The stiffness and damping coefficients of an elastically supported gas foil bearing are calculated. A perfect gas is used as the lubricant, and its behavior is described by the Reynolds equation. The structural model consists only of an elastic foundation. The fluid equations and the structural equations are coupled. A perturbation method is used to obtain the linearized dynamic coefficient equations. A finite difference formulation has been developed to solve for the four stiffness and the four damping coefficients. The effect of the bearing compliance on the dynamic coefficients is discussed in this paper.

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A theoretical model is developed to investigate the effect of Coufoundation. The Puid is modeled with the compressible Reynolds lamb damping i n the sub-foil structure of a foil bearing. Equivalent equation. A perturbation approach is used to deternline the bearing viscous damping is found for the Coulomb friction. The foil is stqfness and damping coefjicients from the coupledfiuid-structural treated as a continuous perfectly extensible surface on a n elastic model. Results are presented for foil bearings with a n elastic foundation constructed of a corrugated foil. Foil Bearing, J o u r n a l Final manuscript approved February 4, 1993 = equivalent viscous damping of the iCh bump bco --normalized damping of the elastic Po foundation -cwBrnn -normalized damping coefficients P, r2 of the bearing; m,n = x o r y = nominal bearing clearance = frictional coefficient = normalized eccentricity of unbalanced mass = Young's modulus = Coulomb friction force of the irh bump h = -= normalized lubricant film clearance = perturbation components of h = horizontal force at the ith bump = second moment of inertia per unit bearing length kc -----normalized stiffness of the elastic Po foundation -cKmn --= normalized stiffness coefficients of pa? the bearing; m,n = x o r y = bump span = bearing Length = number of bumps in contact with the top foil i, -_ -= normalized lubricant film pressure Pa Pa = ambient pressure , , ; = perturbation components o f f r = nominal bearing radius 1 = vt = normalized time variable i = 14 = normalized foil deflection 6 , , , = perturbation components of li v = horizontal displacement of the bump end Wi = vertical load at the it" bump Z ---= norrnalizd axial coordinate L a Pa ---= bearing compliance ck 4 1 F f 2 = --c1m --= average sub-foil damping P Z P n f i Y ---' = whirl frequency ratio W AX, AY = normalized perturbations E = bearing eccentricity ratio 0 = circumferential coordinate 6p,0r2 A --bearing number P,c2 = lubricant viscosity = whirl frequency = bump radius = dissipated energy = half bump arc angle = rotor angular velocity Downloaded by [Johann Christian Senckenberg] at 05:25 28 August 2014

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