Understanding FTF – Fundamental Train Frequency

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Definition: What is FTF?

FTF (Fundamental Train Frequency, also called cage frequency or retainer frequency) is one of the four fundamental bearing fault frequencies, representing the rotational speed of the bearing cage (also called separator or retainer) that holds the rolling elements in position and maintains their spacing. The cage orbits around the bearing, carrying the rolling elements with it, and completes one revolution in the time it takes for all the rolling elements to travel around the bearing once.

FTF is the lowest of the four bearing frequencies, typically ranging from 0.35× to 0.48× shaft speed (sub-synchronous). While it’s the least commonly used for defect detection (cage defects are rare), FTF plays an important role as the modulation frequency that creates sidebands around other bearing fault frequencies, particularly BSF.

Mathematical Calculation

Formula

FTF is calculated using bearing geometry and shaft speed:

• FTF = (n / 2) × [1 – (Bd/Pd) × cos β]

Variables

• n = Shaft rotational frequency (Hz) or speed (RPM/60)
• Bd = Ball or roller diameter
• Pd = Pitch diameter (diameter of circle through rolling element centers)
• β = Contact angle

Simplified Form

For zero contact angle bearings (β = 0°):

• FTF ≈ (n / 2) × [1 – Bd/Pd]
• For typical bearings with Bd/Pd ≈ 0.2, this gives FTF ≈ 0.4 × n
• Rule of thumb: FTF typically 0.4× shaft speed (40% of shaft frequency)

Typical Range

• FTF typically 0.35-0.48× shaft speed depending on bearing geometry
• Example: 1800 RPM (30 Hz) → FTF ≈ 12 Hz (0.4× shaft speed)
• Always sub-synchronous (less than 1× running speed)
• Lowest of the four bearing frequencies

Physical Significance

Cage Motion

The cage’s rotation is determined by the rolling elements:

• Rolling elements roll (no slip) between inner and outer races
• Cage moves at average velocity of rolling element centers
• Speed is approximately midpoint between stationary outer race (0) and rotating inner race (shaft speed)
• Hence cage rotates at approximately 40% of shaft speed

Function of the Cage

• Spacing: Maintains even spacing between rolling elements
• Guidance: Keeps rolling elements in proper orbital path
• Lubrication: May help distribute lubricant
• Prevents Contact: Stops rolling elements from touching each other

When FTF Appears in Vibration Spectra

Direct Cage Defects

Primary FTF peaks appear when the cage itself is defective:

• Broken Cage: Fractured or cracked cage structure
• Worn Pockets: Excessive clearance between cage and rolling elements
• Cage Rubbing: Cage contacting races or seals
• Frequency: Direct FTF peak with harmonics
• Rarity: Cage-only defects are uncommon (< 5% of failures)

As Sideband Modulation (More Common)

FTF more commonly appears as sideband spacing around BSF:

• When rolling element defect present (BSF active)
• Defected ball’s impact severity varies as it orbits
• Variation occurs at cage orbital frequency (FTF)
• Creates sidebands: BSF ± FTF, BSF ± 2×FTF, BSF ± 3×FTF
• Diagnostic pattern for rolling element defects

In Bearing Instability

• Sub-synchronous vibration from bearing-induced instability may occur near FTF
• Can indicate inadequate preload or bearing clearance issues
• Distinguishable from cage defects by different characteristics (continuous vs. impacting)

Cage Defect Diagnosis

Symptoms of Cage Problems

• Peak at FTF frequency in vibration spectrum
• Harmonics at 2×FTF, 3×FTF, etc.
• Often erratic or variable amplitude
• May be accompanied by audible noise (clicking or rattling)
• Sometimes visible in time waveform as periodic impacts

Causes of Cage Defects

• Improper Lubrication: Inadequate lubrication causing cage wear
• High-Speed Operation: Excessive centrifugal forces on cage
• Contamination: Particles damaging cage material or pockets
• Overheating: Thermal distortion or softening of cage material
• Fatigue: High-cycle fatigue in thin cage sections
• Installation Damage: Cage bent or damaged during mounting

Practical Importance

As Diagnostic Marker

FTF’s primary diagnostic value is as sideband spacing:

• 1× Sidebands: Indicate inner race defects (modulation by shaft rotation)
• FTF Sidebands: Indicate rolling element defects (modulation by cage orbital motion)
• Pattern Recognition: Sideband spacing immediately identifies defect type
• Advanced Diagnosis: Understanding FTF enables proper interpretation of complex bearing spectra

In Automated Diagnostics

• Modern vibration analyzers calculate all four frequencies automatically
• Software identifies peaks at BPFO, BPFI, BSF, FTF
• Automatic sideband detection using FTF and 1× as search criteria
• Severity assessed based on amplitude and harmonic content

Relationship to Other Bearing Frequencies

Frequency Hierarchy

The four bearing frequencies in order of magnitude:

• Lowest: FTF (0.4× shaft speed)
• Low-Medium: BSF (2-3× shaft speed)
• Medium: BPFO (3-5× shaft speed)
• Highest: BPFI (5-7× shaft speed)

Mathematical Relationships

• All four frequencies related through bearing geometry
• Knowledge of one frequency and bearing type allows calculation of others
• Ratios between frequencies remain constant for a given bearing model
• Provides cross-verification of diagnosis

FTF, while the lowest and least commonly directly observed of the bearing fault frequencies, plays a crucial role in bearing diagnostics. Its function as the modulation frequency for rolling element defects and its potential indication of cage problems make understanding FTF essential for complete and accurate bearing condition assessment.

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