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In this disseration, the dynamic behaviors and characteristics
of a rotor containing transverse cracks are analyzed by using
the transfer matrix method(TMM) in distributed parameter system.
Two subjects are studied. The first oneis to investigate the
eigenvalue problem for an unrotating and rotating open-cracked
shaft with disk by means of modified TMM and propose a diagnosis
methodto determine the positions and depth of the cracks in
rotor. The second is to develope a new method to determine the
dynamic behavior of a general rotor bearing system with open/
close cracks, and provide more diagnostic informationfor
vibrational monitoring on line. Numerous works are stuied
separately. First, The natural frequencies as wellas the
corresponding mode shapes of unrotating cracked shaft are
solved.Verification of this approach by comparison with some
already existingpublished experimental data is presented. The
position of the crack can bepredicted by comparing the
fundamental mode shapes of the shaft with andwithout a crack.
Furthermore the depth of the crack can be obtained by thechange
of natural frequency of the shaft with and without a crack.
Second, the natural frequencies as well as the corresponding
mode shapes of arotating cracked rotor are solved. To validate
the TMM applied to a crackedrotor, a comparison is made with the
3-dimensinal FEM. Additionally, theeffects of both relative
distances along shaft axis and/or orientations ofcracks of
multi-cracked rotors are considered in free vibration analysis.
Analgorithm, numerical examples and detection of cracks are
presented. Third, the steady state response to the gravity and
unbalance force of ageneral rotors bearing system with open and
open/close crack, are analyzed bythe TMM. The nonlinear equation
are linearized by using the truncated Fourierexpansion as well
as the additional flexibility of the open/close crack.
Itssolutions are given approximately with static deflection, the
1X, 2X, ..., nXwhirling vibrations. By using the concept of
harmonic balance method in solvingnonlinear dynamic problem, the
steady state response of cracked rotor subjectedunbalance and
gravitational load are determined. The results show
thedescrepancy of resonant response and phase lag between open
and open/close-crack rotors, the difference of orbits near the
main critical and subcriticalspeeds between cracked uncracked
rotors. Moreover, the multi-cracked rotorscomposed of round and
square cross-sectional shaft are also discussed inseveral
respects. Finally, a method of identification of crack positions
byinspecting the sharply changed curves of deviation of whirling
shapes betweencracked and uncracked rotor is proposed. The
modified TMM proposed by this study can be well applied to
multi-stepped,multi-disk and multi-crack rotor with various
supporting boundary conditions.No matter how may segment of a
rotor specified, the order of resultant transfermatrix of whole
rotor system is always fixed. The memory requirements are
thenmuch reduced in comparision with those of classical FEM.
Therefore the methodprposed in this investigation are economical
and high efficiency.
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