Displacement and Strain Measurement.pptx

Displacement and Strain Measurement(Mechanical Measurement and Metrology)

1. Dr. Ramesh R. Rajguru Mechanical Measurements and Metrology (Course Code: DJMEC 403 )

2. Module:02 Displacement Measurement: Transducers for displacement, displacement measurement, potentiometer , LVDT, Capacitance Types, Digital Transducers (optical encoder), Nozzle, Flapper Transducer Strain Measurement: Theory of Strain Gauges, gauge factor, temperature Compensation, Bridge circuit, orientation of strain gauges for force and torque, Strain gauge-based load cells and torque sensors

3. Linear Variable Differential Transformer(LVDT): An LVDT is a type of electrical transformer that is used for measuring linear displacement. Figure shows a picture of a standard LVDT. LVDTs are commonly used for position feedback in servomechanisms, and for automated measurement in machine tools and many other industrial and scientific applications

4. Strain Measurement : Strain Gauge: Strain gauge is device whose electrical resistance varies in proportion to the amount of strain in the device. The most widely used gauge is the bonded metallic strain gauge. Gauge factor is defined as the ratio of fractional change in electrical resistance to the fractional change in length (strain):

5. Speed Measurement

6. Torque Measurement Apparatus

7. Collision Avoidance

8. The automated guided vehicle (AGV) system

9. Quantity to be Measured Mechanical Transducer Type of Output Signal (Mechanical) Temperature Bimetallic Strip Displacement and Force Fluid Expansion Displacement and Force Pressure Ring Balance Manometer Displacement Metallic Diaphragms Displacement and Strain Capsules and Bellows Displacement Membranes Displacement Force Spring Balance Displacement and Strain Hydraulic Load Cell Pressure Column Load Cell Displacement and Strain Torque Dynamometer Force and Strain Gyroscope Displacement Spiral Springs Displacement Torsion Bar Displacement and Strain Flow Rate Flow Obstruction Element Strain and Pressure Pitot Tube Pressure Liquid Level Manometer Displacement Float Elements Displacement, Force and Strain Mechanical Transducers

10. Transducer Transducers are generally defined as devices that transform values of physical quantities in the form of input signals into corresponding electrical output signals. The physical quantity may be heat, intensity of light, flow rate, etc . Generally speaking, a Transducer is a device that converts one form of energy into another by the principle of Transduction. Usually, a signal in one form of energy is converted to a signal in another form by a Transducer.

11. Sensing or detecting element: The function of this element is to respond to a physical phenomenon or a change in the physical phenomenon. Hence it is termed a primary transducer. Transduction element: The function of a transduction element is to transform the output obtained by the sensing element to an analogous electrical output. Hence it is termed a secondary transducer.

12. Transducer Example: Mechanical transducer Bourdon tube, Operation pressure to displacement . Strain Gauge (Sensor) and Wheatstone Bridge (Signal Conditioning Unit)

13. Transducer Example: Mechanical transducer Bourdon tube, Operation pressure to displacement . The bourdon tube, which acts as a detecting element, senses pressure and gives the output in the form of displacement. This displacement is further used to move the core of LVDT, and a voltage is obtained as output. Thus, the pressure is converted into displacement, which in turn is transduced into an analogous voltage signal. Thus, the bourdon tube acts as the primary sensing element and the LVDT as the secondary transducer.

14. Transducer Example: In the another example, consider a Strain Gauge as the Sensor. Any changes in the strain will reflect as changes in its resistance. Now, in order to convert this change in resistance into equivalent voltages, you can use a simple Wheatstone Bridge circuit, which acts as the Signal Conditioning Unit . The combination of Strain Gauge (Sensor) and Wheatstone Bridge (Signal Conditioning Unit) is Known as a Transducer.

15. Transducer Sensors and Actuators: Sensors, devices that responds to a physical quantity with a signal. Actuators, devices that respond to signals with physical movement. For example, a Microphone is a Sensor and a Loudspeaker is an Actuator.

