Analytical Tools for Determination of Damped Unbalanced Rotor Response

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Representative Rotor Response Plot (API Standards) & Analytical Simulation

Lateral rotor-dynamic behavior is the most critical aspect in determining the reliability and operability of rotating equipment in the oil and gas industry – be it a centrifugal pump , compressor, steam or gas turbine, motor or generator. One way to evaluate operating reliability is identifying lateral rotor response to unbalance, i.e. by analytically determining damped unbalanced rotor response. Torsional response is sought only for train units comprising three or more coupled machines (excluding any gears). Experience suggests that the effect of other equipment in the train is normally not included in the lateral damped unbalanced response. Hence brief summary of various characteristics and a technique for analytical predictions of lateral behavior deserves attention by all.

The purpose of damped unbalanced rotor response is to identify critical speeds, associated amplification factors-AF (as per API standards AF greater than or equal to 2.5 is considered critical) and ability of rotor dynamics system to meet the separation requirements (margin of operating speed away from critical speed/s). The first step is ‘undamped’ unbalance response analysis for identifying mode shapes and critical speed-support stiffness map.  ‘Damped’ unbalanced response analysis then follows for each critical speed within the speed range of 0 % to 125 % of trip speed. Unbalance or side load is placed at the locations that have been determined by the undamped analysis to affect a particular mode most adversely. The magnitude of the unbalances is four times the value of U as calculated by U = 6350 W/N. The aim then is to identify the frequency of each critical speed, frequency-phase and response amplitude data, deflected rotor shape due to unbalance and bode plots to compare absolute shaft motion with shaft motion relative to the bearing housing (support stiffness <  3.5 times the oil-film stiffness).

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To verify the analytical model, subject to various practical requirements, an unbalanced rotor response test could be performed as part of the mechanical running test. The actual response of the rotor on the test stand to the same arrangement of unbalance as used in the analysis is the criterion for determining the validity of the damped unbalanced response analysis. Sample summary results generated using SoftInWay’s integrated tool for rotor dynamics AxSTREAM®, as shown below indicate a very good agreement between test results and analytical predictions, for both amplitude and frequency.

For further understanding the analytical procedure, testing to validate damped unbalanced rotor response and implications please view or contact us to learn more.

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