A <rotational order> expresses a signal’s <frequency> relative to a specified reference shaft’s rotational <frequency>:
$$
q=\frac{f}{f_{\mathrm{ref}}}.
$$
Thus $q=1$ means one oscillation per reference revolution and $q=1/2$ means one oscillation per two reference revolutions. A <rotational order> is dimensionless and need not be an <integer>. It is especially useful when a machine changes speed: a shaft-synchronous feature can keep the same <rotational order> while moving through many <frequencies> in an ordinary <frequency spectrum>.<Order Analysis of a Vibration Signal in MATLAB documentation>[Introduction and Create RPM-Order Map: rotational-frequency multiples and constant-phase resampling; the helicopter data are simulated]{ref}

The reference is essential. Suppose shaft A turns at $600\,\mathrm{rpm}=10\,\mathrm{Hz}$ and shaft B at $1500\,\mathrm{rpm}=25\,\mathrm{Hz}$. The same $100\,\mathrm{Hz}$ signal has <rotational order> $10$ relative to A and $4$ relative to B. Changing the reference has changed the dimensionless label, not the measured vibration. Likewise, a 24-tooth <gear> turning at $900\,\mathrm{rpm}$ has a <gear mesh frequency> of $24\times15=360\,\mathrm{Hz}$. Its mating 8-tooth <gear> turns at $2700\,\mathrm{rpm}$, giving the same <gear mesh frequency> but <rotational orders> $24$ and $8$ relative to the two shafts.

For a component with unwrapped <phase> $\phi(t)$ and reference angle $\theta(t)$, the instantaneous version is
$$
q(t)=\frac{\dot\phi(t)}{\dot\theta(t)}
$$
where the reference <angular velocity> is nonzero and both angles use the same units. A constant <rotational order> gives $\phi(t)=q\theta(t)+\phi_0$. This explains why <angular resampling> makes a speed-following component periodic as a function of shaft angle. A vibration fixed at $100\,\mathrm{Hz}$ instead changes from <rotational order> $10$ to $5$ when the reference shaft accelerates from $600$ to $1200\,\mathrm{rpm}$.

An <order tracking> measurement therefore pairs a vibration sensor, such as an <accelerometer>, with a shaft-angle or speed reference, such as a <tachometer>. An order peak identifies a speed relationship; it does not by itself establish which part is damaged. A <resonance> can greatly change the amplitude as speed changes even when the excitation’s <rotational order> stays fixed.


 Rotational order (source code)