16. For example, a Microphone is a Sensor, which converts sound waves into electrical signals and a Loudspeaker is an Actuator, which converts electrical signals into audio signals. Both Microphone and Loudspeaker are Transducers in the sense that a microphone converts sound energy into electrical energy and a loud speaker converts electrical energy into sound energy.

17. Classification of Transducers Input Transducers measure non-electrical quantities and convert them into electrical quantities . Output Transducers on the other hand, work in the opposite way i.e. their input signals are electrical and their output signals are non-electrical or physical like force, displacement, torque, pressure etc. Based on input and output

18. Classification of Transducers Depending on the principle of operation, transducers can also be classified into mechanical, thermal, electrical, etc. Also the classification of transducers based on the following three ways: Physical Effect Physical Quantity Source of Energy

19. Classification of Transducers Classification based on Physical Effect (to convert the physical quantity to electrical quantity): Variation in Resistance Variation in Inductance Variation in Capacitance and Piezoelectric Effect An example, is the change in resistance (physical quantity) of a copper element in proportion to the change in temperature.

20. Classification of Transducers Classification based on Physical Quantity: Temperature Transducer – Thermocouple Pressure Transducer – Bourdon Gauge Displacement Transducer – LVDT (Linear Variable Differential Transformer) Level Transducer – Torque Tube Flow Transducer – Flow Meter Force Transducer – Dynamometer For example, a Pressure Transducer is a transducer that converts pressure into electrical signal.

21. Classification of Transducers Classification based on Source of Energy: Active Transducers Passive Transducers E xample: 1) a Strain Gauge is an Active Transducer. 2) a Thermocouple is a passive transducer

22. Applications of Transducers Electromechanical: Accelerometers Pressure Sensors Galvanometers LVDT Load Cells Potentiometers Electromagnetic: Antennas Hall-Effect Sensors Disk Read and Write Heads Magnetic Cartridges Thermoelectric: Thermistors Thermocouples RTD (Resistance Temperature Detectors) Electrochemical: Hydrogen Sensors Oxygen Sensors pH Meters

23. Displacement Transducer A displacement transducer is an electrical transducer used in measuring linear position . A Displacement Transducer is an electromechanical device used to convert mechanical motion or vibrations, specifically rectilinear motion, into a variable electrical current, voltage or electric signals, and the reverse. Precision manufactured displacement transducers are mounted on most modern product lines for automatic gaging in sorting, “go-no go” applications, and quality operations.

24. Linear Variable Differential Transformer (LVDT)

25. Linear Variable Differential Transformer (LVDT) LVDT full form is Linear Variable Differential Transformer. As the name suggests, many people get confused that it is a Transformer. But actually, it is a Transducer not a Transformer. Because its working principle is same as Transformer (i.e. Mutual Induction Principle) and. Also the output across its secondary coil is in the form of differential voltage, that’s why it is named as Linear Variable Differential Transformer (LVDT).

26. Linear Variable Differential Transformer (LVDT) Linear: The cores freedom of motion is straight line. Variable: The core is free to move between the windings. Differential: The way of windings are connected and output of this device will be the difference between the voltage of the two secondary windings. Transformer : Because its working principle is same as Transformer (i.e. Mutual Induction Principle) Linear Variable Differential Transformer (LVDT) is an Electromechanical type Inductive Transducer that converts rectilinear displacement into the AC Electrical Signal.

27. LVDT: Signal conditioning and Manipulation(Inside sensor housing) Since LVDT is a secondary transducer, hence physical quantities such as Force, Weight, Tension, Pressure, etc are first converted into displacement by a primary transducer and then LVDT is used to measure it in terms of the corresponding Electrical signal.

28. LVDT: Electromechanical Transducer Passive Inductive

29. LVDT is placed inside the stainless steel housing because it will provide electrostatic and electromagnetic shielding. LVDT Construction

30. LVDT Construction

31. Linear Variable Differential Transformer (LVDT) LVDT working principle : The working principle of LVDT is based on the mutual induction principle. When AC excitation of 5-15 V at a frequency of 50-400Hz is applied to the primary winding, then a magnetic field is produced. E0 = E1 – E2

32. Case 1: When the core moves towards S1 (Max Left). Case 2: When the core is at Null position. Case 3: When the core moves towards S2 (Max Right).

