Strain Gauge Rosette

9 Key excerpts on "Strain Gauge Rosette"

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  Mechanical Measurements

  Jones' Instrument Technology

  • B E Noltingk(Author)
  • 2016(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  They can be made integral with structural components and are used in this way for pressure measurement (see Chapter 9). Figure 4.5 Examples of semi-conductor gauges. Courtesy, Kulite Semiconductor Products Inc. 68 Measurement of strain 4.2.4 Rosettes We pointed out earlier that a full analysis of strain involves measurements in more than one direction. In fact, three measurements are required on a surface because strain can be represented as an ellipse, for which the magnitudes and directions of the axes must be established. The directions chosen for strain measurements are commonly either at 120° or at 45° and 90° to each other. If we are dealing with large structures, it may be expected that strain will only vary gradually across a surface and three closely spaced individual gauges can be thought of as referring to the same point. When there is little room to spare, it is desirable to have the three gauges constructed integrally, which anyhow simplifies installation. Such a unit is called a rosette. The three units may be either close together in one plane or actually stacked on top of each other (Figure 4.6). Figure 4.6 Rosette of gauges. Courtesy, Micro-Measurements Division, Measurements Group Inc. 4.2.5 Residual stress measurement The state of the surface at the time when a strain gauge is bonded to it has of course to be taken as the strain zero relative to which subsequent changes are measured. The gauge essentially measures increments of strain with increments of load. For many purposes of calculating stresses and predicting life, this is the most important thing to do. However, during fabrication, and before a gauge can be attached, some stresses can be locked up in certain parts and it may be desirable to know these. This cannot be done with any accuracy non-destructively but if we deliberately remove some material the observed strain changes in neighbouring material can tell us what forces were previously applied through the now absent material.

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  Theory and Design for Mechanical Measurements

  • Richard S. Figliola, Donald E. Beasley(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  An example of a two-element rosette is shown in Figure 11.16. For general measurements of strain and stress, commercially available strain rosettes can be chosen that have a pattern of multiple-direction gauges that is compatible with the specific nature of the particular application [ 5 ]. In practice, the applicability of the single-axis strain gauge is extremely limited, and improper use can result in large errors in the measured stress. Strain Gauge Rosettes are commercially available in a variety of configurations, including gauges placed at angles of 0, 45, 90 degrees and 60, 60, 60 degrees. Consider the rectangular rosettes with angles of 0, 45, 90 degrees as shown in Figure 11.17. As we have emphasized, measuring surface strain allows calculation of the principal stresses. Assume that the measured strains from the stacked gauge in Figure 11.17b are ε 1 (from the 0-degree gauge, oriented with the x -axis), ε 2 (from the 45-degree gauge), and ε 3 (from the 90-degree gauge, oriented with the y -axis). From these measured strains, the principal stresses, σ max and σ min, and the maximum shear stress, τ max, may be calculated. as σ max = E m 2 ε 1 + ε 3 1 − υ p + 1 1 + υ p (ε 1 − ε 3) 2 + [ 2 ε 2 − (ε 1 + ε 3) ] 2 σ min = E m 2 ε 1 + ε 3 1 − υ p − 1 1 + υ p (ε 1 − ε 3) 2 + [ 2 ε 2 − (ε 1[--=PLGO. -SEPARATOR=--]+ ε 3) ] 2 τ max = E m 2 (1 + υ p) (ε 1 − ε 3) 2 + [ 2 ε 2 − (ε 1 + ε 3) ] 2 11.39 The angle between the x -axis and the maximum principal stress is given by ϕ = 1 2 tan − 1 2 ε 2 − (ε 1 + ε 3) ε 1 − ε 3 11.40 FIGURE 11.16 Biaxial Strain Gauge Rosettes. (a) Single-plane type. (b) Stacked type. (Courtesy of Micro-Measurements, Raleigh, NC, USA.) FIGURE 11.17 Rectangular (0, 45, 90 degrees) Strain Gauge Rosettes. (a) Planar configuration. (b) Stacked configuration. Example 11.6 A rectangular Strain Gauge Rosette is composed of strain gauges oriented at relative angles of 0, 45, and 90 degrees, as shown in Figure 11.17b

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  Theory and Design for Mechanical Measurements

