The Case For and Against Integration (of Machinery Vibration Signals)

Vibration is typically measured in engineering units for displacement (mils), velocity (in./sec or ips.) or acceleration (g’s). At a given vibration frequency (measured in Hz), there is a specific relationship between displacement, velocity and acceleration. Vibration can be measured in any
one of these units. When one converts acceleration units to velocity units (A/V) or velocity units to displacement units (V/D), it is called single integration; when one converts acceleration units to displacement units (A/D), it is called double integration. This term (integration) results
from the physical and mathematical relationships between acceleration, velocity and displacement units of measure for vibration.When single integrating (A/V or V/D), the relationship between the two units is proportional to: 1/f, (where f = frequency, Hz). When double integrating (A/D), the relationship between the two units is proportional to: 1/f2. Integrating amplifiers circuits electronically alter (integrate) the incoming signal (“A” or “V”) using these proportional  relationships to provide a new signal (“V” or “D”) in the desired units of measure. The
graphs illustrate these relationships.