# Strain Gages Electrical resistance in material changes when the material is deformed R –...

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- Slide 1
- Strain Gages Electrical resistance in material changes when the material is deformed R Resistance Resistivity l Length A Cross-sectional area Taking the differential Change in resistance is from change in shape as well as change in resistivity For linear deformations strain S s sensitivity or gage factor ( 2-6 for metals and 40 200 for semiconductor )
- Slide 2
- The change in resistance is measured using an electrical circuit Many variables can be measured displacement, acceleration, pressure, temperature, liquid level, stress, force and torque Some variables (stress, force, torque) can be determined by measuring the strain directly Other variables can be measured by converting the measurand into stress using a front-end device Output v o Direction of Sensitivity (Acceleration) Strain Gage Housing Seismic Mass m Base Mounting Threads Strain Member Cantilever Strain gage accelerometer
- Slide 3
- Direction of Sensitivity Foil Grid Backing Film Solder Tabs (For Leads) Single Element Two-Element Rosette Three-Element Rosettes Nickle-Plated Copper Ribbons Welded Gold Leads Doped Silicon Crystal (P or N Type) Phenolic Glass Backing Plate Strain gages are manufactured as metallic foil (copper-nickel alloy constantan) Semiconductor (silicon with impurity)
- Slide 4
- Potentiometer or Ballast Circuit v o Output v ref (Supply) Strain Gage + - RcRc R Ambient temperature changes will introduce error Variations in supply voltage will affect the output Electrical loading effect will be significant Change in voltage due to strain is a very small percentage of the output Question: Show that errors due to ambient temperature changes will cancel if the temperature coefficients of R and R c are the same
- Slide 5
- Wheatstone Bridge Circuit v ref (Constant Voltage) - + R 1 A R 2 R 3 R 4 B RLRL vovo - + Load (High) Small i When the bridge is balanced True for any R L
- Slide 6
- Null Balance Method When the stain gage in the bridge deforms, the balance is upset. Balance is restored by changing a variable resistor The amount of change corresponds to the change in stain Time consuming servo balancing can be used Direct Measurement of Output Voltage Measure the output voltage resulting from the imbalance Determine the calibration constant Bridge sensitivity To compensate for temperature changes, temperature coefficients of adjacent pairs should be the same
- Slide 7
- The Bridge Constant More than one resistor in the bridge can be active If all four resistors are active, best sensitivity can be obtained R1 and R4 in tension and R2 and R3 in compression gives the largest sensitivity The bridge sensitivity can be expressed as Bridge Constant
- Slide 8
- Example 4.4 A strain gage load cell (force sensor) consists of four identical strain gages, forming a Wheatstone bridge, that are mounted on a rod that has square cross- section. One opposite pair of strain gages is mounted axially and the other pair is mounted in the transverse direction, as shown below. To maximize the bridge sensitivity, the strain gages are connected to the bridge as shown. Determine the bridge constant k in terms of Poissons ratio v of the rod material. v ref + + vovo 1 2 34 1 Axial Gage 2 Transverse Gage Cross Section Of Sensing Member 3 4 Transverse strain = (-v) x longitudinal strain
- Slide 9
- Calibration Constant k Bridge Constant S s Sensitivity or gage factor
- Slide 10
- Example 4.5 A schematic diagram of a strain gage accelerometer is shown below. A point mass of weight W is used as the acceleration sensing element, and a light cantilever with rectangular cross-section, mounted inside the accelerometer casing, converts the inertia force of the mass into a strain. The maximum bending strain at the root of the cantilever is measured using four identical active semiconductor strain gages. Two of the strain gages (A and B) are mounted axially on the top surface of the cantilever, and the remaining two (C and D) are mounted on the bottom surface. In order to maximize the sensitivity of the accelerometer, indicate the manner in which the four strain gages A, B, C, and D should be connected to a Wheatstone bridge circuit. What is the bridge constant of the resulting circuit? v ref + + v o A B C D W Strain Gages A, B C, D l b h A B C D
