Order Spectrum

Order analysis is the primary technique for analyzing noise and vibration from rotating machinery. Instead of representing the signal as a function of frequency (Hz), order analysis expresses the spectral content in multiples of the rotational speed, called orders. This approach separates speed-dependent components from structural resonances, enabling clear diagnosis of rotating machinery behavior.

Concept of Orders

An order is a frequency component that is a fixed multiple of the shaft rotational frequency. The first order (Order 1.0) corresponds to one event per revolution. Higher orders correspond to events that occur multiple times per revolution:

f_order = Order × RPM / 60

Order	Typical Source
1.0	Unbalance, shaft bow, misalignment (1×)
2.0	Misalignment, looseness, reciprocating forces
N (integer)	Gear mesh (N = number of teeth), blade pass (N = number of blades)
0.43×	Oil whirl in journal bearings
Non-integer	Belt drives, bearing defects (BPFO, BPFI, BSF)

Bearing defect orders are typically non-integer and depend on the bearing geometry. V-Listen can compute these orders automatically from the bearing parameters (number of rolling elements, pitch diameter, contact angle, element diameter).

Resampling to the Angle Domain

In a conventional FFT, a frequency component that tracks the shaft speed will smear across multiple bins as the RPM changes. Order analysis solves this by resampling the time-domain signal to the angle domain (equal angular increments) before computing the spectrum.

The resampling process requires a reference signal that tracks the shaft rotation. This is typically a tachometer pulse (once-per-revolution or multiple-per-revolution trigger). The steps are:

Tacho detection: Identify the time instants of each tacho pulse.
Instantaneous RPM: Compute the rotational speed between consecutive pulses.
Angular resampling: Interpolate the vibration/acoustic signal at equidistant angular positions using the tacho timing information.
Order spectrum: Apply the DFT to the angle-domain signal. The resulting spectrum has the horizontal axis in orders instead of Hz.

Parameters

Parameter	Options	Description
Tacho Channel	Any pulse/TTL channel	Reference signal for angular position tracking.
Pulses per Revolution	1, 2, 4, 8, ...	Number of tacho pulses per shaft revolution.
Trigger Level	Adjustable voltage	Threshold for detecting tacho pulse edges.
Trigger Slope	Rising / Falling	Edge direction for pulse detection.
Max Order	10 – 200+	Highest order to compute. Determines the angular resampling rate.
Order Resolution	0.01 – 1.0 orders	Spectral resolution in the order domain.
Window Type	Hanning, Hamming, etc.	Window function applied to each angle-domain block.
RPM Range	Min – Max RPM	Speed range for the analysis. Data outside this range is excluded.

The maximum detectable order is limited by the angular sampling rate, which depends on the number of tacho pulses per revolution and the original time-domain sampling rate. The rule is: Max Order ≤ (f_s × 60) / (2 × RPM_max), or equivalently, Max Order ≤ Pulses_per_rev × (Samples_between_pulses / 2).

Output

The order spectrum displays amplitude (linear or dB) as a function of order number. Each peak corresponds to a specific mechanical event occurring at that multiple of the rotational speed. The spectrum can be computed at a single RPM, averaged over an RPM range, or displayed as a waterfall across the full speed sweep.

Practical Tips

Ensure the tacho signal is clean and free of electrical noise. False triggers will produce erroneous RPM values and corrupt the resampled data.
Use the highest practical number of pulses per revolution to maximize the order range, especially when analyzing high-order components (gear mesh, blade pass).
Verify the instantaneous RPM profile before proceeding with the order analysis. Check for missing pulses, double triggers, or unrealistic speed jumps.
When no physical tachometer is available, V-Listen supports computed order tracking (COT), which extracts the RPM from the vibration signal itself. This requires a dominant and well-separated order component.
For a comprehensive speed-dependent view, see Campbell Diagram. To extract the level of a single order as a function of RPM, see Order Cut.

If the tacho trigger level is set incorrectly, the system may detect noise as valid pulses or miss legitimate pulses entirely. Always verify the RPM profile before analyzing orders.