strain gauges

Applications of Resistance Strain Gauges

in Measurements

Deepak Garg13209010ME 1st Year

STRAIN GAUGES

• A Strain Gauge is a device used to measure the strain of an object

• The gauge is attached to the object by a suitable adhesive

• As the object is deformed, the foil is deformed, causing its electrical resistance to

change

• The resistance change is commonly measured using a Wheatstone bridge

• The most common type of strain gauge consists of an insulating flexible backing which

supports a metallic foil pattern

What’s the Wheatstone Bridge?

• Wheatstone bridge is an electric circuit suitable for detection of minute resistance

changes., therefore used to measure resistance changes of a strain gage

• The bridge is configured by combining four resistors as shown in Fig.• Initially R1=R2=R3=R4, in this condition no

output voltage is there, e=0

• When one of the Resistances is replaced by strain

Gauge attached to the object whose strain is to be

measured and load is applied, then there is small

change in the resistance of gauge, hence some output

voltage is there which can be related to strain as

From this, strain can be easily determined using the relation

Half Bridge Configuration

To increase the sensitivity of measurement,

two strain gauges are connected in the

bridge, this type of configuration is called as

Half bridge as shown in fig. and the output

voltage and strain can be related as

When gauges are connected to adjacent

arms and

When gauges are connected to opposite

arms

Full Bridge Configuration

To further enhance the sensitivity, all 4

resistances are replaced by strain gauges.

While this system is rarely used for strain

measurement, it is frequently applied to

strain-gage transducers. When the gages at

the four sides have their resistance changed

to R1 + ΔR1, R2 + ΔR2, R3 + ΔR3 and R4

+ ΔR4, respectively, the bridge output

voltage,

e, is

Or

Where K is the Gauge Factor.

Applications of 2-gage system (Strain Cantilever)

The 2-gage system is mostly used for the

following Case

•To measure the bending Strain

•To measure the tensile strain

To measure the Bending Strain,

Configuration 1 is used as shown in fig I

because output voltage from the circuit would

become if fig II is used.

To measure the Tensile strain, Configuration

shown in Fig II is used and not fig I as output

voltage from circuit become zero in the case of

tensile loading.

Fig I

Fig II

Temperature Effects and Need for Temperature Compensation

Measurements are performed with strain gauges in mechanical stress analysis to examine

loading and fatigue. In addition to the desired measurement signal indicating mechanical

strain, each strain gauge also produces a temperature-dependent measurement signal. This

signal, called the apparent strain, is superimposed on the actual measured value.

Various effects contribute to the apparent strain:

• Thermal expansion of the measurement object (i.e. strain due entirely to temperature with

no mechanical loading as the cause)

• Temperature-dependent change in the strain gauge resistance

• Thermal contraction of the strain gauge measuring grid foil

• Temperature response of the connection wires

Methods For Temperature Compensation

•Active Dummy method

•Temperature Response matching or self compensation method

•by connecting several strain gauges together to form a half or full bridge

Active Dummy Method

•The active-dummy method uses the 2-gage system where an active gage, A, is bonded to

the measuring object and a dummy gage, D, is bonded to a dummy block which is free

from the stress of the measuring object but under the same temperature condition as that

affecting the measuring object. The dummy block should be made of the same material as

the measuring object.

•As shown in Fig, the two gages are connected to adjacent sides of the bridge. Since the

measuring object and the dummy block are under the same temperature condition,

thermally-induced elongation or contraction is the same on both of them. Thus, gages A

and B bear the same thermally-induced strain, which is compensated to let the output, e,

be zero because these gages are connected to adjacent sides.

Self-Temperature-Compensation Method

• Theoretically, the active-dummy method described above is an ideal temperature

compensation method. But the method involves problems in the form of an extra task to

bond two gages and install the dummy block. To solve these problems, the self-

temperature-compensation gage was developed as the method of compensating

temperature with a single gage.

• With the self-temperature-compensation gage, the temperature coefficient of resistance

of the sensing element is controlled based on the linear expansion coefficient of the

measuring object. Thus, the gage enables strain measurement without receiving any

thermal effect if it is matched with the measuring object.

