Psychoacoustics vs RPM

Rotating machinery rarely misbehaves at every speed. A gear whine that is inaudible at idle can dominate at 3200 rpm; an electric drive can sound perfectly smooth until a narrow speed window in which the inverter sidebands fall into the roughness-sensitive modulation range. Plotting a psychoacoustic metric against time tells you when the problem occurs; plotting it against speed of rotation tells you where in the operating range it lives — which is the form an engineering team can act on.

Deepsona provides vs RPM variants for five psychoacoustic metrics. All of them are intended for run-up and coast-down measurements, and all of them require a recording that contains speed information.

Available Analyses

Analysis	Standard	Result Form	Detail Page
Sharpness vs RPM	DIN 45631/A1, Aures	Curve over the speed axis, in acum	Sharpness
Hearing Model Roughness vs RPM	ECMA-418-2 (hearing model)	Curve over the speed axis, in asper	Roughness
Fluctuation Strength vs RPM	ECMA-418-2 Edition 4 (hearing model)	Curve over the speed axis, in vacil	Fluctuation Strength
Tonality vs RPM	DIN 45681 / ISO/TS 20065	Colour map: prominence ratio over frequency and speed	Tonality
Tone to Noise Ratio vs RPM	ECMA-418-1	Colour map: tone-to-noise ratio over frequency and speed	Tone-to-Noise Ratio

A sixth speed-resolved psychoacoustic result, Specific Fluctuation Strength (Hearing Model) vs. RPM, is documented together with its band-spectrum and vs Time siblings on the Specific Fluctuation Strength (Hearing Model) page.

Theory

From a Time Axis to a Speed Axis

Every vs RPM analysis starts from the same psychoacoustic model as its vs Time counterpart. The metric is evaluated along the recording, and the result is then expressed over the speed axis instead of the time axis: at each speed step the corresponding result is taken from the underlying analysis. Because a run-up passes each speed exactly once, the mapping is unambiguous and the result reads directly as "metric as a function of operating speed".

Curve Results and Colour-Map Results

Two result forms occur, depending on what the underlying metric produces:

Curve over the speed axis — for metrics that produce one number per instant: sharpness (acum), hearing-model roughness (asper), fluctuation strength (vacil). One curve is produced per sound-pressure channel.
Colour map over frequency and speed — for metrics that produce a whole spectrum per instant: tonality (prominence ratio in dB) and tone-to-noise ratio (dB). The speed replaces the time axis of the corresponding vs Time colour map, so a tonal order appears as a diagonal ridge running across the map.

Common Parameters

All five analyses share the parameters that define the speed axis. Every other parameter is inherited from the corresponding vs Time analysis and is documented on that metric's own page.

Parameter	Options	Description
Speed Step	50 rpm (default)	Spacing of the speed axis. Smaller steps give a finer picture of narrow speed windows but require a slower, more evenly executed run-up
Slope	Automatic (default) / Run-up / Coast-down	Direction of the speed change to be evaluated. Automatic derives the direction from the recorded speed trace
Channel Selection	Sound-pressure channels	Only sound-pressure channels are evaluated; the speed reference and other auxiliary channels are excluded automatically

Recording requirement: the vs RPM analyses are intended for run-up and coast-down operation, and the recording must contain speed information. A measurement made at a constant operating point yields no usable speed axis — use the vs Time variant instead.

Output Quantities

Analysis	Result	Unit	Single Value
Sharpness vs RPM	S(n)	acum	Mean over the speed axis
Hearing Model Roughness vs RPM	R(n)	asper	90th percentile over the speed axis
Fluctuation Strength vs RPM	F(n)	vacil	90th percentile over the speed axis
Tonality vs RPM	PR(f, n)	dB	Tonal level difference with its frequency, the averaged level difference and the uncertainty
Tone to Noise Ratio vs RPM	TNR(f, n)	dB	Not reported (the result is read from the map)

Relationship to the vs Time Variants

The vs RPM and vs Time variants of a metric are two views of the same evaluation, not two different models. Choosing between them is a question of what the result has to answer:

Question	Use
"When during the test does it get bad?"	vs Time
"At which operating speed does it get bad?"	vs RPM
"Is the effect repeatable between run-up and coast-down?"	vs RPM, computed once per direction
"Does the sound stay acceptable at a fixed operating point?"	vs Time, or the stationary variant

Because the speed axis removes the influence of how fast the operator ramped the machine, vs RPM results from different test runs — and from different vehicles or samples — can be overlaid directly. This makes them the preferred form for target setting, benchmarking and pass/fail limits, while vs Time remains the better tool for diagnosing a single event.

Interpretation Guidelines

Isolated narrow peak — A resonance is being excited by an order that crosses it at that speed. Identify the order from an order spectrum, then confirm the structural resonance.
Broad elevation over a speed range — A source that grows with speed (flow noise, inverter switching, bearing excitation) rather than a single resonance.
Peak in roughness or fluctuation strength but not in sharpness — A modulation problem, not a spectral balance problem. The complaint will be described as "buzzy", "beating" or "uneven" rather than "sharp".
Diagonal ridge on a tonality or TNR map — A tonal order: its frequency is proportional to speed. A horizontal ridge is a fixed-frequency tone, typically a structural resonance or an unrelated auxiliary device.
Different run-up and coast-down results — Points to a load-dependent or temperature-dependent mechanism; report both directions.

Practical Application Notes

Keep the run-up rate slow and steady. A fast sweep leaves few result frames per speed step, which makes narrow features unreliable regardless of the step setting.
Use the same speed step across a comparison series. Curves computed with different steps have different smoothing behaviour and should not be overlaid.
Cover the full operating range with margin at both ends. Metrics near the very first and very last speed step are computed from fewer data and are the least robust part of the curve.
When a psychoacoustic vs RPM result shows a peak, follow up with an order-based analysis at that speed. The psychoacoustic curve says how bad it sounds; the order analysis says which component to change.
Report the standard, the sound field and the speed step alongside every vs RPM result. Without them, the numbers are not comparable between laboratories.

Standard References

DIN 45631/A1:2010 — Calculation of loudness level and loudness from the sound spectrum — Zwicker method — Amendment 1: Calculation of the loudness of time-variant sound
DIN 45692:2009 — Measurement technique for the simulation of the auditory sensation of sharpness
ECMA-418-2 — Psychoacoustic metrics for ITT equipment — Part 2: Models based on human perception (hearing-model roughness and fluctuation strength)
ECMA-418-1 — Psychoacoustic metrics for ITT equipment — Part 1: Prominent discrete tones
DIN 45681:2005 + Berichtigung 2006 — Determination of tonal components of noise and determination of a tone adjustment for the assessment of noise immissions
ISO/TS 20065:2022 — Acoustics — Objective method for assessing the audibility of tones in noise — Engineering method