Understanding Gear Mesh Frequency

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Definition: What is Gear Mesh Frequency?

Gear mesh frequency (GMF, also called tooth mesh frequency or tooth engagement frequency) is the vibration frequency generated by the engagement of gear teeth as they enter and exit contact during gear rotation. It is calculated as the number of teeth on a gear multiplied by its rotational speed (GMF = Number of Teeth × RPM / 60). GMF represents the rate at which teeth mesh together and is typically the dominant frequency in gearbox vibration spectra.

Understanding and monitoring GMF is fundamental to gearbox diagnostics because the amplitude, harmonics, and sidebands of the GMF peak provide detailed information about gear condition, including wear, misalignment, tooth defects, and lubrication adequacy.

Calculation of Gear Mesh Frequency

Basic Formula

GMF can be calculated from either gear in a meshing pair:

• GMF = N_pinion × RPM_pinion / 60 (using pinion)
• GMF = N_gear × RPM_gear / 60 (using gear)
• Both methods give the same result (must, since teeth mesh together)

Example Calculations

Example 1: Simple Gearbox

• Input (Pinion): 20 teeth at 1800 RPM
• Output (Gear): 60 teeth at 600 RPM
• GMF = 20 × 1800 / 60 = 600 Hz
• Verification: 60 × 600 / 60 = 600 Hz ✓

Example 2: Multi-Stage Gearbox

• First Stage: 18 teeth at 3600 RPM → GMF₁ = 1080 Hz
• Second Stage: 25 teeth at 1200 RPM → GMF₂ = 500 Hz
• Third Stage: 30 teeth at 400 RPM → GMF₃ = 200 Hz
• Spectrum: Will show peaks at all three frequencies plus harmonics and sidebands

GMF in Vibration Spectra

Normal (Healthy) Gearbox

• GMF Peak: Clear peak at calculated frequency
• Amplitude: Moderate, consistent over time
• Harmonics: 2×GMF and 3×GMF may be present but low amplitude (< 25% of GMF)
• Sidebands: Minimal or absent
• Shaft Speeds: 1× peaks for input and output shafts lower than GMF

Abnormal Signatures Indicating Problems

High GMF Amplitude

• Cause: General gear wear, misalignment, high loads
• Indicator: GMF amplitude increasing over time
• Action: Increase monitoring frequency, plan inspection

Multiple GMF Harmonics

• Cause: Gear tooth defects, heavy wear, poor contact pattern
• Pattern: 2×GMF, 3×GMF, 4×GMF with significant amplitudes
• Severity: More harmonics = more severe condition

Sidebands Around GMF

Sidebands are modulation of GMF by shaft speeds:

• Pinion Sidebands: GMF ± input shaft speed → indicates pinion defects
• Gear Sidebands: GMF ± output shaft speed → indicates gear defects
• Multiple Sidebands: GMF ± n×(shaft speed) where n = 1, 2, 3… → specific tooth defects
• Asymmetric Sidebands: Stronger on one side indicates eccentric gear or unequal tooth spacing

Diagnostic Interpretation

Gear Condition Assessment

Condition	GMF Amplitude	Harmonics	Sidebands
New/Good	Low, stable	Minimal (< 25% of GMF)	Absent or very small
Normal Wear	Moderate, gradual increase	2×GMF present but low	Small sidebands may appear
Moderate Wear	High, continuing increase	2×, 3×GMF visible	Clear sidebands ± shaft frequencies
Severe Wear/Damage	Very high	Multiple harmonics (4×, 5×+)	Multiple sideband families
Localized Defect	Moderate	Present	Strong, regularly spaced sidebands

Specific Fault Signatures

Gear Misalignment

• High 2×GMF and 3×GMF harmonics
• Axial vibration may be elevated
• Improved by gear alignment correction

Eccentric Gear

• Strong sidebands at ±1× shaft speed of eccentric gear
• Tooth contact varies once per revolution
• May see amplitude modulation in time waveform

Broken or Cracked Tooth

• High amplitude sidebands at shaft speed spacing
• One impact per revolution of defective gear
• May show impulsive events in time waveform
• Rapid amplitude growth

Inadequate Lubrication

• Elevated GMF amplitude from increased friction
• High-frequency noise increase
• Temperature rise in gearbox

GMF and Structural Resonance

GMF often falls in range that excites structural resonances:

• Typical GMF: 200-2000 Hz for industrial gearboxes
• Frame Natural Frequencies: Often 50-500 Hz
• Matching: GMF or harmonics can excite frame or housing resonances
• Result: Loud gear whine, excessive casing vibration
• Solution: Stiffen housing, add damping, change gear tooth count (alters GMF)

Monitoring Strategy

Baseline Establishment

• Record GMF amplitude when gearbox new or freshly overhauled
• Document normal harmonic and sideband levels
• Establish alarm limits (typically 2-3× baseline)

Trending Parameters

• GMF Amplitude: Primary indicator of overall gear condition
• Harmonic Ratios: 2×GMF/GMF, 3×GMF/GMF increase indicates deterioration
• Sideband Energy: Sum of sideband amplitudes
• High-Frequency Content: Broadband energy in 5-50 kHz range (gear surface condition)

Alarm Levels

• Alert: GMF amplitude 2× baseline
• Alarm: GMF amplitude 4× baseline or rapid increase
• Critical: Multiple strong harmonics, extensive sidebands, or 10× baseline

Gear mesh frequency is the foundation of gearbox condition monitoring and diagnostics. Understanding GMF calculation, normal vs. abnormal spectral patterns, and the diagnostic significance of harmonics and sidebands enables effective detection of gear problems long before catastrophic failure, allowing planned maintenance and preventing costly production losses.

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