Understanding Bearing Fault Frequencies

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Definition: What are Bearing Fault Frequencies?

Bearing fault frequencies (also called bearing defect frequencies or characteristic frequencies) are specific vibration frequencies generated when rolling elements (balls or rollers) in a bearing pass over defects such as cracks, spalls, or pits on the bearing races or the rolling elements themselves. These frequencies are mathematically predictable based on the bearing’s geometry and the shaft’s rotational speed, making them invaluable diagnostic indicators for early detection of bearing defects.

Understanding and identifying these frequencies through vibration analysis allows maintenance personnel to detect bearing problems months before they would become apparent through temperature rise, noise, or catastrophic failure, enabling planned maintenance and preventing costly unplanned downtime.

The Four Fundamental Fault Frequencies

Every rolling element bearing has four characteristic fault frequencies, each corresponding to a different type of defect:

1. BPFO – Ball Pass Frequency, Outer Race

The rate at which rolling elements pass a fixed point on the outer race:

• Physical Meaning: If a defect exists on the outer race, each rolling element strikes it as it passes, creating a repetitive impact
• Typical Value: 3-5× shaft speed for most bearings
• Formula: BPFO = (N × n / 2) × (1 + (Bd/Pd) × cos β)
• Most Common: Outer race defects are the most frequent bearing failure mode
• Load Zone Effect: Stationary outer race means defect is in constant position relative to load

2. BPFI – Ball Pass Frequency, Inner Race

The rate at which rolling elements pass a fixed point on the inner race:

• Physical Meaning: Inner race rotates with shaft, so a defect on the inner race is struck by each rolling element as they pass
• Typical Value: 5-7× shaft speed for most bearings
• Formula: BPFI = (N × n / 2) × (1 – (Bd/Pd) × cos β)
• Higher Than BPFO: Always higher frequency than BPFO for same bearing
• Sidebands: Almost always shows 1× sidebands due to load zone modulation

3. BSF – Ball Spin Frequency

The rotational frequency of a rolling element spinning on its own axis:

• Physical Meaning: If a rolling element has a defect, it impacts both races at this frequency
• Typical Value: 1.5-3× shaft speed
• Formula: BSF = (Pd / Bd) × (n / 2) × [1 – (Bd/Pd)² × cos² β]
• Least Common: Rolling element defects are less frequent than race defects
• Complex Pattern: Defect contacts both races, creating complex vibration signature

4. FTF – Fundamental Train Frequency

The rotational frequency of the bearing cage (retainer):

• Physical Meaning: Rate at which the cage rotates, carrying rolling elements around the bearing
• Typical Value: 0.35-0.45× shaft speed (sub-synchronous)
• Formula: FTF = (n / 2) × (1 – (Bd/Pd) × cos β)
• Cage Defects: Worn or damaged cages excite this frequency
• Instability Indicator: Can also appear during bearing-induced rotor instabilities

Formula Variables Explained

The fault frequency formulas use these bearing geometric parameters:

• N = Number of rolling elements (balls or rollers)
• n = Shaft rotational frequency (Hz) or speed (RPM)
• Bd = Ball or roller diameter
• Pd = Pitch diameter (diameter of circle through centers of rolling elements)
• β = Contact angle (angle between load direction and bearing axis, typically 0-40°)

Most vibration analysis software includes bearing databases with these parameters pre-calculated for thousands of bearing models.

How Fault Frequencies Appear in Vibration Spectra

Basic Appearance

When a bearing develops a defect:

• Primary Peak: The fault frequency appears as a distinct peak in the frequency spectrum
• Harmonics: Multiple harmonics (2×, 3×, 4×) of the fault frequency appear as defect worsens
• Sidebands: For inner race and rolling element defects, 1× sidebands around fault frequency are common
• Amplitude Growth: Fault frequency amplitude increases as defect progresses

Sideband Patterns

Sidebands provide crucial diagnostic information:

• Inner Race Defects: BPFI with ±1×, ±2× sidebands (defect rotating in/out of load zone)
• Outer Race Defects: BPFO may have 1× sidebands if outer race can rotate slightly
• Rolling Element Defects: BSF with sidebands at FTF spacing (cage frequency modulation)
• Sideband Spacing: Identifies which component is defective

Early vs. Late Stage

• Early Stage: Small peaks barely above noise floor, may require envelope analysis to detect
• Moderate Stage: Clear peaks with harmonics and sidebands in standard FFT
• Advanced Stage: Very high amplitude, numerous harmonics, broadband noise increase
• Late Stage: Spectrum becomes chaotic with raised noise floor and numerous peaks

Detection Techniques

Standard FFT Analysis

• Calculate FFT of vibration signal
• Look for peaks at calculated bearing frequencies
• Effective for moderate to advanced defects
• May miss early-stage defects buried in noise

Envelope Analysis (Most Effective)

Envelope analysis (demodulation) is the gold standard for bearing defect detection:

• Filters out low-frequency, high-energy vibration (from unbalance, etc.)
• Focuses on high-frequency impacts from bearing defects
• Can detect faults 6-12 months earlier than standard FFT
• Envelope spectrum clearly shows fault frequencies and patterns

Time-Domain Techniques

• Shock Pulse Method (SPM): Detects impact energy from defects
• Crest Factor: Ratio of peak to RMS, increases with impacting
• Kurtosis: Statistical measure of impulsiveness, sensitive to early bearing damage

Practical Application

Diagnostic Procedure

1. Identify Bearing: Determine bearing model and location
2. Calculate Frequencies: Use bearing geometry to calculate BPFO, BPFI, BSF, FTF (or look up in database)
3. Collect Vibration Data: Measure at bearing housing with accelerometer
4. Analyze Spectrum: Look for calculated frequencies in FFT or envelope spectrum
5. Confirm Diagnosis: Check for harmonics and sidebands consistent with defect type
6. Assess Severity: Amplitude and harmonic content indicate defect progression stage
7. Plan Action: Schedule bearing replacement based on severity and equipment criticality

Example Diagnosis

Motor with SKF 6308 bearing running at 1800 RPM (30 Hz):

• Calculated Frequencies: BPFO = 107 Hz, BPFI = 173 Hz, BSF = 71 Hz, FTF = 12 Hz
• Observed in Envelope Spectrum: Peak at 173 Hz with harmonics at 346 Hz, 519 Hz
• Sidebands: ±30 Hz sidebands around 173 Hz peak
• Diagnosis: Inner race defect confirmed (BPFI with 1× sidebands)
• Action: Schedule bearing replacement within 2-4 weeks based on amplitude

Importance for Predictive Maintenance

• Early Warning: Detect defects 6-24 months before failure
• Specific Diagnosis: Identify which bearing component is damaged
• Trend Monitoring: Track fault frequency amplitudes to predict remaining life
• Planned Maintenance: Schedule replacements during convenient downtime
• Prevent Secondary Damage: Replace bearing before catastrophic failure damages shaft, housing, or other components
• Cost Savings: Avoid emergency repairs, production losses, and collateral damage

Bearing fault frequencies are among the most powerful diagnostic tools in vibration analysis. Their mathematical predictability combined with modern envelope analysis techniques enables reliable early detection of bearing defects, forming the cornerstone of effective predictive maintenance programs for rotating equipment.

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