Math Bridge: MEMS vibration chain

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Math BridgeAnalytics & MLStruggle-friendly runway

What physically moves when a vibration reading rises from 0.05g to 0.5g?

Trace a downstream RMS alert back to the sensing element.

Data Dora, the guideData Dora guides
The one targetConnect acceleration to displacement and code.
The chapter case0.05g baseline; 0.5g alert; ±4g, 16 bit.
What it buys youA physical threshold audit.

A field team faces an unresolved physical question: What physically moves when a vibration reading rises from 0.05g to 0.5g? They must answer it before changing acceleration 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 acceleration. The middle card applies this page's relationship. The green card is si acceleration. 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.

Acceleration changes si acceleration An input card leads through the page relationship to the si acceleration result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. The 0.5g alert is far above the ideal code step, but that does not eliminate mounting or noise errors.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for acceleration is 0.5.

  2. 2

    Name the relationship. 0.05g → 31.1 pm → 31.1 aF → code 410 0.5g → 311 pm → 311 aF → code 4,096 8g/65,536 = 122 ug/LSB

  3. 3

    Substitute the chapter fixture. Set acceleration to 0.5. The page ledger gives si acceleration as 4.91 m/s^2.

  4. 4

    Read the result. Keep m/s^2 beside the value. Use it only inside the technical boundary on this page.

Predict, then change acceleration

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

0.5
Chapter baseline
SI acceleration

Observe The 0.5g alert is far above the ideal code step, but that does not eliminate mounting or noise errors. Reset the control to 0.5 and compare si acceleration.

Explain Only acceleration 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 acceleration moves. Field effects named in the page's technical boundary stay fixed.

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

1. Begin inside the sensor

A MEMS accelerometer lets a proof mass move against springs. Electronics measure a capacitance change and turn it into a code.

Data Dora: The reported g value is the end of a measurement chain, not a direct touch of acceleration.

2. Name every algebra move

1

Convert ga = g reading × 9.81.

2

Divide by spring frequency squaredx = a/(2πfn)².

3

Scale the differential gapΔC ≈ C0(2x/d0).

4

Divide the rangeq = 8g/2¹⁶.

3. Reproduce the chapter

0.05g → 31.1 pm → 31.1 aF → code 410
0.5g → 311 pm → 311 aF → code 4,096
8g/65,536 = 122 µg/LSB

Linear motion makes the ten-times acceleration change remain ten-times through displacement and capacitance.

4. Try the acceleration

TryMove from the baseline to the alert.

Acceleration
SI acceleration
Proof-mass motion
Capacitance change
Code step
Output code
Baseline multiple

ObserveMotion, capacitance, and code all scale with acceleration in this small-signal model.

ExplainThe 0.5g alert is far above the ideal code step, but that does not eliminate mounting or noise errors.

Technical boundaries.

The chain is quasi-static and idealized.

Mechanics
No damping, cross-axis response, or shock saturation
Capacitance
Small-displacement parallel-plate approximation
Code
No analogue noise, offset, drift, or calibration error

Validate the assembled sensor and mounting.

5. Keep the chain intact

Store range, bandwidth, mounting, calibration, sampling, feature code, and alert threshold with the event.

6. Test more than resolution

Inject known vibration across temperature, axes, fixtures, and frequencies before treating the code gap as certainty.

7. Check yourself

Why does mass cancel?
Answer: Both force and spring stiffness contain it when stiffness is written using resonance.
Why is 0.5g ten times the motion?
Answer: The small-signal equations are linear in acceleration.
Does a large code gap prove a bearing fault?
Answer: No; it proves ideal resolution, not cause.
Honesty boundary.

The g thresholds come from the chapter; sensing-element figures are catalog-typical assumptions.

0.05g and 0.5g
Chapter pipeline
20 kHz, 1 pF, 2 µm
Stated teaching assumptions
±4g, 16 bit
Typical output example

Correct, not complete: this chain does not diagnose a machine.

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