The ring-speed ratio is a comprehensive dynamic index of floating ring bearing structure and operating parameters, which directly affects the dynamic behavior of the turbocharger rotor system. The cross stiffness of ring-speed ratio and floating ring bearing and the work of oil film force are analyzed. The influence of dynamic ring-speed ratio change on the vibration response of floating ring bearing was studied. The finite element model of the rotor-floating ring bearing system is constructed; its model parameters are verified through the measured critical rotor speed. Newmark integral method is used to analyze the nonlinear transient response. The results show that when the ring-speed ratio is between 0.18 and 0.24, the rotor is in a good operating state; when it increases from 0.24 to 0.36, the rotor vibration is dominated by frequency division, and the system will be less stable. The square of the ring-speed ratio is inversely proportional to the rotational speed of the journal where the subfrequency vibration occurs. It helps to know the nonlinear vibration by judging the journal speed when the rotor vibration occurs in subfrequency. The conclusion provides a reference for the mechanical dynamics design and intelligent management and maintenance of this kind of turbine rotors.
According to the diffraction integral theory of vector field and the pupil filtering method with a discrete complex amplitude, we present a tunable pupil filter to achieve and manipulate the focused vector fields with ultra-long depth of focus. The filter consists of a polarization rotator with two /2 wave plates and a discrete complex amplitude filter with six zones. Amplitude transmissions of these zones are different and increase along the radial direction. And every two adjacent transmitted zones have the opposed phases 0 and . With optimized cylindrical polarization (0 =52) and discrete amplitude, the generalized cylindrical vector field can be tightly focused into a three-dimensional (3D) flat-top field with an extended depth of focus (~10 ) by a high numerical aperture lens. For the main outermost zone and the other five inner zones, we analyze the intensity distributions of the three polarized components and the total polarized component in the focal region. We find that the axially and azimuthally polarized components are the major contributors. The outermost zone offers the central field of the focused field while the other five zones affect the side lobe more obviously. Through adjusting the included angle between the double wave plates, we can change the polarization states of the incident vector field and alter the structures of the focused fields among the 3D flat-top focused field, needle-like field, tube-like field and the other fields with intermediate form. Result obtained is superior to that of the past research for the adjustable freedom between these forms, and it reveals the dynamic relation between the evolved vectorial form of incident field and the vector structure of the focused field. Our work paves a way to achieve the controlled dynamical focused field with a long depth of focus. The needle-like field, tube-like field and the well-matched 3D flat-top focused field will meet the demand of applications in optical microscope, optical micro-manipulating, optical micromachining and so on.
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