#### The Importance of Accurately Modeling a Rotor-Bearing System

Hello and welcome to the latest revolution in our series on rotor dynamics and bearing analysis. This month, we’ll be looking at what steps need to be taken to accurately model a rotor train, from the components on the rotors themselves to the bearings and structural components that support the entire machine. If you haven’t had a look at the other entries in this series, you can find them here: Series Preface

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So what is the importance of accurately modeling a rotor-bearing system? Well we already know that an inaccurate analysis can have catastrophic consequences… If you want to know more about why, I also suggest looking at entry 2, titled “Why is Rotor Dynamics so Important?”.

The big reason for accurately modeling the rotor train, is because accurate models and accurate solvers generate accurate results. It makes sense; in order to get the most accurate predictions on how a machine will be behave in the real world, you must make it as close to the real world’s conditions and parameters as possible. If your rotor train is going to be supported by thrust bearings with a specific stiffness coefficient and with a very specific lubricant with its own set of parameters, it wouldn’t do you any good to implement journal bearings or air bearings in the model in their place.

So what steps need to be taken in order to model a rotor train accurately? Well let’s have a look:

1. Generate a mass-elastic lateral model for the rotating assembly – even the stiffest of metals have elastic properties that are apparent when put under loads and are rotating at high speeds! Additional effects such as shrink fits need to be properly assessed and modeled since they will affect the stiffness of the rotor train and therefore its natural frequencies, vibration amplitudes, etc.
2. Calculate the static bearing reactions – this means looking at the gravity loads (some of these machines are really heavy after all), gear loading on coupled rotor trains, and for steam turbines, the loads that come from partial arc steam admission.
3. Calculate the linearized fluid film bearing coefficients
4. Calculate the linearized floating ring oil seal coefficients
5. Determine the Excitation Mechanisms – to do this usually means considering aerodynamic effects and labyrinth seal effects. This is considerably easier when your software for modeling bearings, seals, and the machine’s aerodynamic properties are all connected to your rotor dynamics tool.

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Once you have taken all these steps, the model may need to be refined according to the data that is collected during mechanical testing if the critical speeds differ by more than 5%. It should be noted that most turbomachinery can be adequately modeled using lumped mass-inertia shafts and disk elements.

When modeling a rotor, it should be divided into discrete sections to accurately represent it. Stations as they are called, begin and end at the changes in the outside or the inside of the rotor’s diameter as well as are located where certain elements are (see below).

These stations should adequately approximate the curvature of the rotor’s modes, and these should also be located at the following locations:

• - The centerlines of journal bearings
• - The centerline of stages
• - The centerlines of seals
• - Probe locations
• - The ends of the rotors

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­From there, the external masses and inertia loadings need to be added to the model. These masses include but are not limited to:

• - Impellers/disks
• - Couplings
• - Sleeves
• - Balance pistons
• - Thrust collars
• - Gas seals

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­There are masses that are seen on specific machines and also need to be accounted for such as:

• - Armature windings in electric motors
• - Shrunk-on gear meshes
• - Wet impeller masses and inertia in pumps

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Now this model is coming right along, but we also need to take a closer look at shrunk-on components. These can affect the bending stiffness of the rotating element, in this case our rotor. According to API 684, the vendor must determine the importance of shrink fits for each individual case. If the number, length, and size of these shrunk-on components are sufficiently large, then they must be modeled as contributing to the shaft stiffness. The engineer/vendor performing the analyses and creating the model should do this on a case-by-case basis for the designs, based on prior experience with similar machines, as well as perform modal tests and finite element analyses.

According to API 684, built-up rotors with axially segmented sections that are stacked and bolted together, they can be approximated as being one integral piece of metal, as opposed to fitted parts that are shrunk on; providing that they were properly designed.

Coming up in next month’s rotation…

By now some of you may be wondering, “What about the bearings and structural supports?” Great question! This is an extremely important topic, however, this blog has become quite long, so I think it would be best for us to cover this in a separate blog entry and ensure that we don’t skip any important steps or considerations!

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 info@softinway.com