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.

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The Balancing Act – Rotor Stability

When designing rotating equipment, it is extremely important to take into account the types of unbalance that can occur. Forgetting this step can result in vibrations that lead to damage of the rotating parts, increasing maintenance costs and lowering efficiency. Currently, if a rotating part already vibrates or makes any noises, maintenance engineers rely on OEMs (Original Equipment Manufacturer) or third parties services companies to conduct balancing services.

Types of Unbalances

Figure 1: Static and Couple Forms of Unbalance

The three types of unbalances to consider are static, couple and dynamic. Static unbalance (Figure 1) occurs when a mass at a certain radius from the axis of rotation causes a shift in the inertia axis. Couple unbalance, usually found in cylindrical shapes, occurs when two equal masses positioned at 180 degrees from each other cause a shift in the inertia axis, leading to vibration effects on the bearings. Lastly and most common, dynamic unbalance occurs when you have a combination of both static and couple unbalance.

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The Origin of Rotordynamics

Rotordynamics, the study of vibrational energy in rotors, has a rich history dating back to North America during the 1750’s. This branch of applied mechanics began with theories, but advanced quickly due to practices – starting with Mr. W.J.M Rankine in 1869 and his spinning shaft experiment. Now, decades later, we have strengthened our understanding of rotordynamics and created leading software tools, including AxSTREAM, that are able to simulate analyses to stabilize and increase the reliability of a turbomachinery.

W.J.M Rankine

Not only was W.J.M Rankine a prestigious theoretical scientist and educator, he was a main contributor in the development of rotordynamics and he contributed to thermodynamics and the development of heat engines throughout his lifetime. During his spinning shaft experiment, he concluded that beyond the shaft’s first critical speed, the shaft would be unstable simply because its shape had been bent. By not taking into consideration support damping and Coriolis force in his analysis, many engineers were left confused for almost two centuries, until Gustaf de Laval, a Swedish engineer, ran a steam turbine to supercritical speeds in the late 1880’s. Laval also introduced the use of bearings to oppose absolute motion in his machinery. As the years went by, many other engineers discovered and investigated additional phenomenons (FEM for example) that have an influence in today’s practices.
It is because of these previous innovators that companies like SoftInWay have been able to develop the advanced  rotodynamics modules that we use today.

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