Balancing
Vibration problems in present-day turbomachinery are as pressing andimportant as those encountered in theirdesign， manufacture， and general maintenance. Considerable amounts of precious energy go unused duringmachinery breakdowns， and the associated costs of machine downtime add to unproductive overheads. The modern trend of building high-speedengines requiresnew， dependable techniques to reduce vibrations.
Rotor Imbalance
Of the several factors that can cause vibrations in turbomachines， an unbalanced rotor stands at the top of the list. The lack of balance in a rotor may be caused by internal nonhomogeneity and/or external action. The general sources which can cause this problem are classified in the following categories:
1.
Dissymmetry
2.
Nonhomogeneous material
3.
Eccentricity
4.
Bearing misalignment
5.
Shifting of parts due to plastic deformation of rotor parts
6.
Hydraulic or aerodynamic unbalance
7.
Thermal gradients
A certain amount of the unbalance from factors such as misalignment，aerodynamiccoupling， and thermal gradients may be corrected at runningspeeds using modern balancing techniques; however， in most cases they are basic problems that must be initially corrected before any balancing can be
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done. Rotor mass unbalance from dissymmetry， nonhomogeneous material，distortion， and eccentricity can be corrected so that the rotor can run with-out exerting undue forces on the bearing housings. In balancing procedures only the synchronous vibrations (vibration in which the frequency is the same as the rotor rotating speed) are considered.
In a real rotor system the amount and location of unbalances cannot always be found. The only way to detect them is with the study of rotorvibration. Through careful operation， the amount and the phase angle of vibration amplitude can be precisely recorded by electronic equipment. The relation between vibration amplitude and its generating force for an uncoupled mass station is
F (t)二F ei且t (17-1)
F ei(且t-o)
(t)二F(17-2)
F
F二 叫Y 2 / 叫Y (17-3)
1 -且+i2三且
且 且
叫Y
2且
-1 三且
o二tan叫Y2 (17-4) 1 -且且
where:
F(t)二vibration amplitude
F
二generating force
F
二amplification factor
o二phase lag between force and amplitude
From Equation (17-4)， one will find that the phase lag is a function of the relative rotating speed且/且 and the damping factor三. (See Figure 17-1.) Theforce direction is not the same as the maximum amplitude. Thus， for max-imum benefit， the correction weight must be applied opposite to the force direction.
Figure 17-1. Typical phase lag between force and vibration amplitude chart. 中国航空网 www.aero.cn 航空翻译 www.aviation.cn 本文链接地址：燃气涡轮工程手册 Gas Turbine Engineering Handbook 3(15)
