MAE LAB 2:
Instrument Calibration
OMAR TORRES
3/23/2016
Abstract
In this Lab, we did a set of experiments that taught us how to properly calibrate
measuring instruments. There were two specific instruments that were used for the purpose of
learning how to calibrate: A load cell and an accelerometer. Like the previous lab, all we had to
work with when I came to results was date. This data was a huge column vector of output voltages.
The first instrument that was calibrated was a load cell in which different weights were used to
give out the outputs. The second instrument that was calibrated was the accelerometer which was
on an angled surface and tested at different angles, the moved. In the repot part of the lab, a number
of different plots were done in order to see how the data can be manipulated to calibrate the
instruments. Lastly, the concept of standard deviation is introduce in this lab to see what the
relative error can be.
Introduction
The calibration of instruments is a very important because as engineers, one will always
have to run experiments and simulations, and all these said procedures require measuring
instruments. Many of these instruments nowadays are electrical/digital and the way they hand out
results is by giving a voltage output. Calibrating an instruments is establishing a link between a
system output and a system input. An instrument can be calibrated many ways: however, in this
lab we will focus on two instruments: A load cell and an accelerometer. One thing that is certain
is that when it comes to calibrating instruments, there are always uncertainties. Therefore, it is
crucial to determine the standard deviation of the data given by instruments to find the error that
is associated with the linear fit of data.
The first instrument that the lab focuses on is the Load cell.
As seen in Figure 1, it is simple just a hook mounted to a device
with a sensor and wires coming out of it. This load cell measures
a load with the deformation that is caused when a weight is
placed on it. What deforms are these small load beams in the cell.
There are small electrical circuits called gauges that have a
voltage input going in it. When the beams deform, the resistance
in these small circuits change giving a different voltage output
dddd Figure 1: Load Cell
that came in. using tools like Matlab we can decipher these
voltages and turn them into data that translates to a load.
The second instrument that we focused on was a variable
capacitance accelerometer. This instrument (seen in Figure 2) is a
sealed capacitor. Like all capacitors it has two plates and the
capacitance is determined by the distance between the plates. So how
does it measure acceleration if the plates are fixed? Well that is the
thing the plates are not fixed. They are on a diaphragm where on f the
plates is stationary and the other moves. The distance between the
plates depends on acceleration because it gets displaced different
Figure 2:Accelerometer magnitudes with changing forces. Since the mass of the accelerometer
does not change, it means that the acceleration is what varies. Therefore, when the distance changes
the capacitance changes and it produces a voltage output that is related to the acceleration of the
accelerometer.
Materials & Methods
Since there are two instruments there are two sets of materials and experimental set
ups. For the load cell, we have the stand it will be mounted on, the 3133- micro load cell
(max load 5kg), a LM7805CT voltage regulator (Figure 3), an INA126P amplifier, two 9
volt batteries, different masses and we used DAQ program to record the data.
Figure 3: Voltage regulator and amplifier
1. We connected the batteries to the Load cell circuit and then to the computer.
2. We opened the program and set it up so that the range of the output would be + 5V.
3. We ran the program and recorded data for 5 seconds. We did this for 0-2000 grams
loads.
4. Using Matlab’s mean function, we found the average voltage for each set of data.
The second set or materials we had were the Kister 8305B2 accelerometer, an angled
surface that can have the inclination angle changed (Figure 4), and the computer with the DAQ
program.
Figure 4: Angled surface
1. First we connected the accelerometer to the power supply and adjusted it to 9V.
2. We opened the program and set it up so that the range of the output would be + 5V.
3. We then put the accelerometer on the angled surface with a bit of wax to avoid
slipping.
4. We then ran the program and recorded data for five seconds. This was done a total
of 11 times with the first at 0 o, then four more times with angles between 0-90o,
once at 90o, then four more times for angles between 90-180o and lastly once at
180o.
5. Then we recorded data for five seconds while we constantly moved the
accelerometer up and down.
6. Lastly, we used Matlab to gee the average voltage for each set of data and change
the angles to acceleration.
Results
Figure 5: Vavg vs Load
To find the equation of the trend line, two points were chosen on the line (see Figure 5)
𝑌 −𝑌
and the slope formula 𝑆 = 𝑋2 −𝑋1 was used to find the slope. Then the standard equation of
2
1
a line 𝑦 = 𝑆𝑥 + 𝑏 and a point on the line, was used to find the y-int. The equation is:
𝑽𝒂𝒗𝒈 = 𝟎. 𝟎𝟎𝟏𝟎𝟖𝟗𝑳 − 𝟎. 𝟒𝟗𝟕𝟎𝟒
Figure 6: Points used to find Line Equation
Figure 7: STDV vs Load
Figure 8: Vavf vs Acceleration
Figure 9: Vavg vs Acceleration
In order to convert degrees to acceleration, the formula given to us during lecture
𝐴 = −𝑔𝑐𝑜𝑠𝜃 was used. Then after the plot was made, the same procedure explained
before, was used (look at Figure 9 for the points used) to find the trend line equation which
is:
𝑽𝒂𝒗𝒈 = −𝟎. 𝟓𝟑𝟑𝒂 + 𝟐. 𝟒𝟖𝟗
Figure 10: points used to find line equation
Figure_11: Acceleration vs Time
In order to get this plot, we had to convert the voltage output from the five seconds
that the accelerometer was in motion. The equation found in the previous step was used to
get a bunch of values for acceleration and the plotted.
