![MANIPAL INSTITUTE OF TECHNOLOGY
Department of Mechanical & Manufacturing Engineering, MIT, Manipal 87
MANIPAL INSTITUTE OF TECHNOLOGY
In a solid shaft of diameter d, rotating with rpm N, subjected to torque T,
Power = (2 x π x N x T) / 60
Also, Torque, T= [(fs x π x d3) / 16] ……………………..{ from DDHB }
where fs = Shear stress induced in the shaft.
Shear strain = Shear stress induced in the shaft / Shear modulus
Longitudinal strain in the shaft at 45º to the axis of the shaft, ε45 = Shear strain / 2](https://image.slidesharecdn.com/strainmeasurementnew-240314065338-ac066b76/85/Strain-Measurement-NEW-pptx-81-320.jpg)
Strain Measurement (NEW).pptx .
- 1. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 1 MANIPAL INSTITUTE OF TECHNOLOGY STRAIN Measurement
- 2. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 2 MANIPAL INSTITUTE OF TECHNOLOGY
- 3. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 3 MANIPAL INSTITUTE OF TECHNOLOGY Electrical resistance strain gauges are very widely used for strain measurement. Its operation is based on the principle that the electrical resistance of a conductor changes when it is subjected to a mechanical deformation. Typically an electric conductor is bonded to the specimen with an insulating cement under no-load conditions. A load is then applied, which produces a deformation in both the specimen and the resistance element.
- 4. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 4 MANIPAL INSTITUTE OF TECHNOLOGY This deformation is indicated through a measurement of the change in resistance of an element as follows: Resistance of a conductor, Where L = Length of the electrical conductor, A = Cross sectional area of the conductor, ρ = Resistivity of the conductor material. In other words when the conductor is stretched, its length (L) will increase, area (A) will decrease and hence the resistance (R) will increase. Similarly, when the conductor is compressed resistance (R) will decrease. 2 ..................(1) l l C R A D
- 5. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 5 MANIPAL INSTITUTE OF TECHNOLOGY Bonded Resistance-strain Gauge The bonded gauge is a suitably shaped piece of resistance metal which is bonded close to the surface whose strain is to be measured. The exploded view Fig. shows a thin wire shaped into a grid pattern, which is cemented between thin sheets of insulating material such as paper or plastic. The grid can also be made from thin metal foil. The assembled gauge is bonded to the surface with a thin layer of adhesive and finally waterproofed with a layer of wax or lacquer. The grid experiences the same strain as the material to which it is bonded.
- 6. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 6 MANIPAL INSTITUTE OF TECHNOLOGY The gauge is most sensitive to the strain along its axial direction X-X while the strain in the Y-Y direction occurs due to Poisson's ratio effect. This causes change of resistance, and may lead to an error of 2% in the measured strain when using the wire bonded gauge. However, in the foil gauge the thickened ends reduce this cross-sensitivity effect to virtually zero. If the direction of principal strain is not known then cluster of three or more strain gauges are used, which are called rosettes.
- 7. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 7 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 7 MANIPAL INSTITUTE OF TECHNOLOGY
- 8. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 8 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 8 MANIPAL INSTITUTE OF TECHNOLOGY
- 9. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 9 MANIPAL INSTITUTE OF TECHNOLOGY
- 10. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 10 MANIPAL INSTITUTE OF TECHNOLOGY a) Single element b) Two-element rosette c) Three – element rosette d) Special – purpose gauges (used on pressurized diaphragms)
- 11. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 11 MANIPAL INSTITUTE OF TECHNOLOGY
- 12. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 12 MANIPAL INSTITUTE OF TECHNOLOGY
- 13. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 13 MANIPAL INSTITUTE OF TECHNOLOGY
- 14. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 14 MANIPAL INSTITUTE OF TECHNOLOGY
- 15. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 15 MANIPAL INSTITUTE OF TECHNOLOGY 15
- 16. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 16 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 16 MANIPAL INSTITUTE OF TECHNOLOGY 16
- 17. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 17 MANIPAL INSTITUTE OF TECHNOLOGY
- 18. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 18 MANIPAL INSTITUTE OF TECHNOLOGY
- 19. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 19 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 19 MANIPAL INSTITUTE OF TECHNOLOGY
- 20. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 20 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 20 MANIPAL INSTITUTE OF TECHNOLOGY
- 21. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 21 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 21 MANIPAL INSTITUTE OF TECHNOLOGY
- 22. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 22 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 22 MANIPAL INSTITUTE OF TECHNOLOGY
- 23. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 23 MANIPAL INSTITUTE OF TECHNOLOGY
- 24. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 24 MANIPAL INSTITUTE OF TECHNOLOGY Wire type: It consists of a very fine wire of diameter 0.025 mm wounded into a grid shape as shown in figure and the grid is cemented between two pieces of thin paper with plastic or ceramic backing. This is done in order that the grid of the wire may be easily handled. This is securely bonded with a suitable cement to the surface of the member in which the strain has to be measured.
