vibration-testing

name	vibration-testing
description	Vibration testing — accelerometers, modal testing (EMA/OMA), frequency response functions (FRF), coherence, impact hammer, shaker setup, ODS, data acquisition, resonance identification.
metadata	{"priority":7,"promptSignals":{"phrases":["vibration testing","modal testing","accelerometer","frequency response","FRF","impact hammer","shaker test","ODS","modal analysis"],"minScore":4}}

Vibration Testing — Complete Skill

Measurement Hardware

Accelerometers

Piezoelectric: charge-mode or IEPE (voltage-mode, built-in amplifier) IEPE (ICP): 2-wire, constant current excitation (4mA typ.), industry standard Sensitivity: 10-100 mV/g typical; frequency range: 0.5 Hz to 10 kHz Mounting: stud mount (best, highest frequency range), adhesive, magnetic, hand-held (worst)

MEMS (capacitive): low frequency, low cost, suitable for 0-Hz (DC capable) Good for: structural health monitoring, slow machinery

Selection criteria: Mass loading: m_acc/m_structure < 5-10% at resonance (else shifts frequency) Frequency range: f_max,usable ≈ 1/3 of sensor resonant frequency g-range: ±50g (general), ±500g (shock), ±10g (low-level vibration) Temperature: standard -40 to +120°C; high-temp variants to +650°C

Signal Conditioners / DAQ

Sample rate: ≥ 2.56× bandwidth (anti-alias filter at 40% of sample rate) Resolution: ≥ 24-bit for vibration (avoids quantization noise at small amplitudes) Anti-aliasing: low-pass filter at < f_sample/2 (Nyquist) Dynamic range: 80-100 dB typical for vibration analyzers

Force Transducers

Load cell for static/quasi-static; piezoelectric force sensor for dynamic Impact hammer: built-in force transducer + accelerometer on tip Tip hardness: soft rubber (low-frequency, wide excitation), hard steel (high-freq, narrow excitation) Double hits: ringing after first strike — check coherence (< 0.9 = problem)

Frequency Response Function (FRF)

Definition

H(ω) = X(ω)/F(ω) [complex, function of frequency] Where X = response (accel, velocity, or displacement), F = force input

Types:

• Accelerance (inertance): a/F [m/s²/N]
• Mobility: v/F [m/s/N]
• Receptance (compliance): x/F [m/N] Related: H_accel = ω² × H_recept, H_mob = ω × H_recept

FRF Estimators

H1 = S_XF / S_FF (best when output noise dominates) H2 = S_XX / S_FX (best when input noise dominates) Coherence γ² = |S_XF|² / (S_FF × S_XX) γ² = 1: perfect causal linear relationship (no noise, no nonlinearity) γ² < 0.9: problem (noise, double impact, nonlinearity, leakage)

Processing

FFT size: longer record → better frequency resolution Δf = f_sample / N Averaging: minimum 5-10 linear averages; 50-100 for noisy signals Windowing:

• Rectangular: exact for hammer impact (short transient in window)
• Hanning: for shaker (continuous signal) — reduces leakage
• Force window: apply to force channel (hammer); Exponential window: response channel

Leakage: frequency not exact multiple of Δf → energy spreads to adjacent bins → use Hanning or zoom FFT

Modal Parameter Extraction

Peak Picking (SDOF approximation)

Natural frequencies: peaks in FRF magnitude Damping from half-power bandwidth: ζ = Δω/(2ω_n) where Δω = ω at A_max/√2 Only valid for well-separated modes (modal overlap factor < 0.3)

SDOF Curve Fitting (Circle Fit — Ewins)

Plot Im{H(ω)} vs. Re{H(ω)} → Nyquist circle at each mode Diameter = 1/(2ζk_modal), center location → natural frequency, damping

Global Curve Fitting (MDOF — PolyMAX, LSCF)

Fits all measured FRFs simultaneously Stabilization diagram: mode indicator vs. polynomial order → stable poles = physical modes Extract: ω_n, ζ, mode shape coefficients {φ} for all modes Software: LMS Test.Lab, Brüel & Kjær Connect, ME'scope, pyEMA (open source)

MAC (Modal Assurance Criterion)

MAC_ij = |{φ_i}ᵀ{φ_j}|² / ({φ_i}ᵀ{φ_i} × {φ_j}ᵀ{φ_j}) MAC = 1: identical shapes; MAC = 0: orthogonal (independent) Used to: compare experimental modes to FEA modes (model correlation) Off-diagonal MAC > 0.1: possibly confused modes (sensor placement issue)

Experimental Modal Analysis (EMA)

Roving Hammer

Fix single reference accelerometer (good sensor location — all modes excited well) Impact at all DOF nodes on structure FRF matrix column: all rows at fixed reference Mode shapes: from FRF amplitudes at resonance frequencies

Roving Accelerometer

Fix impact location (reference DOF) Move accelerometers to all DOF nodes FRF matrix row: all columns from fixed input

Test Planning

Sensor locations: every node of interest + sufficient to define mode shapes (avoid nodal points of modes of interest) Rule: minimum 2× DOF sensors per mode to be identified Pre-test FEA: compute expected mode shapes → place sensors at high-amplitude DOFs

Operational Modal Analysis (OMA)

Input force not measured — uses ambient/operational excitation Output-only modal analysis: output PSD and correlation functions as inputs Assumes: broad-band white-noise excitation (often valid for ambient vibration) Methods: SSI-COV (Stochastic Subspace Identification), FDD (Frequency Domain Decomposition), p-LSCF

Advantages: no shutdown required, actual operating conditions Limitations: cannot get modal scaling (mass-normalized), cant distinguish closely-spaced modes with correlated inputs

Operating Deflection Shape (ODS)

Not modal analysis — shows how structure vibrates at operating speed/frequency FRF not needed — just measure response amplitude/phase at all points Phase coherence: reference sensor + roving sensors measured simultaneously Phase relationships show wave patterns (traveling waves vs. standing waves) Cannot separate modes (superposition of all modes at that frequency)

Shaker Testing

Excitation Signals

Swept sine: slow sweep through frequency range; high SNR; reveals nonlinearity Burst random: random excitation, burst within window (leakage-free); multiple averages Periodic random: random, repeating each cycle; most efficient averaging Chirp (swept sine in time window): linear or log sweep in one burst

Shaker attachment: stinger (thin rod, axial force only, decouples lateral) → prevents shaker from applying moment to structure Force measurement: force transducer between stinger and structure (NOT at shaker)

Drive Point FRF

FRF measured at same point and direction as force input Must be: positive imaginary part (receptance) at resonance, phase 0-180° Used for: damping estimation, structural dynamic modification

Key Frequency Domain Quantities

RMS = √(Σa_i²/2) [for sinusoidal, from FFT amplitude] VRMS from PSD: a_rms = √(∫G(f)df) [integrate PSD over frequency band] Peak: a_peak = crest_factor × a_rms (crest factor = 1.41 for sine, 3-6 for random) OA (overall): sum over all frequencies

Standards

ISO 5348: mechanical mounting of accelerometers ISO 7626: mechanical mobility measurement (FRF) ASTM E756: material damping by cantilever beam IEC 60068-2-6: sinusoidal vibration test MIL-STD-810H: environmental vibration test requirements

Output

Provide: accelerometer specification (sensitivity, g-range, mounting), FRF processing settings (Δf, averages, window), natural frequencies and damping [Hz, %], MAC comparison to FEA, ODS animation description.