noise-vibration-harshness

name	noise-vibration-harshness
description	NVH (Noise, Vibration, Harshness) — NVH metrics, transfer path analysis (TPA), panel contribution analysis, NVH simulation (SEA, FEA, BEM), sound quality, acoustic materials, vehicle NVH.
metadata	{"priority":7,"promptSignals":{"phrases":["NVH","noise vibration harshness","transfer path analysis","TPA","panel contribution","sound quality","NVH simulation","SEA","vehicle noise","interior noise"],"minScore":3}}

NVH (Noise, Vibration, Harshness) — Complete Skill

NVH Fundamentals

Noise and Vibration Metrics

Sound Pressure Level: L_p = 20 log₁₀(p/p_ref) [dB] p_ref = 20 μPa (threshold of hearing) p in Pa (RMS)

Sound Power Level: L_W = 10 log₁₀(W/W_ref) [dB] W_ref = 10⁻¹² W

Addition of uncorrelated sources: L_total = 10 log₁₀(10^(L₁/10) + 10^(L₂/10) + ...) Two equal sources: L_total = L₁ + 3 dB

A-weighting: dB(A) — frequency-weighted to human hearing sensitivity Peak sensitivity: ~3-4 kHz; reduced below 500 Hz and above 10 kHz Most vehicle interior noise specs in dB(A)

Vibration metrics: RMS acceleration a_RMS [m/s² or g] Vibration Dose Value (VDV): VDV = (∫ a(t)⁴ dt)^(1/4) [m/s^1.75] — includes peaks

Frequency Ranges of Interest

Vehicle NVH: 20-200 Hz: powertrain, road, structure-borne noise (FEA domain) 200-2000 Hz: mid-range, panel vibration (hybrid FEA-SEA) 2000-10000 Hz: high-frequency, airborne noise (SEA, ray tracing) Human sensitivity to harshness: 50-500 Hz (smooth torque feel) Idle boom: 50-100 Hz; road noise: 500-2000 Hz; wind noise: 1000-5000 Hz

Transfer Path Analysis (TPA)

Classical TPA (Blocked Force / Operational TPA)

Concept: separate system into source + transfer paths Source (active): engine, wheel, suspension → forces/moments at mount points Transfer path: structure + cavity from mount to target (ear position) Receiver: driver/passenger ear

TPA equation: p_ear(ω) = Σ_k H_k(ω) × F_k(ω) H_k = Frequency Response Function (FRF) from source k to ear [Pa/N] F_k = active force at source k [N]

Steps:

1. Measure FRFs H_k(ω): impact hammer on mounts, microphone at ear
2. Measure operational forces F_k: accelerometers + mount stiffness, or direct force cells
3. Synthesize: p_syn(ω) = Σ H_k × F_k; compare to measured p_ear
4. Path contribution: p_k = H_k × F_k (rank paths by contribution)
5. Countermeasure: target highest contributing path

Component TPA (CTPA): Uses blocked forces (independent of receiver system) F_k^blocked = measured with rigid blocking at connection More accurate for structurally complex systems

Operational Transfer Path Analysis (OTPA)

Matrix method: uses only operational data (no direct FRF measurement) H_approx = P_target × P_sources⁺ (pseudo-inverse) Limitation: neglects partial coherence; use with care (reference selection critical)

Transmissibility matrix approach: T_ij = p_i / x_j (transmissibility from reference j to target i) Reference sensors must be linearly independent (near different source contributions)

Panel Contribution Analysis

Panel Acoustic Contribution

Interior cavity pressure from vibrating panels: p_ear(ω) = Σ_panels H_panel(ω) × v_panel(ω) H_panel = transfer admittance from panel velocity to ear pressure [Pa·s/m] v_panel = panel normal velocity [m/s] (from FEA or measurement)

Panel ranking: identify largest acoustic contribution panels Efficient countermeasure: add damping, mass, stiffness to highest-contributing panels

Measurement: scanning laser Doppler vibrometer (LDV) → velocity field on panel surface OR: FEA vibration → acoustic BEM for radiation

Radiation Efficiency

σ_rad = W_rad / (ρ_air c_air S <v²>) (radiation efficiency, normalized to plane wave) σ_rad << 1 below coincidence frequency (low radiation; bending waves shorter than acoustic wavelength) σ_rad = 1 at and above coincidence: efficient radiator

Coincidence frequency: f_c = c²/(2π) × √(m/B) [Hz] c = speed of sound, m = mass per unit area, B = bending stiffness For steel 1mm plate: f_c ≈ 12,000 Hz (high — not a problem in audible range) For concrete: f_c in audible range → important for building acoustics

NVH Simulation Methods

Finite Element Method (FEA) — Low Frequency

Vibroacoustic FEA: structural + acoustic coupled Structural: [M_s]{ü} + [C_s]{u̇} + [K_s]{u} = {F_s} + [K_c]ᵀ{p} Acoustic: [M_a]{p̈} + [C_a]{ṗ} + [K_a]{p} = {F_a} - ρ[K_c]{ü} [K_c] = coupling matrix (structural-acoustic interface)

