|
  
|
||
|
|
||
The strain gage measurement is a very nice principle of measurement strain, and with that also stress of the materials. Strain gages are basically foil resistors which are using the principle that the line resistance of the wire is proportional to the length and inversely to the area of the cross section. A typical strain gage material is constantan (copper-nickel alloy), which has a constant resistance over a big temperature range. The change, however, of resistance with strain is very small, so we need a good amplifier and measurement principle to measure such small differences. |
|
Wheatstone bridge
The most widely used principle to measure strain gage is the Wheatstone bridge. This bridge consists of four resistors. On the inputs, we supply the so-called excitation voltage and measures the voltage of the outputs. If the bridge is balanced, the output voltage will be zero. |
|
There are now several ways to mount the strain gages. This depends a lot on the specific application. For a better understanding on how to use the software and what the values mean, let's take a look at the basic equation of the bridge.
One of the more common configurations of the bridge is a quarter-bridge. In this case, only one resistor is a strain gage while the other three are fixed resistors with equal resistance, which use the nominal resistance of the strain gage (this shows that the bridge is balanced). Therefore let's say that R4=R+dR and all the rest are equal R1=R2=R3=R. Now let's put this in the equation above.
The 2*dR/R part is quite small (1% of elongation gives a 1% error), so this can simplify the equation to:
The basic parameter of the strain gage is a so-called gage factor k. This gage factor tells us the amount of change of the resistance in relationship to the strain.
|
→ therefore the dR / R=k · ε |
If we insert this in equation above, we get:
If the user has a different bridge configuration, this factor needs to be entered in the DEWESoft program. This is the so-called bridge factor. The equation thus changes to:
The bridge factors are given in the table for all bridge configurations.
The measured value from the strain gage is therefore the strain:
ε = dL / L
The strain is usually presented in um/m, so the ratio of elongation in micrometers comparing to the length of a specimen in meters. So what does that really mean if we measured a value of 2000? First of all, we can also express this in percent. Strain in um/m divided by 10000 is elongation in percent. In the case of 2000, the elongation will be 0.2%.
We can also judge from this value how close the material is from its limit of elasticity. For steel, this limit is app. 2% (this depends heavily on the type of steel), so were exceed 20000 um/m, the specimen would be over its tolerance of elasticity and would be permanently stretched. The full bridge example will demonstrate how to calculate stress and force from the strain.
Bridge configurations
There are several configurations for basic measurements. First, we need to know the special effects of the materials - that is when the material is stretched, the material (usually) gets thinner in the other (two) directions. The ratio of transverse strain to extension strain is called Poisson's ratio ν.
When strain gages are positioned 90 deg. towards each other, it becomes very important to know the ratio of transverse strain and to include this in the equation.
The Poisson's factor is 0.27 to 0.31 for steel (usually 0.3 is used) and 0.33 for aluminum.
The following table shows several basic configurations for the gages. Basically the configurations are divided in quarter, half and full bridge circuits.
MEASURES |
TYPE |
BRIDGE |
EQUATION |
BRIDGE |
LINEAR |
DESCRIPTION |
tension, compression |
quarter |
|
|
1 |
no |
Single gage measuring tension and compression - basic configuration |
|
half |
|
|
(1+ν) |
no |
One gage in principal direction and one in transverse direction - usually used for temperature compensation |
|
half |
|
|
2 |
yes |
Two gages with opposite strain - usually used for measurement of bending |
|
half |
|
|
2 |
no |
Two gages with same strain - usually used for bending cancellation |
|
full |
|
|
2 ⋅ (1+ν) |
no |
Two pairs of gages where one is in the principal direction and the other one is in transverse direction used in temperature compensation and bending cancellation |
|
full |
|
|
2 ⋅ (1+ν) |
yes |
Two pairs of gages where one is in the principal direction and the other one is in transverse direction used in temperature compensation and tension cancellation |
|
full |
|
|
4 |
yes |
Two pairs of gages in opposite strain - usually used for measurement of bending |
Sensor mounting
The mounting of the strain gage is a process where we need to clean the surface, glue the strain gage, connect lead wires and protect the strain gage. The detailed process is beyond the scope of this manual; please refer to the web pages or handbooks of strain gage manufacturers for specific information. Since the different configurations must be connected in the correct way, as shown in the above picture, it is very important to use special care when connecting the gages to the amplifier.
A little story about the strain gage connections is very fitting in this context. Most people are likely familiar with Murphy's Law. It originally states that "Whatever can go wrong, will go wrong". This is very well known, but what is not as well known is that it originates from the strain gage measurements. The "inventor" of this law, Capt. Ed Murphy, made a strain gage measurement system for a g-force testing system at Edwards Air Force Base, where the maximum g force that the human body could take was to be tested. As a side-note, a real human was used, and the maximum force was 40 g.
The result of the first measurement was zero, simply because the strain gages were connected in such a way that they gages canceled out each other. Capt. Ed Murphy blamed his assistant for the error, who had connected the gages in the wrong way. The other, even more interesting part of the story for the process of measurement was that Murphy simply declined a verification of the system, which was offered to him before performing the test.
The point of this story is this: Connect - CALIBRATE - VERIFY - Measure. If Capt. Ed Murphy had followed this procedure Murphy's Law would not have been invented (at least not on that occasion).
