Understanding BSF – Ball Spin Frequency

Devices

Portable balancer & Vibration analyzer Balanset-1A

$2,358.31

Parts

Vibration sensor

$107.47

Parts

Optical Sensor (Laser Tachometer)

$148.07

Devices

Balanset-4

$8,123.32

Parts

Magnetic Stand Insize-60-kgf

$54.93

Parts

Reflective tape

$11.94

Devices

Dynamic balancer “Balanset-1A” OEM

$2,071.73

Definition: What is BSF?

BSF (Ball Spin Frequency, also called rolling element spin frequency) is one of the four fundamental bearing fault frequencies that represents the rotational speed of a rolling element (ball or roller) spinning about its own axis. When a rolling element has a surface defect such as a spall, crack, or inclusion, the defect impacts both the inner and outer races twice per revolution of the rolling element, creating periodic impacts at the BSF frequency.

BSF is the least commonly observed of the four bearing frequencies because rolling element defects are relatively rare compared to race defects, accounting for only about 10-15% of bearing failures. However, when present, BSF produces a distinctive and complex vibration signature that can be identified through careful vibration analysis.

Mathematical Calculation

Formula

BSF is calculated using bearing geometry and shaft speed:

• BSF = (Pd / 2×Bd) × n × [1 – (Bd/Pd)² × cos² β]

Variables

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

Simplified Form

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

• BSF ≈ (Pd / 2×Bd) × n × [1 – (Bd/Pd)²]
• For typical bearings with Bd/Pd ≈ 0.2, this gives BSF ≈ 2.4 × n
• Rule of thumb: BSF typically 2-3× shaft speed

Typical Values

• BSF typically ranges from 1.5× to 3× shaft speed
• Lower than both BPFI and BPFO
• Higher than FTF (cage frequency)
• Example: Bearing at 1800 RPM (30 Hz) → BSF ≈ 71 Hz (2.4× shaft speed)

Physical Mechanism

Rolling Element Rotation

Understanding BSF requires visualizing the rolling element’s motion:

1. Rolling element orbits around bearing at cage frequency (~0.4× shaft speed)
2. Simultaneously, it spins on its own axis at BSF
3. Spin rate depends on ratio of pitch diameter to ball diameter
4. Each complete spin brings defect into contact with both races

Double Impact per Revolution

A defect on a rolling element creates a unique pattern:

• First Impact: Defect strikes inner race
• Half Revolution Later: Same defect (now rotated 180°) strikes outer race
• Result: Two impacts per ball revolution = 2×BSF
• Actual Frequency Observed: Often see peaks at both BSF and 2×BSF

Modulation by Cage Frequency

Additional complexity arises from the rolling element’s orbital motion:

• Defected ball passes through load zone once per cage revolution
• Impact severity modulated by loading (high in load zone, low elsewhere)
• Creates sidebands at FTF (cage frequency) spacing
• Sideband pattern: BSF ± n×FTF, where n = 1, 2, 3…

Vibration Signature

Spectrum Characteristics

• Primary Peak: At BSF or 2×BSF frequency
• FTF Sidebands: Spaced at cage frequency intervals (unlike BPFI’s 1× sidebands)
• Multiple Harmonics: 2×BSF, 3×BSF often present
• Complex Pattern: More complicated than race defect patterns
• Variable Amplitude: Can vary significantly between measurements as defected ball’s position in load zone changes

Envelope Spectrum

Envelope analysis is particularly important for BSF detection:

• BSF peaks often clearer in envelope than standard FFT
• FTF sideband structure more visible
• Early detection possible before peaks visible in standard spectrum

Why Rolling Element Defects Are Less Common

Several factors make rolling element defects relatively rare:

Load Distribution

• Rolling elements rotate, distributing load and wear around entire surface
• Races (especially outer race) have concentrated load zones
• More uniform stress distribution delays fatigue in rolling elements

Manufacturing Quality

• Balls and rollers typically receive highest quality control
• Harder material and better surface finish than races in many bearings
• Less likely to have material defects

Stress Patterns

• Rolling contact stress distributed over surface
• Races experience higher maximum Hertzian contact stresses
• Edges and corners of races more prone to stress concentration

Diagnostic Challenges

Complexity

• BSF signature more complex than race defects due to FTF sidebands
• Can be confused with other machinery frequencies
• Variable amplitude makes trending more difficult
• Multiple defected balls create overlapping signatures

Detection Difficulty

• BSF peaks sometimes lower amplitude than race defect peaks for similar defect sizes
• Frequency may fall in range with other machinery components
• Requires experience to distinguish BSF patterns from race defects

Practical Diagnosis

Confirmation Steps

1. Calculate BSF: From bearing specifications
2. Look for BSF Peak: Search envelope spectrum at calculated frequency
3. Check for 2×BSF: Often stronger than fundamental BSF
4. Verify FTF Sidebands: Look for sidebands at cage frequency spacing (NOT 1× spacing)
5. Amplitude Variability: BSF amplitude may vary between measurements (characteristic of ball defects)
6. Elimination: Rule out BPFI and BPFO before concluding BSF

When Multiple Balls Defected

• Multiple defected balls create complex overlapping patterns
• BSF peaks may broaden or show multiple nearby frequencies
• Indicates advanced bearing deterioration
• Immediate replacement recommended

Causes and Prevention

Common Causes of Rolling Element Defects

• Material Inclusions: Internal voids or foreign material in ball/roller
• Installation Damage: Brinelling from impacts during handling
• Contamination: Hard particles embedding in or damaging ball surface
• Electrical Damage: Electric current arcing through bearing creating pits
• False Brinelling: Fretting from vibration while stationary
• Corrosion: Moisture or chemical attack creating surface pits

Prevention Strategies

• Use high-quality bearings from reputable manufacturers
• Careful handling during installation
• Effective contamination control (seals, clean environment)
• Proper lubrication preventing corrosion
• Electrical insulation for motors with VFD drives
• Vibration isolation during storage and shipping

While BSF is less frequently encountered than BPFO or BPFI, understanding its characteristics enables complete bearing diagnostics. The distinctive FTF sideband pattern and potential for rapid progression once detected make BSF an important part of comprehensive bearing condition monitoring programs.

---

← Back to Main Index