Page 122 - Improving Machinery Reliability

94 Improving Machinery Reliability

can contribute to rotordynamic instabilities, which will be discussed later. If the
critical speeds are in the area of low support stiffness (stiff shaft region), the
critical speeds are strongly dependent upon the bearing stiffness and damping
parameters and the critical speeds can shift considerably.
3. The mode shape of the critical speed. The mode shapes are used to assess the
response of the rotor to potential unbalances. For example, a rotor that has a
conical whirl mode (second critical) would be sensitive to coupling unbalance,
but not strongly influenced by midspan unbalance.

Seal Stiffness and Damping Coefficients. In addition to the bearing stiffness and
damping effects, the seals and labyrinths can influence the rotor critical speeds and
response. Generally, oil ring seals are designed to float with the shaft since they are
held in place by frictional forces dependent upon the pressure balance force and the
coefficient of friction. Lubrication and seal oil systems are discussed elsewhere.6 If
the seals do not float with the shaft and lock up, they can add additional stiffness and
damping. In such cases, they are treated as additional bearings in the rotordynamic
calculations. The seal stiffness and damping coefficients are calculated by assuming
that the seals are locked at some eccentricity ratio and that the seals are non-cavitat-
ing. Typical values of seal stiffness and damping for centrifugal compressors will be
less significant than the bearings; however, in some designs they can change the
rotor response characteristics.
Rotor Response to Unbalance. Computer programs are available today that can
calculate the elliptical shaft orbit at any location along the length of a rotor for vari-
ous types of bearings, pedestal stiffnesses, pedestal masses, seals, labyrinths, unbal-
ance combinations, etc. These programs are used to determine the installed rotor’s
response to unbalance and accurately predict the critical speeds over the entire range
of variables. The actual critical speed locations as determined from response peaks
caused by unbalance are strongly influenced by the following factors’?

1. Bearing direct stiffness and damping values
2. Bearing cross-coupled stiffness and damping values
3. Location of the unbalance
4. Location of measurement point
5. Bearing support flexibility

To illustrate the sensitivity of the peak response critical speeds for the compressor
whose critical speed map is given in Figure 3-2, the responses due to coupling unbal-
ance and midspan impeller unbalance were calculated. The allowable vibration
amplitude (API 617) for this compressor was 1.03 mils peak-to-peak since its maxi-
mum continuous speed was 1 1,300 rpm.
The normal unbalance used in an analysis produces a force equal to 10% of the
rotor weight. Usually, rotor response to unbalance calculations are made for midspan
unbalance, coupling unbalance, and moment type unbalance. An unbalance equal to a
force of 5% rotor weight is usually applied at the coupling to excite the rotor. For
moment unbalances, an unbalance equal to the 5% rotor weight is used at the cou-