The existence of unbalance in a rotor system may be in continuous formor discreteform， as shown in Figure 17-2. Ascertaining an exact distributionis an extremelydifficult， if not impossible， task by today"s techniques.
For a perfectly balancedrotor， not only should the center of gravity belocated at the axis of rotation， but also the inertial axis should coincide with the axis of rotation shown in Figure 17-3. This condition is almost impos-sible to achieve. Balancing may be defined as a procedure for ad.usting the mass distribution of a rotor so that the once-per-revolution vibration motion of the .ournals or forces on the bearings is reduced or controlled. Balancing functions can be separated into two ma.or areas: (1) determining the amount and location of the unbalance and (2) installing a mass or masses equal to
Figure 17-.. Balanced rotor.
the unbalance to counteract its effects or removing the mass of the unbal-ance exactly at its location.
Static techniques to determine unbalance can be performed by setting a rotor on a set of frictionless supports; the heavy point of the rotor will havea tendency to roll down. Noting the location of this point， the resultant unbalance force canbe found， and the rotor can be statically balanced. Static balancing makes the center of gravity of the rotor approach the centerline of two end supports.
Dynamic balancing can be achieved by rotating the rotor either on its own supports or on an external stand. .nbalance can be detected by studying rotor vibration with various types of probes or sensors. Balancing is then achieved by placing correction weights in various planes that are perpen-dicular to the rotor axis. The weights reduce both the unbalanced forces and unbalanced moments. Placing the correction weights in as many planes as possible minimi.es the bending moments along the shaft introduced by the original unbalance and/or the balance correction weights.
Flexible rotors are designed to operate at speeds above those correspond-ing to their first natural frequencies of transverse vibrations. The phase relation of the maximum amplitude of vibration experiences a significant shift as the rotor operates above a different critical speed.Hence， the unbalance in a flexible rotor cannot simply be considered in terms of a force and moment when the response of the vibration system is in-line (or in-phase) with the generating force (the unbalance).Consequently， the two-plane dynamic balancing usually applied to a rigid rotor is inadequate to assure the rotor is balanced in its flexible mode.
The best balance technique for high-speed flexible rotors is to balancethem not in low-speed machines， but at their rated speed. This is not alwayspossible in the shop; therefore， it is often done in the field. New facilities are being built that can run a rotor in an evacuated chamber at running speedsin a shop. Figure 17-4 shows the evacuation chamber， and Figure 17-5 shows the control room.
High-speed balancing should be considered for one or more of the follow-ing reasons:
1. The actual field rotor operates with characteristic mode shapes sig-nificantly different than those that occur during a standard produc-tion balance.
2. Flexible rotor balancing must be performed with the rotor whirl configuration approximating the mode in question. The operating speed(s) is in the vicinity of a ma.or flexible mode resonance (dampedcritical speed). As these two speeds approach one another， a tighter
Figure 17-4. Evacuation chamber for a high-speed balancing rig. (Courtesy ofTransamericaDelaval， Inc.)
Figure 17-5. Control room for high-speed balancing rig. (Courtesy of TransamericaDelaval， Inc.)
balance tolerance will be required. Those designs that have a low rotor-bearing stiffness ratio or bearings in the vicinity of mode nodal points are of special concern.
3. The predicted rotor response of an anticipated unbalance distribution is significant. This type of analysis may indicate a sensitive rotor which should be balanced at rated speed. It will also indicate which components need to be carefully balanced prior to assembly.
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