EXPERIMENT 6B: ACCELEROMETERS, FUNCTION
GENERATOR, AND FREQUENCY SPECTRA
What are accelerometers used for???
Air bags
You don’t want them to deploy unless you are rapidly de-accelerating,
or, in a wreck…
http://auto.howstuffworks.com/airbag1.htm
Airplanes to submarines…
Want to know if you are right side up or not? Use an
accelerometer!
roll stabilization of aircraft, flight simulators, and torsional
effects on rotating machinery.
This lab – test packing materials
How fast does an object de-accelerate for a given
packing material?
Wiring for accelerometer:
+5V = excitation voltage
Ground (black wire) to ch 8 and
AIgrnd
Signal (white wire) to ch 0
Oscillation:
Hang accelerometer off of table with rubber band and C-clamp….
Shock with an Accelerometer
Q5 Try 3 different materials @ the same height
Q6 Try different drop heights, orientations, and material thicknesses
Q8-10 Triggering
Trigger around the at rest voltage
Experiment 6B Preparation
try and get this done during the 6A lab so that you can see the
equipment you will be using ahead of time!
1. What voltage outputs do you predict when the 5•g accelerometer is (a) standing up, (b)
on its side, and (c) upside down? (15 pts)
The accelerometer is a linear transducer, like the pressure transducers
that you used in lab 5. You can plot V vs acceleration for this lab like
you plotted V vs. pressure
for L5.
2.4
Vout = sensitivity * acceleration +
2
1.8
Zero offset
Vout of accelerometer
2.2
1.6
1.4
1.2
Upside-down
Righ
1
-15
-10
acceleration (m/s2)
-5
0
5
Sensitivity =slope of line = 400mV/g (sensitivity varies from
accelerometer to accelerometer)
Zero offset = 1.8V
Vout from the accelerometer represents acceleration
parallel to the horizontal bar:
Consider how gravity is acting with respect to the accelerometer…
Right side up
upside-down
Horizontal
at some angle
g=0
+g
Pictures courtesy of Janine – Thanks Janine!
-g
2. Develop the equation to calculate velocity of the oscillating wooden block (with
embedded accelerometer) from measured voltage. Show the steps clearly and
completely. Define any variables. (15 pts)
The accelerometer acts like a spring holding up a weight.
Depending on the direction of gravity, the spring will
deform varying amounts.
dv
dx 2
F  k  ma  m
m 2
dt
dt
g
k = spring constant
 = how much the spring is stretched from it’s equilibrium
length
m = mass
a = acceleration = change in velocity with time
There are two different ways to integrate – numerical and analytical
Analytical = what they taught you in your math class
Numerical = what you do if you have a string of data:
So… you will have data of time, and vout. For this one, set up an excel
spreadsheet that creates columns of :
Acceleration from vout
dt from time
dv from acceleration and dt
And velocity from dv…
time
dt
Vout
acceleration
dv
Velocity
seconds dt =t2 - t1 from LabVIEW calc from Vout (a = dv/dt) dv = v2 - v1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.1 - 0 = 0.1
