ME411 Engineering Measurement & Instrumentation. Winter 2017 Lecture 9

Transcription

1 ME411 Engineering Measurement & Instrumentation Winter 2017 Lecture 9 1

2 Introduction If we design a load bearing component, how do we know it will not fail? Simulate/predict behavior from known fundamentals if simple enough! Even with a model, we need verification or at least information to develop a model! Stress analysis measure the deformation of a part then infer the stresses from the deformation 2

3 Stress & Strain For a rod under tension d L where d is the d diameter Lateral strain is related to chance in diameter of the rod (has to narrow conservation of mass 3

4 Stress & Strain Elastic region In the elastic region there is a constant rate of chance in the lateral strain as the axial strain increases Poisson s ratio 4

5 2D strains For 2D cases, all the stress and strain components lie in the same place Measurement made at surface of part (in plane) Can only measure surface stresses 5

6 Strain measurement techniques Contact method: A sensor in contact with the test specimen LVDT (Linear variable differential transformer; used in tensile testing) Strain gauge (gage adhere to the test specimen surface) Optical: use of a material that will produce patterns that can be used to determine strain Photoelasticity Moiré interferometry 6

7 Ideal Instrument to Measure Strain Good spatial resolution Unaffected by ambient condition change High frequency response for dynamic strain A sensor that closely meets these characteristics is the bonded resistance strain gauge

8 Resistance strain gauges Consider a conductor ( wire ) with uniform crosssectional area, A and length L made of a material having a resistivity,. This wire has a resistance given by: If subjected to a normal stress along the axis of the wire, A and L change change in R A single wire would work, but practically the signal would be too weak for sufficient resolution Increase signal by bending wire back and forth! 8

9 Resistance strain gauges Gauge length is the ultimate resolution strain is averaged over that size Choice of strain gauge used depends on application Special construction Special bonding techniques Resolution (both spatially and the change in resistance) Sensitivity! 9

10 Resistance strain gauges Change in resistance of strain gauge is expressed empirically in terms of the gauge factor, GF GF depends on Poisson s ratio (usually about 0.3) and piezoresistivity typically GF = 2 A Wheatstone bridge is generally used to detect the small changes in resistance that are the output of a strain gauge measurement circuit. Equipment is commercially available that can measure changes in gauge resistance of less than Ω ( µε). A simple strain gauge Wheatstone bridge circuit is shown next. 10

11 Strain gauge electrical circuit If bridge is initially balanced (Eo = 0), and all the fixed resistors and strain gauge resistance are initially equal then: 11

12 Strain Gauge Electrical Circuits The Wheatstone bridge has several distinct advantages for use with electrical resistance gauges. The bridge may be balanced by changing the resistance of one arm of the bridge. Therefore, once the gauge is mounted in place on the test specimen under a condition of zero loading, the output from the bridge may be zeroed. There are two schemes for circuits to accomplish this balancing.

13 Strain Gauge Electrical Circuits Shunt balancing is the best, since changes in resistances are small. The strategic placement of multiple gauges in a Wheatstone bridge can both increase the bridge output and cancel out certain ambient effects and unwanted components of strain.

14 Multiple Gauge Bridge The output from a bridge circuit can be increased by the appropriate use of more than one active strain gauge. The use of multiple gauges can be used to compensate for unwanted effects, such as temperature or specific strain components. Consider the case when all four resistances in the bridge circuit represent active strain gauges.

15 Multiple Gauge Bridge In general, the bridge output is given by: If these gauges are now subjected to strains such that the resistances change by dri, where i = 1, 2, 3, and 4, then the change in the bridge output voltage can be expressed by:

16 Multiple Gauge Bridge Evaluating the appropriate partial derivatives from Eq yields:

17 Multiple Gauge Bridge Assuming dri << Ri, the resulting change in output voltage δeo may now be expressed as δeo where: If R1= R2= R3= R4, then

18 Multiple Gauge Bridge It is possible to purchase matched sets of strain gauges for a particular application, so that GF1 = GF2 = GF3 = GF4, and:

19 Multiple Gauge Bridge The last equation shows that for a bridge containing one or more active strain gauges, equal strains on opposite bridge arms sum, whereas equal strains on adjacent arms of the bridge cancel. These characteristics can be used to increase the output of the bridge, to provide temperature compensation, or to cancel unwanted components of strain.

20 Bridge Constant Commonly used strain gauge-bridge arrangements may be characterized by a bridge constant, k, defined as the ratio of the actual bridge output to that output of a single gauge sensing the maximum strain, ε max (assuming the remaining bridge resistances remain fixed).

21 Common gauge mountings 21

22 Apparent Strain Compensation Apparent strain is manifested as any change in gauge resistance that is not due to the component of strain being measured. Techniques for accomplishing temperature compensation, eliminating certain components of strain, and increasing the value of the bridge constant can be devised. The bridge constant is influenced by (1) the location of strain gauges on the test specimen and (2) the gauge connection positions in the bridge circuit.

23 Apparent Strain Compensation A component of strain can be removed (compensation) from the measured signal. Consider a beam having a rectangular cross-section and subject to the loading condition, shown in the next slide, where the beam is subject to an axial load F N and a bending moment, M.

24 Apparent Strain Compensation Source: Figliola and Beasley

25 Apparent Strain Compensation To remove the effects of bending strain, identical strain gauges are mounted to the top and bottom of the beam. They are connected to bridge locations 1 and 4 (opposite bridge arms). The gauges experience equal but opposite bending strains and both strain gauges are subject to the same axial strain caused by F N.

26 Apparent Strain Compensation The bridge output under these conditions is: Where ε 1 = ε a1 + ε b1 and ε 4 = ε a4 - ε b4,with subscripts a and b referring to axial and bending strain, respectively.

27 Apparent Strain Compensation Hence, the bending strains cancel but the axial strain will sum, giving:

28 Strain Gauge Arrangement for Temperature Compensation Source: Figliola and Beasley

29 Optical Strain Measurement Techniques Photoelasticity - is the study of stress and strain field distributions within a loaded photoelastic specimen, as viewed under a polariscope. Moiré Interferometry - is a high-sensitivity method for measuring in-plane deformations over the surface of specimens. Full-field deformation contour maps in both the x and the y direction can be observed and recorded.

30 Photoelasticity Circular polariscope ( hotoelasticity)

31 Photoelasticity Example

32 Moiré Interferometry From

33 Residual stresses in friction stir welded aluminum alloy plates

34 Strain GaugeTraining videos Be sure to watch the following videos before you go to the lab: Strain Gage Surface Preparation for Steel and Aluminum Alloys CEA Strain Gage Installation with M-Bond 200 Adhesive Soldering and Coating a CEA Strain Gage 34

35 Image credits All images from Figliola and Beasley, Mechanical Measurements 5 th edition unless otherwise stated 35