33. Case 1 .: Null Position

34. Case 2: When the core moves towards S1 (Max Left).

35. Case 3: When the core moves towards S2 (Max Right).

36. Linear Variable Differential Transformer (LVDT) If the output voltage E0 is positive then this means an object is moving towards the Left from the Null position . If the output voltage E0 is negative then this means the object is moving towards the Right of the Null position. The Graph of variation of output with respect to its position is shown in the below figure.

37. Linear Variable Differential Transformer (LVDT) Advantages of LVDT Smooth and Wide Range of Operation. 1.25mm to 250 mm. High Sensitivity 40V/mm. Low Friction Losses Lower Power consumption, 1W Disadvantages of LVDT Affected by the vibrations and temperature variation . It is sensitive to Stray Magnetic Field LVDT is used to measure the physical quantities such as Force, Tension, Pressure, Weight, etc.

38. RESISTIVE TRANSDUCERS The design basis of an electrical resistive transducer: The resistance of a metal conductor is expressed by a simple equation that involves a few physical quantities. The relationship is Ω where R = resistance ; Ω , L = length of conductor ; m, A = C/S area of conductor ; m 2 , and p = resistivity of conductor material; Ω – m.   Examples: The translational and rotational potentiometers which work on the basis of change in the value of resistance with change in length of the conductor can be used for measurement of translational or rotary displacements . Strain gauges work on the principle that the resistance of a conductor or a semi-conductor changes when strained. This property can be used for measurement of displacement, force and pressure.

39. RESISTIVE TRANSDUCERS The resistivity of materials changes with change of temperature thus causing a change of resistance. This property may be used for measurement of temperature. Various types of resistive transducers are: Potentiometer Strain gauges Thermistor Resistance thermometer/ Resistance Temperature Detector (RTD).

40. Potentiometer : Basically a resistance potentiometer consists of a resistive element provided with a sliding contact. This sliding contact is called a wiper. The motion of the sliding contact may be translatory or rotational. A linear pot and a rotary pot are shown in Figs. a) and (b) respectively . RESISTIVE TRANSDUCERS

41. The resistive element of the POT may be excited by either d.c. or a.c . voltage . Motion of wiper (sliding contact): Translatory or Rotational. The helical resistive elements are multiturn rotational devices which can be used for measurement of either translational or rotary motion. Resolution : 0.05% to 0.1% Helipot : Some POTs have resistive elements which are multi turn and can be used for measurement of translator as well as rotational motion. The POT is a passive transducer since it requires an external power source for its operation . A translational potentiometer has about 500 turns of a resistance wire on a card of 25 mm in length and for this device the resolution is limited to 25/500 = 0.05 mm = 50 µm.

42. Wire : Wires (0.01mm) are platinum, nickel chromium, nickel copper, or some other precious resistance elements. Resistance temperature co-efficient is usually small is of the order of 20x10- 6 / o C . Resistance element: The resistance elements are also made up from cermet, hot moulded carbon, carbon film and thin metal.

43. Let us consider a translational potentiometer as shown in Fig. = Input and output voltages respectively, V. Total length of translational pot, m = displacement of wiper from its zero position, m. = Total resistance of the potentiometer, Ohm If the distribution of the resistance wrt translational movement is linear, the resistance per unit length = /   = ( = [ / / ]*  

44. Variation of error due to loading effect of a potentiometer. Figure: shows a plot of the variation in error with the slider position for different ratios of the load (output device or meter) resistance to the potentiometer resistance. The maximum error is about 12 per cent of full scale if Rm / Rp = 1. This error drops down to about 1.5% when Rm / Rp = 10. For values of Rm / Rp > 10, the position of maximum error occurs in the vicinity of xi/ xt = 0.67.

