Understanding BPFI — Ball Pass Frequency, Inner Race
บีพีเอฟไอ (ความถี่ในการส่งบอล, ระยะภายใน) เป็นหนึ่งในสี่ปัจจัยพื้นฐาน ความถี่ความผิดพลาดของตลับลูกปืน and represents the rate at which rolling elements pass over a defect on the rotating inner race of a bearing. When a spall, crack, or pit forms on that inner raceway, every rolling element strikes the flaw as the race carries it past, generating periodic impacts that show up in the การสั่นสะเทือน signal at the BPFI frequency. What sets BPFI apart from the other characteristic frequencies is its near-constant escort of ±1× แถบข้าง — a fingerprint that makes inner-race defects among the most confidently diagnosed faults in การวิเคราะห์การสั่นสะเทือน.
1. Definition: What is BPFI?
BPFI counts how many rolling-element passes occur over one point on the inner race per unit time. Because the inner race turns with the shaft while the elements orbit more slowly at cage speed, the relative motion between race and elements is high — and so is the frequency. The defect sits on the rotating race, so it is repeatedly hammered by each ball or roller that sweeps past. Together with the outer-race frequency (สมาคมป้องกันประเทศ (BPFO)), the cage frequency (เอฟทีเอฟ), and the rolling-element spin frequency (บีเอสเอฟ), BPFI forms the standard set of frequencies an analyst calculates to localise damage within a bearing. The faults themselves belong to the wider topic of ข้อบกพร่องของตลับลูกปืน.
2. การคำนวณทางคณิตศาสตร์
สูตรและตัวแปร
BPFI follows from bearing geometry and shaft speed:
BPFI = (N × n / 2) × [1 − (Bd/Pd) · cos β]
- เอ็น = number of rolling elements in the bearing.
- n = ความถี่การหมุนของเพลาในเฮิรตซ์ (หรือ RPM ÷ 60).
- บีดี = เส้นผ่านศูนย์กลางของลูกบอลหรือลูกกลิ้ง.
- พีดี = pitch diameter (the circle through the rolling-element centres).
- เบต้า = มุมสัมผัส.
Why BPFI is always higher than BPFO
For the same bearing, BPFI always exceeds BPFO, and the formula shows exactly why:
- The inner race rotates with the shaft, while the rolling elements orbit at roughly 0.4× cage speed, so the relative velocity at the inner race is greater.
- BPFI uses the term [1 − Bd/Pd], whereas BPFO uses [1 + Bd/Pd].
- Subtracting a fraction from one keeps BPFI’s multiplier larger than BPFO’s.
- The typical ratio BPFI/BPFO works out to about 1.6–1.8.
Typical values
- For common bearings, BPFI lands around ความเร็วรอบเพลา 5–7 เท่า.
- ตัวอย่างที่ทำงานแล้ว: a 10-ball bearing at 1800 RPM (30 Hz) gives BPFI ≈ 173 Hz, about 5.8× shaft speed.
Rather than evaluate this by hand for every machine, most analysts read the value — alongside BPFO, BSF, and FTF — straight from the เครื่องคำนวณความถี่ข้อบกพร่องของแบริ่ง, entering the bearing geometry and running speed once.
3. Physical Mechanism and Load-Zone Modulation
The rotating defect
An inner-race flaw creates a situation the outer race never sees, because the defect itself moves:
- The defect rides on the rotating inner race.
- As the race turns, the flaw travels around the bearing circumference.
- Each rolling element strikes it on passing — that is the BPFI rate.
- But the force of each strike depends on where the defect sits relative to the load zone at that instant.
The load-zone effect
Every loaded bearing has a region — the load zone — where the rolling elements press hardest against the races. As the inner-race defect rotates through and out of this zone once per shaft turn, the impact strength rises and falls:
- Defect inside the load zone: high contact force, a strong impact as each element strikes it.
- Defect opposite the load zone: little or no contact force, a weak or absent impact.
- Modulation frequency: the defect completes this cycle once per shaft revolution — i.e. at ความเร็วในการวิ่ง 1×.
- ผลลัพธ์: the BPFI impacts are amplitude-modulated at 1× shaft speed.
Sideband generation
That amplitude modulation is what produces the diagnostic sideband comb:
- Carrier frequency: BPFI.
- Modulation frequency: 1× shaft speed.
- แถบข้าง: BPFI ± 1×, BPFI ± 2×, BPFI ± 3×, symmetrically spaced about the carrier.
- ค่าการวินิจฉัย: this regular 1× sideband family is all but pathognomonic for an inner-race defect — and it is precisely what distinguishes BPFI from the FTF-spaced sidebands of a BSF fault.
4. Vibration Signature Characteristics
Typical spectrum appearance
- Central peak ที่ความถี่ BPFI.
