gear-noise

name	gear-noise
description	Gear noise and vibration — transmission error (TE), gear mesh frequency, tooth profile modification (tip relief/lead crowning), whine noise, rattle, dynamic factor, AGMA 2000 accuracy, gear measurement (STE/DTE), NVH in automotive transmissions.
metadata	{"priority":7,"promptSignals":{"phrases":["gear noise","gear whine","transmission error","gear mesh frequency","tooth profile modification","gear NVH"],"minScore":3}}

Gear Noise and Vibration — Complete Skill

Fundamentals of Gear Noise

Primary noise mechanism: transmission error (TE) — deviation of driven gear from perfect kinematic motion due to manufacturing errors, elastic deflections, and tooth geometry Vibration path: TE → dynamic mesh force → shaft → bearings → housing → acoustic radiation

Gear mesh frequency (GMF): f_GMF = N_teeth × RPM / 60 [Hz; for each gear; pinion and gear have same GMF] GMF and its harmonics: 2×GMF, 3×GMF, etc. are primary noise frequencies

Sidebands: modulation of GMF by shaft rotational frequency → sidebands at f_GMF ± n × f_shaft Sidebands indicate: tooth-to-tooth pitch error, tooth form error variation around gear, eccentricity

Transmission Error (TE)

Static transmission error (STE): TE(θ) = θ_driven × N_driven/N_driving - θ_driving [rad; deviation from ideal kinematics under load] Measured by encoder difference between input and output at quasi-static speed

Sources of STE:

• Tooth spacing error (pitch error): e_p — periodic at shaft frequency
• Profile error: deviation from involute → periodic at GMF
• Lead error: helix angle error → periodic at shaft frequency
• Elastic deflection under load: mesh stiffness variation → periodic at GMF

Dynamic transmission error (DTE): TE(t) = STE(t) + dynamic response [amplified at resonance; DTE >> STE near critical speed] Critical speed: f_n ≈ GMF → amplification by Q (quality factor) → loud gear whine

TE Peak-to-Peak (pp) targets: Automotive final drive (quiet): < 2 μm STE pp Industrial gearbox: 5–15 μm STE pp Typical improvement with profile modification: 30–70% reduction in STE pp

Tooth Profile Modification

Tip Relief

Purpose: remove material at tooth tip to compensate for tooth bending and approach path error; reduces mesh stiffness variation → reduces TE Amount of tip relief: α_tip = load-dependent deflection at tip engagement α_tip ≈ F_t × C_te [μm; C_te = tip relief compliance factor from tooth FEA or handbook] Typical: 5–25 μm tip relief at nominal load

Long relief vs. short relief: Long (full profile): relief extends 1/3–1/2 of active tooth flank; effective at multiple loads Short (tip only): < 1/4 of active flank; optimized for single operating load

Lead modification (crowning): Crowning: barrel-shaped tooth along facewidth → reduces sensitivity to misalignment Crown amount: C_crown = K_crown × β_error [μm; K_crown = sensitivity factor; β_error = lead error / misalignment] Typical crowning: 10–50 μm maximum crown for spur/helical automotive gears

Helix Angle Modification

For helical gears: progressive tooth engagement → smoother contact; εβ = 1 → one full pitch of helical overlap εβ = F × sin(β) / (π × m_n) [F = facewidth; β = helix angle; m_n = normal module] Higher εβ (> 1.5): smoother load sharing; lower TE; lower gear whine

Dynamic Factor and Resonance

Dynamic factor K_v (AGMA): K_v accounts for dynamic mesh load increase at high speed K_v = [A / (A + √(200V))]^B [AGMA 2001; A, B depend on accuracy grade; V = pitch line velocity in m/s] Or Barth velocity factor: K_v = (6.1 + V) / 6.1 [V in m/s; simplified for AGMA 6]

