Knowledge Base:  
Tech Note 114: Double Integration of Vibration Signals
Last Updated: 05/10/2017

Double Integration of Vibration SignalSTI recommends performing double integration (Acceleration to Displacement) when required by using a CMCP793V Velocity Output Accelerometer and a CMCP535(A) Transmitter or Monitor. As each integration stage can require significant gain to the raw dynamic signal this method keeps amplified noise to a minimum as the first level of integration (acceleration to velocity) is performed within the Accelerometer before the field wiring and external noise is introduced.

The second level of integration (Velocity to Displacement) is then performed within the CMCP535 Transmitter or Monitor. Noise sources that create issues with double integration include field wiring, hand held radios, ground loops, VFDs (Variable Frequency Drives) and AC power.

Portable data collection instruments and analyzers that are not connected to the real world (battery powered) are not subject to the same noise and interference sources as permanently installed systems and thus perform double integration quite well.

As can be seen in the following calculation the machine speed must be considered. Low speed machines in general are not good candidates for double integration (<600 RPM). The following calculation can only be used for discrete frequencies and cannot be used for broadband vibration.

D = 19.57 g/f2

D = Displacement (mils Peak to Peak) g = Acceleration (gs 0 to Peak) f = frequency Hz

As can be seen in the following table, machine speed and frequencies of interest are critical to having a viable output for double integration from a case mounted industrial accelerometer that will not be effected by field wiring noise and interference.




Output @ 100 mv/g

2 mils


0.368 gs

36.8 mv

2 mils


0.092 gs

9.2 mv

2 mils


0.023 gs

2.3 mv

2 mils


0.01 gs

1 mv

2 mils


0.003 gs

0.3 mv

Displacement readings on rotating machinery have historically been requested on Journal Bearing Machines where economic decisions do not justify the installation of Proximity Probes that provide a true relative measurement of displacement (shaft to bearing). Additionally as Operators have historically used displacement on Journal Bearing Machines the same engineering term was desired. Rolling Element Bearings (REB) should always be monitored using Velocity (single integration) as provided by a standard 100 mv/g industrial accelerometer and the CMCP530(A) Transmitter/Monitor.

Displacement readings provided by double integrating a acceleration signal from a case mounted sensor are not the same nor will they agree with the displacement signal provided by a Proximity Probe System. In general the case reading may be 3 to 5 times lower than the actual shaft displacement internal to the bearing.

  • Case Mounted Sensors are a Absolute Measurement (Case to Free Space)

  • Proximity Probes are a Relative Measurement (Shaft to Bearing)

  • Journal Bearings provide Damping (like a shock absorber)

Double Integration Checklist:

  • Machine Speed >600 RPM

  • Journal Bearing

  • CMCP793V (Accelerometer w/Velocity Output)

  • CMCP535(A) Transmitter or Monitor

  • Painted Steel or Stainless Steel Enclosure for Transmitter or Monitor (if field mounted)

  • Extension Cable (793V to Transmitter) short as possible and in metal conduit

  • Cross all power lines at 90 degree angle (Do not Parallel)

  • Extension Cable Shield landed at Transmitter/Monitor

  • No Ground Loops

  • Proper Grounds Established for Enclosure and Power Supply

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