0.2 - 0.1 = 0.1
0.3 - 0.2 = 0.1
1.392252803
1.433027523
1.473802243
1.514576962
1.555351682
1.596126402
1.636901121
-10
-9
-8
-7
-6
-5
-4
dv = a * dt
let v1 = 0
v2 = dv + v1
v3 = dv + v2
etc…
1
Open up the acquire waveforms.vi, and make sure you know how to
record vout data with time.
What sampling rate will you need to use?
How is time being plotted? In seconds? ms?
How many data points will you have to take?
Specify all of the setting you will need to use to take data next week…
3. Develop an equation for displacement of the block from measured voltage. Show steps
clearly and completely. Define any variables. (15 pts)
recall that velocity (v) is a measure of displacement (x):
dv
dx 2
F  k  ma  m
m 2
dt
dt
add on some new columns to your spreadsheet to calculate x and dx…
show all of the equations that you are using.
time
dt
Vout
acceleration
dv
Velocity
seconds dt =t2 - t1 from LabVIEW calc from Vout (a = dv/dt) dv = v2 - v1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 - 0 = 0.1
0.2 - 0.1 = 0.1
0.3 - 0.2 = 0.1
1.392252803
1.433027523
1.473802243
1.514576962
1.555351682
1.596126402
1.636901121
-10
-9
-8
-7
-6
-5
-4
dv = a * dt
4. Graph the relationship between potential, kinetic and total energy waveform. Assume
sinusoidal shapes with amplitude of 10 and frequency of 2 for potential and kinetic
waveforms. Draw a graph with the three different waveforms with the correct
relationship between maximum and zero points. Attach the graph.(15 pts)
For this, use the spreadsheet you created in #3, fill in some predicted
times and vout’s, and use these to test all of your calculations…
1 2
mv
2
1
PE  k 2
2
TE  KE  PE
KE 
Prepare a place in your spreadsheet to place values for constants such
as m and k. For now, make up your own values, in lab we can measure
these.
PE – potential energy = potential from the spring or rubber band.
Measure the equilibrium position (how far down the wooden block
hangs at rest) and the distance you displace it to vibrate it. – Note: To
get a nice vibration, do not displace it too much, or it will be bouncing
all over the place…
let v1 = 0
v2 = dv + v1
v3 = dv + v2
etc…
m = ???
k = ???
x1 = ???
time
seconds
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
dt
dt =t2 - t1
0.1 - 0 = 0.1
0.2 - 0.1 = 0.1
0.3 - 0.2 = 0.1
Vout
from LabVIEW
acceleration
calc from Vout
dv
(a = dv/dt)
Velocity
dv = v2 - v1
dx
(from v=dx/dt)
1.392252803
1.433027523
1.473802243
1.514576962
1.555351682
1.596126402
1.636901121
-10
-9
-8
-7
-6
-5
-4
dv = a * dt
let v1 = 0
v2 = dv + v1
v3 = vd + v2
etc…
?
?
?
x
from dx 1
5. Attach copies of the procedures that you plan to use for the oscillation and shock
experiments. (20 pts)
6. Attach copy of the wiring diagram that you plan to use. (20 pts)
Analytic solutions:
Find v as a function of voltage….
d 2x
F   kx  ma  m 2
dt
2
d x k
 x0
dt 2 m
@t  0
x  A  max deflection
v0
and
solve :
x  A cos t

