Practical Modal Testing and Analysis Applied to Rotating Equipment Diagnostics

by Ray Kelm, P.E. and Malcolm E. Leader, P.E.


The use of modal analysis to help understand the vibration characteristics of rotating machinery is explored. The basic tools that one needs to extract modal quantities are described as well as the types of instrumentation setups. Ways to calibrate a modal analysis test are shown using simple easily understood concepts. Several single and multiple degree of freedom examples are presented with comparisons of theoretical and experimental results. The use of modal analysis to augment rotor dynamic analyses is examined. The loss of effective stiffness and damping of fluid film bearings is shown as result of flexible bearing pedestals. Rotor free-free mode shapes are discussed and determined experimentally using specific test techniques and compared to the calculated results from rotor models.


This tutorial is limited to the use of modal testing and analysis in the rotating equipment field. Many of the techniques and principals can be applied to other structures. However, testing the bearing pedestal of a fan requires different techniques than testing a suspension bridge. Modal analysis is a tool that we can use to determine the resonant frequencies of a machine or one of its parts. Additionally, the modal test tells us the shape of the vibrations or how one part moves relative to other parts. Each frequency has a unique mode shape associated with that resonance. Modal testing ranges from a simple mobility test with an impact hammer to multi-shaker testing of large structures with hundreds of response accelerometers. Modal testing is an experimental means of determining the dynamic characteristics of a structure through mechanical excitation, created either by forced response (shaker) or impact methods. This excitation is done to stimulate the mode shapes of the test item that are measured by accelerometers or other transducers. The data from these transducers is then analyzed to develop the dynamic structural characteristics of the machine being tested.

Modal Testing: Modal testing is the practice of gathering empirical test data that can be used to define dynamic response of a structure. The name “modal” implies that the data gathered will be adequate to define one or more dynamic mode shapes of response to some stimulus. The values often calculated from measured data include modal stiffness, damping, mass, natural frequency, and the deformed shape of the structure corresponding with each natural frequency.

In addition to defining the dynamic response of the structure in question at or near resonance, the same test data can be used to predict off-resonant response based on the characteristics of the modal data.

Single Degree of Freedom System: The Figure 1.1 below shows a single degree of freedom (SDOF) dynamic system. By definition, such a system will have one mode, or natural frequency, that is completely defined by a very limited number of parameters including modal mass, stiffness, and damping.

The calculated frequency response is shown in Figure 1.2 for an example undamped system including a 10 Lb mass with 10,277 Lb/in stiffness to produce a 100 Hz natural frequency. The response is scaled for 1 Lb of applied force. Several observations can be made from the plot below that can have a huge significance on modal testing:

  • Response at relatively low frequency is controlled by support stiffness
  • Response at relatively high frequency is controlled by the moving mass
  • The response will produce a peak at the natural frequency, with amplitude near resonance controlled by the available modal damping at that mode.”

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