Critical speed (gear pair torsional resonance): ω_critical = √(k_mesh / (m_eff)) [k_mesh = mesh stiffness ≈ 0.8–1.5 × 10⁹ N/m for steel; m_eff = effective mass] Avoid operation at ω_critical or GMF = ω_critical / (2π × N_teeth)

Dynamic magnification factor (Q-factor): Q = 1/(2ζ) → near resonance: DTE = Q × STE [ζ = damping ratio ≈ 0.01–0.05 for gears]

AGMA 2000 Accuracy Classification

Quality number (QN 6–13): Higher QN → tighter tolerances; QN 11–13: precision gear; QN 6–7: commercial grade

Total accumulated pitch error (F_p): At QN 6: F_p ≈ 50–100 μm (depending on module and diameter) At QN 11: F_p ≈ 5–10 μm At QN 13: F_p ≈ 2–3 μm (master gears)

Profile error (f_f): At QN 6: f_f ≈ 25 μm At QN 11: f_f ≈ 3 μm

Lead error (F_β): At QN 6: F_β ≈ 30 μm At QN 11: F_β ≈ 5 μm

Effect on noise: QN 11 vs. QN 6 → 10–15 dB reduction in gear whine (approximate; highly geometry-dependent)

Gear Measurement

CMM (Coordinate Measuring Machine) / Gear Measuring Center: Profile measurement: continuous involute check from root to tip; compare to theoretical involute Helix measurement: scan along tooth for lead accuracy Pitch measurement: cumulative pitch error; spacing error between teeth

Single Flank Test (SFT): Measures STE directly; most relevant NVH test Output: TE spectrum (amplitude vs. order); total TE pp [μm]

Double Flank Test (backlash control): Checks total composite error; backlash variation; useful for production screening

Gear Rattle (Impact Noise)

Mechanism: in loose gear pairs (clutch packs, gear pairs not under torque) → backlash-induced impacts → rattle noise Common: automotive transmission at idle (non-engaged gears rattle from torsional excitation)

Rattle threshold: Δθ_excitation > backlash / (R_pitch) → impact; Δθ_excitation from engine cylinder firing excitation Mitigation: reduce backlash (increases rattle sensitivity to TL); add friction material; change gear mass/inertia

Backlash optimization: Minimum backlash (gear expansion under thermal): b_min = f(ΔT, α, d) Design for backlash = thermal expansion + manufacturing tolerance; AGMA 2002: minimum backlash tables

Housing and System NVH

Gear housing radiation: Sound power: Lw ∝ 10 log₁₀(P_radiation) = 10 log₁₀(σ_rad × S_housing × ρ₀c₀ × <v²>) Housing stiffness: increase ribbing → raise modes above GMF; add damping treatments

NVH path reduction:

• Engine mounts: isolate transmission from body (rubber mounts ≈ 10–15 dB isolation)
• Gear shaft bearing preload: reduce housing vibration transmission
• Acoustic covers / foam inserts in hollow housings

Order analysis (rotating machinery): Track GMF as multiple of shaft order → identifies speed-dependent gear noise Campbell diagram: frequency vs. speed; shows resonance crossings

Standards

Standard	Scope
AGMA 2000-A88	Gear classification and inspection
AGMA 2001-D04	Fundamental rating factors (dynamic factor)
ISO 1328	Cylindrical gear — accuracy grade
AGMA 2015-1	Accuracy classification system (new standard)
VDI 2608	Flank line modifications
SAE J1297	Measurement of gear rattle

Output

Provide: gear accuracy class (AGMA QN or ISO class), pitch line velocity V [m/s], GMF [Hz] and critical speed [RPM], STE pp [μm] measured or predicted, tip relief applied (amount [μm] at nominal load), crowning (crown amount [μm] and facewidth), profile modification effectiveness (STE reduction [%]), dynamic factor K_v, housing resonance modes vs. GMF (separation margin), gear rattle assessment (backlash [μm] vs. excitation amplitude), overall gear whine level estimate [dB] and dominant order, and applicable standard (AGMA 2000, ISO 1328, AGMA 2015).