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By Katherine Reiss | October 11, 2020
Overview
Overview
Strain gages have a number of applications across various engineering disciplines. Paired with a Wheatstone bridge circuit, as outlined below, a strain gage can provide information about the force applied to an object given a change in resistance.[1] Among these applications, strain gages are helpful in determining the pressure inside an object. In this experiment, we explore the use of a strain gage to understand what happens to pressure as a soda can's condition is changed. First, we investigate a soda can at its resting, initial and unopened position. Next, we shook the unopened can and repeated these measurements. Lastly, we opened the can and recorded the data in this condition. With the use of the strain gage, Wheatstone bridge circuit, and the calculations outlined below, we were able to interpret our readings to find out information about the soda can. Ultimately, we used this information to decide whether removing 1 gram of aluminum from the can would be detrimental or effective for its design.
What is a strain gage?
What is a strain gage?
A strain gage is used in a number of applications in order to detect the difference in strain of a given object when some external factor influences its condition.[1] Depending on the experiment, calculations are made in order to answer a question about the system. In this case, the strain gage was used to understand more about the pressure inside the can during three different conditions. The calculations for the pressure originally came from the data coming from the strain gage. But what exactly does the gage detect? Let's explore the internal workings of the strain gage. Figure 1 depicts the types of strain gages used in this experiment. As seen in this photo, there appears to be wire inside the gage. When the gage is glued flat onto the soda can, this wire has an initial, resting length. When the soda can is shaken, the pressure inside increases. As a result, the can gets slightly bigger.
Figure 1: Strain Gages[1]
This causes the wires in the adhered strain gage to lengthen which, in turn, increases the resistance in the wire.[2] Likewise, when the can is opened, the pressure decreases, the length of the wire in the strain gage decreases, and the resistance decreases. This change in resistance is ultimately the measurement taken in this experiment. As one can imagine, the change in resistance must be very small. There is not a visible change in the size of a can when the pressure inside it increases or decreases. So how exactly do we detect such an incremental difference in resistance? Next, we will delve into the design of a Wheatstone bridge and discuss why this circuit is ideal in strain gage applications.
Can Preparation
Can Preparation
The following steps were used in order to effectively attach a strain gage to a soda can.
Sandpaper was used to remove the paint off the side of an unopened can.
This sanded area was cleaned using alcohol and a cleansing pad. This step was complete once the cleansing pad did not pick up any more paint.
Scotch tape was used to create a vertical and horizontal reference so that the strain gages could adhere in the correct orientations.
Gloves were put on before using superglue to adhere the strain gage to the sanded portion of the can. One strain gage was placed parallel to the veritcal tape, while the other was placed parallel to the horizontal tape. The flat side of the gages were placed against the can.
Wheatstone Bridge Circuit
Wheatstone Bridge Circuit
A Wheatstone bridge circuit is a circuit that is used to detect very small measures of resistance. Figure 2 below depicts a TinkerCad model of the Wheatstone bridge used in this project. As one can see, the power supply is supplying a voltage of 5V. This supply feeds into two 120Ohm resistors, each followed by another resistance of 120Ohms. The bottom right resistor is representing the strain gage location in the circuit. The strain gage was measured to have a resistance of 120Ohms. This is why the three other resistor values in the circuit are 120Ohms. A very important part of the Wheatstone bridge is that all of the components must be of equal resistance. This results in what is called a balanced circuit.[3] The reason this balance is so important in the circuit is because any deviation from the balance is what is measured as the resistance. Therefore, when the resistance in the strain gage changes as a result of the pressure change in the soda can, this circuit design is able to detect this change, even though it may be small.[3]
Figure 2: A TinkerCad design of a Wheatstone bridge circuit
Figure 3: The Wheatstone bridge
Figure 3 above is a photo of the actual Wheatstone bridge circuit used in this experiment. A digital multimeter was set up to detect voltage values across point V0 as seen in Figure 2. These values were then used in calculations to determine the pressure inside the can. Other measurements needed to be made for the completion of the calculations. This included the external diameter and the wall thickness of the can as well as the elastic modulus and strain value of the strain gage.
Calculations
Calculations
Below are the equations[2] used in the calculations of this experiment in order to find the strain, logitudinal stress, hoop stress, and the pressure using both types of stresses. The two different stresses are both considered because each represent a different force that is important in understanding whether or not the soda can is able to handle removing 1 gram of aluminum from its design. These stresses can be seen in figure 4. As pictured, the longitudinal stress runs parallel to the length of the can while the internal pressure comes from inside the can and pushes out against its sides. Understanding the difference between these stresses, we can use the equations outlined below in order to solve for the pressures. When one gram is removed from the can, its radius will change based on the percent decrease of the can's weight. In turn, the radius will decrease. The pressure calculations can be used with these new numbers in order to find out how the pressure will change after the gram is removed. Depending on the results of the pressure, the can will be able to function properly without this 1 gram, or it will fail as the pressure will be too much for its design.
Figure 4: Longitudinal stress vs. hoop stress.[2]
Strain:
Longitudinal Stress:
Hoop Stress:
Pressure (hoop stress):
Pressure (longitudinal stress):
where ϑ = 0.33, elastic modulus (E) = 75 GPa, yield strength = 170MPa, can density = 2.7g/cm3, S = 2.14, r = radius, V0 = measured voltage, Vs = system voltage, t = wall thickness, and p = pressure.[2]
In our own conduction of this experiment, it was found that the pressure would have decreased, had a gram been removed from the design. While this may be true, there were many factors that went into measuring and calculating values which could have introduced error. For that reason, it is important to properly set up the can and strain gage and the Wheatstone bridge. Failing to do so may result in deviations from an accurate result.
References
References
[1] “What Is a Strain Gauge? | Omega Engineering,” accessed October 11, 2020, https://www.omega.co.uk/prodinfo/StrainGauges.html.
[2] "Strain Gage Project," accessed October 11, 2020, EGR311 Project Guide.
[3] “Wheatstone Bridge Circuit and Theory of Operation,” Basic Electronics Tutorials(blog), October 15, 2013, https://www.electronics-tutorials.ws/blog/wheatstone-bridge.html.
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