Vibrational Analysis and its Meaning

I tried to locate a simple layman explanation of vibrational analysis on the web to help those who do not have a technical background understand the results of the vibration data recorded from the Corvair engines.  Not finding any that I found satisfactory, I am going to attempt to explain, in layman terms, what it all means.  This information is based on what I have learned from the mechanical and vehicle engineers with whom I have worked with over the years. If any information in the below abstract is in error it is my sole responsibility for not grasping their explanations correctly.  I would appreciate and request that if any errors are found or my assumptions are incorrect, please notify me and I will make the proper corrections.

Vibration is the repetitive movement of an object. The movement can be oscillatory like the movement of a speaker to create a tone, or it can be random like the static you may hear when an AM radio is tuned off of a radio station. The vibrations that are of the most interest to us are the oscillatory vibrations. These are the vibrations caused by the operation of the pistons and the rotation of the propeller. 

The measurement of these vibrations is accomplished by the use of accelerometers mounted on the engine. Accelerometers measure a change in motion. Everyone has experienced being pushed back in their seat when a car is accelerated rapidly from a stop. Accelerometers measure the magnitude of the acceleration in units of G where 1G is the force of gravity and represents an acceleration of 32 feet per second per second (32ft per second^2). To help understand let us picture a car accelerated from a stop at 1G of constant acceleration for 10 seconds. At the end of the first second the car would be traveling at 32 feet per second or about 21 MPH. At the end of second 2 the car is traveling at 64 feet per second at about 43 MPH and so on until at the end of second 10 the car is traveling at 320 ft per second or 218 MPH.  While these numbers are not exact they are close enough to convey the basic principal of acceleration.

Now let us look at this rate in fractional seconds which is what we need for our analysis. 1 G means we moved 9.77 inches in 1 second, we must have moved 0.09 inches in one tenth of a second or 0.0009 inches in 1/100^th of a second.  The frequencies of interest all lay below 200 Hz or 1/200^th of a second so the actual displacement of the motor at 1 G is 0.0002 inches.  My source for this information comes from a vibration calculator from Wilcoxon Research Inc. and can be downloaded at

http://www.wilcoxon.com/knowdesk_calculator.cfm

l. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma.

III. For every action there is an equal and opposite reaction.

Now we need to understand how this applies to our engine. Let us assume the following graph shows the output of our sensor. NOTE: this is an illustration only.

This graph was created by adding two sine waves at two different frequencies but both have the same magnitude.  As can be seen the lower frequency seems to be the most dominant but when we look at this graph in the frequency spectrum, you can see that they have the same magnitude.

It is the ability to separate these frequencies from the signals that is important to our analysis.  So now let us tie all of this together.

If we assume that our engines weight about 220 lbs  and we expose them to 1G at 1 Hz we get 220lbs * 32feet per second^2  is about equal to 218 foot pounds of force. Now granted we do not expose our engines to that kind of force so let us pick a more reasonable number.  One that is typical from the data collected.

220lbs * .4 G at 100 Hz = 82 foot pounds of force.

I wish to make a final point about vibration and my understanding of vibrations in metal structures like our engines.  Random forces like noise are not damaging and can be ignored. Likewise vibrations above 200 Hz can generally be ignored as the metal molecules cannot respond fast enough and tend to transmit those frequencies directly through the metal without internal structural damage.

It is the oscillatory sinusoidal vibrations below 200 Hz that cause the most problems for metal structures and it is these forces that we need to look at closely.

For more technical explanations of vibrational analysis the following websites are available for reference.  Please feel free to contact me with corrections and opinions about this abstract at JohnKearneyATatt.net.  Exchange the AT with @ sign to email.

http://www.cage.curtin.edu.au/mechanical/info/vibrations/intro.htm

http://www.sensorsmag.com/articles/0899/14/index.htm