Introduction to Performing Torsional Rotor Dynamics Analysis

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Hello and welcome to the last part of our series on Rotor Dynamics! In today’s blog we’ll be concluding with torsional analysis, and the steps needed to perform this type of analysis. If you haven’t had a look at the other entries in this series, you can find them here:

Series Preface

  1. What is Rotor Dynamics? And Where is it Found?
  2. Why is Rotor Dynamics so Important?
  3. What API Standards Govern Rotor Dynamics Analysis?
  4. Basic Definitions and Fundamental Concepts of Rotating Equipment Vibrations
  5. The Purposes and Objectives of Rotor Dynamics Analyses
  6. The Importance of Accurately Modeling a Rotor-Bearing System­
  7. Modeling Bearings and Support Structures in a Rotor Bearing System
  8. Introduction to Performing Lateral Rotor Dynamics Analysis


In an earlier blog, we covered the basic definitions of lateral and torsional analysis. Lateral analysis is concerned with the bending behavior of a rotor train. Torque is a measurement of force that causes an object to rotate on an axis such as when a component needs to be “torqued to spec” in a car’s engine, for example. Torsional analysis, meanwhile, looks at the twisting behavior of the rotor train.

In the context of rotor dynamics, torsional vibrations refer to the oscillatory torsional deformations encountered by the shafts in the rotor train.

Pictured - A shaft undergoing torsional vibration
Pictured: A shaft undergoing torsional vibration.

If these torsional vibrations and excitations are left undamped and aren’t analyzed properly, breakages and catastrophic failures can occur similar to undamped lateral excitations. For more on that, you can read up on the importance of rotor dynamics analysis here.

So what are the goals and steps of torsional analysis? The objectives and steps should be the following:

  1. Identify possible torsional excitations
  2. Predict the torsional natural frequencies
  3. Sensitivity analysis: Evaluate the effect on the natural frequencies and vibration amplitudes from changing one or more design parameters or components in the train
  4. Screen for resonances (Campbell diagram)
    – In case of a resonance, modify the system to remove it
    – In case it is not possible to remove the resonance, demonstrate that the system is reliable (does not break):
    —- Calculate pulsating torque amplifications
    —- Obtain stress levels on shafts
    —- Verify system against low/high cycle fatigue
  5. Compute the vibration amplitudes and peak torques under steady state torsional excitation
  6. Compute the dynamic torque and gear tooth loads under transient conditions

Using this basic outline, a torsional analysis can be completed. But it’s important to understand the tools and methods of going through these steps. Additionally, it’s important to understand the context of why we perform torsional analysis.

Illustrated examples of torsional excitation, including blade passing frequency, shaft runout, and piston reciprocation
Illustrated examples of torsional excitation, including blade passing frequency, shaft runout, and piston reciprocation

All rotating machines (not just turbomachinery!) have torsional excitations of one form or another. Some examples include blade passing frequency in turbomachines, shaft runout, and the torque exerted by pistons in reciprocating machines. Unlike lateral excitations, torsional natural frequencies are not influenced in any way by rotation speed. Additionally, while lateral analysis performed on the individual rotors in a train, for torsional analyses, the entire rotor train needs to be analyzed in one model.

Once the potential torsional excitation sources are recognized, it’s time to move into the undamped natural frequency analysis. The results that we want to get from this are the rotor train’s torsional natural frequency and torsional mode shapes. The natural frequencies are shown in the form of a Campbell diagram, like the one below.

A Campbell diagram for torsional natural frequencies, with the rotortrain in this example being a motor gear compressor train.
A Campbell diagram for torsional natural frequencies, with the rotortrain in this example being a motor gear compressor train.

So what is this Campbell Diagram displaying, exactly? Along the X axis we see the machine’s rotating speed measured in the typical revolutions per minute (RPM), and along the Y axis the steady-state natural frequencies measured in hertz (Hz). Additionally, on the right Y axis we can see the Electrical frequency, also measured in hertz (Hz).  Based on this information, we can see the coincidence of the steady state natural frequencies and the torsional natural frequencies.

If there is a coincidence of the torsional natural frequency with any steady state excitation frequency, it must meet the API separation margin, or it must be demonstrated that the torsional natural frequency is nonresponsive.

Now let’s have a look at the torsional mode shapes. These mode shapes show the way in which the system is displacing as a result of the natural frequencies coinciding with the speed of the machine.

Torsional 2D Mode Shapes
Pictured above are the mode shapes for a turbine-gearbox-pump rotor train, and the undamped in natural frequency 1st Mode 36.5 Hz ( model generated in AxSTREAM RotorDynamics )

The mode shapes will plot the rotor’s relative angular deflection vs. the axial distance of the coupled rotors. The mode shape information is critical for the proper interpretation of the analysis results. If a torsional interference exists, a study of the train’s mode shape can give an engineer information on nodal point locations and damped nodal points along the rotor train. This will allow the engineer to understand where the rotor is sensitive to flexibility, and where it is sensitive to inertia.

Other things that may need to be considered in torsional analyses include forced analysis and transient torsional analyses if there is a synchronous electric motor or variable frequency drive. However since this is blog is meant to provide a general overview of torsional rotor dynamics, we will not be delving into these topics here. Maybe in our next series 😊.

This marks the end of our introductory series on rotor dynamics analyses. Thank you to those who have been following along!

If you want to learn more about the importance of rotor dynamics, or about the tools our engineers and thousands of others around the world rely on for their turbomachinery designs, reach out to us at

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