- Slide 11
- Obtain an expression relating applied acceleration a (in units of g) to bridge output (bridge balanced at zero acceleration) in terms of the following parameters: W = Mg = weight of the seismic mass at the free end of the cantilever element E = Youngs modulus of the cantilever l = length of the cantilever b = cross-section width of the cantilever h = cross-section height of the cantilever S s = gage factor (sensitivity) of each strain gage v ref = supply voltage to the bridge. If M = 5 gm, E = 5x10 10 N/m 2, l = 1 cm, b = 1 mm, h = 0.5 mm, S s = 200, and v ref = 20 V, determine the sensitivity of the accelerometer in mV/g. If the yield strength of the cantilever element is 5xl0 7 N/m2, what is the maximum acceleration that could be measured using the accelerometer? If the ADC which reads the strain signal into a process computer has the range 0 to 10 V, how much amplification (bridge amplifier gain) would be needed at the bridge output so that this maximum acceleration corresponds to the upper limit of the ADC (10 V)? Is the cross-sensitivity (i.e., the sensitivity in the two directions orthogonal to the direction of sensitivity small with this arrangement? Explain. Hint: For a cantilever subjected to force F at the free end, the maximum stress at the root is given by
- Slide 12
- Mechanical Structure Signal Conditioning MEMS Accelerometer Applications: Airbag Deployment
- Slide 13
- Data Acquisition AC Bridge Calibration Constant OscillatorPower Supply Amplifier Demodulator And Filter Dynamic Strain Reading Supply frequency ~ 1kHz Output Voltage ~ few micro volts 1 mV Advantages Stability (less drift), low power consumption Foil gages - 50 k Power consumption decreases with resistance Resolutions on the order of 1 m/m
- Slide 14
- Semiconductor Strain Gages Single Crystal of Semiconductor Gold Leads Conductor Ribbons Phenolic Glass Backing Plate Gage factor 40 200 Resitivity is higher reduced power consumption Resistance 5k Smaller and lighter
- Slide 15
- MaterialCompositionGage Factor (Sensitivity) Temperature Coefficient of Resistance (10 -6 / C) Constantan45% Ni, 55% Cu 2.015 Isoelastic36% Ni, 52% Fe, 8% Cr, 4% (Mn, Si, Mo) 3.5200 Karma74% Ni, 20% Cr, 3% Fe, 3% Al 2.320 Monel67% Ni, 33% Cu 1.92000 Siliconp-type 100 to 17070 to 700 Siliconn-type -140 to 10070 to 700 Properties of common strain gage material
- Slide 16
- Disadvantages of Semiconductor Strain Gages The strain-resistance relationship is nonlinear They are brittle and difficult to mount on curved surfaces. The maximum strain that can be measured is an order of magnitude smaller 0.003 m/m (typically, less than 0.01 m/m) They are more costly They have a much larger temperature sensitivity. 321123 0.2 0.1 0.1 0.2 0.3 0.4 0.3 Strain 10 3 Resistance Change = 1 Microstrain = Strain of 110 -6 321123 0.2 0.1 0.1 0.2 0.3 0.4 0.3 Strain 10 3 Resistance Change P-type N-type
- Slide 17
- For semiconductor strain gages S 1 linear sensitivity Positive for p-type gages Negative for n-type gages Magnitude is larger for p-type S 2 nonlinearity Positive for both types Magnitude is smaller for p-type
- Slide 18
- Linear Approximation Strain Change in Resistance Quadratic Curve max max Linear Approximation 0 Error Quadratic Error Minimize Error = 0 Maximum Error
- Slide 19
- Range change in resistance Percentage nonlinearity error
- Slide 20
- Temperature Compensation Compensation Feasible Compensation Not Feasible Compensation Feasible () Concentration of Trace Material (Atoms/cc) Temperature coefficients (per F) 0 1 2 3 = Temperature Coefficient of Resistance = Temperature Coefficient of Gage Factor Resistance change due to temperature Sensitivity change due to temperature
- Slide 21
- R4R4 R1R1 R2R2 R3R3 v o + Compensating Resistor R c v ref + vivi R R + vivi R R + RcRc Self Compensation with a Resistor For self compensation the output after the temperature change must be the same Possible only for certain ranges

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