Critical
Speeds in Rotating Machinery
Mohsen Nakhaeinejad, Suri Ganeriwala
SpectraQuest Inc., 8201 Hermitage Road, Richmond, VA 23228
Published: October 2008
Abstract
Critical
speeds of rotating machinery in presence of different couplings
and bearing faults are studied. A rotating
machine including motor, coupling, rolling element bearings, shaft
and disks was modeled in XLRotor, a powerful software
for rotordynamics analysis. Effects of rotor/disks configurations
and coupling stiffness on critical speeds were studied.
The SpectraQuest Machinery Fault Simulator (MFS) Magnum
was used to conduct series of experiments with four types of coupling:
beam, lovejoy, gear and rigid couplings with different
shaft/disk configurations. Also, bearing faults were introduced
to the machine and the change of critical speeds was
observed. Observations validate the XLRotor model and show the
critical speed behavior of the MFS machine.
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Introduction
All objects exhibit at least
one natural frequency. This is the frequency at which the object
will vibrate if struck once. The classic example is a bell or tuning
fork. Resonance occurs when the object is repeatedly excited at
the natural frequency. Physically, energy is confined within the
boundaries of the structure and cannot escape or dissipate quickly,
creating standing wave deformations at the natural frequencies.
The standing waves displaying the actual motion at a natural frequency
are known as mode shapes. Since resonance results in large amplitudes
that can be both noisy and destructive, good machine design calls
for avoiding such conditions. As a result, in designing a machine,
modeling and calculations are performed to estimate the natural
frequencies of the various parts and the entire structure. With
this knowledge, the machine design can be altered during the design
stages to avoid resonant conditions.
The expression critical speed or simply critical applies to
a rotating system, particularly shaft and rotors, as opposed
to stationary structures. The critical speed of a rotating
system occurs when the rotational speed matches a natural frequency.
Resonance occurs as the rotating speed passes through each
natural frequency. Minimizing rotational unbalance and unnecessary
external forces are very important to reducing the overall
forces, which initiate resonance. The lowest speed at which
a natural frequency is encountered is called the first critical.
As the speed increases, additional critical speeds may be observed.
For example, there might be second and third criticals. Critical
speeds significantly greater than the maximum operating speed
of the machine are of less interest and importance.
Since the real dynamics of machines in operation is difficult
to model theoretically, calculations are based on the simplified
model which resembles the various structural components. Obtained
equations from models can be solved either analytically or
numerically. Also, Finite Element Methods (FEM) is another
approach for modeling and analysis of the machine for natural
frequencies. Resonance tests to confirm the precise frequencies
are often performed on the prototype machine and then the design
revised as necessary to assure that resonance does not become
an issue. In addition, resonance testing may be required when
troubleshooting the machine or components that experience unexpected
failures or short lives. Transient or startup/coastdown test
which is used in this study is an excellent way to quickly
scan the whole machine
for natural. The machine starts up and accelerates to a maximum
speed and coast down to the rest with constant acceleration
and deceleration rates. The machine is excited by itself as
the dynamic forces come into play. Vibration signals are collected
and the high spectral peaks represent the natural frequencies.
The
objective of this technical note is to study the critical
speeds in rotating machinery. To achieve this goal, a rotating
system including motor, shaft, disks, coupling and rolling
element bearings is considered and the XLRotor is used for
modeling and analysis. The stiffness and damping associated
with the rolling element bearings are calculated in software
and the whole rotating system is solved for damped critical
speeds. Experiments were conducted on a SpectraQuest’s
Machinery Fault Simulator (MFS) Magnum to validate the XLRotor
data. Also, changes of critical speeds due to locations of
disks on the shaft, type of coupling and faulted bearings were
studied by experiments.
Fig 1: Effect of bearing faults on the
1st (left) critical speed. Inner race and outer race faults are
introduced on the left bearing.
Fig 2: Effect of bearing faults on the
2nd (right) critical speed. Inner race and outer race faults are
introduced on the left bearing.
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