  • Richard S. Figliola, Donald E. Beasley(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  The result of these measurements yields the principal strains and allows determination of the maximum stress [3]. 414 STRAIN MEASUREMENT FIGURE 11.15 Hysteresis in initial loading cycles for two strain gauge materials. (Courtesy of Micro- Measurements, Raleigh, NC, USA.) +1000 0 +2000 +3000 +4000 +5000 Applied strain level in microstrain Applied strain level in microstrain R/R o (μΩ/Ω) –2500 0 +2500 +5000 +7500 +10,000 +12,500 +15,000 +17,500 +20,000 +22,500 1 +25,000 ST cycle +1000 0 +2000 +3000 +4000 +5000 +6000 R/R o (μΩ/Ω) 0 +1000 +2000 +3000 +4000 +5000 +6000 +7000 1ST cycle +1000 0 +2000 +3000 +4000 +5000 +6000 5TH cycle (There were 3 additional cycles to 6000 microstrain) +1000 0 +2000 +3000 6TH cycle +1000 0 +2000 +3000 +4000 +5000 2ND cycle +1000 0 +2000 +3000 +4000 +5000 3RD cycle The multiple-element strain gauges used to measure more than one strain at a point are called Strain Gauge Rosettes. An example of a two-element rosette is shown in Figure 11.16. For general measurements of strain and stress, commercially available strain rosettes can be chosen that have a pattern of multiple-direction gauges that is compatible with the specific nature of the particular application [5]. In practice, the applicability of the single-axis strain gauge is extremely limited, and improper use can result in large errors in the measured stress. Strain Gauge Rosettes are commercially available in a variety of configurations, including gauges placed at angles of 0, 45, 90 degrees and 60, 60, 60 degrees. Consider the rectangular rosettes with angles of 0, 45, 90 degrees as shown in Figure 11.17. As we have emphasized, measuring surface strain allows calculation of the principal stresses. Assume that the measured strains from the stacked gauge in Figure 11.17b are ε 1 (from the 0-degree gauge, oriented with 11.6 Apparent Strain and Temperature Compensation 415 (a) (b) FIGURE 11.16 Biaxial Strain Gauge Rosettes.

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  Mechanical Testing of Bone and the Bone-Implant Interface

  • Yuehuei H. An, Robert A. Draughn(Authors)
  • 1999(Publication Date)
  • CRC Press

    (Publisher)

  Misalignment errors are less critical if rosettes are used for measuring principal strains. 76-78 However, it should be noted that accurate principal strain measurements are dependent on accurate gauge orientation measurements. As such, careful alignment of gauges should not be abandoned when rosettes are utilized. Their relative insensitivity to misalignment makes these the gauges of choice when it is difficult to align gauges accurately along specific axes or landmarks or when only peak strains are of interest. Although the alignment of the rosettes during installation is not critical, as already noted, the accurate measurement of gauge orientation is critical in order to be able to complete the strain analysis. The equations used to assess the principal strains and principal strain directions are dependent on the type of rosette utilized and can be found in many fundamental mechanics books. 72,79 Rosettes are generally available in several different configurations (Figure 20.3) and the choice of a configuration usually depends on the proposed location of the gauge on the test specimen. Another choice that an investigator must make when using rosettes is whether to use a single-plane rosette (i.e., one in which all elements are in one plane) or a stacked rosette (i.e., one in which the elements are stacked on top of each other) (see Figure 20.3). The advantage of the single-plane rosette is that it has better heat dissipation properties and thus its measurements are more accurate when it is used on relatively flat specimens experiencing small strain gradients. Single-plane rosettes are more flexible than stacked rosettes and can be contoured to a specimen surface better. However, principal strain measurements can be extremely inaccurate when used on curved surfaces with large strain gradients because each element collects strain from a different location.

