#### 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.

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!

#### 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

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.

Balancing Methods used Today

Two of the most popular balancing methods that are performed on existing turbine rotors are low-speed balancing and high-speed balancing methods. A low-speed balance helps determine wear and tear on rotor under minimum speed conditions. This method is generally used by companies who lack access to a high-speed balance cell. A high-speed balance (Figure 2) allows the test be run at or passed operating speed, and even though it is more expensive, it tends to be a more accurate method of testing. The primary reason why  more end users are opting for this type of balance, for both turbine rotors and power generator fields, is that all major components can be tested under rigorous conditions. By doing this, the full operating lives of these components can accurately be determined.

Want to make sure you’re taking into account unbalances when designing rotors in rotating equipment? Look into our rotordynamics software capabilities

References:

Reciprocating Machinery Dynamics by Abdulla S. Rangwala – Chapter 9

http://www.powermag.com/high-speed-turbine-rotor-balancing-lowers-costs-improves-operation/?printmode=1

#### 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.

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.

AxSTREAM, for example is a prime example of this. The software tool saves engineering time and cost and it ensures that no destructive vibration will occur in the rotor-bearing system. It is able to perform many analyses like Static Gravity Deflection, Critical Speeds, Damped Unbalance Response, Modal and Transient. It is because of the rich history of rotordynamic development that software platforms like AxSTREAM are able to ensure the best design and performance for your turbomachinery.

Figure 2: Demostration of AxSTREAM RotorDynamics

Reference:
1)http://www.universitystory.gla.ac.uk/biography/?id=WH0067&type=P
2)https://www.turbomachinerymag.com/vibration-the-pulse-of-rotating-machinery
3)http://www.softinway.com/engineering-services/rotor-dynamics