- 25. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 25 MANIPAL INSTITUTE OF TECHNOLOGY Foil type resistance strain gauge: These gauges usually employs a foil less than 0.005 mm thick. The common form of foil type gauge consists of a metal foil grid element on a thin epoxy support. Epoxy filled with fiber glass is used for high temperatures. These foil type gauges are manufactured by printing on a thin sheet of metal alloy with an acid-resistant ink, and then the unprinted portion is etched away. Foil gauges have the advantages of improved hysteresis, better fatigue life and lateral strain sensitivity.
- 26. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 26 MANIPAL INSTITUTE OF TECHNOLOGY It is thinner and more flexible, thus permitting it to be applied to fillets and sharply curved surfaces. The common wire or foil gauges are called metallic gauges.
- 27. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 27 MANIPAL INSTITUTE OF TECHNOLOGY Semiconductor or Piezoresistive strain gauge: Semiconductor gauges are cut from single crystals of silicon or germanium in which are combined exact amounts of impurities such as boron which impart certain desirable characteristics. The same types of backing, bonding materials, and mounting techniques as those used for metallic gauges can be used for semiconductor gauges. When the gauge is bonded to a member which is strained, causes changes of current in the semi-conductor material. The advantages of semiconductor gauges is their high strain sensitivity which allows very small strains to be measured accurately.
- 28. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 28 MANIPAL INSTITUTE OF TECHNOLOGY A gauge whose electrical resistance increases in response to tensile strain is known as positive or p-type semiconductor gauge. On the other hand when the resistance decreases in response to tensile strain then it is known as negative or n-type semiconductor gauge. The semiconductor gauge consists of a rectangular filament of about 0.05 mm thick by 0.25 mm wide and gauge length varies from 1.5 to 12 mm as shown in Figure.
- 29. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 29 MANIPAL INSTITUTE OF TECHNOLOGY Strain Gauge Metals: The most common metals used for the manufacture of metallic strain gauges are: alloys of copper and nickel or, alloy of nickel, chromium and iron with other elements in small percentages. Gauges with resistances varying from 60 Ω to 5000 Ω are available. The current carried by the gauges for long periods is around 25 mA to 50 mA.
- 30. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 30 MANIPAL INSTITUTE OF TECHNOLOGY Strain Gauge Backing Materials: The strain-gauges are normally supported on some form of backing material. This provides not only the necessary electrical insulation between the grid and the tested material, but also a convenient carriage for handling the un-mounted gauge. Certain types of gauges intended for high temperature applications use a temporary backing which will be removed when the grid is mounted. In this case, at the time of installation the grid is embedded in a special ceramic material that provides the necessary electrical insulation and high-temperature adhesion.
- 31. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 31 MANIPAL INSTITUTE OF TECHNOLOGY The desirable characteristics for backing materials are as follows: 1. Minimum thickness consistent with other factors 2. High mechanical and dielectric strength 3. Minimum temperature restrictions 4. Good adherence to cements used, and should be non- hygroscopic in nature. Common backing materials include thin paper, phenolic- impregnated paper, epoxy type plastic films, and epoxy- impregnated fiber glass.
- 32. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 32 MANIPAL INSTITUTE OF TECHNOLOGY Bonding Materials and Methods: Strain gauges are attached to the test item by some form of cement or adhesive. The adhesives commonly used are cellulose, phenolic, epoxy, cyanoacrylate, or ceramic etc. The desirable characteristics of strain-gauge adhesives are as follows: 1. High mechanical and dielectric strength 2. High creep resistance 3. Minimum temperature restrictions and moisture absorption 4. Good adherence with ease of application 5. The capacity to set fast
- 33. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 33 MANIPAL INSTITUTE OF TECHNOLOGY Treatment Regarding Preparation and Mounting of Strain Gauges: The following steps should be strictly followed for proper mounting of the strain gauges: 1. The surface on which the strain gauge has to be mounted must be properly cleaned by an emery cloth and bare base material must be exposed. 2. Various traces of grease or oil etc must be removed by using solvent like acetone. 3. The surface of the strain gauge coming in contact with the test item should also be free from grease etc.
