The collective model of an odd neutron in an axially symmetric deformed Woods–Saxon potential, coupled to a rotating core, and containing the full RPC and pairing corrections has been used to predict the full low lying rotational band spectrum of the nuclei with N = 91 to 97. Only three adjustable parameters were used in each nucleus to fit the complete spectrum. It was possible in several nuclei to obtain the correct level sequence and in most to confirm level assignments, and the adjusted parameters were in good agreement with accepted values. However, the accuracy of this method is insufficient, in most nuclei, to provide reliable predictions for as yet unidentified bands. The lack of good overall agreements in the low lying spectra of these nuclei confirms that the core shape parameters do change from one band to another.

In this study the global assumed mode method (GAMM) is used to analyze the dynamic behavior of a spinning Timoshenko beam subjected to a moving skew force with general boundary conditions. The moving skew force is usually caused by the frictional effect or the weight of the components. Considering three general geometric boundaries, i.e. hingedhinged, clamped-clamped, and clamped-hinged, the system equations of motion are derived by the Lagrangian approach combining with the GAMM. The transient response of the system due to a moving skew force is evaluated by the Runge-Kutta method. The numerical results show that the lateral deflections due to the skew force for the hinged-hinged boundary case are smaller than those in the case of a clamped-clamped or clamped-hinged boundary. And the axial deflections due to the skew force are larger in the case of a hinged-hinged boundary.

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The nonlinear dynamic behaviors of rotor-bearing system for ball end milling are studied in this paper. The rotor system is supported by bearings with nonlinear spring effects. The nonlinear cutting force can be calculated by using the Tlusty proposed 3/4 rule for chip thickness. The effects of design parameters on system dynamic behaviors including critical speeds and stability under the dynamic cutting forces are numerically investigated in the time domain. For linear system case or the nonlinear system with small depth-of-cut or feed per tooth under linear cutting force, the results show that the critical speeds of system are proportional to the corresponding system natural frequencies, but inversely to the cycle number of tool vibration multiplying by the number of flutes during the cutting time from one flute to another. With large depth-of-cut or feed per tooth, the differences of the critical speeds become larger between linear and nonlinear rotor systems and so are the dynamic responses at critical speeds milling. The critical speed under nonlinear cutting force milling is found to be always higher than that under linear cutting force. Furthermore, the chatter stability lobes are studied for various cutting conditions. The intervals between critical speeds increase gradually, and the axial depths of cut of nonlinear system for stability are lower than those of linear system.