Rotor Dynamics for Turbomachinery Engineers

A rotor is a body suspended through a set of cylindrical hinges or bearings that allow it to rotate freely about an axis fixed in space. It is the most critical component of any rotating machine; often operating at high speeds and within a wide speed range (Figure 1). Rotor dynamics is the branch of engineering that studies the lateral and torsional vibrations of rotating shafts. The main purpose of rotor dynamics is to predict the rotor vibrations and keep the vibration level under an acceptable limit. To meet stringent reliability requirements, each step of the rotor design should be based on an accurate rotor dynamics prediction.

Figure 1 The components of a rotating machine
Figure 1 The components of a rotating machine, [1]
A rotor dynamics analysis should accomplish several goals. It should predict critical speeds at which vibration due to rotor unbalance is severe and should be avoided. Relatedly, it should suggest modifications that would allow designers to increase a machine’s critical speeds. Rotor dynamics analysis should also predict natural frequencies of torsional vibration, as well as amplitudes of synchronous vibration caused by rotor unbalance. In addition, the analysis should predict dynamic instability (including oil whip), and suggest design modifications to suppress it. Lastly, the analysis should recommend balance correction masses and locations from measured vibration data.

Real-world rotor dynamic systems are typically too complex for existing models to solve in all but the simplest cases. Still, numerical solutions for simplified 2D and 3D models of rotor dynamic systems are standardly used, as they provide decent data for engineers to go on. The Jeffcott rotor is one example of such a simplified model that is commonly employed (Figure 2).

Jeffcott rotor,
Figure 2 Jeffcott rotor, [2]
Nevertheless, these numerical solutions do not provide the kind of deep insight that can be had from a step-by-step derivation of an analytical solution. Such a derivation can tell us how the different system response characteristics are interconnected in the final design, and thereby provides higher quality data than 2D / 3D models alone do.

A software tool such as AxSTREAM RotorDynamics™ lets us perform exactly that step-by-step analysis. The software provides a comprehensive rotor modeling capability, including shaft design, mass-inertia elements, bearings and supports, couplings, as well as forces and accelerations affecting the rotor stress state and its prestress conditions (Figure 3).

Rotor dynamics model in AxSTREAM RotorDynamics
Figure 3 Rotor dynamics model in AxSTREAM RotorDynamics

Each rotor’s unique features impose strict limitations on the structural finite-element method that engineers use to predict vibration response. This method should be capable of calculating the dynamic characteristics of the rotor auxiliary components, such as bearings, supports, and seals.

With AxSTREAM RotorDynamics, users get the required solution settings for obtaining accurate results that satisfy modern API requirements. Engineers are thus able to analyze a rotor’s safe operation with regard to its stress state, vibration response, stability, transient issues occurring during its operation, and more. (Figure 4).

Figure 4 Results for the rotor lateral vibrations (from top to bottom – deflection form, bearing reactions, amplitude-frequency characteristic, and bearing-supports response characteristic)

Errors in prediction of the peak values of the rotor deflection and stress amplitudes can have severe consequences. If the amplitudes are overestimated, necessary design changes cannot be accurately determined in the early stages of the project. If the amplitudes are underestimated, the safety of the rotor operation would be compromised, risking catastrophic failure. It is also important to account for the influence of rotor components such as bearings and supports, since they too can impact the peak values of the rotor deflection and stress amplitude.

The real dynamics of a machine are difficult to model perfectly. Instead, the calculations engineers often use are based on simplified models that resemble various structural components (lumped parameters models), and on equations obtained both from solving models numerically (Rayleigh-Ritz method), and from the finite element method (FEM).

For all the reasons mentioned, engineers need rotor dynamics, and therefore software that can simplify their work. AxSTREAM RotorDynamics and AxSTREAM Bearing™ provide users with comprehensive modeling of the rotor and bearing operation based on recognized approaches and API standards—allowing engineers to take into account all of the important rotor dynamic effects needed to achieve accurate results.

To learn more about AxSTREAM RotorDynamics and AxSTREAM Bearing, feel free to reach out to our team at


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