Tham khảo tài liệu 'rotating machinery vibration 2011 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 4 Chapter 1 eral expression for the motion of the unforced underdcunped system is commonly expressed in any one of the following four forms. sin Ct dt ự or sin wdt ự s v t Xea OR cos dt or cos wdt dv 5 X single-peak amplitude of exponential decay envelope at t 0 wd wnor damped natural frequency phase angle f ột ộc 90 and ị ộc yield same signal a dim real part of eigenvalue for underdamped system n y khn undamped natural frequency i V 1 . Self-Excited Dynamic-Instability Vibrations The unforced underdamped system s solution as expressed in Eq. 5 provides a convenient way to introduce the concept of vibrations caused by dynamic instability. In many standard treatments of vibration theory it is tacitly assumed that c 0. However the concept of negative damping is a convenient way to model some dynamic interactions that tap an available energy source modulating the tapped energy to produce so-called self-excited vibration. Using the typical later shown multi-degree-of-freedom models employed to analyze rotor-dynamical systems design computations are performed to determine operating conditions at which self-excited vibrations are predicted. These analyses essentially are a search for zones of operation within which the recd part a of any of the system s eigenvalues becomes positive. It is usually one of the rotor-bearing system s lower frequency corotational-orbit-direction vibration modes at a natural frequency less than the spin speed frequency whose eigenvalue real part becomes positive. That mode s transient response is basically the same as would be the response for the 1-DOF system of Eq. 3 with c 0 and c2 4km which produces a 0 a positive real part for the two complex conjugate roots of Eq. 4 . As Fig. 3 shows this is the classic self-excited vibration case exhibiting a vibratory motion with an exponential growth envelope as opposed to the exponential decay envelope for c 0 shown in Fig. 2. The widely accepted fact that safe reliable operation of rotating .
