Tonal NVH During Battery Preconditioning

What the field is reporting

A narrow-band tone, only in one operating mode.

Warranty and quality channels logged a consistent description: a steady tonal drone or whine, perceived from the cabin and engine bay, present only while preconditioning is active and the vehicle is stationary, predominantly in cold ambient. It is absent while driving and absent during summer cabin cooling. Subjective pitch reports cluster in the low-kilohertz range.

Because preconditioning activates several subsystems at once — the traction inverter's active-heating injection, the coolant pump, valves, and sometimes the compressor — the symptom is operationally entangled. Multiple subsystems are "on" together, which is precisely the condition under which correlational reasoning misleads. The study was designed to break that entanglement.

The measured fleet

320 vehicles were logged during preconditioning events with synchronized electrical, thermal, and acoustic channels. Each record carries the calibration identity, the commanded heating current and its injection frequency, auxiliary-pump duty, the motor structural variant (which sets the stator modal frequency), and the extracted tonal sound-pressure level at the complaint frequency. Signals were drawn from CAN, inverter telemetry, and a cabin microphone with order/spectral post-processing.

The dataset is synthetic, generated from a physics-based model with a known ground truth so the diagnostic method can be validated against the answer (full generator in the appendix). The d-axis current is the only true electromagnetic driver; pump duty is deliberately built as a calibration-linked proxy with no path to the tonal peak.

The field of suspects

Six hypotheses were carried forward, spanning the failure-mode families so the true cause could not be excluded by assumption. Each is stated with the prediction it makes — the prediction is what later lets us reject or retain it.

Note that H4, H5, and H6 are not rivals — they are links in one chain (a calibration sets the current; the current creates the force; the structure amplifies it). Recognizing that early prevents the common error of treating a multi-stage mechanism as competing single-cause explanations.

First pass: what correlates with the tone

Ranking each logged channel against the tonal SPL gives the starting leaderboard:

Pump duty (r = ) is the dangerous result: a mechanically plausible, strongly correlated feature with an obvious story. It clears the first three diagnostic gates — association, significance, materiality. It fails the fourth, and the failure is only visible under control.

A confounder, not a cause

The pump correlation looks like this — tight enough to close a hasty investigation:

The test is partial correlation: hold the d-axis current constant and ask whether pump duty retains any association with the tone. It does not.

H2 is rejected. Two independent lines of evidence converge: the partial correlation eliminates the statistical association, and the order analysis in §7.1 shows the tonal frequency does not track pump speed at all. The pump is loud, but it is not this tone.

Why d-axis current alone doesn't close the case

Holding pump aside, d-axis current is a strong, surviving cause — and it has a mechanism (more on that in §7). But fitting the tone to current alone leaves a large unexplained residual: a meaningful population of high-current vehicles stays quiet. A cause that is real but incomplete is a signal that a second variable is in play.

The regression makes the gap explicit. Adding the saturation term (current²) to the pump model lifts explanatory power; adding the resonance gain lifts it sharply:

The pump coefficient decays toward zero as real causes enter; the resonance term is what closes the case. This is the abductive move: the best explanation for "high current, yet quiet" is that the audible outcome requires the current-driven force to land on a structural resonance. The refined hypothesis becomes specific and testable — loud iff i_d is high and 6·f_inj ≈ stator mode — and it is that conjunction the physics in §7 confirms.

Where the statistics meet the electromagnetics

Statistical survival is necessary but not sufficient; a root cause must show its mechanism in the raw physics. Three independent confirmations follow.

7.1 — Order tracking: the tone is electromagnetic, not mechanical

If the tone were a bearing or pump artifact it would track a rotational or pump-speed order. It does not. The measured tonal frequency tracks 6 × f_inj across the fleet — a clean line of slope 6 against injection frequency, with the vehicle at standstill (no shaft rotation to produce a mechanical order at all).

7.2 — Saturation enriches the 5th and 7th harmonics

Why a 6th-order force? In a three-phase winding the 5th and 7th MMF harmonics beat against the fundamental to produce a 6th-order radial force. Their amplitude is small in the linear regime but grows super-linearly once the high d-axis current drives the stator teeth into magnetic saturation, flattening and distorting the airgap flux.