- 34. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 34 MANIPAL INSTITUTE OF TECHNOLOGY 4. Sufficient quantity of cement is applied to the cleaned surface and the cleaned gauge is then simply placed on it. Care should be taken to see that there should not be any air bubble in between the gauge and the surface. The pressure applied should not be heavy so that the cement may puncture the paper and short the grid 5. The gauges are then allowed to set for at least eight or ten hours before using it. If possible a slight weight may be placed by keeping a sponge or rubber on the gauge. 6. After the cement is fully cured, the electrical, continuity of grid must be checked by ohm meter and the electrical leads may be welded.
- 35. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 35 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 35 MANIPAL INSTITUTE OF TECHNOLOGY Theory of strain gauges
- 36. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 36 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 36 MANIPAL INSTITUTE OF TECHNOLOGY
- 37. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 37 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 37 MANIPAL INSTITUTE OF TECHNOLOGY
- 38. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 38 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 38 MANIPAL INSTITUTE OF TECHNOLOGY
- 39. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 39 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 39 MANIPAL INSTITUTE OF TECHNOLOGY
- 40. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 40 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 40 MANIPAL INSTITUTE OF TECHNOLOGY
- 41. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 41 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 41 MANIPAL INSTITUTE OF TECHNOLOGY
- 42. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 46 MANIPAL INSTITUTE OF TECHNOLOGY
- 43. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 47 MANIPAL INSTITUTE OF TECHNOLOGY Resistance Strain Gauge Bridge Unbalanced Strain Gauge Bridge
- 44. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 48 MANIPAL INSTITUTE OF TECHNOLOGY
- 45. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 49 MANIPAL INSTITUTE OF TECHNOLOGY
- 46. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 50 MANIPAL INSTITUTE OF TECHNOLOGY
- 47. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 51 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 51 MANIPAL INSTITUTE OF TECHNOLOGY 51 2. Voltage Sensitive bridge:
- 48. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 52 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 52 MANIPAL INSTITUTE OF TECHNOLOGY 𝑖1=𝑖3 & 𝑖2=𝑖4 Assume that input impedance of the meter is infinite and therefore 𝑖𝑚=0 Output voltage 𝑒0 = 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑐𝑟𝑜𝑠𝑠 𝑡ℎ𝑒 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙𝑠 𝑏 𝑎𝑛𝑑 𝑑 = 𝑖1𝑅1 − 𝑖2𝑅2 𝑖1= 𝑒𝑖 𝑅1 + 𝑅3 𝑖2= 𝑒𝑖 𝑅2 + 𝑅4 𝑒0 = 𝑅1 𝑅1 + 𝑅3 − 𝑅2 𝑅2 + 𝑅4 𝑒𝑖 𝑅1𝑅2 + 𝑅1𝑅4 − 𝑅1𝑅2 − 𝑅3𝑅2 (𝑅1 + 𝑅3)(𝑅2 + 𝑅4) 𝑒𝑖 = Suppose 𝑅1 changes by an amount Δ𝑅1. This causes a change in output voltage Δ𝑒0 (𝑅1+Δ𝑅1)𝑅4 − 𝑅3𝑅2 (𝑅1 + Δ𝑅1 + 𝑅3)(𝑅2 + 𝑅4) 𝑒𝑖 𝑒0 + Δ𝑒0 = Deviding by 𝑅1𝑅4
- 49. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 53 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 53 MANIPAL INSTITUTE OF TECHNOLOGY 𝑒0 + Δ𝑒0 = (1 + Δ𝑅1 𝑅1 )𝑅4 − 𝑅3𝑅2 𝑅1𝑅4 (1 + Δ𝑅1 𝑅1 + 𝑅3 𝑅1 )(1 + 𝑅2 𝑅4 ) 𝑒𝑖 To simplify the relationship assume 𝑅1 = 𝑅2 = 𝑅3 = 𝑅4 = 𝑅 Under these conditions 𝑒0=0 Δ𝑅 𝑅 (4 + 2 Δ𝑅 𝑅 ) 𝑒𝑖 Δ𝑒0 = Resistance change is very small compared to initial resistance 4 >> 2 Δ𝑅 𝑅 Δ𝑒0 = Δ𝑅 𝑅 4 𝑒𝑖 Hence Bridge sensitivity =𝑆𝐵 = Δ𝑒0 Δ𝑅 = 𝑒𝑖 4𝑅
- 50. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 54 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 54 MANIPAL INSTITUTE OF TECHNOLOGY 𝑅1 = 𝑅2 = 𝑅3 = 𝑅4 = 𝑅𝑔 the strain gauge resistance and changes to ∆𝑅𝑔 Δ𝑒0 = ∆𝑅𝑔 𝑅𝑔 (4 + 2 ∆𝑅𝑔 𝑅𝑔 ) 𝑒𝑖 4 >> 2 ∆𝑅𝑔 𝑅𝑔 Δ𝑒0 = ∆𝑅𝑔 𝑅𝑔 4 𝑒𝑖 𝐺𝑓.𝜀 4 𝑒𝑖 Δ𝑒0 =