Figure 12: STDV vs Acceleration
Discussion
What voltage values would you expect to measure for loads of 175 g and 1.3 kg? What
is the maximum voltage you would expect to measure for this load cell?
In order to calculate these values, all we have to do is plug in the loading the
equation we derived from the trend line.
𝑽𝒂𝒗𝒈 = 𝟎. 𝟎𝟎𝟏𝟎𝟖𝟗𝑳 − 𝟎. 𝟒𝟗𝟕𝟎𝟒 = 𝟎. 𝟎𝟎𝟏𝟎𝟖𝟗(𝟏𝟕𝟓) − 𝟎. 𝟎𝟒𝟗𝟕𝟎𝟒 = 𝟎. 𝟏𝟒𝟎𝟖𝟕 𝑽
𝑽𝒂𝒗𝒈 = 𝟎. 𝟎𝟎𝟏𝟎𝟖𝟗(𝟏𝟑𝟎𝟎) − 𝟎. 𝟒𝟗𝟕𝟎𝟒 = 𝟎. 𝟗𝟏𝟖𝟔𝟔 𝑽
We had to convert 1.3kg to grams since those are the proper units for the equation. Since
the Max load on the load cell is 5kg, the maximum voltage expected to be read is 5.395 V.
What load values would give you voltages of 1V and 2V respectively?
In order to do this, we have to solve for L in our previous equation and plug in the
values for voltage.
𝑳=
𝑽𝒂𝒗𝒈 + 𝟎. 𝟎𝟒𝟗𝟕𝟎𝟒 𝟏 + 𝟎. 𝟎𝟒𝟗𝟎𝟒
=
= 𝟗𝟔𝟑 𝒈
𝟎. 𝟎𝟎𝟏𝟎𝟖𝟗
𝟎. 𝟎𝟎𝟏𝟎𝟖𝟗
𝟐 + 𝟎. 𝟎𝟒𝟗𝟎𝟒
= 𝟏𝟖𝟖𝟐 𝒈
𝟎. 𝟎𝟎𝟏𝟎𝟖𝟗
Discuss any trends that you see in the standard deviation vs. load plot. What are some
ways that you can think of to reduce the standard deviation?
The standard deviation slowly increases, it has two spots where it spikes up rapidly.
If the load cell were to keep getting tested by further adding mass, I feel like the same trend
would continue where it will just spike up rapidly. Also, the deviation also seems to
increase at a faster rate as the mass increases. One way to reduce the standard deviation is
by changing the material of the load beams to a material in which the thermal expansion
coefficient is so that it doesn’t expand and contract as much with changes in temperature.
What would you expect to happen if you exceeded the maximum load of 5 kg?
I would expect it to give very erroneous reading that make no sense. The reason I
believe is because once it exceeds the load value, the voltage output will want to go over.
However, it will not be allowed to do so and it will start fluctuating thus giving erroneous
results.
Why wouldn’t we want to use the Voltage vs. Angle for our calibration?
Well for one, the angle was used for this specific experiment, but there are different
ways of calibrating accelerometers. Especially if they have more than one axis, so that
means that angle is not important. The main reason is because if one looks at Figure_, we
can observe that the plot is not linear which is not ideal for calibration.
Discuss any trends that you see in the standard deviation vs. acceleration plot. What
are some ways that you can think of to reduce the standard deviation?
The most noticeable trend in the deviation plot is that at around + 6 m/s2 the rate of
change of deviation is great. Also, in the range between the said accelerations, the standard
deviation stays high. Outside of that range the standard deviation stays pretty low. One way
that the standard deviation can be lowered is by placing the plate that moves of flexes on a
diaphragm that is more sensitive to movement. Meaning it can be moved more easily. The
reason for this suggestion is that it seems that at lower accelerations, the voltage output is
erroneous so I believe that the plate movement needs more force to accurately move. If it
was place on a surface more susceptible to movement it would take less force therefore
reaction more accurately.
What else could be done to improve the accuracy of the calibration?
The experiments that are performed can be optimized for better accuracy. For
example instead of putting it on an angled surface you can put it on a gyroscopic device to
increase the range of motion and therefore acquiring more data that can be used to more
accurately calibrate the accelerometer.
References
https://ublearns.buffalo.edu/bbcswebdav/pid-3668910-dt-content-rid12157623_1/courses/2161_17836_COMB/MAE%20334%20-%20Lab%202%20%20Procedure.pdf
https://ublearns.buffalo.edu/bbcswebdav/pid-3674001-dt-content-rid12215304_1/courses/2161_17836_COMB/Lecture%206%20Calibration%20%26%20Electronics.pdf