#### Rotor Dynamics Challenges in High-Speed Turbomachinery for HVAC Applications

In comparison to large steam and gas turbines, the rotating equipment found in heat ventilation and air conditioning (HVAC) applications is often seen as more simplistic in design. However, sometimes a simpler model of a rotating machine does not mean a simpler approach can be used to accurately investigate its rotor dynamics behavior. For example, a large number of effects should be taken into account for single-stage compressors used in HVAC applications. Three important ones include:

1. High values of rotational speeds above the first critical speed;
2. Rigid rolling element bearing used in the design and therefore a relatively flexible foundation which should be modeled properly;

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All these effects should be modeled properly when performing lateral rotor dynamics analyses of HVAC machines. And, in some cases, this simpler model can prove a much more challenging task than building the complex model of a steam turbine rotor.

Let’s consider a seemingly simple example of a high-speed single-shaft compressor for HVAC application (Figure 1). It consists of the compressor and motor rotors, the flexible coupling connecting them, the ball bearings connecting the rotors to the bearing housing joined with the compressor volute, and the structural support.

The compressor rotor is connected with the motor through a flexible coupling. Its lateral vibrations can be considered uncoupled from the motor rotor vibrations, and the lateral rotor dynamics model appears pretty straightforward (Figure 2).

However, additional factors are discovered if you include the mechanical properties of the supporting structure when considering the lateral rotor dynamics calculations. These factors are very important to an accurate model.

Accurate Models of a Single-Stage Compressor

A model of a single-stage compressor can be done by a simple connection of the spring-damper element, describing the bearing properties to the spring-damper-mass element, and describing the support properties. However, this approach is pretty basic and does not account for all the effects of the supporting structure on the vibration response of the rotor. The model may be usable for some applications, but it will not be as accurate as other applications require (Figure 3).

A more complicated yet much more accurate approach is to include the whole spectrum of the supporting structure modal properties by executing the preliminary calculation of the three-dimensional modal analysis of the supporting structure. Further, the calculated modal mass and stiffness coefficients are accompanied by the relative maximal displacements of the corresponding natural mode and are applied to the model for the rotor dynamics analyses.

These additional considerations introduce significant differences in the results. The more natural modes that are taken into account, the less value the peak amplitude of the rotor unbalance response has.

This has a very significant role in the interpretation of the results. As we discussed earlier, the compressors used in HVAC applications very often have rotational speed values higher than (or in the range of) their first critical speeds. The erroneous determination of the peak values of the rotor deflection and stress amplitudes may result in an erroneous conclusion regarding the safe operation of the machine. If the amplitudes are overestimated, necessary design changes can not be accurately determined in the early stages of the project. On the other end, if the amplitudes are underestimated, then poor conclusions can be made about the safety of the rotor operation, allowing a dangerous design to be used.

In this case, taking into account the supporting structure modal properties decreases the peak vibration amplitude at the resonant regime by almost 10 times! This occurs because we introduce the additional compliance in the structure which decreases the sharpness of the peak rotor amplitude. However, as the example shows, these additional considerations resulted in additional resonances in the system which were safe in this case but may become dangerous under other operational or design conditions. Therefore it is extremely important to consider all the elements affecting the rotor response, even for a simple rotor dynamics model.

Even simple rotor dynamics analyses of HVAC applications have challenges which if not properly accounted for, can have disastrous results. Fortunately, there are comprehensive standards and complex engineering tools which make this task much simpler for engineers. AxSTREAM Bearing and RotorDynamics provide their users with comprehensive modeling of bearing and rotor operation based on recognized approaches and API standards and allows designers to take into account all of the important rotor dynamic effects affecting the accuracy of the results. To learn more about how the tools used in this blog can work for your workflow, send us an email at Sales@SoftInway.com or fill out the below form: https://www2.softinway.com/Software-Trial-Request-Form

References

• Moroz, L, Romanenko, L, Kochurov, R, & Kashtanov, E. “Prediction of Structural Supports Influence on Rotating Machinery Dynamics.” Proceedings of the ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition. Volume 7B: Structures and Dynamics. Charlotte, North Carolina, USA. June 26–30, 2017. V07BT33A001. ASME. https://doi.org/10.1115/GT2017-63035