Software: ANSYS Mechanical + Acoustic, Abaqus Acoustic, LMS Virtual.Lab Acoustics Modal: compute modes → superposition for forced response Frequency domain: direct frequency response (full FRF computation)

Upper frequency limit for FEA: ~200-500 Hz (require 6+ elements per acoustic wavelength) At 500 Hz: λ = c/f = 340/500 = 0.68 m → element < 0.11 m; manageable At 2000 Hz: λ = 0.17 m → element < 28mm; mesh becomes very large

Statistical Energy Analysis (SEA) — High Frequency

Energy balance between coupled subsystems P_in = W_ij (power flow from subsystem i to j) + D_i (power dissipated in i) W_ij = ω η_ij E_i - ω η_ji E_j (power flow proportional to energy difference) η_ij = coupling loss factor (CLF, depends on junction type) η_ii = damping loss factor (DLF, from measurements or material data)

SEA software: AutoSEA, VAone (ESI), NOVA Validity: high modal overlap (M > 3-5); many modes per frequency band; wavelength << subsystem size Typical: valid above ~500 Hz for vehicle body panels

Boundary Element Method (BEM) — Acoustic Radiation

Solve acoustic problem using only surface mesh (not volume mesh) For exterior radiation and scattering problems: efficient vs. FEA Direct BEM: p + u_n boundary conditions → solve for unknown p or u_n CHIEF (Combined Helmholtz Integral Equation Formulation): avoids interior resonances

Indirect BEM (ESI, MSC Actran): pressure jump across thin shell → efficient for thin structures

Hybrid FEA-SEA

FEA for structural components (few modes, well-characterized) SEA for acoustic cavities and high-frequency panels (many modes) Coupling at shared interfaces via power flow equations

Sound Quality (SQ) Metrics

Psychoacoustic Metrics

Loudness (sone): N = f(A-weighted SPL); accounts for masking and frequency dependence Sharpness (acum): high-frequency content feel; sharp/harsh sounds score high Roughness (asper): modulation at 20-200 Hz; engine combustion harmonics Fluctuation strength (vacil): slow AM modulation (< 20 Hz) Tonality (tuHMS): ratio of tonal to broadband energy

Target SQ by vehicle segment: Luxury: low roughness, low sharpness, consistent sound signature Sports: acceptable higher level, emphasized exhaust harmonics (intentional) EV: near-zero powertrain noise → high-frequency road/wind noise becomes prominent

Order Analysis

Engine orders: n-th order = f at n × RPM/60 4-cylinder: dominant orders 2nd (firing), 4th (secondary) 6-cylinder: 3rd order dominant firing Gear whine: gear mesh frequency = n_teeth × RPM/60

Waterfall plot (Campbell diagram): SPL vs. frequency vs. RPM Identifies: order-related noise (diagonal lines), resonances (vertical lines), mode shapes

Acoustic Materials and Treatments

Noise Reduction Methods

Mass law (sound insulation): TL = 20 log(m×f) - 47.5 [dB] (single panel, field incidence) Double mass: TL increases 6 dB; double frequency: TL increases 6 dB Rule: add 6 dB TL by doubling panel mass — expensive and heavy

Damping treatments: CLD (Constrained Layer Damping): η_system = 3E₂t₂/(E₁t₁) for thin viscoelastic layer Application: 1-2 kg/m² patch on high-radiation panels; 60-80% coverage often sufficient Free layer damping (FLD): cheaper but less effective (1/3 of CLD)

Absorption: Open-cell foam: efficient absorber at high frequency (f > 500 Hz); QWL resonance at t = λ/4 Fiber (glass wool, mineral wool): similar; sound absorption coefficient α → 0.9 at high f NRC (Noise Reduction Coefficient): average of α at 250, 500, 1000, 2000 Hz

Barriers: Mass-spring-mass (double-wall): resonance at f_0 = c/2π √(ρ_air/m × (1+1/n)); deep TL dip at f_0 Typical automotive dash isolation: composite of barrier (lead, mass) + absorber (foam)

Vehicle NVH Targets (Passenger Car)

Condition	Typical Target
Idle (in vehicle)	≤ 42 dB(A)
Cruising 100 km/h	≤ 68 dB(A)
Full acceleration	≤ 75 dB(A)
Road noise 80 km/h rough	≤ 70 dB(A)
Wind noise 140 km/h	≤ 68 dB(A)

Output

Provide: SPL L_p [dB(A)] at target position, dominant frequency bands [Hz], TPA path ranking (top 3 contributing paths), panel contribution ranking (top panels), suggested treatment (CLD, barrier, absorber, mount stiffness change), predicted attenuation [dB] from treatment, simulation method recommendation (FEA/SEA/Hybrid based on frequency).