Variable-Speed Order Tracking

A conventional FFT spectrum is computed over time. When machine speed changes, speed-related components (1×, 2×, gear mesh orders) move across the spectrum with speed, so peaks smear, amplitudes are wrong and faults cannot be located. The module converts the time signal to the angle domain, so that each revolution has a fixed number of samples and speed-related components become fixed lines in the order spectrum. Order spectra are then computed for segments of equal revolutions and shown as a 3D waterfall and a 2D color map.

Screen layout

The left panel groups channel selection, analysis parameters, tachometer mode, curve window content, amplitude scale, run direction, map Y axis and display controls; all changes take effect immediately.

Five curve window contents

1. Speed curve: instantaneous speed against time (rpm vs s), showing run-up, run-down and steady speed — the first check of speed extraction quality.
2. Order spectrum slice: click a speed row in the color map to show the order spectrum at that speed, for quantitative reading of each order (for example at 2905 rpm).
3. Channel waveform: the complete acceleration waveform of the channel, to confirm signal validity and range.
4. Pulse voltage: the raw once-per-revolution signal of the tachometer sensor (5 V square wave), to check probe mounting and triggering.
5. Cumulative angle: the rotation angle integrated from speed (rad vs s), the intermediate result of the time-to-angle mapping; it should rise smoothly and monotonically.

3D order map

The 3D surface shows orders on the X axis, speed (rpm) or time (s) in depth and amplitude vertically, colored by amplitude, with scales for amplitude, speed and order.

The surface is drawn back to front (painter's algorithm), so hidden surfaces are correct from any angle; while dragging it is drawn at half density to keep interaction smooth. Example readout: order 5.55, 4925 rpm, amplitude 0.514.

2D color map

The color map condenses the speed–order–amplitude data into one image: order horizontally, speed (or time) vertically, color for amplitude with a nine-step scale. Pixel-level bilinear interpolation gives smooth transitions between segments and orders, and segment boundaries are joined at the mid-point between neighboring speeds. Moving the mouse shows order, speed and amplitude; clicking selects the nearest segment and shows its order spectrum in the curve window. The vertical axis always runs from low speed at the bottom to high speed at the top, for both run-up and run-down, so the two can be compared directly; the rows of the 3D waterfall match the color map.

Amplitude scales and axes

Analysis parameters

The panel calculates and shows three engineering constraints, so wrong settings are obvious. Defaults are shown for a sampling rate of 10240 Hz.

• Lower limit of samples per revolution: more than 2.56 times the maximum order (angle-domain Nyquist plus margin for the Hanning window); otherwise high orders alias.
• Upper limit of samples per revolution: not more than the samples per revolution of the original signal at maximum speed (sampling rate ÷ maximum speed in Hz); beyond that, interpolation adds no information.
• Revolutions per segment: more revolutions give finer order resolution but a larger speed change within a segment. A speed change of no more than 5 % within a segment is a common industrial guideline; more broadens resonance peaks.

Tachometer mode and channels

Tachometer channel: a once-per-revolution pulse from an optical, eddy-current or magnetic sensor; rising edges are captured at a 2.5 V threshold for the most accurate speed. Tachless self-tracking: no tachometer sensor is needed; speed is extracted by tracking the 1× component in the vibration signal with a sliding window, which suits machines without a tachometer probe and the reanalysis of recorded data. The enabled channels are listed with their units. Test mode generates a standard signal — a triangular speed profile 1000 → 5000 → 1000 rpm with orders 1, 2 and 3, fixed resonances at 400 and 500 Hz and tachometer pulses — for demonstration, training and self-checks without hardware.

Supporting functions

Stay on top, built-in PDF help, copy the 3D waterfall to the clipboard, export the order spectrum matrix as CSV, and Chinese or English interface.

Run-up and run-down of variable-speed drives

Motors, spindles, fans and pumps on frequency converters or servo drives pass through their critical speeds during run-up and run-down, the most effective condition for revealing resonance. Order tracking fixes speed-related components on the order axis and, with automatic run separation, distinguishes order peaks — proportional to speed, from unbalance, misalignment or gear defects — from fixed resonances at constant frequency (natural frequencies of the structure). Where a resonance band crosses an order line is a critical speed.

Automotive and rotating machinery NVH

Engine run-up and coast-down, transmission gear mesh orders and reducer whine in electric vehicles require order spectra normalized to engine speed and color maps as standard deliverables. Speed or time axes and linear, dB or log scales produce these charts directly.

Start-up and shutdown of large machines

Start-up and shutdown analysis of steam turbines, compressors and large fans needs the complete speed–order–amplitude data to identify critical speeds. Run-up and run-down are mapped separately to compare their dynamics.