- 51. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 55 MANIPAL INSTITUTE OF TECHNOLOGY Signal enhancement factor of the Wheatstone bridge is defined as the maximum output due to changes in various strain gauges of the bridge to the maximum output obtainable with the use of only one strain gauge on the member. In other words, more than one active gauge (subjected to strain), suitably arranged, can leads to increased sensitivity or signal enhancement. Strain gauge arrangement
- 52. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 56 MANIPAL INSTITUTE OF TECHNOLOGY Strain gauge arrangement The following two factors are kept in mind while deciding the arrangements of strain gauges on elastic members, for measuring various physical variables: High sensitivity and Temperature compensation
- 53. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 57 MANIPAL INSTITUTE OF TECHNOLOGY All the possible arrangement of four strain gauges on elastic members, for measuring axial force with signal enhancement factor. Signal enhancement factor = 2(1 + ν)
- 54. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 58 MANIPAL INSTITUTE OF TECHNOLOGY All the possible arrangement of four strain gauges on elastic members, for measuring bending force with signal enhancement factor. Signal enhancement factor = 2(1 + ν)
- 55. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 59 MANIPAL INSTITUTE OF TECHNOLOGY
- 56. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 60 MANIPAL INSTITUTE OF TECHNOLOGY
- 57. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 61 MANIPAL INSTITUTE OF TECHNOLOGY
- 58. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 62 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 62 MANIPAL INSTITUTE OF TECHNOLOGY
- 59. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 63 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 63 MANIPAL INSTITUTE OF TECHNOLOGY
- 60. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 64 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 64 MANIPAL INSTITUTE OF TECHNOLOGY
- 61. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 65 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 65 MANIPAL INSTITUTE OF TECHNOLOGY
- 62. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 66 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 66 MANIPAL INSTITUTE OF TECHNOLOGY
- 63. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 67 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 67 MANIPAL INSTITUTE OF TECHNOLOGY
- 64. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 68 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 68 MANIPAL INSTITUTE OF TECHNOLOGY
- 65. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 71 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 71 MANIPAL INSTITUTE OF TECHNOLOGY
- 66. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 72 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 72 MANIPAL INSTITUTE OF TECHNOLOGY
- 67. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 73 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 73 MANIPAL INSTITUTE OF TECHNOLOGY
- 68. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 74 Department of Mechanical & Manufacturing Engineering, MIT, Manipal 74 MANIPAL INSTITUTE OF TECHNOLOGY
- 69. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 75 MANIPAL INSTITUTE OF TECHNOLOGY Temperature Compensation One of the most important and critical factors in the use of resistance strain gauges is temperature sensitivity. Although compensation is provided in the electrical circuitry, for a majority of the applications, the problem is not eliminated completely. The following three factors are involved: 1. The gauge is unable to differentiate the strain resulting from the differential expansion existing between the grid support and the proper grid from the load strain. 2. The resistivity changes with the change in temperature. 3. The strong magnetic field has an influence on the gauge performance.