45. = ( = [ / / ]*   The under ideal circumstances, the output voltage varies linearly with displacement as shown in Fig

46. potentiometers Advantages of potentiometers They are inexpensive. They are simple to operate. They are very useful for measurement of large amplitudes of displacement . Their electrical efficiency is very high . Disadvantages of potentiometers The chief disadvantage of using a linear potentiometer is that they require a large force to move their sliding contacts (wipers ). The other problems with sliding contacts are that they can be contaminated, can wear out, become misaligned and generate noise. So the life of the transducer is limited

47. Q1The output of an LVDT is connected to a 5 V voltmeter through an amplifier whose amplification factor is 250. An output of 2 mV appears across the terminals of LVDT when the core moves through a distance of 0.5 mm. Calculate the sensitivity of the LVDT and that of the whole set-up. The milli -voltmeter scale has 100 divisions . The scale can be read to 1/5 of a division. Calculate the resolution of the instrument in mm.

48. Q2 A steel cantilever is 0.25 m long, 20 mm wide and 4 mm thick. ( a) Calculate the value of deflection at the free end for the cantilever when a force of 25 N is applied at this end. The modulus of elasticity for steel is 200 GN/m2. ( b) An LVDT with a sensitivity of 0.5 V/mm is used. The voltage is read on a 10 V voltmeter having 100 divisions. Two tenths of a division can be read with certainty . ( c) Calculate the minimum and maximum value of force that can be measured with this arrangement.

49. Q2 A steel cantilever is 0.25 m long, 20 mm wide and 4 mm thick. ( a) Calculate the value of deflection at the free end for the cantilever when a force of 25 N is applied at this end. The modulus of elasticity for steel is 200 GN/m2. ( b) An LVDT with a sensitivity of 0.5 V/mm is used. The voltage is read on a 10 V voltmeter having 100 divisions. Two tenths of a division can be read with certainty . ( c) Calculate the minimum and maximum value of force that can be measured with this arrangement.

50. Example: Figure shows a capacitive transducer using five plates. The dimensions of each plate are 25 x 25 mm and the distance between plates is 0.25 mm. This arrangement is to be used for measurement of displacement by observing the change in capacitance with distance x. Calculate the sensitivity of the device. Assume that the plates are separated by air. The permittivity of air is 8.85 x 10~12F/m.

51. A capacitive transducer is made up of two concentric cylindrical electrodes. The outer diameter of the inner cylindrical electrode is 3 mm and the dielectric medium is air. The inner diameter of the outer electrode is 3.1 mm. Calculate the dielectric stress when a voltage of 100 V is applied across the electrodes. Is it within safe limits ? The length of electrodes is 20 mm. Calculate the change in capacitance if the inner electrode is moved through a distance of 2 mm. The breakdown strength of air is 3 kV/mm.

52. Uses of LVDTs LVDTs are used for measurement of weight or pressure exerted by liquid in a tank. They (LVTDs) are excited in parallel to increase the sensitivity . Two LVDTs which are used for measurement and control of thickness of a metal sheet being rolled. When the thickness equals the desired value, the two LVDTs are balanced out . LVDT being used for measurement of tension in a cord while

53. The capacitive transducer is used for measuring the displacement, pressure and other physical quantities. It is a passive transducer that means it requires external power for operation . By measuring the change in capacitance one can infer the displacement. Capacitance is measured in units of farads (F ). The capacitive transducer contains two parallel metal plates. In the normal capacitor the distance between the plates are fixed, but in capacitive transducer the distance between them are varied. CAPACITIVE TRANSDUCERS

54. The capacitive transducer works on the principle of change of capacitance which may be caused by : Change in overlapping area A CAPACITIVE TRANSDUCERS

55.   Principle of Operation The equations below express the capacitance between the plates of a capacitor Where A – overlapping area of plates in m2 d – The distance between two plates in meter Relative permittivity ε –permittivity of the medium in F/m – The permittivity of free space  

56. The capacitive transducer works on the principle of change of capacitance which may be caused by : Change in the distance ‘d’ between the plates, and Change in dielectric constant. CAPACITIVE TRANSDUCERS

57. The capacitive transducers are used for measuring the large displacement approximately from 1mm to several cms . The area of the capacitive transducer changes linearly with the capacitance and the displacement. The capacitive transducer is used for measuring the angular displacement. CAPACITIVE TRANSDUCERS

