What is Hunting Tooth Frequency? Gear Pattern Repeat • Portable balancer, vibration analyzer "Balanset" for dynamic balancing crushers, fans, mulchers, augers on combines, shafts, centrifuges, turbines, and many others rotors What is Hunting Tooth Frequency? Gear Pattern Repeat • Portable balancer, vibration analyzer "Balanset" for dynamic balancing crushers, fans, mulchers, augers on combines, shafts, centrifuges, turbines, and many others rotors

What is Hunting Tooth Frequency? Gear Pattern Repeat

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Understanding Hunting Tooth Frequency

Definition: What is Hunting Tooth Frequency?

Hunting tooth frequency (HTF, also called assembly phase frequency or greatest common divisor frequency) is a low-frequency vibration component in gear pairs that represents the rate at which the same individual teeth on the pinion and gear come back into contact with each other. This frequency is determined by the greatest common divisor (GCD) of the number of teeth on each gear and appears as a modulation frequency creating sidebands around the gear mesh frequency (GMF).

Hunting tooth frequency is diagnostically significant because vibration at HTF indicates problems with specific individual teeth (such as a cracked tooth, localized wear, or eccentricity) rather than general gear condition, helping pinpoint the exact location and nature of gear defects.

Mathematical Basis

Calculation Method

HTF is calculated using the greatest common divisor (GCD) of the tooth counts:

Formula

  • HTF = GCD(N₁, N₂) × RPMpinion / 60
  • Where N₁ = number of teeth on pinion
  • N₂ = number of teeth on gear
  • GCD = greatest common divisor of N₁ and N₂

Examples

Example 1: Hunting Tooth Pair

  • Pinion: 23 teeth at 1800 RPM
  • Gear: 67 teeth
  • GCD(23, 67): 1 (prime numbers, no common factors)
  • HTF = 1 × 1800 / 60 = 30 Hz (same as pinion shaft speed)
  • Meaning: Each pinion tooth meshes with each gear tooth before pattern repeats
  • Result: Hunting tooth gear — optimal wear distribution

Example 2: Non-Hunting Pair

  • Pinion: 20 teeth at 1800 RPM
  • Gear: 60 teeth
  • GCD(20, 60): 20
  • HTF = 20 × 1800 / 60 = 600 Hz
  • Meaning: Same 20 tooth pairs mesh repeatedly
  • Result: Concentrated wear pattern on same teeth

Example 3: Intermediate Case

  • Pinion: 18 teeth at 3600 RPM
  • Gear: 54 teeth
  • GCD(18, 54): 18
  • HTF = 18 × 3600 / 60 = 1080 Hz
  • Pattern: 18 different tooth contact pairs repeat

Hunting vs. Non-Hunting Gear Sets

Hunting Tooth Design (GCD = 1)

Achieved when tooth numbers are relatively prime (no common factors):

  • Advantages:
    • Each pinion tooth eventually meshes with every gear tooth
    • Wear distributed uniformly across all teeth
    • Manufacturing errors averaged out
    • Longer gear life
    • Preferred for most applications
  • Disadvantages:
    • Specific tooth defects create vibration at shaft speed (HTF = shaft speed)
    • May require more precise manufacturing

Non-Hunting Design (GCD > 1)

Occurs when tooth numbers share common factors:

  • Advantages:
    • Simpler tooth count selection
    • May allow standard gear sizes
  • Disadvantages:
    • Same teeth repeatedly mesh (only GCD unique pairs)
    • Wear concentrated on same tooth pairs
    • Manufacturing errors on specific teeth repeated every cycle
    • Shorter gear life typically
    • Generally avoided in quality gearbox design

Vibration Signature

HTF as Sideband Spacing

HTF appears primarily as sideband spacing around GMF:

  • Central Peak: GMF (gear mesh frequency)
  • Sidebands: GMF ± HTF, GMF ± 2×HTF, GMF ± 3×HTF
  • Interpretation: Sidebands at HTF spacing indicate individual tooth defects or eccentricity
  • Amplitude: Sideband amplitude indicates severity of localized defect

Diagnostic Patterns

Single Damaged Tooth

  • Strong sidebands at HTF spacing around GMF
  • HTF = shaft speed of gear with damaged tooth
  • Impact once per revolution of defective gear
  • Time waveform shows periodic impulse

Gear Eccentricity

  • HTF sidebands from runout (eccentric mounting)
  • Tooth engagement depth varies once per revolution
  • Creates amplitude modulation of GMF
  • Correctable through remounting or runout compensation

Unequal Tooth Spacing

  • Manufacturing error in tooth spacing
  • Creates pattern repeating at HTF
  • May require gear replacement or acceptance if within tolerances

Practical Diagnosis

Identifying Defective Gear

Determine which gear (pinion or main gear) has the defect:

  1. Calculate Both Shaft Speeds: Input and output RPM
  2. Measure Sideband Spacing: From vibration spectrum
  3. Compare: If sideband spacing = input shaft frequency → pinion defect
  4. Compare: If sideband spacing = output shaft frequency → gear defect
  5. Conclusion: Sideband spacing identifies which shaft (and thus which gear) has the problem

Severity Assessment

  • Sideband Amplitude: Higher amplitudes indicate more severe localized defect
  • Number of Sidebands: More sidebands (higher orders) indicate worse condition
  • Time Waveform: Clear periodic impulse confirms individual tooth impact
  • Comparison to GMF: Sidebands > 25% of GMF amplitude indicates significant defect

Design Considerations

Selecting Tooth Numbers

Best practice for gear design:

  • Use Prime Numbers: Ensures GCD = 1 (hunting tooth design)
  • Avoid Common Factors: Don’t use tooth counts like 20:60 (GCD=20)
  • Example Good Pairs: 17:51, 19:57, 23:69 (all GCD=1)
  • Trade-off: May limit gear ratio options slightly

When Non-Hunting Acceptable

  • Low-load applications where wear not critical
  • Standard gear sets where exact ratios required
  • Short-life applications (wear distribution less important)
  • When manufacturing advantages outweigh wear considerations

Relationship to Other Gear Frequencies

Frequency Hierarchy in Gearbox

  • Shaft Speeds: 1× for input and output (lowest frequencies)
  • HTF: Equal to shaft speed (hunting design) or higher (non-hunting)
  • GMF: Number of teeth × shaft speed (highest primary frequency)
  • GMF Harmonics: 2×GMF, 3×GMF, etc. (from non-linearities)

Sideband Analysis Strategy

  • Sidebands at shaft speed spacing → eccentric gear or individual tooth defect
  • Sidebands at HTF spacing (if HTF ≠ shaft speed) → repeating tooth pattern issue
  • No clear sidebands → general distributed wear or good gear condition

Hunting tooth frequency, while a subtle aspect of gear dynamics, provides powerful diagnostic information. Understanding HTF calculation and recognizing HTF sidebands enables precise identification of which gear has a defect and whether the problem is a specific damaged tooth or a more distributed condition, guiding targeted maintenance actions in gearbox troubleshooting.

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