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  Hole-Drilling Method for Measuring Residual Stresses

  • Gary S. Schajer, Philip S. Whitehead, Gary S., Philip Schajer(Authors)
  • 2022(Publication Date)
  • Springer

    (Publisher)

  This arrangement increases the effective strain sensitivity of the rosette and also provides compensation for thermal strains, both very useful features when measuring small strains. The thermal strain compensation also greatly stabilizes measurements on low- conductivity materials that do not provide adequate heat dissipation for strain gauges when connected within quarter-bridges. In general, this rosette pattern should be used only for these purposes because the half-bridges are costly and time consuming to assemble. 4.2. SPECIMEN PREPARATION 71 In general, strain gauges are manufactured either as “open” rosettes or with encapsulated grids. Various hole-drilling rosette patterns beyond the three types specified in E837 are com- mercially available from several different manufacturers and can also give satisfactory results pro- viding that the associated calibration constants are used when computing the residual stresses from the measured strain data. Gauge manufacturers typically provide these calibration con- stants either explicitly or within available computer software. It is usual for the selection of the Strain Gauge Rosette to be based on the layout of the specimen, the size of the available target site and the depth to which residual stress data is required. The most commonly used rosette choice is the 1/16”-size. This rosette is drilled with 20 x 0.050 mm increments (as recommended in ASTM E837), which provides a good level of stress distribution detail and a final stress depth approaching 1 mm. If a greater level of stress distribution detail is required (especially close to the surface) then the 1/32”-size rosette (drilled with 20 x 0.025 mm increments to a final depth of 0.50 mm) may be more appropriate, provided that the hole can be drilled with the commensurate level of precision. Alternatively, if residual stress data is required to a greater depth, then the 1/8”-size rosette can provide data to depth 2 mm.

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  Mechanics of Materials Laboratory Course

  • Ghatu Subhash, Shannon Ridgeway, Ghatu Zimmerman(Authors)
  • 2022(Publication Date)
  • Springer

    (Publisher)

  4.2 THEORY OF STRAIN ROSETTE In Fig. 4.2, a strain rosette is oriented at an arbitrary angle ˛ to the horizontal (H ) and vertical (V ) axes. Here we use a 0 ı –45 ı –90 ı strain rosette to measure strains on a beverage can. Note that the outer two strain gages are at 0 ı and 90 ı and hence they form a convenient rectangular coordinate system with axes denoted as x and y. The x-axis is oriented at an angle ˛ to the H - axis. The student will bond a 0 ı –45 ı –90 ı strain rosette at an arbitrary angle ˛ to the axes of the cylindrical pressure vessel. Recall that each strain gage measures strain along its length direction. For a 0 ı ı 90 ı strain rosette, the following equations are relevant. Upon application of pressure, the following strains are measured by the strain gages along these directions: " x D " D0 D " 0 (4.1) " D " x cos 2 C " y sin 2 C xy sin cos D " x C " y 2 C " x " y 2 cos 2 C xy 2 sin 2 (4.2) " y D " D90 D " 90 (4.3) Although we have noted that the strain rosette is bonded at an arbitrary angle to the axis of the cylindrical beverage container, for convenience, we have chosen the x-axis as the axis of strain gage-1 ( D 0 ı ) irrespective of its orientation to the axis of the container. Also, for the middle gage, the generalized equation for strain in any orientation is given in Eq. (4.2), although in the strain rosette chosen here, the middle strain gage is at D 45 ı . In general, shear strain ( xy ) cannot be measured directly by a single strain gage because each strain gage can measure only axial strain in the direction of gage wire lay up and hence it needs to be calculated from Eq. (4.2). In this laboratory, we use strain measurements from the three gages in the strain rosette and Eqs. (4.1)–(4.3) to calculate shear strain ( xy /. Both " x and " y are measured directly dur- ing the experiment. Knowing the value of strain from strain gage at D 45 ı , i.e., " D45 , and

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  Handbook of Measurement in Science and Engineering, Volume 1

  • Myer Kutz(Author)
  • 2015(Publication Date)
  • Wiley

    (Publisher)

  2 ), and only two independent strain measurements are required.

  Conceptually, three uniaxial strain gages (or two uniaxial gages, if there are only two unknowns) could be used to measure strains in three (or two) different directions. However, as a practical matter it is easier to precisely align the gages in the intended orientation if three (or two) strain gages are bonded to the same backing by the gage manufacture. Strain gages produced in this manner are called strain gage rosettes.