- Sideband family of peaks at BPFI ± n×(1×).
- Harmonic families at 2×BPFI and 3×BPFI, each carrying its own ±1× sidebands.
- Visual pattern: a “picket fence” or comb of evenly spaced peaks.
Why the envelope spectrum is decisive
Inner-race impacts excite high-frequency bearing resonances rather than depositing all their energy at BPFI directly, so a raw เอฟเอฟที can look unremarkable in the early stages. การวิเคราะห์ซองจดหมาย demodulates those resonant bursts, and in the resulting สเปกตรัมซองจดหมาย the BPFI peak dominates and the 1× sidebands stand out with exceptional clarity — often months before the standard สเปกตรัม shows anything. As the defect grows, the envelope amplitude climbs steeply.
5. Detection, Diagnosis, and Field Practice
A reliable recognition sequence
- Calculate BPFI from the bearing model number or geometry.
- Search the spectrum for a peak at the calculated frequency, allowing about ±5% tolerance.
- Verify the ±1× sidebands — the key confirming feature.
- Check the harmonics (2×BPFI, 3×BPFI) for their own sidebands.
- Assess amplitude against baseline or severity guidelines.
- Confirm: BPFI plus 1× sidebands equals an inner-race defect.
In the field, the same workflow runs on a portable two-channel instrument. An analyst can mount an accelerometer on the bearing housing, capture the high-frequency vibration at operating speed, and screen the envelope on-site — the very kind of measure-it-where-it-runs task a tool such as the บาลานเซ็ต-1A is built for, doubling as a field vibration analyser alongside its rotor-balancing role.
BPFI versus BPFO at a glance
| คุณสมบัติ | BPFI (เชื้อชาติภายใน) | BPFO (เชื้อชาติภายนอก) |
|---|---|---|
| ความถี่ | Higher (5–7× shaft speed) | Lower (3–5× shaft speed) |
| แถบข้าง | มีอยู่เกือบตลอดเวลา (±1×) | อาจมีหรือไม่มีก็ได้ |
| Sideband pattern | ระยะห่างสม่ำเสมอและชัดเจน | Less regular when present |
| การเกิดขึ้น | เกิดขึ้นน้อยกว่า (~25% ของความล้มเหลว) | ความล้มเหลวที่พบบ่อยที่สุด (~40%) |
6. Progression, Severity, and Remaining Life
Defect development stages
- การเริ่มต้น: รอยแตกหรือหลุมขนาดเล็กที่ยังไม่สามารถตรวจพบได้
- จุดเริ่มต้น: a small BPFI peak emerges in the envelope spectrum (≈ 0.1–0.5 g).
- แต่แรก: a clear BPFI peak with one or two harmonics and sidebands (≈ 0.5–2 g).
- ปานกลาง: multiple harmonics, prominent sidebands, a spall visible on inspection (≈ 2–10 g).
- ขั้นสูง: very high amplitude, numerous harmonics, a rising noise floor (> 10 g).
- รุนแรง: broadband noise dominates, the discrete peaks wash out, and catastrophic failure is imminent.
Remaining-life guidance
- Incipient to early: typically 6–18 months remaining.
- Early to moderate: 3–6 months.
- Moderate to advanced: 1–3 months.
- Advanced to severe: days to weeks.
- Caveat: the real timeline depends on load, speed, lubrication, and bearing size — figures are guides, not guarantees, and feed into any formal อายุการใช้งานที่เหลืออยู่ estimate.
7. Causes and Corrective Actions
Common causes of inner-race defects
- ความเหนื่อยล้า: high-cycle subsurface fatigue from repetitive loading, the classic end-of-life mechanism.
- Improper installation: mounting damage, such as driving the bearing on by striking the inner race.
- Shaft damage: a rough or scored shaft seat causing fretting.
- Excessive interference fit: over-tight press-fitting raising hoop stress.
- การจัดตำแหน่งที่ไม่ถูกต้อง: non-uniform loading that accelerates fatigue.
- การปนเปื้อน: hard particles denting the raceway.
- Lubrication failure: inadequate film leading to surface distress and การแตกเป็นสะเก็ด.
Response and replacement planning
On detection, step up the monitoring interval (monthly → weekly → daily as severity rises), schedule replacement for the next convenient outage, and trend the amplitude to forecast remaining life. Avoid lingering at ความเร็ววิกฤต that could hasten failure. When planning the swap, order the correct bearing model, inspect the shaft (an advanced inner-race defect can score the seat), and run a root-cause review so the replacement does not fail the same way. Folded into a disciplined การติดตามสภาพ programme, BPFI detection becomes a cornerstone of bearing reliability — its unmistakable high-frequency peak with 1× sidebands giving timely, unambiguous warning that prevents secondary damage to shafts and housings.
