Basic Definitions and Fundamental Concepts of Rotating Equipment Vibrations

Hello and welcome or welcome back to the January 2020 edition of our Rotor Dynamics Blog series! Here are the other entries in the series for those who are just joining us:

  1. Series Preface
  2. What is Rotor Dynamics? And Where is it Found?
  3. Why is Rotor Dynamics so Important?
  4. What API Standards Govern Rotor Dynamics Analysis?

In our previous blogs we established that rotor dynamics is a branch of applied mechanics in mechanical engineering and is concerned with the behavior of all rotating equipment, but let’s have a closer look at some of the factors that affect the behavior of rotating equipment.

Here’s a non-exhaustive list of the different static and dynamic forces and phenomena that can act on a rotor train:

  • – Unbalance
  • – Gravity
  • – Bearing reaction
  • – Inertia
  • – Seals
  • – Fluid-rotor interaction
  • – Impeller aerodynamic loadings
  • – Misaligned couplings and bearings
  • – Rubbing between rotating and stationary components


Rotor Train Schematic
Rotor Train Schematic

As you can see there’s no shortage of different forces and factors which must be considered to ensure the smooth operation of your turbomachinery and other rotating equipment. While some of these factors are very familiar such as gravity, some factors like rotor unbalance have numerous causes. Here’s another (non-exhaustive) list of different factors that can cause rotor unbalance:

  • – Blow holes in castings
  • – Eccentricities
  • – Addition of keys and keyways
  • – Distortion
  • – Clearance tolerances
  • – Corrosion or wear
  • – Deposit build-up (dirt, lime, etc.)
  • – Asymmetrical manufactured configurations
  • – Hydraulic or aerodynamic unbalance


Rotor Imbalance
Rotor Imbalance

It might be hard to fathom, but something as minor as some deposit build up or corrosion/wear on the rotor train or the machine’s blades and other rotating components can have a serious effect on the balance of the machine. But keep in mind, when a machine is spinning at potentially tens or hundreds of thousands of RPMs, the slightest eccentricity or added/lost weight can completely throw off the balance of a rotor. It’s similar to how a car’s drive shaft may need to have weight added on in certain areas to balance it, or why car tires can have little weights added to the rim in specific places.

Some other forces that need to be considered don’t even come from the rotor itself, however. They come from the components and other machines the rotor may be coupled to; for example, a motor-driven centrifugal compressor rotor would have an electric motor connected to a rotor which is connected to an impeller that may be “overhung”. Overhung here meaning that the impeller for the compressor hangs out at the end of the rotor train, with the support bearings on one side. Here are some of the cross-coupled forces that can affect a rotor’s behavior:

  • – Fixed geometry bearings
  • – Seals
  • – Compressor impellers
  • – Shrink fittings
  • – Gear type couplings
  • – Rubs
  • – Steam whirl
  • – Flow differences in the uneven clearances around impeller/seals caused by lateral motion


All of these forces that are external to the rotor itself can affect the behavior of the rotor train and can severely impact the rotor dynamics.

Some other definitions in rotor dynamics which should be covered while we’re here include critical speeds, Campbell diagrams, vibration amplitude, and separation margins.

So, first things first, what’s a critical speed?

A critical speed occurs or is reached when a machine’s rotation speed coincides with the natural frequencies of the machine itself (measured in Hertz). When this happens, the machine will operate in a state of resonance, or vibration. You can notice this, for example, when a jet engine starts on an airplane and as the entire engine accelerates up to idle speed, it will resonate and vibrate for a very short period of time if appropriate damping is present. It should be noted that in lateral rotor dynamic systems, natural frequencies often depend on the rotation speed.

Below you can find the API’s definitions of Critical Speed:

  • – API 613, 1995, 4th Ed.
    If the frequency of any harmonic component of a periodic forcing phenomenon is equal to or approximates the natural frequency of any mode of rotor vibration, a condition of resonance may exist; if resonance exists at a finite speed, that speed is called a critical speed
  • – API 684, 2005, 2nd Ed.
    When the synchronous rotor frequency equals the frequency of a rotor natural frequency, the system operates in a state of resonance, and the rotor’s response is amplified if the resonance is not critically damped
  • – API 684 defines a critical speed as any rotor resonance with an amplification factor of > 2.5


Next, we have vibration amplitude; vibration amplitude is the characteristic that describes the severity of the machine’s vibration. The measurement of vibration amplitude is known as the amplification factor, or AF. The higher the AF, the more severe the vibration. Below you can see an example of the amplification factor being calculated based on the operating speed and the vibration amplitude at the critical speeds.

The equation for amplification factor calculation is:

Equation for Amplification Factor

Example of a Rotor Forced Response
Example of a Rotor Forced Response

The above diagram is an example of a forced response, with the critical speed being the peak of the vibration level and its corresponding rotor speed measured in RPM. A large amplification factor corresponds to a steep resonance peak with low damping.

This leads us to discuss the topic of separation margins. Separation margins, or SM’s, are required to ensure smooth operation of the machine. With regards to API standards, separation margins come into play when the amplification factor of a rotor train’s critical speed is higher than 2.5. You can find the rules for separation margins according to API 684 below:

Separation Margins Rule as per API Standards

Finally, let’s touch on Campbell diagrams. A Campbell diagram is the evolution of the natural frequencies corresponding to a mode as a function of the shaft rotation speed. In short, it is where the output of the critical speed is displayed, with the X axis being rotation speed and the Y axis being natural frequencies. You can see what a typical lateral analysis Campbell diagram looks like below.

Lateral Analysis Campbell Diagram
Lateral Analysis Campbell Diagram

To wrap this entry up, let’s do a quick review. First, a number of different factors and forces play into the rotor dynamics of a machine that need to be accounted for, from imperfections in the rotor from the machining process, to accumulation of dirt/wear on the rotor blades/attachments. Secondly, the supports, couplings, and other external forces can affect the rotor dynamics of the machine and must be considered as part of the analysis process. Lastly, the critical speed and amplification factor, which are plotted on a Bode plot, are essential to rotor dynamics, and if the amplification factor is too significant (greater than 2.5), separation margins must exist in order for the machine to operate safely; its required minimum value depends on whether the considered critical speed is above or below the machine operating range.

Coming up in next month’s rotation…

Next month, we’ll look more closely at the purposes and objectives of rotor dynamics analyses, the different kinds of rotor dynamics analyses, and what the end results of a successful rotor dynamics analysis look like. We’ll see you then!

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