58. Capacitive transducers are used for measurement of humidity in gases since the dielectric constant of gases changes with change in humidity thereby producing a change in capacitance. the example of air. The dry air at 45°C has a dielectric constant of 1.000247 and that of air saturated with water is 1.000593 at the same temperature. These measurements are carried out with microwave techniques and the frequency is of the order of 10 GHz. CAPACITIVE TRANSDUCERS Capacitive transducers can also be used directly as pressure transducers in all those cases where the dielectric constant of a medium changes with pressure. For instance, the dielectric constant of Benzene changes by 0.5 per cent in the range of pressure of 1 to 1000 times the atmospheric pressure. Similarly, the dielectric constant of air at 19°C changes from 1.0006 to 1.0548 in the same pressure range.

59. The nozzle flapper is a displacement transducer that translates displacements into a pressure change. The general form of a nozzle flapper is shown schematically in Figure. The body whose displacement is being measured is connected physically to the flapper plate. The output measurement of the instrument is the pressure, Po, in the chamber shown in Fig. Nozzle Flapper

60. Air is used very commonly as the working fluid, which gives the instrument a time constant of about 0.1 second . A typical measurement range is ±0.05mm with a measurement resolution of ±0.01µm. One very common application of nozzle flappers is measuring displacements within a load cell, which are typically very small. Nozzle Flapper

61. Strain Measurement : Strain Gauge: Strain gauge is device whose electrical resistance varies in proportion to the amount of strain in the device. The most widely used gauge is the bonded metallic strain gauge.

62. Module:02 Strain Measurement: Theory of Strain Gauges, gauge factor, temperature Compensation, Bridge circuit, orientation of strain gauges for force and torque, Strain gauge-based load cells and torque sensors

63. Strain Gauge A strain gauge (or strain gage) is a device used to measure strain on an object. It is also termed as Load cell. Invented by Edward E. Simmons and Arthur C. Ruge in 1938 T he most common type of strain gauge consists of an insulating flexible backing which supports a metallic foil pattern.

64. Theory of Strain Gauges: The strain gauge is the most popular secondary transducer employed for the measurement of force. The strain gauge operates on a simple principle . When force is applied on an elastic member, a steel cylindrical rod in this case, the dimensions undergo a change. Axially loaded bar Prismatic bar

65. Theory of Strain Gauges: The strain gauge is the most popular secondary transducer employed for the measurement of force. The strain gauge operates on a simple principle. When force is applied on an elastic member, a steel cylindrical rod in this case, the dimensions undergo a change. If the strain gauge is bonded to the cylinder, the gauge is stretched or compressed, resulting in a change in its length and diameter. The dimension of the strain gauge changes due to a change in resistance . This change in resistance or output voltage of the strain gauge gives a measure of the applied force.

66. Theory of Strain Gauges: Normally , measurements are made over the shortest gauge lengths . The change in length measured over a finite length does not give the value of strain at a fixed point but rather gives. The average strain over the entire length. A magnification system is essential since the change in length is over a small gauge length. Two types of strain gauges are employed: 1 . Mechanical strain gauges, 2 . Electrical strain gauges

67. Strain Gauge Applications 1 . To determine the state of strain existing at a point on a loaded member for carrying out strain analysis 2. To act as a strain-sensitive transducer element in the measurement of quantities such as force, pressure, displacement, and acceleration.

68. Theory of Strain Gauges: Load cells and proving rings that employ strain gauges are the two most common instruments used for force measurement.

69. Strain Measurement : Strain can be measured using various types of devices classified depending upon their principle of operation. Some of them are as follows : 1. Mechanical type, extensometer 2. Optical type: Photoelectric strain gauge was also introduced which uses a light beam to produce electric current corresponding to deformation. 3. Pneumatic type 4. Electrical type: The most commonly used strain gauge is an electrical resistance strain gauge

70. The strain gauge operates on a simple principle Tension Compression Principle : If a metal conductor is stretched or compressed, its resistance changes on account of the fact that both length and diameter of the conductor changes.

