Foundations of Rotordynamics – Part 1

In order to succeed as an engineer focused on rotor dynamics in rotating equipment, it is important to be fully aware of its foundation. The foundations of rotor dynamics consists of two parts, lateral analysis and torsional analysis. For part one of this blog, I will be focusing on lateral analysis and then exploring torsional analysis in part two next week.

Lateral analysis, also referred as critical speed analysis, is the study of when rotational speed meets or exceeds the shaft natural frequency. This is important since not knowing the critical speed can lead to instability, unbalance or even cause unknown forces to alter the functionality of rotating machinery. Since a rotating machinery consists of many components (rotor, bearing, motor, seals, etc), lateral analysis is made up of three categories: undamped critical speed analysis, steady state synchronous analysis (also known as damped unbalance response analysis) and stability analysis.

Influenced by the rotor’s mass and stiffness properties, undamped critical speed analysis is used for the estimation of critical speeds, mode shape characteristics and eigenvalues. Generally, this analysis excludes any damping in the system as well as any unbalance forces. For the estimation of undamped critical speed, an undamped critical speed map is a common tool that can be used. This map generally represents the first four undamped, forward-whirling modes as a total bearing/support stiffness. Calculated using bearing principles stiffness, mode shapes are helpful because they provide an approximate indication of the relative displacements that the shaft undergoes when the rotor operates in the vicinity of the associated critical speeds.

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Figure 1: Example of critical speed calculation on front bearing using AxSTREAM RotorDynamics

Next, unbalance response analysis takes into consideration all damping effects. There are three requirements needed to satisfy unbalance performance: separation between critical speeds and operational speeds, operational speed should not be exceeded, and no rubbing should occurs when the rotor’s balance stage degrades to the probe vibration limit. Performing this analysis confirms whether or not these requirements have been achieved. It is a good idea to keep your API requirements handy when evaluating this analysis for reference.

Latestly, stability analysis calculates damped eigenvalues, and also takes into consideration oil whirl and shaft whip to avoid self-exited instabilities. It is known, that if the damping exponent of an eigenvalue is negative, then stable rotor vibrations occur, and if positive, the oppsite effect will occur. Understanding these categories relating back to lateral analysis as a whole, will allow the respective engineer, to design and analyze a stable and reliable rotating machinery.

Check in for next week’s blog post – Foundations of Rotor Dynamics: Part 2  and check out AxSTREAM RotorDynamics or SoftInWay’s upcoming webinar on rotordynamics!

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