2. The mode shapes (problem unbalance distributions) of the rotor at the criticals.
3. The most probable distribution of unbalance in the finally installedrotor， considering manufacturing tolerances， balancing residuals afterlow-speedbalance， assembly tolerances， etc.
4. The
response of the entire rotor-bearing system to thisunbalance，considering damping in bearings，.oints， dampers， etc.
5. Provisions for eliminating ..unbalance distribution problems"" at eachmanufacturingstep， whether by machining， low-speed balancing， or high-speed balancing.
6.
Provisions for future balancing of the final rotorassembly， when and if necessary.
All of the previous steps are now commercially available at a small fraction of the cost of a replacement rotor.
Component balancing in the factory is required for a very simple reason: the mass center of the component design (or the mass center of each section of long components) does not lie on the intended axis of rotation. The problem occursbecause of machining tolerances， void inclusions in themetal， etc. As a result， the component is sub.ected to one or more balancingsteps. In the balancing operation， rotor unbalance sensitivities (interference coefficients) are determined for a sampling of rotors and stored.
Design of the production-rotor balancing process begins with an analyt-ical optimi.ation process， usually best conducted during system design. An unbalance-response computer program is coupled with a balancing com-puter program to calculate vibration amplitude as a function of unbalance.These programs yield the optimum location of vibration sensors， correctionplanes， and optimum balance speeds. Multiplane balancing of the rotor assembly may be done conveniently in a balancing fixture that simulates dynamically the actual environment in which the rotor will operate. A drivemotor is required， and possibly a vacuum system， depending on rotor con-figuration and balancing speed.
It is important that final balancing corrections not be made on any components that are later to be replaced under field operation conditions.Items such as turbine wheels， which are to be replaced as balanced itemsduring field maintenance， obviously cannot be removed and replaced with-out altering the assembly balance if they have been utili.ed for balance corrections. The balancing process design should therefore also be integrated with the maintainability design for best results.
Once the rotor system has been installed， downtime is the key cost asso-ciated with vibration. For example， it is not unusual for lost production costs to be measured in tens of thousands of dollars per day for a chemical plantcompressor. Obviously， shutting down the machine to rebalance the rotor is a decision not taken lightly. The optimum approach is to determine cor-rections while the machine isrunning， and shutdown only long enough to install the trim balance weights. The multiplane balancing procedure permits this procedure to be done with ease after the rotor sensitivities have been measured.
In field balancing (trim balancing)， however， rotor speed and system temperatures are the key considerations. It will often be difficult to control speed because of process considerations; system temperatures may requirehours， or evendays， to stabili.e. Vibration should be recorded each time the unit is stopped for trial weight insertion to determine the length of timerequired for thermal stabili.ation. Consideration of critical speed locations，vibratory modeshapes， and the like obtained by a separate rotor dynamics study can also greatly improve the results by providing better guidance to the best sensor and balancing plane locations.
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