71. R= ρ (1) Let the tensile stress ‘ s’ applied to the wire . With result change in length Δ L , Change in area Δ A , change in diameter Δ D. In order to find Δ R ; R is differentiated w.r.t. stress ‘s’ = (2) Dividing equation (2) throughout with R= ρ = (3) In equation (3) per unit change in resistance is due to (a) per unit change in length Δ L/L per unit change in area Δ A/A and ( c) per unit change in resistivity Δ /   Tension

72. A= = 2. D. (4) Dividing both sides by A (5) = = (6)  

73. Now Poisson's ratio = =- = - (7) Putting equation (7) in equation (6) = For small variation above van be written as = + 2 + = Gauge factor ( ) is defined as the ratio of per unit change in resistance to per unit change in length = = Gauge factor= 1 + 2 or = 1 + 2 Gauge factor= 1 + 2 as the strain is in the term of microstrain  

74. Types of Strain gauge Unbounded Strain gauge Bonded (wire & Metal foil) Strain gauge Vacuum deposit Strain gauge Semiconductor S train gauge Diffused metal Strain gauge

75. A Strain Gauge is a device used to measure the strain of an object The gauge is attached to the object by a suitable adhesive As the object is deformed, the foil is deformed, causing its electrical resistance to change The resistance change is commonly measured using a Wheatstone bridge The most common type of strain gauge consists of an insulating flexible backing which supports a metallic foil pattern

76. Construction of bonded-wire-type strain gage

77. Materials used for wire Strain Gauge Materials Composition Gauge Factor Resistivity ohm m Nichrome Ni: 80% Cr:20% 2.0 100 X10 -8 Constantan Ni:45% Cu:55% 2.1 48 X10 -8 Isoelastic Ni:36% Cr:8% Mo:05% 3.6 105 X10 -8 Nickel - 12.1 6.5 X10 -8 Platinum 4.8 10 X10 -8

78. Unbonded strain gauge Wire Diameter 0.003mm Length of wire 25mm Resistance of each arm 120-1000 ohms Input Voltage 5-10V DC

79. Bonded Wire Strain Gauge Fine wire with diameter about .025 mm Grid of wire is cemented to the carrier (Base)-sheet of paper, thin sheet of Bakelite or Teflon Small as 3X3mm, larger 25X12.5mm

80. Bonded metal foil strain gauge Grater heat dissipating capacity Formed from a sheet of metal less than 0.005mm thick by photo-etching process Easy manufacturing process Can be apply in curved surface 10 million cycles at +- 1500 micro-strain can be applied to foil gauge

81. Materials used for wire Strain Gauge Materials Composition Gauge Factor Resistivity ohm m Nichrome Ni: 80% Cr:20% 2.0 100 X10 -8 Constantan Ni:45% Cu:55% 2.1 48 X10 -8 Isoelastic Ni:36% Cr:8% Mo:05% 3.6 105 X10 -8 Nickel - 12.1 6.5 X10 -8 Platinum 4.8 10 X10 -8

82. Semiconductor Strain gauge S emiconducting wafers or filaments of length varying from 2 mm to 10 mm and thickness of 0.05 mm are bonded on suitable insulating substrates (for example Teflon). The gold leads are usually employed for making electrical contacts. The electrodes are formed by vapour deposition. The assembly is placed in a protective box

83. Advantages of Semiconductor Strain Gauge The gauge factor of semiconductor strain gauge is very high, about ±130.  Semiconductor strain gauge exhibits very low hysteresis i.e., less than 0.05%.  They are useful in measurement of very small strains of the order of 0.01 micron The semiconductor strain gauge has much higher output, but it is as stable as metallic strain gauge. It has a large fatigue life i.e., 10 x 10 6 operations can be performed. It possesses a high frequency response of 1012 Hz. can be manufactured in very small sizes, their lengths ranging from 0.7 to 7.0 mm.

84. Strain Measurement : Drawbacks of Strain gauge 1. A strain gauge is capable only of measuring strain in the direction in which gauge is oriented. 2. There is no direct way to measure the shear strain or to directly measure the principal strains as directions of principal planes are not generally known.

