ArticleRotordynamics Case Histories
by Malcolm E. Leader, P.E.
This paper provides three case histories that show how applying rotor dynamic analysis can solve serious machinery problems. The 1st case study is about a three stage centrifugal compressor with reliability problems. The bearings had been replaced and resulted in the 1st critical being at run speed. The rotor dynamic analysis resulted in a bearing redesign and adding mass to the compressor rotor to lower the 1st critical speed. The 2nd case study is an aero-derivation gas turbine instability problem. The vibration data showed sub-synchronous vibration when rotor speed was above 10,000 RPM. A very elaborate rotor-casing model was developed which provided response predictions that matched the field test data well. A bearing was designed to replace the existing bearing resulting in elimination of the sub-synchronous vibration. The 3rd case study is a newly installed steam turbine operating near its 1st critical speed. Squeeze film damper design is discussed and some equations used in the design are provided. The bearing design was modified; squeeze film dampers installed and addition mass added to the rotor to lower the 1st critical speed successfully.
The rotordynamics modeling of rotating machinery has become a relatively mature science in the past 30 years. While many different mathematical techniques have been applied including matrix transfer and polynomial expansion, the use of finite element modeling techniques has allowed for faster and more realistic system modeling. This paper will show how some of these techniques are applied including the ability to analyze complete coupled trains where flexible couplings connect two or more rotors. In the past couplings were included as lumped masses and inertias. Although the flexible parts of modern couplings do somewhat isolate rotors laterally from one another, there are some dynamic effects that are transmitted through these couplings. In Case 1 the coupling played an integral part in the compressor rotor’s dynamics.
The ability to include substructures such as bearing housings, casings, flexible supports and foundations has greatly improved the accuracy of rotordynamics analysis. In Case 2 in this paper, an aero-derivative gas turbine had a very complex substructure. Without a concentrated effort to include all of the elements of the casing and foundation, the problem could not have been solved. Extensive modal testing was used in this case to get effective stiffness and mass properties but finite element modeling of structures can also be used to determine these properties.
One of the biggest gains in the last decade for rotordynamics modeling and analysis is the production of very high quality graphics, some of which are displayed in this paper. Although it can’t be shown on paper, animations have become a very useful tool to help visualize the dynamic behavior of rotor bearing systems. It is especially useful as a learning tool or to convince a skeptical boss that the proposed fix is the right one.
There are three principal cases when a rotordynamics study is appropriate. The most obvious is to help resolve vibration problems that have resisted normal maintenance attempts such as balancing and alignment. Some machines just have design flaws or need improvement in order to withstand operational abuse such as surging or contaminant buildup. The three cases presented in this paper all cover the analysis of problem machines and the applied measures to solve the vibration problems. The next appropriate time to seek out a rotordynamics analysis is when system modifications are planned. This might be changing coupling designs or it might involve a complete revamp, adding impellers or other modifications. The rotordynamics analysis can tell ahead of time if the modifications will cause any problems.”
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