  Strain gage rosettes are commonly available in three forms, as shown in Figure 11.7 . A biaxial rosette (also known as a T-rosette) consists of two perpendicular and electrically independent gage elements. Two types of three-element rosettes are available: the rectangular rosette, where the three gage elements are orientated in 45° increments, and the delta rosette, where the three gage elements are oriented in 60° increments.3

  FIGURE 11.7

  Common strain gage rosettes. (a) Biaxial rosette. (b) Rectangular rosette. (c) Delta rosette.

  11.2.4.1 Rosette Equations

  Three strain gages oriented at distinct angles θa , θb , and θc relative to the x-axis are shown in Figure 11.8 . Applying the first of Equation (11.2) to each of these gages in turn, we have

  (11.17)

  FIGURE 11.8

  A rectangular rosette relative to an x-y coordinate system.

  Equation (11.17) is called the general rosette equations. Since εa , εb , εc , θa , θb , and θc are all measured, we have three equations involving three unknowns, εxx , ε

  yy

  , and γxy .

  A rectangular rosette is shown relative to an x–y coordinate system in Figure 11.8

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  Theory and Design for Mechanical Measurements, International Adaptation

  • Richard S. Figliola, Donald E. Beasley(Authors)
  • 2023(Publication Date)
  • Wiley

    (Publisher)

  484 Chapter 11 | Strain Measurement 11.3 RESISTANCE STRAIN GAUGES The measurement of the small displacements that occur in a material or object under mechanical load can be accom- plished by methods as simple as observing the change in the distance between two scribe marks on the surface of a load- carrying member or as advanced as optical holography. In any case, the ideal sensor for the measurement of strain would (1) have good spatial resolution, implying that the sensor would measure strain at a point, (2) be unaffected by changes in ambient conditions, and (3) have a high-frequency response for dynamic (time-resolved) strain measurements. A sensor that closely meets these characteristics is the bonded resistance strain gauge. In practical application, the bonded resistance strain gauge is secured to the surface of the test object by an adhesive so that it deforms as the test object deforms. The resistance of a strain gauge changes when it is deformed, and this is easily related to the local strain. Both metallic and semiconductor materials experience a change in electrical resistance when they are subjected to a strain. The amount that the resistance changes depends on how the gauge is deformed, the material from which it is made, and the design of the gauge. Gauges can be made quite 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. In an 1856 publication in the Philosophical Transactions of the Royal Society in England, Lord Kelvin (William Thomson) [4] laid the foundations for understanding the changes in electrical resistance that metals undergo when sub- jected to loads, which eventually led to the strain gauge concept. Two individuals began the modern development of strain measurement in the late 1930s—Edward Simmons at the California Institute of Technology and Arthur Ruge at the Massachusetts Institute of Technology.

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  Sensor Systems

  Fundamentals and Applications

  • Clarence W. de Silva(Author)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  This process is much more economical and is more precise than making strain gauges with metal filaments. The strain-gauge element is formed on a backing film of electrically insulated material (e.g., polyamide plastic). This element is cemented or bonded using epoxy onto the member whose strain is to be measured. Alternatively, a thin film of insulating ceramic substrate is melted onto the measure-ment surface, on which the strain gauge is mounted directly. The direction of sensitivity is the major direction of elongation of the strain-gauge element (Figure 9.4a). To mea-sure strains in more than one direction, multiple strain gauges (e.g., various rosette con-figurations) are available as single units. These units have more than one direction of sensitivity. The principal strains in a given plane (the surface of the object on which the strain gauge is mounted) can be determined by using these multiple strain-gauge units. Output v o Direction of sensitivity (acceleration) Strain gauge Housing Seismic mass m Base Mounting threads Strain member cantilever FIGURE 9.3 A strain-gauge accelerometer. 441 Effort Sensors Typical foil-type gauges are shown in Figure 9.4b, and an SC strain gauge is shown in Figure 9.4c. A direct way to obtain strain-gauge measurement is to apply a constant DC voltage across a series-connected strain-gauge element (of resistance R ) and a suitable (complementary) resistor R c and to measure the output voltage v o across the strain gauge under open-circuit conditions (i.e., using a device of high input impedance). This arrangement is known as a “potentiometer circuit” or “ballast circuit” and has several weaknesses. Any ambient temperature variation directly introduces some error because of associated change in the strain-gauge resistance and the resistance of the connecting circuitry. Also, measurement accuracy will be affected by possible variations in the supply voltage v ref .

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