Detecting rolling bearing damage early: what envelope analysis and bearing defect frequencies reveal
Incipient bearing damage produces tiny impacts at a fixed repetition rate. If you know which frequency to look for, you will find them in the envelope spectrum long before the bearing becomes audible.
A rolling bearing rarely fails suddenly. It almost always starts with a small defect on a raceway or a rolling element: a pit, a crack, a spot with a damaged surface. Every time a rolling element rolls over this spot, a short impact is produced. At first these impacts are so weak that they are lost in the overall vibration level. Their repetition rate, however, is precisely determined by the bearing geometry and the speed. Rolling bearing diagnostics is built on this.
Why bearing damage has its own frequency
A bearing consists of an outer race, an inner race, rolling elements and a cage. When the spindle is running, the inner race turns with the shaft, the outer race is stationary in the housing, and the rolling elements travel round with the cage. This gives each component its own defect frequency:
- BPFO (ball pass frequency, outer race): how many times per second a rolling element passes over a given point on the outer race.
- BPFI (ball pass frequency, inner race): the same for a point on the inner race.
- BSF (ball spin frequency): how many times per second a rolling element turns about its own axis.
- FTF (fundamental train frequency): the rotational frequency of the cage.
If the defect is on the outer race, the impacts repeat at BPFO. If it is on the inner race, at BPFI. So the diagnosis does not ask ‘Is the vibration high?’, but ‘Is there energy at exactly the frequency that belongs to this component?’. That is why a frequency-based analysis shows damage much earlier than an RMS value.
The formulas for BPFO, BPFI, BSF and FTF
The defect frequencies can be calculated from four geometry values and the shaft rotational frequency fr. The formulas apply to rolling without slip with a stationary outer race:
The geometry values are in the bearing manufacturer's datasheet. You should never estimate them: even a wrong number of rolling elements shifts all the frequencies, and the diagnosis then looks in the wrong place. Spindle bearings are usually angular contact ball bearings. That is why the contact angle α enters the calculation; for deep groove ball bearings it is zero.
Worked example
For an assumed angular contact ball bearing with 16 balls, a d/D ratio of 0.2 and a 15° contact angle at 6,000 rpm (fr = 100 Hz), the result is:
| Characteristic frequency | Value | Multiple of shaft frequency |
|---|---|---|
| FTF, cage | 40.3 Hz | 0.40 × |
| BSF, rolling element | 240.7 Hz | 2.41 × |
| BPFO, outer race | 645.4 Hz | 6.45 × |
| BPFI, inner race | 954.6 Hz | 9.55 × |
Because all values are proportional to speed, they are often given as multiples of the shaft frequency. That way the figure stays the same when the spindle runs at a different speed. For the diagnosis, the current speed must still be known. On CNC machines it comes from the CNC control.
Envelope analysis: how the impacts become visible
An impact in the bearing excites the structure around the bearing, usually at a high natural frequency in the kilohertz range. In the normal frequency spectrum you therefore do not see the defect frequency itself, but a broad high-frequency band that swells and fades in time with the impacts. Envelope analysis extracts this rhythm:
- Measure: an accelerometer on the spindle housing records the raw signal at a high sampling rate.
- Filter: a band-pass filter cuts out the frequency range in which the impacts excite the structure. Shaft frequency, gear mesh and cutting forces are usually lower and are removed.
- Demodulate: the envelope is formed from the filtered signal, i.e. the amplitude over time.
- Transform: the spectrum of the envelope shows how many times per second the impacts occur. This is where the defect frequencies appear as lines.
Why a dedicated sensor is needed
The standard interfaces of CNC controls deliver values at well below 1 kHz. Envelope analysis needs signals in the kilohertz range. Spindle bearing diagnostics is therefore only possible with a vibration sensor mounted directly on the spindle housing. Speed and load come from the CNC control as a supplement.
Which pattern belongs to which defect
In the envelope spectrum each defect has a typical signature. These patterns have been described in vibration diagnostics for decades:
| Defect | Typical pattern in the envelope spectrum |
|---|---|
| Outer race | Line at BPFO and its harmonics. Because the outer race is stationary, the load zone stays the same. Sidebands are usually absent. |
| Inner race | Line at BPFI with sidebands spaced at the shaft frequency. The defect turns with the shaft through the load zone, so the impact becomes stronger and weaker once per revolution. |
| Rolling element | Often clearer at 2 × BSF than at BSF, because a damaged rolling element touches both raceways once per rotation about its own axis. Frequently with sidebands spaced at the cage frequency. |
| Cage | Line at FTF, often also as modulation of other lines. Hard to detect and frequently a sign of lubrication problems. |
Two practical pitfalls: first, real bearings slip by around one to two per cent, so the lines are not exactly where the calculation puts them. The search therefore needs a tolerance band. Second, harmonics of different defect types can almost coincide, for example 3 × BPFO and 2 × BPFI on some bearings. Our system therefore only treats a defect as detected if the fundamental frequency itself is visible, not just a harmonic.
How bearing damage develops
The progression of bearing damage follows a well-known pattern, even though the duration of each stage depends heavily on load, speed, lubrication and bearing design:
- Onset: first impacts. A weak line appears at the defect frequency in the envelope spectrum. RMS and noise are unchanged. This is the stage at which frequency-based monitoring pays off most.
- Propagation: the line becomes stronger, harmonics and sidebands appear. Features such as crest factor and kurtosis rise because the signal becomes more impulsive.
- Advanced: the damage grows and the impacts smear. The overall level rises, the bearing becomes audible and runs warm.
- Final stage: broadband noise masks the clear lines. Failure is imminent.
Nobody can give a general figure for how much time passes between the first line and failure. Sound statements on this are only possible for a specific machine and only after a period of observation. Anyone who promises you a fixed number of weeks does not know your spindle.
How we implement this in our system
The bearing frequencies are the foundation. Whether a line that has been found is actually significant, however, is decided in our system by comparison with the learned baseline, i.e. the normal state of this spindle. Every spindle has its own background noise, depending on installation, age and machining. The edge box calculates the features directly at the machine and transmits only the results. An alert is only raised if a deviation persists over several measurements, so that a single impact during a tool change does not trigger an alarm. More on this in the article Fixed thresholds or learned baseline.
Every alert names the suspected component, the frequency and the size of the deviation. So the maintenance engineer sees not just a red light, but the reason: ‘Line at BPFO with three harmonics, clearly above the learned baseline’.
Frequently asked questions
Can bearing damage be detected from the RMS value of the vibration?
Only late. The RMS value usually rises only once the damage is advanced. Early damage shows up as weak lines at the bearing frequencies in the envelope spectrum, long before the overall level changes.
Where do I get the geometry data for my spindle bearing?
From the bearing manufacturer's datasheet or from the spindle manufacturer's documentation. You need the number of rolling elements, rolling element diameter, pitch diameter and contact angle. Estimated values lead to wrong frequencies.
Is CNC control data enough for bearing diagnostics?
No. The standard interfaces of the controls deliver values well below 1 kHz. Envelope analysis needs signals in the kilohertz range, so a vibration sensor on the spindle housing is required. The control does, however, supply the speed, without which the bearing frequencies cannot be calculated.
How long before failure is bearing damage detected?
That depends on bearing design, load, speed and lubrication and cannot be given as a general figure. Frequency-based methods do, however, typically show the damage much earlier than overall level, temperature or noise.
About the author
Sascha P. Forbach is the founder of Forbach & Partners and the software architect of its spindle monitoring system. For twelve years he has advised manufacturers on process quality and machine availability. About us