85. Strain rosettes: Since for strain analysis in biaxial state of stress we should know strain in three directions and due to drawbacks in a strain gauge, Strain rosettes came in to picture. Strain rosette can be defined as the arrangement of strain gauges in three arbitrary directions. These strain gauges are used to measure the normal strain in those three directions. Depending on the arrangement of strain gauges, strain rosettes are classified in to:- 1. Rectangular strain gauge rosette 2. Delta strain gauge rosette 3. Star strain gauge rosette

86. Strain rosettes: 1 . Rectangular strain gauge rosette:Rectangular strain gauge rosette A rectangular strain rosette consists of three strain gauges arranged as follows : 2. Delta strain gauge rosette: A delta strain gauge also consist of three strain gauges arranged as shown below. 3. Star strain gauge rosette: This rosette consist of three strain gauges in three directions as shown below

87. Wheatstone Bridge

88. Wheatstone Bridge

89. Wheatstone Bridge

90. Temperature Compensation: The strain gauge would change its resistance with respect to the temperature. Gauge resistance is affected by many reasons in which temperature plays an important role. Total indicated strain= Mechanical Strain + Apparent Strain When temperature increases Gauge grid will elongate ∆ 𝑙, 𝑙 =∝.∆𝑇 Base material mounted on gauge will elongate ∆𝑙, 𝑙 = β.∆𝑇 Resistance of the gauge will increase, ∆ 𝑅 , 𝑅 = γ.∆𝑇 The combined effect of these three factors will produce a temperature induced change in resistance of the gauge as ∆𝑅, 𝑅 = 𝛽−𝛼 ∆𝑇.𝐹+𝛾∆ 𝑇, α = Thermal coefficient of expansion of the gauge material, β = Thermal coefficient of base material, γ = Thermal coefficient of gauge material and F = Gauge factor.

91. Temperature Compensation : In order to prevent significant errors due to “Temperature Compensation” current available methods are Compensating dummy gauge Self temperature compensated gauge Compensation by Dissimilar gauge Compensation by Similar gauge Compensation by Computation

92. Temperature Compensation : Compensating Dummy Gauge This is the earliest form of temperature compensation technique. The active gauge is connected with a dummy gauge to balance out the unwanted temperature induced resistance change. The dummy gauge is identical to active gauge mounted on unstressed specimen exposed to same thermal environment . Disadvantages This method is failure if temperature variations are not uniform in both the gauges.

93. Temperature Compensation : Self-Temperature Compensated Gauge The term temperature compensated denotes that change is resistance due to temperature is zero. This method is successful only when materials having specific value of thermal expansion coefficient. It must be 0-25 ppm/ Deg C. In First method- Self temperature Compensation is created by altering the temperature coefficient of grid material. So that when mounted on materials having a certain thermal expansion coefficient thermal expansion will be low.

94. Temperature Compensation : Self-Temperature Compensated Gauge The Second method includes forming a grid with two different lengths of gauge wires in series so that resultant apparent strain is zero . The gauge in the first arm should have relatively small temperature effect in same direction In the Second arm series and shunt resistance are connected in series so that the temperature effects of two arms cancel each other . Advantages This method is more successful than Self temperature compensated gauge because of relative resistance of the filament is not critical. Compensation over a greater temperature is easily achieved. Disadvantages: At higher temperature, Value will not be known accurately

95. Temperature Compensation : Compensation by Similar gauge Best Suitable method for Unpredictable and Predictable Effects of temperature. It is achieved by connecting by two similar gauges in series like Wheatstone Bridge Circuit. One gauge connected in direction of maximum principal strain. Other gauge in the direction of minimum principal strain . Advantages It can easily eliminated hydrostatic component of stress from reading. Shear component of stress can be easily predictable. Best suited method if the direction of principle strain is known.

96. Temperature Compensation : Compensation by Computation By knowing the temperature characteristics of Strain gauge and the base metal, temperature correction can be easily calculated theoretically.