k
m
dx
 A sin t
dt
dv
a
  2 A cos t
dt
re  arrange
v
cos t  
a
2A
 a 

2
 A
t  cos 1 
 A a
4
2
2
2A
so...
a 

v  A sin cos 1 2 
 A

and
   4 A2  a 2
v  A
2A

v
  4 A2  a 2

Acceleration:
-a
  A a
4



2
2
2A
a
V  Vo
s / 9.8
s  sensitivit y in V
g
 4 A 2  96V  Vo 2 / s 2
v

k
2

 2f 
(sec 1 )
m
T
A=max amplitude
V = voltage
Position:
x  A cos t
a 


2
  A
a 
a

x  A  2    2

  A
t  cos 1  
 V  Vo 
if a  9.8

 s 
where s  slope  sensitivity in V g
x
9.8V  Vo 
 2s
Look at the equipment before leaving lab 6A so that the wiring diagram
will be accurate…
Experiment 6B Report
Old notes: http://www.mines.edu/fs_home/jmoss/6B.html
Harmonic Oscillation with an Accelerometer
If you have just gotten back from the circuits test – do things in red first.
(Calculations, graphs, etc can be done at home – just make sure you get the data you
need in class)
1. *Report measured and predicted values from the accelerometer in the table below.
Explain any differences. (5 pts)
Note: Some of the accelerometers have different sensitivities than those reported in the
lab manual – so it is OK if the measured values are not what you expect…
Predicted V
Measured V
Upright
Side
Up Side Down
This is to calibrate your accelerometer – ie – get data so that you can
make a graph like:
2.4
Vout = sensitivity * acceleration + zero offset
Vout of accelerometer
2.2
2
1.8
1.6
1.4
1.2
1
-15
-10
acceleration (m/s2)
-5
0
5
10
15
For your specific piece of equipment. If you do not see a large voltage
change for different block orientations, get a new block.
2. *Write 2000 points of 1000-samples/s harmonic-oscillation data from the wooden
block accelerometer to a spreadsheet file. Calculate acceleration, velocity, and
displacement for each point in different columns of an EXCEL spreadsheet. Graph
acceleration, velocity, and displacement and attach a printed copy of the graph.
Format the graph properly. Scale velocity and displacement so they are similar in
magnitude to acceleration. Make sure that your graph shows correct data. For
example what is the value of acceleration, velocity, and displacement when time is
zero? When time approaches infinity? Do not print and attach the 2000 lines of
spreadsheet data. (33 pts)
Use the spreadsheet you created in your pre-lab for this…
time
dt
Vout
acceleration
dv
Velocity
seconds dt =t2 - t1 from LabVIEW calc from Vout (a = dv/dt) dv = v2 - v1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1 - 0 = 0.1
0.2 - 0.1 = 0.1
0.3 - 0.2 = 0.1
1.392252803
1.433027523
1.473802243
1.514576962
1.555351682
1.596126402
1.636901121
-10
-9
-8
-7
-6
-5
-4
dv = a * dt
Note: if your graph does not stay centered around zero, change your
initial value for velocity from zero to whatever number makes things
look right…
To calculate velocity, ignore acceleration due to gravity – ie, subtract 9.8 from all of your
acceleration values.
3. *Add columns to the question 2 spreadsheet to calculate total, potential, and kinetic
energy. Attach a graph of total, potential, and kinetic energy. You must know
velocity and displacement at the beginning of your data set. Save often, at least every
5 minutes. Do not attach the 2000 lines of spreadsheet data. Give the equations used
for the calculations in the space below this question. Define all variables. (10 pts)
let v1 = 0
v2 = dv + v1
v3 = dv + v2
etc…
Again, copy and paste your data into the spreadsheet from the prelab…
Note: KE + PE would be constant in an ideal world, but with energy
dissipation, this value should decrease with time.
m = ???
k = ???
x1 = ???
time
seconds
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
dt
dt =t2 - t1
0.1 - 0 = 0.1
0.2 - 0.1 = 0.1
0.3 - 0.2 = 0.1
Vout
from LabVIEW
acceleration
calc from Vout
dv
(a = dv/dt)
Velocity
dv = v2 - v1
dx
(from v=dx/dt)
1.392252803
1.433027523
1.473802243
1.514576962
1.555351682
1.596126402
1.636901121
-10
-9
-8
-7
-6
-5
-4
dv = a * dt
let v1 = 0
v2 = dv + v1
v3 = vd + v2
etc…
?
?
?
4. Discuss the relationship between kinetic and potential energy as shown in the graph
from 9. Explain increases and decreases in each and how they are related. (4 pts)
Remember learning about a pendulum in physics? When it is up E =
PE, when it is down E = KE, and the total energy (in an ideal system)
remains constant.
Shock with an Accelerometer
x
from dx 1
5. *List the drop height, average value, and the standard deviation for the peak shock
acceleration for 3 drops onto each packing material in the table below. Note any
observations about the packing material thickness, drop height, etc. (10 pts)
poly-foam
polystyrene insulation
bubble-wrap
Drop Height
Average of 3 drops
Standard Deviation
For these you are comparing how fast the block deaccelerates.
Stopping fast = bad
Stopping slow = good…
6. *Repeat the shock experiment in question 8, but vary the dropping technique, drop
height, and material thickness. (4 pts)
Why is drop technique important and how do different techniques affect the data?
How do different drop heights affect the data?
How do different material thickness affect the data?
7. Explain why the peak acceleration is a critical measurement in the characterization of
packing materials. (4 pts)
8. What was the best voltage level for triggering? Why? (4 pts)
9. How many pre-trigger points did you use? (see the VI block diagram) Why? (3 pts)
10. Did you use a rising or falling trigger slope? (see the VI block diagram) Why? (3 pts)