Order tracking
= Order tracking
<Order tracking> follows vibration or other signal components according to their ratio to a reference shaft's rotational frequency. That ratio is the <rotational order>:
$$
q=\frac{f}{f_{\rm rot}},\qquad f_{\rm rot}=\frac{r}{60},
$$
where $r$ is speed in revolutions per minute and $f,f_{\rm rot}$ are measured in hertz. A component at three cycles per reference revolution has order 3 even while its ordinary <frequency> changes. The reference shaft must be specified; changing the reference changes the order value.<Order Analysis of a Vibration Signal in MATLAB documentation>[Introduction, order definition and reference-speed ratios]{ref}
For an original example, a shaft accelerates from 600 to 1200 revolutions per minute. Its third-order component sweeps from 30 to 60 hertz, while its seventh-order component sweeps from 70 to 140 hertz. A <Fourier transform> over the entire time record spreads those components over frequency. An unrelated fixed 90-hertz tone instead retains its frequency but changes from order 9 to order 4.5.
<Angular resampling> expresses the record on a uniform shaft-angle grid. A speed-locked component $\cos(q\theta(t)+\phi)$ then becomes $\cos(q\theta+\phi)$, with fixed angular periodicity. An order spectrum or order-versus-speed map can separate that structure from a frequency-domain smear. MathWorks demonstrates this distinction with explicitly simulated helicopter-vibration data.<Order Analysis of a Vibration Signal in MATLAB documentation>[Visualize Data Using an RPM-Order Map; example-data introduction]{ref}
\Image[/order-tracking-angle-resampling.png]
{title=Angular resampling concentrates speed-locked components during a chosen run-up}
{description=Original synthetic signal with third- and seventh-order components and an independent 90-hertz tone. Left: stipulated shaft speed. Middle: windowed spectrum of uniform time samples. Right: spectrum after <angular resampling>. The two speed-locked components concentrate at their orders; the fixed-frequency tone spreads in order. This is a mathematical demonstration, not measured machinery data.}
In an apparatus, an <accelerometer> can record housing motion while a <tachometer> or <rotary encoder> records the reference. Tracking an order's amplitude and phase over a run-up can reveal where the machine's response grows, but a large amplitude need not identify the forcing mechanism by itself. Mechanical resonance, load changes and sensor placement can also change the response.
<Time-synchronous averaging> is related but answers a different question: it estimates a waveform repeatable over the chosen reference period. <Order tracking> can retain amplitude variation over speed and inspect selected components. Record speed-estimation assumptions, angular resolution and amplitude normalization with either analysis.