What is Strain?

Alexander M. Tomsick - P.E. Director of Engineering

This is the first in a series of videos that are being produced to discuss the Voyager FDS sensor. This video discusses the unit that the Voyager FDS sensor measures, which is strain. This video will provide some background on the purpose of the Voyager FDS sensor, as well as background knowledge on the unit of strain for those who may not have been exposed to it before.

Figure 1: Voyager FDS Sensor

The Voyager FDS sensor, shown in Figure 1, is designed to be mounted onto bearing housings for fluid film bearing machines and measures strain in the direction of the arrows on the top of the sensor. The Voyager FDS sensor was originally developed to monitor the health of unprotected fluid film bearings on turbo machinery.

Strain is typically denoted with the Greek letter epsilon (ε), and is the measure of a body's change in length compared to its original length in response to a load. Strain can be calculated using Equation 1:

From the equation, you can see that the unit of strain is dimensionless, as strain is calculated by dividing a length by a length.

Beam Under Tension:

A tensile force (F)acts on the beam shown in Figure 2, which has an original length (L) of 12 inches. Due to the applied force, the beam elongates to a length of 12.25 inches. This means the beam's length changes by (ΔL) 0.25 inches when loaded.

Figure 2: Beam Under Tension

Using this information, the strain in the beam can be calculated as:

The same relationship is true for a beam acted on by a compressive force, but the strain experienced by the beam will be negative.

Beam Under Compression:

A compressive force (F)acts on the beam shown in Figure 3. The beam had an original length (L) of 12 inches. Due to the applied force, the beam compresses to a length of 11.75 inches. This means the beam’s length changes by (ΔL) -0.25 inches when loaded.

Figure 3: Beam Under Compression

Using this information, the strain in the beam can be calculated as:

Static Strain of a Bearing Housing:

If we extend this idea to a hydrodynamic bearing, the load from the shaft is transmitted to the bearing by the high-pressure oil, which supports the rotating shaft. Due to this transmitted load, the bearing housing experiences a correlated strain shown in Figure 4.

Figure 4: Bearing Housing Strain Distribution

Given the bearing geometry, the compressive load acting on the bottom of the bearing will cause a localized region of high strain, shown by the bright green area on the bearing housing. The magnitude of the strain in this region decreases the further from the bearing surface it is measured. To measure the bearing strain, the sensor should be mounted on the bearing housing as close to the bearing surface as possible.

The strains discussed in this video are static strains due to the static loads that were applied in the examples. The Voyager FDS sensor cannot measure static strain but instead is designed to measure dynamic strain. The next video in this series will discuss the differences between static and dynamic strains.