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Rotating Machinery Vibration 2011 Part 9

Tham khảo tài liệu 'rotating machinery vibration 2011 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 180 Chapter 5 equations is a considerable abridgement from the full Navier-Stokes equations for this problem obtaining general solutions is nevertheless still a formidable task given that the BFM equations are coupled nonlinear partial differential equations. However based on computational solutions plus experiments over a static eccentricity ratio e C range from zero to 0.9 strong arguments are made that for practical purposes the seal rotor vibration coefficients expressed in Eq. 16 are nearly constant out to e c 0.3. The mitigating factors that make static eccentricity of less importance to ungrooved annular seals than to journal bearings are that a seal clearances are typically more than twice the clearances of the journal bearings which are the primary enforcers of rotor centerline static position and b turbulent flow inherently acts to desensitize the circumferential variation of pressure to static eccentricity because of the corresponding reduction of the local Reynolds number where the seal film thickness is smaller and increase where it is larger. This second effect is similar to a hypothetical circumferentially cyclic variation in viscosity oc h with the maximum viscosity at the maximum film thickness and the minimum viscosity at the minimum film thickness. Such a phenomenon in a journal bearing would obviously desensitize it to static eccentricity. It would thus appear that the isotropic model of Eq. 16 is justified for seals much more so than for journal bearings. Childs 10 presents in considerable detail the formulation for extracting annular seal rotor vibration characteristic coefficients from the BFM. Perturbation pressure solutions Ap o zp are formulated and obtained for a small circular rotor orbital motion of radius e C about the centered position i.e. about the position for which seal flow is rotationally symmetric. Integration of the perturbation pressure distribution similar to Eqs. 2 for journal bearings yields the orthogonal components of .