Order tracking

Order tracking is one thing for which I have not found a good all-in-one reference. There are various resources on specific methods, but no one resource with all at once. If you know of such a resource, please let me know.

Order tracking is a method of analysis used for analyzing rotating machinery ⁷. Typically such a machine will have one or more shafts and the frequency of vibration will depend on some way on the speed of the shaft. For example, if a turbine shaft has 20 blades and runs at 10 Hz, we may find a vibration signal at 200 Hz. But if the speed increases to 20 Hz, we will not be surprised to find that the vibration is now at 400 Hz.

To put another way, you have a vibration signal versus time denoted by v(t). You know that v(t) can be described by the following:

v(t) = A(t)cos($\theta$(t) + $\phi$(t)) + B(t)

where $\theta$ is the angle of the shaft at a given time, and $\dot{{\theta}}$ = $\omega$(t) is the speed of the shaft. $\omega$ is known a priori, or from some tachometer processing algorithm 4.2, A(t) is an amplitude signal that varies slowly relative to $\omega$, $\phi$(t) is a phase difference between the shaft angle and the vibration angle, and B(t) is any arbitrary vibration signal (e.g. a fixed frequency sinusoid, random noise, or something that varies with a different speed). The goal of order tracking is to recover the signals A(t) and $\phi$(t) from the signal v(t). In other words, eliminate the undesired content B(t), and recover the slowly varying component that is modulating the higher frequency component.

Footnotes

...⁷

Of course, all of the methods described herein are also application to non-rotating machinery where the frequency of forced vibration changes as a function of time. It just won't be called ``order tracking'' by people in those industries.

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