EXAMPLE 2 A resistive position transducer with a resistance of 5000 and a shaft stroke of 5.0 in. is used in the arrangement of Fig. (4). Potentiometer R 3 R 4 is also 5000, and V T = 5.0 V. The initial position to be used as a reference point is such that R 1 =R 2 (i.e.. the shaft is at midstroke). At the start of the test, potentiometer R 3 R 4 is adjusted so that the bridge is balanced (V E =0). Assuming that the object being monitored will move a maximum distance of 0.5 in. toward A, what will the new value of V E be?

9. Solution If the wiper moves 0.5 in. toward A from midstroke, it will be 3.0 in. from B.

10. Resistive Position Transducer(cont’d) This answer is a measure of the distance and direction that the object has traveled. Fig (2) Basic voltage divider and resistance bridge circuits

11. 2-Strain Gauge Transducers The strain gauge is an example of a passive transducer the; uses electrical resistance variation in wires to sense the strain produced by a force on the wires. It is a very versatile detector and transducer for measuring weight pressure mechanical force, or displacement.

12. Strain Gauge Transducers(cont’d) The construction of a bonded strain gauge Fig (3) shows a fine- wire element looped back and forth on a mounting plate, which is usually cemented to the member undergoing stress. A tensile stress tens to elongate the wire and thereby increase its length and decrease its cross-sectional area. The combined effect is an increase in resistance as seen from Eq. (1) (1) Where = the specific resistance of the conductor material in ohm L = the length of the conductor in meters A = the area of the conductor in square meters

13. Strain Gauge Transducers(cont’d) Fig (3) Resistive strain gauges; wire construction

14. Strain Gauge Transducers(cont’d) As a consequence of strain two physical qualities are of particular interest: (1) the change in gauge resistance and (2) the change in length. The relationship between these two variables expressed as a ratio is called the gauge factor. K. Expressed mathematically as (2) Where K = the gauge factor R = the initial resistance in ohms (without strain) = the change in initial resistance in ohms L = the initial length in meters (without strain) = the change in initial length in meters

15. Strain Gauge Transducers(cont’d) Note that the term IL in the denominator is the same as the unit strain G. Therefore. Eq. (2) can be written as (3) Robert Hooke pointed out in the seventeenth century that for many common materials there is a constant, ratio between stress and strain.

16. Strain Gauge Transducers(cont’d) Stress is defined as the internal force per unit area. The stress equation is (4) Where S = the stress in kilograms per Square meter F= the force in kilograms A= the area in square meters

17. Strain Gauge Transducers(cont’d) The constant of proportionality between stress and strain for a linear stress-strain curve is known as the modulus of elasticity of the material. E or Young's modulus. Hooke's law is written as (5) Where E=Young's modulus in kilograms per square meter S= the stress in kilograms per square meter G = the strain (no units)

18. Strain Gauge Transducers(cont’d) For strain gauge applications, a' high degree of sensitivity is very desirable. A high gauge factor means a relatively large resistance change for a given strain. Such a change is more easily measured than a small resistance change. Relatively small changes in strain can be sensed.

19. Strain Gauge Transducers(cont’d) EXAMPLE 3 A resistant strain gauge with a gauge factor of 2 is fastened to a steel member, which is subjected to a strain of 1 X 10 -6. If the original resistance value of the gauge is 130. Calculate the change in resistance.

20. Solution

21. Example 4 A round steel bar, 0.02 m in diameter and 0.40 m in length, is subjected to a tensile force of 33.000 kg, where E=2x10 10 kg/m 2. Calculate the elonga­tion, L, in meters. Solution:

22. Strain Gauge Transducers(cont’d) Semiconductor strain gauges are often used in high-output transducers as load cells. These gauges are extremely sensitive, with gauge factors from 50 to 200. They are however, affected by temperature fluctuations and often behave in a nonlinear manner. The strain gauge is generally used as one arm of a bridge. The simple arrangement shown in Fig. (2-a) can be employed when temperature varia­tions are not sufficient to affect accuracy significantly, or in applications for which great accuracy is not required.

23. Strain Gauge Transducers(cont’d) The strain gauge is generally used as one arm of a bridge. The simple arrangement shown in Fig. (4-a) can be employed when temperature varia­tions are not sufficient to affect accuracy significantly, or in applications for which great accuracy is not required.

24. Strain Gauge Transducers(cont’d) However, since gauge resistance is affected by temperature, any change of temperature will cause a change in the bridge balance conditions. This effect can cause an error in the strain measurement. Thus, when temperature variation is significant, or when un­usual accuracy is required an arrangement such as that illustrated in Fig. (4) may be used.

25. Strain Gauge Transducers(cont’d) Here two gauges of the same type are mounted on the item being tested close enough together that both are subjected to the same temperature. Consequently, the temperature will cause the same change of resistance in the two, and the bridge balance will not be affected by the temperature. However one of the two gauges is mounted so that its sensitive direction is at right Angles to the direction of the strain.

26. Strain Gauge Transducers(cont’d) The resistance of this dummy gauge is not affected by the deformation of the material. Therefore, it acts like a passive resistance (such as R 3 of Fig. 4-b) with regard to the strain measurement. Since only one gauge responds to the strain, the strain causes bridge unbalance just as in the case of the single gauge. Fig (4) Basic gauge bridge circuits.