1. The Trinity: Acceleration, Velocity, Displacement

Vibration can be measured in three different physical parameters. Choosing the right one depends on the frequency of interest and the type of defect. Understanding the mathematical relationship between these units ($D \rightarrow V \rightarrow A$) via integration and differentiation is fundamental to vibration analysis.

• Displacement ($\mu m$, mils): Measures the total distance the shaft moves. It is heavily weighted toward Low Frequencies ($< 10$ Hz). It is the standard for monitoring Sleeve Bearings (Journal Bearings) using Eddy Current Probes (Proximity Probes), where the critical concern is the shaft physical movement relative to the babbitt lining (oil film clearance). It typically ignores high-frequency bearing noise because a very high frequency vibration often has a microscopic displacement amplitude.
• Velocity (mm/s, ips): Measures the speed of the vibration. It is the ISO standard because it represents the Energy (Destructive Power) of the vibration. Energy is proportional to velocity squared ($E \propto v^2$). It is relatively flat across the frequency spectrum (10 Hz - 1000 Hz), making it the ideal "General Health" indicator for detecting unbalance, misalignment, and looseness in general rotating machinery.
• Acceleration ($g$, m/s²): Measures the force ($F=ma$). It is heavily weighted toward High Frequencies ($> 1 kHz$). It is the primary tool for detecting Rolling Element Bearing faults and Gear Mesh issues. A tiny pit in a bearing race generates a sharp impact (high force/acceleration) but negligible movement (displacement). Therefore, acceleration is the earliest warning indicator for bearing failure.

The Mathematical Link: Physics dictates that these are related by integration/differentiation. If you know the frequency ($\omega = 2\pi f$), you can convert them. Note that as frequency ($f$) increases, Displacement drops rapidly, while Acceleration rises.

2. Decoding ISO 10816-3 Standards

ISO 10816 is the global standard for evaluating vibration severity on non-rotating parts (bearing housings). It replaces the older ISO 2372. It categorizes severity not just by the vibration number, but by the machine size and foundation stiffness. A vibration of 5 mm/s might be acceptable for a giant fan on flexible springs but catastrophic for a rigid pump.

The 4 Zones:

• Zone A (Green): Vibration of newly commissioned machines. Ideal state.
• Zone B (Yellow-Green): Acceptable for unrestricted long-term operation. Normal aging.
• Zone C (Orange): Unsatisfactory. The machine can operate for a limited time to reach the next maintenance window, but remedial action is required. This is typically the "Alarm" or "Alert" level in a DCS.
• Zone D (Red): Unacceptable. Vibration is sufficient to cause structural damage. Immediate trip/shutdown recommended. This is the "Trip" or "Danger" level.

Rigid vs. Flexible Foundations: This is a critical distinction often missed. A machine on a massive concrete block (Rigid) has lower vibration tolerance limits because the foundation doesn't move with the machine; high vibration measurements indicate high internal stress on the bearings and housing. A machine on a flexible steel skid (Flexible) is allowed higher vibration numbers because the whole skid moves with the machine, absorbing some of the energy and reducing the internal stress on the bearings. **Always classify your foundation correctly to avoid false alarms.**

3. The 4-20mA Transmitter Logic

Vibration transmitters (like the IFM VTV122, PCB 603C01, or Hansford HS-420) convert the complex dynamic vibration waveform into a simple DC current proportional to the RMS velocity. This allows a PLC or DCS to monitor health without needing expensive spectrum analyzers or high-speed DAQ cards.

Scaling Calculation: The transmitter has a "Full Scale" range (e.g., 25 mm/s). The 4-20mA output maps linearly to this range.

Example: A transmitter range is 0-25 mm/s. The machine is vibrating at 4.5 mm/s.
Ratio = 4.5 / 25 = 0.18 (18% of scale).
Current = 4 + (0.18 * 16) = 4 + 2.88 = 6.88 mA.

Troubleshooting:

• If the DCS reads 4.0 mA but the machine is running, the vibration is very low (Good).
• If it reads < 3.6 mA, the wire is cut (Open Circuit) or the sensor has failed.
• If it reads > 21 mA, the sensor is overloaded, the cable is shorted, or the machine is destroying itself.

4. RMS vs. Peak vs. Peak-to-Peak

Confusion between these units is the #1 cause of alarm errors in vibration monitoring.

• RMS (Root Mean Square): Represents the "Area under the curve" or power content. ISO 10816 uses RMS velocity. Most 4-20mA transmitters output RMS. It is a statistical average that correlates well with destructive energy.
• Peak (0-pk): The maximum distance from zero to the top of the wave. Often used for Acceleration to catch impulsive impacts (like a hammer blow inside a bearing). For a pure sine wave, $Peak = RMS \times 1.414$. However, for a spiky waveform (like a bad bearing), Peak can be 5x or 10x the RMS value (High Crest Factor).
• Peak-to-Peak (pk-pk): The total distance from the bottom trough to the top crest. Standard for Displacement (Orbit analysis) on sleeve bearings. $Pk-Pk = Peak \times 2$.

Warning: If your DCS expects RMS but you program the alarm limits using Peak values from a chart, you will alarm too late (under-sensitive). If you use Peak values for RMS limits, you will false alarm constantly (over-sensitive). This calculator handles the conversions automatically for sinusoidal inputs.

5. Sensor Mounting Best Practices

The method used to mount the sensor dictates the frequency response range.

• Stud Mount (Drilled & Tapped): The gold standard. Direct mechanical transfer allows reading frequencies up to 10-15 kHz. Essential for high-speed gearboxes.
• Adhesive/Glue Mount: Good for up to 5-8 kHz if done correctly with a stiff epoxy.
• Magnet Mount: Convenient for walk-around routes but acts like a low-pass filter. Typically loses accuracy above 2 kHz. Fine for unbalance (1X), bad for early bearing faults.
• Hand-Held Probe (Stinger): The worst method. Severely dampens signal. Only useful for very low frequency (< 500 Hz) measurements.