- 70. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 76 MANIPAL INSTITUTE OF TECHNOLOGY The Adjacent-Arm Compensating Gauge The active strain gauge is installed on the test specimen while the dummy gauge is installed on a like piece of material and is not subjected to any strain. The bridge is initially balanced and therefore If the gauges in arms 1 and 2 are alike and mounted on similar materials and if both gauges experience the same resistance shift, Rt caused by temperature change, then
- 71. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 77 MANIPAL INSTITUTE OF TECHNOLOGY We see that the bridge remains in balance and the output is unaffected by the change in temperature. When the compensating gauge is used merely to complete the bridge and to balance out the temperature component, it is often referred to as the "dummy" gauge.
- 72. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 78 MANIPAL INSTITUTE OF TECHNOLOGY Temperature compensation using more than one active strain gauge
- 73. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 79 MANIPAL INSTITUTE OF TECHNOLOGY
- 74. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 80 MANIPAL INSTITUTE OF TECHNOLOGY Calibration of strain gauges Normally, calibration of a measuring system means introducing an accurately known sample of the variable that is to be measured and then observing the system`s response. Once a bonded strain gauge is mounted on the structure under study, it cannot be removed or transferred. Moreover the value of the gauge factor specified by the manufacturer of the gauge has to be taken for granted. With these constraints, the relationship between the strain and the output of the Wheatstone bridge has to be established. When the gauge factor and gauge resistance are known, the shunting method is used to calibrate strain gauge.
- 75. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 81 MANIPAL INSTITUTE OF TECHNOLOGY In the shunting method, a small known resistance change is introduced at the strain gauge and then an equivalent strain is calculated. This small known resistance change is introduced at the strain gauge by shunting a high resistance across the strain gauge as shown in diagram.
- 76. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 82 MANIPAL INSTITUTE OF TECHNOLOGY
- 77. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 83 MANIPAL INSTITUTE OF TECHNOLOGY
- 78. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 84 MANIPAL INSTITUTE OF TECHNOLOGY Strain measurement on rotating shaft The mounting of four resistance strain gauges on rotating shaft for measuring the torque transmitted by a shaft with Wheatstone bridge arrangement.
- 79. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 85 MANIPAL INSTITUTE OF TECHNOLOGY
- 80. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 86 MANIPAL INSTITUTE OF TECHNOLOGY During torsion of cylinder, the principal strains (tensile or compressive) exist at 45º to the axis. These can be measured by bonded resistance gauges, as shown in the figure. The output is increased by using four strain gauges so that adjacent arms of the Wheatstone bridge have strains of opposite nature. For taking signals in and out of the rotating shaft, slip rings and brushes are used as shown in the figure.
- 81. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 87 MANIPAL INSTITUTE OF TECHNOLOGY In a solid shaft of diameter d, rotating with rpm N, subjected to torque T, Power = (2 x π x N x T) / 60 Also, Torque, T= [(fs x π x d3) / 16] ……………………..{ from DDHB } where fs = Shear stress induced in the shaft. Shear strain = Shear stress induced in the shaft / Shear modulus Longitudinal strain in the shaft at 45º to the axis of the shaft, ε45 = Shear strain / 2
- 82. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 88 MANIPAL INSTITUTE OF TECHNOLOGY
- 83. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 89 MANIPAL INSTITUTE OF TECHNOLOGY
- 84. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 90 MANIPAL INSTITUTE OF TECHNOLOGY The voltage output, e, is given as Signal enhancement factor = 2 X 2 Battery Voltage E = Battery Current (R1+R4) Sensitivity = Voltage output / Strain
- 85. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 91 MANIPAL INSTITUTE OF TECHNOLOGY
- 86. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 92 MANIPAL INSTITUTE OF TECHNOLOGY
- 87. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 93 MANIPAL INSTITUTE OF TECHNOLOGY
- 88. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 94 MANIPAL INSTITUTE OF TECHNOLOGY The voltage output, e, is given as Signal enhancement factor = 2(1 + ν) X 2(1 + ν) Poisson’s ratio ν = 0.3 Bridge excitation voltage E = 6V Gauge Factor GF = 2.2 Area of the Strip A = 10 mm2
- 89. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 95 MANIPAL INSTITUTE OF TECHNOLOGY = 4.785 mV Deflection of the trace = 4.785/10 = 0.478 cm
- 90. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 96 MANIPAL INSTITUTE OF TECHNOLOGY
- 91. MANIPAL INSTITUTE OF TECHNOLOGY Department of Mechanical & Manufacturing Engineering, MIT, Manipal 97 MANIPAL INSTITUTE OF TECHNOLOGY The voltage output, e, is given as Signal enhancement factor = 4) X 4