Strain Gauge PDF

Resistive Strain Gages Bonded gages: fine wire or conducting film cemented to a structural member to measure its strain. Unbonded gages: wires not bonded to any structure, but may be originally under some tension. Generally, elongation or compression of the gage wires, in response to mechanical l...

Resistive Strain Gages Bonded gages: fine wire or conducting film cemented to a structural member to measure its strain. Unbonded gages: wires not bonded to any structure, but may be originally under some tension. Generally, elongation or compression of the gage wires, in response to mechanical load, causes a change in the resistance of the gage conductor (wire), which can be accurately sensed using a wheatstone bridge circuit.  Features of the metallic bonded strain gauge It is composed of a thin metal (e.g., constantan) wire or film, approximately 0.025 mm thick, that is deposited on a base (e.g., polyimide backing material) for protection and electric insulation. The strain gauge wire or film can also be sandwiched between two polymeric protective transparent layers with the solder tabs exposed at the up-facing side during mounting. The strain gauge package is bonded to the surface by using an adhesive bonding agent Strain gauge wired and soldered using a connector (bondable) terminal At a given temperature, the resistance of a wire is given by: L R=  A If a load W is applied, the wire will be stressed by: W s=σ = (stress) A ΔL s σ ε= = = (strain) L Y E where; Y = E = Young's modulus of elasticity for the wire material  L R=  Applying Taylor’s series expansion on R yields; A − L L  R = 2 A +  + L A A A The fractional change in R, R A  L =− + + R A  L the gage factor can be defined as; R / R R / R  /  A / A GF = = = 1+ − L / L  L / L L / L  ΔL dA ΔA dD 2ΔD Note that : = ε , also, = =2 = L A A D D From the definition of Poisson's ratio  ; ΔD ΔL = -μ = -μ ε D L The gage factor can then be written in the following form; ΔR/R ΔR/R Δρ/ρ -2μ ε GF = = = 1+ − ΔL/L ε ε ε 1 dρ 1  R  GF = 1+ 2μ + , local strain =  =   ε ρ GF  R  Typical value of Poison’s ratio for many materials is 0.3  1  R  local strain =  =   GF  R  The value of gage factor and the resistance are usually specified by the manufacturer. User only needs to measure the value of ∆R in order to determine the local strain. For most gages GF is constant over wide range of strains. If the resistivity ρ of the material does not vary with strain, then: 0 1 d GF = 1 + 2  +  GF = 1+ 2 μ    A high gage factor GF is desirable in practice because a larger change in resistance ∆R is produced for a given strain input, thereby necessitating less sensitive readout circuitry. Resistance element must be securely bonded to its mounting (strong bond). (any slip ➔ error) 1. Surface must be absolutely clean (cleaning with emery cloth followed by acetone). 2. Sufficient time must be allowed for the cement to dry and harden completely.  Types of bonded strain gages: Wire gage Foil gage Semiconductor gage (high GF) - Output of strain gage bridges generally need amplification (Op-amps). - Sensitivity to temperature changes can be reduced by using two matched gauges on one side of the bridge. (one gauge unstrained and acts as a thermal compensator for the active bottom gauge). - Both gauges are at the same temperature! Gage Compensation Gage 2 Gage 1 R2 Active gage R1 Inactive gage - Frequency response of the bonded strain gauges is largely dependent on the mechanical properties of the structure to which it is bonded. - Power excitation voltage is limited by power dissipation in the wire and heating in the resistances/gages. - Strain sensitivity: is the minimum deformation that can be indicated by the gage per unit base length. (base length = the length over which the average strain measurement is taken) Unbonded Resistance Strain Gage Two pairs of wires initially under tension. When force is applied, one pair is strained more and the other less in equal amounts. Fine-wire filaments are stretched around the mounting pins. Unbonded strain gauge with four active sets of resistance wires Unbonded Resistance Strain Gage - Mounting pins must be rigid and also serve as electrical insulators. - Mechanical resonance limits high frequency response (spring-mass system). - Power excitation voltage is limited by power dissipation (I2R) in the wire and heating in the resistances. - No means for heat dissipation other than convection to surrounding air. - Unbonded gage has been successfully used in acceleration and diaphragm pressure transducers. Different states of stress One important objective of stress analysis is to locate the orientation of principal stresses at arbitrary points on a component.  x = E x Uniaxial loading (Tension or where, compression) ➔ single gage can determine the P force state of stress. x = = A cross - sectional area or , Papplied = AE x Biaxial loading axial stress Loading in two r orthogonal directions  y strain gage  x strain gage hoop stress Cylindrical (thin-walled) Pressure vessel For a thin-walled pressure vessel (t/r < 0.1), the stresses are approximated by:  x = transverse or hoop stress  y = axial or longitudinal stress Substituting for the stresses from the previous slide, pressure in the vessel based on the strain gage measurements yields: Strain gages ➔ Pressure gage? For complex loading or complex geometry three directions are needed.➔ strain gage rosette. General state of planar stress on component surface Rectangular strain gage rosette Rectangular strain gauge rosette  Most common strain gage rosette configurations From principles of solid mechanics, magnitudes and direction of principal stresses can be determined (for a rectangular rosette): If the numerator is positive then 2θp lies in the first or second quadrant so 0 < θp < 90°, Otherwise, 2θp lies in the 3rd or 4rth quadrant so -90° < θp < 0. Similar relations exist for the equiangular (delta) and the T-delta rosettes.