• The apparent strain that comes into play as the temperature changes can be represented

in a simplified manner as follows

Where:

εs = apparent strain of the strain gauge

∝r = temperature coefficient of the electrical resistance of the measuring grid foil

∝b = thermal expansion coefficient of the measurement object

∝m = thermal expansion coefficient of the measuring grid material

k = gauge factor (sometimes called k factor) of the strain gauge

∧ϑ = temperature difference that triggers the apparent strain

•The temperature coefficient of the electrical resistance of the measuring grid foil is

adapted by technical production measures so that the terms of the equation cancel each

other out; thus r = ( m - b) • k. ∝ ∝ ∝•Accordingly, there are different types of strain gauges that are identical in terms of

geometry and resistance values, but differ in temperature response matching for the

material on which the strain gauge is installed. Temperature response matching to a wide

range of thermal expansion coefficients is available (for example, to ferritic steel with a

thermal expansion coefficient of 10.8 • 10-6/K, or aluminum with 23 • 10-6/K).

Applications of strain Gauges

Strain gauges are basically strain transducers which converts the mechanical signals into

electrical signals and hence measure the strain produced. This strain can be utilized further

to measure the following quantities as given:

•Force

•Torque

•Pressure

•Flow Rate

•Residual Stresses

Measurement of Force•Force can be measured using strain gauge load cells

•A load cell is a transducer that is used to convert a force into electrical signal

•A load cell is made by bonding strain gauges to a spring material. To efficiently detect

the strain, strain gauges are bonded to the position on the spring material where the strain

will be the largest

•Two gauges are along the direction of

applied load and other two are at right

angle to these.

•When there is no load, all gauges have

same resistance and bridge is balanced

•When load is applied, there is change in

resistance and hence some output voltage

is there which is the measure of applied load.

e= V/2*(1+µ)*(K*P)/(A*E)

P= Load to be Measured Tension-compression resistance strain-gage load cell

Pressure Measurement • Use elastic diaphragm as primary pressure transducer

• Apply strain gage directly to a diaphragm surface and calibrate the measured strain in

terms of pressure

• Pressure is measured through force that is exerted on the diaphragm where the force will

be detected by the strain gauge and resistance change will be produced

Location of strain gages on

flat diaphragm

The central gage is subjected

to tension while the outer

gage senses compression

Flow Measurement

Torque Measurement

• Four bonded-wire strain gauges are mounted on a 450 helix with axis of rotation and

place in pairs diametrically opposite as shown in figure

• If gauges are accurately placed and have matched characteristics, the system is

temperature compensated and insensitive to bending, thrust or pulls

• Any change in resistance is purely due to torsion of shaft, hence the torque can be

determined by measuring change in voltage which can be written as

T=e/(V*K)[J*E/r(1-µ)]

Where

e= Change in Voltage

V=Applied Voltage

K=Gauge Factor

J=Polar Moment of Inertia

E=Young’s Modulus

r= Radius of Member

Amplification and Digitization of Output

Electronic Circuitry for Gain and Digitization

Measurement of Cutting Force and Torque in Drilling By Drill Tool Dynamometer

Measurement of Residual Stresses by Hole-Drilling Strain Gage Method

The most widely used modern technique for measuring residual

stress is the hole-drilling strain-gage method of stress relaxation,

Shown in fig. Briefly summarized, the measurement procedure

involves six basic steps:

•A special three element strain gage rosette is installed on the test

part at the point where residual stresses are to be determined

•The gage grids are wired and connected to a multi channel static

strain indicator

•After zero-balancing the gage circuits, a small, shallow hole is

drilled through the geometric center of the Rosette

•Readings are made of the relaxed strains, corresponding to the

initial residual stress

•Using special data-reduction relationships, the principal residual

stresses and their angular orientation are calculated from the

measured strains

Three-Element Rosettes

Through-Hole Analysis

Depicted in Figure (a) is a local area within a

thin plate which is subject to a uniform residual

stress, σx. The initial stress state at any point P

(R, α) can be expressed in polar coordinates by:

Figure (b) represents the same area of the plate

after a small hole has been drilled through it.

The stresses in the vicinity of the hole are now

quite different which can be given as:

Subtracting the initial stresses from the final (after drilling) stresses gives the change in

stress, or stress relaxation at point P (R, α) due to drilling the hole. That is:

Selection and Installation Factors for Bonded Metallic Strain Gages

•Grid material and configuration

•Backing material

•Bonding material and method

•Gage protection

•Associated electrical circuitry

Desirable Properties of Grid Material

•High gage factor, F

•High sensitivity

•Low temperature sensitivity

•High electrical stability

•High yield strength

•High endurance limit

•Good solderability or weldability

•Low hysteresis

•Low thermal emf when joined to other materials

•Good corrosion resistance

Properties of Common Grid Materials

Common Backing Materials

•Thin paper

•Phenolic-impregnated paper

•Epoxy-type plastic films

•Epoxy-impregnated fiberglass

•Most foil gages use an epoxy film backing

Bonding Procedure• Select Strain Gauge

The two primary criteria for selecting the right type of

strain gauge are sensitivity and precision. So Select

the strain gauge model and gage length which meet

the requirements of the measuring object and

purpose

• Remove Dust and Paint

Using a sand cloth polish the strain-gage bonding site

over a wider area than the strain-gage size. Wipe

off paint, rust and plating, if any, with a grinder or

sand blast before polishing

• Decide Bonding Position

Using a pencil or a marking-off pin, mark the

measuring site in the strain direction. When using a

marking off pin, take care not to deeply scratch the

strain-gage bonding surface

Bonding Procedure

• Remove grease from bonding surface and clean

Using an industrial tissue paper (SILBON paper)

