What Is Gear Mesh Frequency (GMF)?

Gear Mesh Frequency (GMF) is the rate at which gear teeth come into contact with each other.

Every time a tooth on the pinion engages with a tooth on the gear, it produces vibration. These repeated impacts create a measurable vibration frequency. That frequency is GMF.

Basic GMF Formula

The standard equation is:

GMF = Shaft Speed (Hz) × Number of Teeth

If speed is given in RPM:

GMF = (RPM ÷ 60) × Number of Teeth

That’s it. Simple and direct.

Example Calculation

Let’s say:

• Input speed = 3000 RPM
• Pinion teeth = 19

Step 1: Convert RPM to Hz
3000 ÷ 60 = 50 Hz

Step 2: Multiply by tooth count
50 × 19 = 950 Hz

So the gear mesh frequency is 950 Hz.

That means the gear teeth are engaging 950 times per second.

Why Gear Mesh Frequency Matters

Gear mesh frequency is the foundation of gearbox vibration analysis. It helps you:

• Detect gear wear
• Identify cracked teeth
• Diagnose pitting or spalling
• Spot eccentricity and misalignment
• Perform NVH analysis
• Prevent catastrophic gearbox failure

When a gearbox develops a fault, the first change often appears at GMF or its harmonics.

If you monitor the amplitude of GMF over time, you can predict failures early.

Inputs Used in the Gear Mesh Frequency Calculator

The calculator you shared includes the following inputs:

1. Input Shaft Speed

You can enter speed in:

• RPM
• Hz

The calculator automatically converts Hz to RPM when needed.

2. Pinion Tooth Count

This is the number of teeth on the driving gear.

3. Gear Tooth Count

This is the number of teeth on the driven gear.

4. Calculation Mode

The tool offers three modes:

• Fundamental Mesh Frequency
• Sideband Analysis
• Harmonic Series

Each mode gives different diagnostic insight.

5. Fault Type Detection (Optional)

You can choose:

• General wear
• Localized pitting
• Tooth crack
• Gear eccentricity

The calculator then highlights the frequencies you should monitor.

6. Sensor Sample Rate (Optional)

This is used to check for aliasing risk.

Aliasing happens when your sampling rate is too low to capture high-frequency vibration correctly.

The calculator warns you if:

GMF > Sample Rate ÷ 2.56

This follows common vibration analysis practice.

Understanding the Output

The calculator provides:

• Gear Mesh Frequency (Hz, kHz, CPM)
• Gear ratio
• Output shaft speed
• Pinion shaft frequency
• Gear shaft frequency
• Harmonics (if selected)
• Sideband frequencies (if selected)
• Fault-specific diagnostic notes

Let’s break down the most important parts.

1. Fundamental Gear Mesh Frequency

This is the primary tooth engagement frequency.

If this amplitude increases over time, you likely have wear.

2. Harmonics (GMF × n)

Real gear vibration does not appear only at one frequency.

You will often see:

• 2× GMF
• 3× GMF
• 4× GMF

Higher harmonics often indicate:

• Advanced wear
• Poor lubrication
• Surface damage

If harmonics rise evenly, suspect distributed wear.

3. Sidebands (GMF ± Shaft Frequency)

Sidebands are critical for fault detection.

They appear when modulation occurs.

For example:

GMF ± Pinion Shaft Frequency

If GMF = 950 Hz
And pinion speed = 50 Hz

Sidebands will appear at:

• 900 Hz
• 1000 Hz

Sideband spacing equal to shaft frequency often indicates:

• Eccentricity
• Misalignment
• Localized damage

Gear Fault Detection Explained

The calculator includes logic for common gear faults. Here’s how they relate to frequency behavior.

1. General Wear

Symptoms:

• Elevated GMF
• Elevated harmonics
• Uniform increase across spectrum

Why it happens:
Surface roughness increases vibration energy.

2. Localized Pitting or Spalling

Symptoms:

• Sidebands around GMF
• Modulation at shaft frequency
• Increasing amplitude over time

Reason:
A damaged tooth causes impact once per rotation.

3. Tooth Crack

Symptoms:

• Strong sidebands
• Irregular amplitude changes
• Transient impacts

Cracks cause uneven tooth engagement.

4. Gear Eccentricity or Runout

Symptoms:

• Clear sidebands at exactly 1× shaft frequency
• Dominant first-order sidebands

Often caused by:

• Bent shaft
• Mounting issue
• Machining error

Harmonic Series in Detail

When you enable harmonic mode, the calculator shows:

1× GMF
2× GMF
3× GMF
4× GMF
5× GMF
6× GMF

Why this matters:

Some faults appear more clearly at 2× or 3× GMF than at the fundamental.

Monitoring harmonic growth helps detect faults earlier.

Aliasing Risk and Sample Rate

This part is often ignored, but it should not be.

If your vibration analyzer sample rate is too low, high-frequency GMF will fold into lower frequencies. This creates misleading data.

The calculator checks:

Minimum Sample Rate ≈ GMF × 2.56

If GMF = 950 Hz:

Minimum recommended sample rate:
950 × 2.56 ≈ 2432 Hz

If your device samples at 2000 Hz, your data may be unreliable.

Gear Ratio and Output Speed

The calculator also computes:

Gear Ratio = Gear Teeth ÷ Pinion Teeth
Output RPM = Input RPM ÷ Gear Ratio

This ensures:

• Pinion GMF
• Gear GMF

Both match properly.

If they don’t match, you may have entered incorrect tooth counts.

Practical Example: Full Calculation

Let’s use:

• Input Speed = 3000 RPM
• Pinion Teeth = 19
• Gear Teeth = 41

Step 1: Gear Ratio
41 ÷ 19 = 2.158

Step 2: Output Speed
3000 ÷ 2.158 = 1390 RPM

Step 3: Pinion Frequency
3000 ÷ 60 = 50 Hz

Step 4: GMF
50 × 19 = 950 Hz

Step 5: Sidebands
950 ± 50 → 900 Hz and 1000 Hz

This is exactly what your calculator produces.

Why Engineers Use a Gear Mesh Frequency Calculator

Manual calculation is easy once.

But during:

• Condition monitoring
• Commissioning
• Root cause analysis
• Spectrum interpretation

You need fast, repeatable results.

A calculator ensures:

• No math mistakes
• Instant harmonic analysis
• Automatic sideband detection
• Aliasing validation
• Fault guidance

That saves time and prevents incorrect diagnoses.

Industry Relevance

Gear mesh frequency is widely used in vibration standards such as:

• ISO 10816 (machine vibration evaluation)
• Predictive maintenance programs
• Automotive NVH testing
• Industrial gearbox diagnostics

GMF is the anchor frequency in gearbox health monitoring.

Who Should Use This Calculator?

This tool is useful for:

• Vibration analysts
• Reliability engineers
• Maintenance planners
• Mechanical engineers
• Automotive NVH specialists
• Rotating equipment technicians

If you work with gears, you will use GMF regularly.