Page 196 - Subyek Teknik Mesin - Forsthoffers Best Practice Handbook for Rotating Machinery by William E Forsthoffer

Be st Practice 3 .18 Compressor Best Practices
B.P. 3.18. Supporting Material natural frequency, it is said that the rotor is operating at its
critical speed. The critical speed of a rotor is commonly desig-
The term ‘critical speed’ is often misunderstood. In nature, all nated as NC and the corresponding natural frequencies or
things exhibit a natural frequency. This is defined as that fre- critical speeds are: NC 1 ,NC 2 ,NC 3 , etc.
quency at which a body will vibrate if excited by an external Every turbo-compressor that is designed must have critical
force. The natural frequency of any body is a function of its speeds of the rotor system determined prior to manufacture. In
stiffness and mass. As mentioned, for a body to vibrate, it must this section, we will follow the procedure for the determination
be excited. A classical example of natural frequency excitation is of the necessary parameters to define a rotor system’s critical
the famous bridge ‘Galloping Gerty’ in the state of Washington. speed. The procedure is commonly known as determination of
That bridge vibrated to destruction when its natural frequency rotor response. Figure 3.18.1 is a representation of a critical
was excited by prevailing winds. speed map for a rotor system.
In the case of turbo-compressor rotors, their natural fre- It should be understood that all stiffness values are ‘calcu-
quency must be excited by some external force to produce lated’ and will vary under actual conditions. As an exercise,
a response that will result in increased amplitude of vibration. determine NC 1 ,NC 2 and NC 3 for the horizontal and vertical
One excitation force that could produce this result is the speed directions for each bearing in Figure 3.18.1 (assume bearing 1
of the rotor itself. Thus the term ‘critical speeds’. The term and 2 stiffness are the same)
‘critical speed’ defines the operating speed at which a natural Critical speed Horizontal (X) Vertical (Y)
frequency of a rotor system will be excited. All rotor systems
have both lateral (horizontal and vertical) and torsional (twist NC 1 3,300 rpm 3,000 rpm
about the central shaft axis) natural frequencies. Only lateral NC 2 9,700 rpm 8,000 rpm
critical speeds will be discussed in this section. NC 3 16,000 rpm 15,000 rpm
In the early days of rotor design, it was thought that the rotor
system consisted primarily of the rotor supported by the bear- Based on a separation margin of 20% from a critical speed,
ings. This led to the assumption that only the stiffness of the what would be the maximum allowable speed range between
rotor supported by rigid bearings needed to be considered in the NC 1 and NC 2 in Figure 3.18.1?
analysis of the natural frequency. Countless machinery prob-
lems have proven this assumption to be false over the years. The - Maximum speed 6,600 rpm
concept of the ‘rotor system’ must be thoroughly understood. - Minimum speed 4,000 rpm
The rotor system consists of the rotor itself, the characteristics Remember, changing of any value of support stiffness will
of the oil film that support the rotor, the bearing, the bearing change the critical speed. Support stiffness, in lbs/inch, is
housing, the compressor case that supports the bearing, com- plotted on the x axis. The primary components of support
pressor support (base plate), and the foundation. The stiffness stiffness in order of decreasing increasing influence are:
and damping characteristics of all of these components together
result in the total rotor system that produces the rotor response - Oil support stiffness
to excitation forces. - Bearing pad or shell
We will examine a typical rotor response case in this section - Bearing housing
and note the various assumptions, the procedure modeling, the - Bearing bracket
placement of unbalance, the response calculation output and - Casing support foot
discuss the correlation of these calculations to actual test results. - Baseplate
- Foundation
Note that this analysis of the critical speed does not include
Critical speeds oil film damping. It is common practice to first determine the
‘undamped critical speeds’ to allow for necessary modifications
The natural frequency of any object is defined by the to the rotor or support system. This is because the effects of
relationship: stiffness on the location of critical speed are significantly greater
K
r ffiffiffiffiffi than damping. Figure 3.18.1 shows four (4) distinct critical
F NATURAL ¼ speeds. Operation within 20 of actual critical speeds is to be
M
avoided. Also plotted are the horizontal (x) and vertical (y)
Where: K ¼ Stiffness bearing stiffness for each bearing. Note that these values vary
M ¼ Mass with speed and are the result of changes in the oil stiffness.
When excited by an external force, any object will vibrate at Therefore, a change in any of the support stiffness components
its natural frequency. If the frequency of the exciting force is noted above can change the rotor critical speed. Experience has
equal to the natural frequency of the object, and no damping is shown that critical speed values seldom change from 5% of
present, the object can vibrate to destruction. Therefore, if the their original installed values.
frequency of an exciting force equals the natural frequency of If a turbo-compressor with oil seals experiences a signifi-
an object, the exciting force is operating at the ‘critical cant change in critical speeds, it is usually an indication of
frequency’. seal lock-up. That is, the seal does not have the required
Rotor speed is one of the most common external forces in degrees of freedom and supports the shaft acting like
turbo-machinery. When the rotor operates at any rotor system abearing.Sincethesealspanislessthanthe bearingspan,

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