dipped in acetone, clean the strain-gage bonding

site. Strongly wipe the surface in a single direction

to collect dust and then remove by wiping in the

same direction. Reciprocal wiping causes dust to

move back and forth and does not ensure cleaning

• Apply adhesive

Ascertain the back and front of the strain gage. Apply

a drop of adhesive to the back of the strain gage.

Do not spread the adhesive. If spreading occurs,

curing is adversely accelerated, thereby lowering

the adhesive strength

Bonding Procedure• Bond strain gage to measuring site

After applying a drop of the adhesive, put the strain gage on

the measuring site while lining up the center marks with

the marking off lines

• Press strain gage

Cover the strain gage with the accessory polyethylene sheet

and press it over the sheet with a thumb. Once the strain

gage is placed on the bonding site, do not lift it to adjust

the position

• Complete bonding work

After pressing the strain gage with a thumb for one minute or

so, remove the polyethylene sheet and make sure the

strain gage is securely bonded. The above steps complete

the bonding work. However, good measurement results

are available after 60 minutes of complete curing of the

adhesive

Some Adhesives and Their Preferred Curing Time

Protecting the Strain Gage

• The strain gages must be protected from ambient conditions e.g. moisture, oil, dust and

dirt•Protective materials used are Petroleum waxes, silicone resins, epoxy preparations,

rubberized brushing compounds

Many materials can be used to protect strain gage installations. Perhaps

none is more versatile for short-term applications than room-temperature

vulcanizing (RTV) silicone rubber. The list of this material's capabilities

is indeed impressive:

• Available as an easy-to-apply single-component coating with uncured

consistencies ranging from a low-viscosity brush-on material for thin

coats, to a medium viscosity self-levelling form for use on level surfaces,

to a high-viscosity no-run paste for vertical and overhead applications.

• Cures at room temperature, yet is usable over a temperature range of -

75° to +550°F (-60° to +290°C).

• Has a low modulus of elasticity that is ideal for thin or flexible

structures for which coating reinforcement effects may become

significant.

• Provides good short-term protection from water; resists many

chemicals; and can be used in radiation and vacuum environments.

RTV Silicone Rubber Coatings

Some Gage Orientation and Interpretation of Results

Bar with Axial Loading

Bar with Transverse Loading

Torsion

Possible sources of error in strain gauge signals

1- Cross-sensitivity

Because a strain gauge has width as well as length, a small proportion of the resistance

element lies at right angles to the major axis of the gauge, at the points where the conductor

reverses direction at the ends of the gauge. So as well as responding to strain in the direction

of its major axis, the gauge will also be somewhat responsive to any strain there may be at

right angles to major axis.

2- Bonding faults

For perfect bonding, the suitable adhesives and procedures for bonding gauges to the strain

surface should be complied. If the bonding is unsatisfactory, creep may occur. Creep is a

gradual relaxing of the strain on the strain gauge, and it has the effect of decreasing the gauge

factor, so that the output of the bridge becomes less than it should be. Creep may also occur

where gauges have been used to measure dynamic strain, and have been subjected to many

thousands of cycles of strain.

3- Hysteresis

If a strain gauge installation is loaded to a high value of strain and then unloaded, it may be

found that the gauge element appears to have acquired a permanent set, so that resistance

values are slightly higher when unloading. The same effect continues when the direction of

loading is reversed. To manipulate this problem, repeating cycles of loading/unloading

should cause the hysteresis loop to narrow to negligible

4- Effects of moisture

The gauges or the bonding adhesive may absorb water. This can cause dimensional changes

which appear as false strain values. Another effect when moisture connections forms high

resistance connected in parallel with the gauge. To prevent this, gauges should be bonded in

dry condition or a suitable electrically insulating water repellent, such as a silicone rubber

compound.

5- Temperature change

One possible source of temperature difference is the heat produced by the current through a

strain gauge. When the bridge is first switched on, the gauges may warm up, so the bridge

should not be used for measurement until sufficient time for temperature to stabilize.