Squeeze film dampers introduce nonlinear motion dependent damper forces into otherwise linear rotor bearing systems, thereby considerably complicating their analysis. Noncircular orbit type dampers, such as unsupported or uncentralized dampers, have generally necessitated transient solutions, which are computationally prohibitive for design studies of large order systems, particularly for systems with low damping. By utilizing harmonic balance with appropriate condensation, it is possible to considerably reduce the number of simultaneous nonlinear equations inherent to this approach. The stability (linear) of the equilibrium solutions may be conveniently evaluated using Floquet theory, particularly if the damper force components are evaluated in fixed, rather than rotating, reference frames. The versatility of this technique is illustrated on systems of increasing complexity with and without damper centralizing springs. Of particular interest, is its applicability to unsupported systems illustrating how such systems can lift off and, with further increase in speed, the damper forces can be linearized about the orbit center.
This paper investigates squeeze film bearings supporting a centrally preloaded rigid rotor mounted in antifriction bearings. Assuming the short bearing approximation and isothermal, incompressible lubrication, design data are presented for such a system over a wide range of operating conditions. Design considerations include the possibility of undesirable operation modes, the maximum unbalance for which the squeeze film support is superior to the rigid mount, the transmissibility at design speed and the forces transmitted during start-up. It is shown that unbalance force attenuations by factors of three or more are a practical possibility with a consequent increase in antifriction bearing life. A numerical example is included.
Experimental obseruations on unpressurized dynamically loaded compressible fluid. Assuming this to be a homogeneous gas-liquid hydrodynamic bearings and squeeze-film dampers indicate that caumixture, with density and viscosity dependent on pressure, the load itation bubbles, once formed, do not completely redissolve upon the capacity of squeeze-film dampers is compared with that obtained reappearance of positive pressures. Iratead, one is left with a spongy using hitherto adopted cauitation models which assume an incompressible lubricant with the fluid-film pressures being set to the saturated vabor bressure (SVP) of the lubricant whenever the firessure a ' , , . , Presented at the 40th Annual Meeting In Vegas, Nevada falk below the SVP. T o save computation effort, a short bearing May 6-9, 1985 approximation is derived for the compressible Reynolds equation, -. Final manuscript approved January 11, 1985 A = constant, (lV,dNe)H + Po a = unbalance eccentricity C = radial clearance D = bearing diameter e = eccentricity F,t = film force -F = F C ' I (~~R L~R ) H = Henry's constant h = film thickness -11 = hlC K = adiabatic exponent L = bearing length M = ratio of molecular weights,
Assuming the short bearing approximation and symmetric motions, the stability of the steady-state synchronous operation of centrally preloaded single-mass flexible rotors supported in squeeze-film bearing dampers is theoretically investigated. The stability regions are depicted over a wide range of system parameters and allow for easy determination of the stability of existing steady-state design data. The influence of rotor flexibility, rotor speed, bearing dimensions, lubricant viscosity, rotor mass distribution, and rotor unbalance on rotor-bearing system stability may be readily seen. In the absence of pressurization, instability regions were possible even with relatively high support damping, though no instability was indicated for speeds below the support natural frequency, or for bearing eccentricity ratio <0.4 at any speed. Pressurization of the lubricant supply was found to stabilize the system over the whole range of parameters investigated, regardless of unbalance, which would then be limited only by the bearing clearance. Data are presented which enable the minimum supply pressure to ensure full film lubrication to be conveniently determined.
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