Vibration Data Basics: Displacement, Velocity, Acceleration & Frequency Bands

In equipment diagnosis, correctly evaluating vibration strictly requires understanding three metrics: "Displacement," "Velocity," and "Acceleration," and using them appropriately according to the target anomaly (frequency band).

The "sensitivity" of these metrics varies greatly depending on the frequency of the target vibration. To get straight to the point, as the frequency increases, the "change per unit of time" becomes much steeper, causing the values (sensitivity) for velocity and acceleration to jump significantly.

Why Does Sensitivity Increase at Higher Frequencies? (An Intuitive Explanation)

Why does the sensitivity of velocity and acceleration increase as the frequency rises? Imagine shaking an object with the "same amplitude (displacement)."

• Displacement (Constant Sensitivity)
  Since it measures the physical distance of "how much it moved," the maximum distance remains the same whether moved slowly or quickly, keeping the value constant.
• Velocity (Proportional to Frequency)
  Doubling the frequency means you are required to "travel the same distance back and forth in half the time." Naturally, the moving speed (velocity) must double to keep up, making it proportional to the frequency.
• Acceleration (Proportional to the Square of Frequency)
  Acceleration is the "rate of change of velocity." When the frequency doubles, not only does the "velocity itself double," but the "timing of changing direction" also becomes twice as frequent. Because you must reverse a higher speed in a shorter amount of time, the load (energy) applies as a squared factor.

Mathematical Reasoning: Proof by Differentiation Rules

The relationship between vibration metrics can be clearly explained mathematically using "differentiation." If we consider vibration as a simple sine wave, the relationships are as follows.

* Let $t$ be time, $f$ be frequency, and $A$ be amplitude (displacement).

Application Approach with conanair: Balancing Velocity and High-Frequency Acceleration

In actual field diagnostics, it is necessary to select sensors while understanding the relationship between frequency and sensitivity. The wireless vibration sensor "conanair" adopts a unique design that covers both the "mid" and "high" frequency ranges, which are practically the most important.

• [Trend Management of Velocity]
  It performs general-purpose "velocity" trend management based on ISO standards to monitor overall machinery condition deterioration, such as unbalance and looseness. This is ideal as the primary purpose of simplified diagnosis.
• [Detection of High-Frequency Acceleration via Under-Sampling]
  Normally, accurately capturing high-frequency acceleration over 1kHz (such as early-stage bearing anomalies) entails massive data transmission and power consumption. conanair uses its patented "Under-Sampling Technology" to intentionally utilize aliasing, ensuring that high-frequency acceleration peaks (bearing damage) are reliably detected even at a low sampling rate.

[Important] The Limits of Under-Sampling and the Significance of Saving Raw Data

Here, we honestly share the facts with our field users. Because under-sampling technology reflects high frequencies into lower frequency bands, there is a clear limitation (disadvantage): "precise absolute value measurement of high-frequency vibration is impossible."

However, when focusing strictly on the bearings of general-purpose rotating machinery, high-frequency vibrations do not occur during normal operation. In other words, rather than knowing "exactly what the absolute value is," reliably capturing the fact that "a high frequency that shouldn't normally occur has appeared" is the most critical factor in trend management (relative comparison) when an anomaly occurs.

The biggest reason we accept the disadvantage of not measuring absolute values—in exchange for drastically reducing data size—is to prevent the "black-boxing of edge processing" that has become mainstream recently.

Most edge processing transmits only "results" such as pass/fail judgments, summarized data (averages, peaks), FFT results, or AI scores, discarding the most crucial "raw waveforms." This makes it impossible for engineers to later verify "why that anomaly judgment was made."

conanair continuously saves the "Raw Data itself," made lightweight by under-sampling, to the cloud or a local environment. This provides an environment where field engineers can check the waveforms with their own eyes and achieve correct predictive maintenance based on facts.

Common Questions Engineers Ask Before Implementation

Q1: I don't know whether I should look at displacement, velocity, or acceleration.

A: As a strict rule, check "velocity" for monitoring general rotating machinery unbalance or looseness, and "acceleration" if you want to catch early-stage bearing anomalies (flaws or chipping) as quickly as possible. conanair measures these simultaneously and saves them as raw data.

Q2: Do the values change depending on the installation direction of conanair?

A: Yes, they change significantly. It is crucial to know "in which direction the vibration is transmitting from the source." As explained in detail in the "Correct Installation Direction" article within this category, the basic approach is to install the sensor while being mindful of the 3 axes: vertical, horizontal, and axial.

Q3: Why is "Raw Data" considered so important?

A: Because relying solely on an "anomaly score" from AI or edge processing prevents engineers from later identifying the root cause (verifying why it was judged as an anomaly). If you have the raw data, you can perform follow-up FFT analysis and make maintenance decisions with confidence.

30-Day Free Trial & Inquiry

Try Conan Air for free for 30 days. Here is what our users are saying:

• Easy installation for immediate use
• No app required; operate via web browser
• No cloud required for fully automatic measurement
• Affordable, including dedicated software

Try equipment anomaly detection and predictive maintenance for free. Please feel free to contact us.

30-Day Free Trial & Inquiry

Try Conan Air for free for 30 days. Here is what our users are saying:

• Easy installation for immediate use
• No app required; operate via web browser
• No cloud required for fully automatic measurement
• Affordable, including dedicated software

Try equipment anomaly detection and predictive maintenance for free. Please feel free to contact us.

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Correct Vibration Sensor Installation: 3-Axis (XYZ) vs. Single-Axis