Strain rosette analysis 1

Study and analysis of strain rosette

1. STRAIN ROSETTE ANALYSIS By, TUSHAR GHAG ME-MACHINE DESIGN ROLL NO-221603

2. Introduction A strain gauge is a passive transducer that converts mechanical displacement into change of resistance. It is a thin, wafer like material than can be attached to a variety of material to measure their strain. 2

3. Principle : The basic concept of an electrical strain gauge is attributed to Lord Kelvin who in 1856 expounded the theory that the resistance of a copper or iron wire changes when subjected to tension. The resistance of the wire changes as a function of strain, increasing with tension and reducing with compression. Types Of Electrical Strain Gauges : Wire Gauges Wrap-around Type Unbonded Strain Gauges Foil Gauges Bonded Strain Gauge   3

4. Axial Sensitivity It is very important that the strain gauge be properly mounted onto the test specimen so that the strain is accurately transferred from the test specimen, through the adhesive and strain gauge backing, to the foil itself. A fundamental parameter of the strain gauge is its sensitivity to strain, expressed quantitatively as the Gauge Factor (GF). Gauge factor is defined as the ratio of fractional change in electrical resistance to the fractional change in length (strain). The gauge factor for metallic strain gauges is typically around 2.   4

5. Cross Sensitivity Transverse sensitivity in a strain gauge refers to the behaviour of the gauge in responding to strains which are perpendicular to the primary sensing axis of the gauge. Ideally, it would be preferable if strain gauges were completely insensitive to transverse strains. However in practice, most gauges exhibit some degree of transverse sensitivity; but the effect is ordinarily quite small, and of the order of several percent of the axial sensitivity. 5

6. Cross Sensitivity In simple words, the gauge in addition to measuring the strain along the axis also measures the strain transverse to it. This is known as cross-sensitivity or transverse sensitivity. Axial Strain Sensitivity: Normal Strain Sensitivity:   6

7. CROSS SENSITIVITY FACTOR IS GIVEN BY, 7

8. Strain Gauge Rosettes Introduction : A strain gauge rosette is, by definition, an arrangement of two or more closely positioned gauge grids, separately oriented to measure the normal strains along different directions in the underlying surface of the test part. It is often desired to measure the full state of strain on the surface of a part, i.e. to measure not only the two extensional strains, and but also the shear strain with respect to some given xy- axis system. A single gauge is capable only of measuring the extensional strain in the direction that the gauge is oriented.   8

9. Rosettes are designed to perform a very practical and important function in experimental stress analysis. It can be shown that for a general biaxial stress state, with the principal directions unknown, three independent strain measurements (in different directions) are required to determine the principal strains and stresses. When the principal directions are known in advance, two independent strain measurements are needed to obtain the principal strains and stresses. 9

10. To meet the requirements, manufacturers offer three basic types of strain gauge rosettes (each in a variety of forms): Tee: Two mutually perpendicular grids. 45°- rectangular: Three grids, with the second and third grids angularly displaced from the first grid by 45° and 90°, respectively. 60°- delta: Three grids, with the second and third grids 60° and 120° away, respectively, from the first grid. 10

11. Representative gauge patterns for the three rosette types are reproduced in figure. 11

12. Rosette Selection Considerations Basic parameters are strain-sensitive alloy, backing material, self temperature-compensation number, gauge length which must be considered in the selection of any strain gauge. Two other parameters are important in rosette selection. These are: (1) the rosette type — tee, rectangular or delta and (2) the rosette construction — planar or stacked . The tee rosette should be used only when the principal strain directions are known in advance from other considerations. If there is uncertainty about the principal directions, a three-element rectangular or delta rosette is preferable . 12

13. All three types of rosettes (tee, rectangular, and delta) are manufactured in both planar and stacked versions. The stacked rosette will cover more area than planar rosette and hence will give an accurate result. However if this rosette is mounted on a thin member subjected to severe bending, a considerable error will be introduced since each gauge is at different distance from neutral axis. 13

14. Gauge Element Numbering “Numbering” refers to the numeric sequence in which the gauge elements in a rosette are identified during strain measurement. With any three-element rosette, misinterpretation of the rotational sequence (cw or ccw) can lead to incorrect principal strain directions To obtain correct results, the grids in three-element rosettes must be numbered in a particular way. 14

15. Gauge Element Numbering It is always necessary in a tee rosette, for instance, that grid numbers 1 and 3 be assigned to two mutually perpendicular grids. Any other arrangement will produce incorrect principal strains. Following are the general rules for proper rosette numbering: With a rectangular rosette, the axis of grid 2 must be 45° away from that of grid 1; and grid 3 must be 90° away, in the same rotational direction. With a delta rosette, the axes of grids 2 and 3 must be 60° and 120° away, respectively, in the same direction from grid 1. 15

16. Numbering the grids can be in either the clockwise or counterclockwise direction, as long as the sequence is correct. Counterclockwise numbering is preferable, because it is consistent with the usual engineering practice of denoting counterclockwise angular measurement as positive in sign. 16

17. Stress Strain Relationship   17

18. Stress Strain Relationship   18

19. Stress Strain Relationship Having three unknowns and three equations, , and can be evaluated. The principal strains are then given by;   19

20. Strain Rosette -     To increase the accuracy of a strain rosette, large angles are used. In a three gauge rectangular rosette gauges are separated by 45 o ; and . The three equations can then be simplify to:   20

21. Strain Rosette -     Solving for  , and gives,   21

22. STRAIN ROSETTE - 60 O   Similarly, if the angles between the gauges are , 60 o ; and . The unknown strains, for  , and will be,   22

23. Applications Structural health monitoring ( railroads, bridges, dams etc.) Vehicle classifications using strain gauge 23