7.3 — Resonance: the gate that decides who is loud

The 6th-order force is present on every heating event, but it becomes audible only when its frequency meets a stator structural mode. Sweeping the ratio of forcing frequency to modal frequency reproduces the classic single-degree-of-freedom resonance peak, with magnification set by the modal quality factor (Q ≈ ):

7.4 — The mechanism, end to end

Assembled, the confirmed chain runs from a calibration choice to an audible tone, with a structural resonance acting as the gate that decides which vehicles are affected:

The investigation, distilled to a field test

Once the mechanism is known, the recurring per-vehicle diagnosis compresses into three questions. This is what a service tool or an on-board monitor evaluates — each leaf names both the cause and the action. Split points come from the data: the heating current separates the calibrations (~240 A vs ~110 A), and the resonance window is set by the modal bandwidth.

The ordering encodes the analysis: the order check first (it cleanly excludes the mechanical and PWM families), then the saturation gate (the primary cause), then the resonance gate (the co-cause that decides audibility).

Silencing the order

With the mechanism identified, two mitigations follow directly — one electromagnetic, one structural-avoidance — and a third at the calibration level. Each was evaluated in simulation.

8.1 — Harmonic current injection (HCI)

Because the offending force is a specific order (6th), it can be cancelled at the source by injecting an anti-phase current component tuned to that order. Modeling % cancellation of the 6th-order force removes the dominant peak from the radial-force spectrum:

8.2 — Injection-frequency dithering & calibration

Moving the injection frequency so that 6·f_inj sits off the structural mode walks the operating point down the resonance curve. A % detune yields ≈ dB of relief on resonant vehicles — smaller than HCI but trivially deployable as an interim calibration patch. A variant-aware calibration that caps i_d for the susceptible stator variant is the conservative fallback, at the cost of a slower heating rate.

Predicting the complaint wave before it lands

Because the root cause is mechanistic, the diagnosis becomes a forward forecast. The quality-relevant "failure" here is a logged customer complaint, and its likelihood grows with cold-season exposure: each preconditioning event on a resonant, aggressive-calibration vehicle has a chance of being audibly annoying, and repeated annoyance drives complaints. We run a Monte Carlo over the at-risk cohort — 5,000 customers, weekly preconditioning events through a six-month cold season — and track when each first complains, with and without the HCI fix.

10.1 — Accumulating exposure

10.2 — Probability of a complaint

10.3 — Time to first complaint

The forecast generalizes to a fleet screen: every vehicle on the aggressive calibration whose stator variant places its mode within the resonance window is in the at-risk cohort, before any complaint is filed. The prognosis tells the program both how many and how soon — and how completely the HCI fix removes the exposure.

Fleet action

The diagnosis converts directly into a screen and a remedy. Because the root cause is mechanistic, the affected population can be identified before complaints arrive: any vehicle on the aggressive calibration whose stator variant places its mode within the resonance window of 6·f_inj is at risk.

Recommended sequence: deploy the HCI 6th-order cancellation as the primary OTA controller fix; ship the injection-frequency dither as an immediate interim relief for in-warranty resonant vehicles; and fold a variant-aware heating calibration into the next release so the regime is avoided by design. Post-fix, verify by confirming the 6·f_inj tonal peak has dropped below the audibility threshold in re-instrumented vehicles, and track complaint rate by calibration-and-variant cohort.

Why each suspect was kept or dropped

Reproducibility

The fleet dataset and the full analysis are provided alongside this report as nvh_precond_rca.py (physics-based generator + diagnostic pipeline) and nvh_fleet.csv (320-vehicle mockup). The essential physics of the generator:

# saturation enriches 5th/7th -> 6th-order radial force
H57   = (i_d / I_d0) ** 2                  # harmonic content vs current
f_force = 6.0 * f_inj                       # dominant radial-force order
A_res = 1 / sqrt((1-(f_force/f_mode)**2)**2 + (f_force/(Q*f_mode))**2)
F_radial  = H57 * A_res                     # amplitude (norm.)
SPL_tonal = 20*log10(F_radial) + 42 + noise # dB(A) at 6*f_inj

# confounder: aggressive cal drives BOTH i_d and pump duty
i_d       = where(cal_aggressive, ~240A, ~110A)
pump_duty = where(cal_aggressive, ~72%, ~46%)   # proxy, no path to tone

The diagnostic pipeline reproduces every figure: the correlation screen, the partial-correlation confounder test (pump → r ≈ ), the staged regression (R² ), order tracking, the saturation and resonance curves, and the HCI mitigation.