| 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).
