4. The available balance planes are far removed from locations of expected unbalance and are thus relatively ineffective at the operating speed. The rule of balancing is to compensate in the planes of unbal-ance when possible. A low-speed balance using inappropriate planes has an adverse effect on the high-speed operation of the rotor. Inmanycases， implementation of an incremental low-speed balance asthe rotor is assembled will provide an adequatebalance， since com-pensations are being made in the planes of unbalance. This is particu-larly effective with designs incorporating solid-rotor construction.
5. A very low-production balance tolerance is needed to meet rigorous vibration specifications. Vibration levels below those associated with a standard production-balanced rotor are often best obtained with a multiple-plane balance at the operating speed(s).
6. The rotors on other similar designs have experienced field vibration problems. Even a well-designed and constructed rotor may experience excessive vibrations from improper or ineffective balancing. This situation can often occur when the rotor has had multiple rebalances over a long service period and thus contains unknown balance dis-tributions. A rotor originally balanced at high speed should not be rebalanced at low speed.
A wealth of technical literature concerning balancing has been published. Various phases of a variety of balancing procedures have been discussed in these papers. .ackson and Bently discuss in detail the orbital techniques.Bishop and .ladwell， as well as .indsey， discuss the modal method of balan-cing. Thearle， .egrow， and .oodman discuss early forms of influence coeffi-cient balancing. The author， Tessar.ik， and Badgley have presented improved forms of the influence coefficient method that provide for the balancing of flexible rotors over a wide speed range and multiple-bending critical speeds.
Practical applications of the influence coefficient method to multiplane， multispeed balancing are presented by Badgley and the author. The separate problem of choosing balancing planes is discussed at some length by DenHartog， .ellenberger， and Miwa for the ( N +2)-planemethod， and by Bishop and Parkinson in the N-plane method.
Balancing Procedures
There are three basic rotor balancing procedures: (1) orbital balancing，
(2) modal balancing， and (3) multiplane balancing. These methods are sub-
.ect to certain conditions that determine their effectiveness.
Orbital Balancing
This procedure is based on the observation of the orbital movement of theshaft centerline. Three signal pickups are employed， of which two probes measure the vibration amplitudes of the rotor in two mutually perpendicular directions. These two signals trace the orbit of the shaft centerline. The third probe is used to register the once-per-revolution reference point and is called the keyphazor. A schematic arrangement of these probes is shown in Figure 17-6.
The three signals are fed into an oscilloscope as vertical-， hori.ontal-， and external-intensity marker input. The keypha.or appears as a bright spot on the screen. In cases where the orbit obtained iscompletely circular， the maximum amplitude of vibration occurs in the direction of the keypha.or.To estimate the magnitude of the correction mass， a trial-and-error processis initiated.认ith the rotor perfectlybalanced， the orbit finally shrinks to a point. In the event of an elliptic orbit， a simple geometric construction allows for the establishment of the phase location of the unbalance (force).Through the keypha.orspot， a perpendicular is dropped on the ma.or axis of the ellipse to intersect its circumcircle as shown in Figure 17-7. This intersecting point defines the desired phase angle. Correction mass is found as described earlier. It is important to note that for speeds above the firstcritical， the keypha.or will appear opposite the heavy point.
In the orbitalmethod， the damping is not taken into account. Therefore，inreality， this method is effective only for very lightly damped systems.Further， as no distinction is made between the deflected mass and thecentrifugal unbalance due to its rotation， the balance weights are mean-ingful only at a particular speed. The optimum balancing plane considered is the plane containing the center of gravity of the rotor systemor，alternately， any convenient plane that allows for the orbit to be shrunk to a spot.
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