Field diagnosis without a tachometer

Many machines have no tachometer sensor. Tachless self-tracking performs order analysis from one vibration signal, and recorded data acquired without a tachometer can be reanalyzed.

Training and demonstration

The test signal with orders 1, 2 and 3 and fixed resonances at 400 and 500 Hz shows the typical pattern of order lines crossed by resonance bands, without a signal generator or sensors.

Speed extraction

Tachometer mode: all rising edges of the tachometer signal are captured at a 2.5 V threshold; the reciprocal of the interval ΔT between pulses is the instantaneous speed, rpm = 60 / ΔT, time-stamped at the mid-point, so accuracy is not limited by the sampling grid.

Tachless mode has four steps:

1. FFT of a 1024-point sliding window with a step of 256 points (75 % overlap).
2. Search only within the band [rpm_min / 60, rpm_max / 60] for the largest line, to avoid picking up 2× or 3× components or fixed resonances.
3. Parabolic interpolation through the peak and its two neighbors refines the frequency below one Δf and removes steps in the speed curve.
4. Rotational frequency × 60 gives rpm(t).

Time-to-angle mapping and equal-angle resampling

The speed is converted to rotational frequency f(t) and integrated sample by sample to give the cumulative angle θ(t). This is the core of the conversion: components whose frequency changes with speed in the time domain become stationary components with a fixed period in the angle domain. Resampling takes points at equal angle intervals on θ(t), with a set number of points per revolution (default 128), and finds the values by cubic Hermite interpolation. A forward-only pointer keeps the complexity O(N).

Segmentation and order spectra

The total revolutions are divided into segments of a set number of revolutions (default 5). Each segment is resampled, Hanning-windowed and transformed by a radix-2 FFT (length rounded up to a power of two) into a single-sided magnitude spectrum.

• Order line spacing = samples per revolution ÷ FFT length (for example 128 points per revolution × 5 revolutions = 640 points, padded to a 1024-point FFT, gives 0.125 order); the resolution limit is 1 ÷ revolutions per segment = 0.20 order.
• Mean speed of each segment = actual revolutions in the segment ÷ segment duration × 60, using the real angle difference rather than a nominal value; the segment mid-point time is used for the time axis.
• Two boundary protections: segmentation stops when a segment has fewer than 10 time samples (end of signal) or fewer than 50 % of the nominal revolutions (speed too high or end of record), so empty segments do not produce false lines.

Run-up and run-down separation and monotonic check

Segments are split at the speed maximum into run-up (before) and run-down (after). Each group is forced to be strictly monotonic in speed, which prevents segments from folding back and overlapping in the color map when speed dips slightly — a common defect in waterfall plots.

Row normalization and rendering

Rows are ordered by ascending vertical value, so the color map always has low speed at the bottom and the 3D waterfall low speed at the front, for both run directions. Slices are taken by the nearest speed value, independent of row order. The color map uses bilinear interpolation between segment centers and between order lines, with amplitude normalized for linear, dB or log scaling. The 3D surface is drawn back to front with the same amplitude normalization as the color map, so both read the same values. Cursor positions are projected back to world coordinates to find the order and segment indices.

1. Select the vibration channel to analyze (only enabled channels, shown with units).
2. Check the parameters — minimum and maximum speed, sweep rate, maximum order and revolutions per segment — and the three constraint hints for sampling rate, points per revolution and record length.
3. Select the tachometer mode: tachometer channel with its channel number, tachless self-tracking, or test mode for a demonstration.
4. Click Refresh; the title bar shows the calculation progress.
5. Read the maps: move the mouse over the color map and click for a slice; rotate the 3D map and click to place cursor lines.

Data quality checks

Reading the maps

• Order peaks: lines that run along the speed direction at constant order (1, 2 …) — speed-related excitation.
• Fixed resonances: bands at constant frequency whose order changes with speed — natural frequencies of the structure. Where they cross an order line is a critical speed.
• dB scale: emphasizes weak orders, for example half orders or gear mesh sidebands.
• Slices: read the amplitude of each order at a given speed for a quantitative diagnosis.

Adjusting parameters

Image copy and CSV export

Both require a completed calculation. Copy places the 3D waterfall, without temporary cursor lines, on the clipboard for Word, presentations or e-mail. Export saves the order spectrum matrix as CSV (default name OrderTrackWaterfall.csv, with a warning before overwriting).

Confirm the display scale before exporting. Run-up and run-down data in one file are both ordered by ascending Y value, as displayed.