Math Bridge: Vibration sampling before compression

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Math BridgeAnalytics & MLStruggle-friendly runway

Why must bearing-fault sampling be settled before compression?

Preserve the fault physics before reducing the payload.

Data Dora, the guideData Dora guides
The one targetChoose a rate from the highest retained harmonic.
The chapter case1,800 RPM; 8 elements; third harmonic; 4 kHz.
What it buys youAn auditable 67× reduction.

A field team faces an unresolved physical question: Why must bearing-fault sampling be settled before compression? They must answer it before changing sample rate on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is sample rate. The middle card applies this page's relationship. The green card is shaft. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Sample rate changes shaft An input card leads through the page relationship to the shaft result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. Choose filtering and sampling first, then prove that the 120 B/s feature record retains the decision evidence.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for sample rate is 4000.

  2. 2

    Name the relationship. 1,800/60 = 30.0 Hz; 8(30) = 240 Hz; 3(240) = 720 Hz Nyquist minimum = 1,440 Hz; 2.5x target = 3,600 Hz 4,000(2) = 8,000 B/s; 8,000/120 = 66.7x; 16 bit = 98.1 dB

  3. 3

    Substitute the chapter fixture. Set sample rate to 4000. The page ledger gives shaft as 30.0 Hz.

  4. 4

    Read the result. Keep Hz beside the value. Use it only inside the technical boundary on this page.

Predict, then change sample rate

Try Predict the direction of shaft. Move one control, calculate, then check your prediction.

4000
Chapter baseline
Shaft

Observe Choose filtering and sampling first, then prove that the 120 B/s feature record retains the decision evidence. Reset the control to 4000 and compare shaft.

Explain Only sample rate moves here. The other chapter fixtures remain fixed.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only sample rate moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only sample rate. It replays the chapter fixture; it is not a field prediction.

1. Start with rotation

The shaft sets a base frequency. Bearing geometry creates a fault component; its retained harmonics set the acquisition band.

Data Dora: Compression cannot recover a harmonic that the ADC aliased first.

2. Name every algebra move

1

Convert minutesfshaft=RPM/60.

2

Multiply geometryffault=nfshaft.

3

Keep the harmonicfh=3ffault.

4

Double and marginfs,target=2.5(2fh).

5

Compare payloadsratio=raw bytes/feature bytes.

3. Reproduce the chapter

1,800/60 = 30.0 Hz; 8(30) = 240 Hz; 3(240) = 720 Hz
Nyquist minimum = 1,440 Hz; 2.5× target = 3,600 Hz
4,000(2) = 8,000 B/s; 8,000/120 = 66.7×; 16 bit = 98.1 dB

At only 100 Hz, the 240 Hz component folds to 40.0 Hz.

4. Try the sample rate

TryMove from an unsafe rate toward the 4 kHz design.

Sample rate
Shaft
Fault
Third harmonic
Nyquist minimum
Practical target
Fault alias
Raw payload
Reduction
Payload removed
Ideal SNR

ObserveThe physical frequencies stay fixed while alias location and raw payload move with sample rate.

ExplainChoose filtering and sampling first, then prove that the 120 B/s feature record retains the decision evidence.

Technical boundaries.

The bearing relation is a simplified teaching chain.

Geometry
No contact angle, slip, load, or exact bearing kinematics
Sampling
No anti-alias filter response or spectral leakage
Compression
No proof that top peaks retain every fault mode

Validate spectra and decisions on the target machine.

5. Preserve anomaly context

Transmit compact features routinely but retain raw windows around anomalies for audit and model change.

6. Bind the release

Version bearing assumptions, sensor mounting, filter, sample rate, window, FFT, selected peaks, and raw retention.

7. Check yourself

Why is the third harmonic 720 Hz?
Answer: 1,800 RPM is 30 Hz; eight elements give 240 Hz; three times that is 720 Hz.
Why is 4 kHz above strict Nyquist?
Answer: The chapter applies a 2.5× margin to the 1,440 Hz minimum and rounds 3,600 Hz upward.
Does 66.7× prove evidence retention?
Answer: No; labeled fault tests must prove it.
Honesty boundary.

The rotation, element count, harmonic, rate, and payloads are the chapter case.

1,800 RPM, 8, third
Teaching bearing chain
4 kHz, 2 B
Chapter raw record
120 B/s
Chapter feature record

Correct, not complete: sampling and byte arithmetic do not qualify condition monitoring.

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