Let's talk about sensors, baby.

In my drop tower post, I mentioned that I plan on adding a force transducer to the penetrator so I could get more useful data. For my part, the really fun thing is that setting this kind of thing up from nothing is pretty new to me. Additionally, being able to set up sensors will really open up the opportunities I have for experiments.

So let's talk about these force transducer thingies.

What is a force transducer?

A force transducer or load cell is an electromechanical device that converts an input load to an output electronic signal (usually a voltage change). They are used everywhere from laboratory experiments to bathroom scales. There are a wide variety of different types, each suited to different applications, load ranges and loading rates.

Here are a couple links that include photos of what load cells look like.

The particular type of load cell I'm interested in are called strain gauge compression load cells. The name comes from the fact they are designed to measure a force acting to compress the load cell and use devices called strain gauges to achieve that. They are also very commonly used and can be had fairly cheap.

What is a strain gauge?

A strain gauge (or strain gage) is another electromechanical device, this time used for measuring strain. The most common type is a small metallic foil resistor that changes resistance as the foil deforms. The change in resistance (or measured voltage change) is correlated to the deformation through a calibration curve. A typical strain gauge looks like: 

Schematic of typical strain gauge. Source: Wikimedia Commons. 

The two large rectangular sections at the bottom are the contacts for the sensing wires. The arrows are for alignment. 

Measuring deformation with strain gauges

One aspect of note for strain gauges is that the resistance change is relatively small.  So measuring the change directly can be very difficult. However, there is a special circuit called a Wheatstone Bridge that is intended for this purpose.

Wheatstone Bridge with 1 unknown resistance. From here.

The way the bridge works is that the known input voltage, \(V_{in}\) is applied to the top and bottom nodes. The output voltage, \(V_{out}\), is measured between the left and right nodes. If the ratio of the resistances on the left side (R1/R2) is equal to the ratio of resistances on the right side of the bridge (Rg/R3), then the measured output voltage is zero. Since a strain gauge is just a variable resistor, any deformation will result in a change in the measured output voltage. If all of the resistances are known, as well as the input voltage, you can calculate the output voltage as follows:
\[V_{out} = \left(\frac{R_2}{R_1 + R_2} - \frac{R_3}{R_g+R_3}\right) V_{in}\]

Ideally, we'd choose our 3 known resistances to be equal to the unloaded resistance of our strain gauge. That way, at zero load, we'd get a zero output voltage. But in practice, resistors are only commonly available in certain increments. If \(R_1\) and \(R_2\) are equal, our equation looks like:
\[V_{out} = \left(\frac{1}{2} - \frac{R_3}{R_g+R_3}\right) V_{in}\]
If our resistances were all equal to the unloaded strain gauge resistance, as \(R_g\) increased, the term \(\frac{R_3}{R_g + R_3}\) decrease from 1/2. As a result, our output voltage would end up no larger than 1/2 of the input voltage. On the other hand, if \(R_g\) was much less than \(R_3\), we could actually have a negative coefficient in the equation above: our output voltage would be reversed (as well as scaled down).

In practice, the measured output voltage from a strain gauge in a Wheatstone bridge is very small, on the order of millivolts. Therefore, in order to improve measurement accuracy it is necessary to amplify the signal to a more easily measurable level, on the level of volts. This is accomplished with a device called an Instrumentation Amplifier. The amplified signal is often communicated to a computer with a data acquisition system (DAQ), which includes a sensor interface (monitors the output voltages of attached sensors), a power supply for the sensors and a data logging program for actually recording the data.

Depending on the goal, more than a single strain gauge may be necessary. Companies that produce the gauges, such as Omega Engineering, provide technical documentation that detail various setups. Each setup is intended to measure a different type of strain. A group of strain gauges mounted in roughly the same location, but with different orientations, is called a rosette. Strain gauge rosettes are used when strain along multiple directions is of interest, and also can be used to determine the state of strain at a location.