Effects of Fluid Inertia on Finite-Length Squeeze-Film Dampers

Abstract

The itr/luelrce r,fll~rid i~lcrticc, on the SFD force response to circularadded mass coefficients remain invariant as the Reynolds number ccrr/ar(:!rl t t~o / i o~~v (f arbitrary aini~litude i s analyzed i n detail. For increases from small values to a moderate Reynolds number equal fii~itl! leir.gth, locally senled SFDs, integro-differential equations are to 10. A n approximate, finile-length, solution for the fluid-film cl(!i-ivc(l i~r tertr~v of the mean pow components. Numerical predicforces has been analytically obtained which accounts for the fluidtiow, u.siirg the finite-element method, show that the damping and inertia effeck as well as local end seal effects in symmetric SFD configurations. The approximate solution, strictly valid for small Presented as an Amerlcan Society of Lubrlcatlon Engineers Reynold numbers (Re<l), agrees well with the results from the paper at the ASMEIASLE Tribology Conference in Pittsburgh, Pennsyivanla, October 20-22, 1986 numerical solution for most SFD cotzfigurations and orbit radii ~l n a i manuscript approved June 2, 1986considered. NO~IENCI.K~UHE -Dij = Dij 63w/(p,~). Dimensionless inertia coefficient. = -,,,ze, ~~~~~~~~i center radial acceleration in circular sl~e = Dij 6l(p L R'). Dimensionless added mass coefficient. centerctl t~~o t i o n s [Lrp]. e = orbit amplitude for circular-centered motions [L] -(8,. = rr,./wzc = -E. Di~iiensionless journal center radial acFi = fluid film force in i-th direction [MLIT~] c e l e~~t i o n . f; = FiICf. Dimensionless fluid-film force in i-th direction. . A,;Hr,Ct = radial force coefficients for finite-length SFD (CCO) h = fluid-film thickness in squeeze film [L] 48 6 H = hlc = 1 + E cos0. Dimensionless fluid-film thickness. A t = -(loo1 + Q 11o1)le --Iincl~ 35 35 Iij -H -1 iri ii, dn. Momentum integrals 2 7 ~j r = -7 (1oo1 + 2 Q 1101 + Q~~~O I ) I E 35 !ilk = film thickness integrals. 27 ~r = --~( 1~~1 + 2 1121 + 1021)lb2 2x . j 35 sln 0 cos ' 0 dB, At,Bt,Ct = r;lngcntial force coefficients for finite-length SFD (CCO) 2x , = sin 0 ln(H) d0 2x I , = cos 0 in(H) d0Cij = tl;lmping cocfficicnt [MIT]. First subscript indicates force 1 lolo = -2, Itlo = -In (E) ,12 10 = -2/y2. 1rrU = -direction. Sccond subscrtpt denotes velocity direction. Cij A = Cij 6 " l ( d ) . Ditnensionless damping coefficient. 1 1 1 0 + 2(1 -171~) CIA = Local encl seal loss coefficient --CI = CLI(C1, cash(,\) + sinh(s)/h2}. Local end seal function Iy21 = ~7114, 1121 = 122112, 1021 = 0 Ibt. linite length locally sealcd SFDs. I1 = SI'D journ;~l d i ;~~n e t e r 12:+,) = -4(5 + e2)115, 1050 = 1130 = -413 11(j = incrti:~ force coefficient [MI. First subscript indicates J , = inertia vector components force direction. Second subscript denotes acceleration ke, kc = global resistance factors direction. L = squeeze-film damper length [L] 384 Downloaded by [LMU Muenchen] at 09:03 27 December 2014 Effects of Fluid Inertia o n Finite-Length Squeeze-Film Dampers 385 LID = squeeze-film damper -slenderness ratio L,,Lb,L, = functions of LID, A, CL sinh(s) La($) = DIL I)uD Z(5) d...

A Study of Lubricant Inertia Effects for Squeeze Film Dampers Incorporated into High-Speed Turbomachinery

“…For a π-film SFD model at small to moderate inertia effects, the contribution of the inertia forces to the radial force component is a positive value. This positive contribution is added to the negative viscous radial forces and reduces the magnitude of the radial force component relative to the inertialess model, which diminishes the likelihood of bi-stable rotor operation [16]. Furthermore, the magnitude of the inertialess radial forces is negative, meaning that the force is directed towards the center of the bearing (i.e., inwards).…”

“…Subsequently, the terms in the equations are approximated by assuming that the shape of the velocity profiles is not strongly influenced by the inertia forces [15]. San Andres and Vance [16] implemented the momentum approximation technique to determine the force coefficients for finite-length SFDs executing CCOs. They included convective fluid inertia as well as end seal effects in the calculations.…”

“…This perturbation technique separates the flow equations into a set of inertialess equations that are characterized by using the classic Reynolds equation, and a set of first-order inertial correction equations. According to [16,17,21] it is suggested that the first-order perturbation is applicable for SFD flow regimes with Re ≤ 25. Finally, the energy approximation [14,22] firstly develops the expressions for the fluid kinetic energy.…”

Effects of Nanoparticle Enhanced Lubricant Films in Dynamic Properties of Plain Journal Bearings at High Reynolds Numbers

“…They have gotten a comprehensive type of Reynolds equality counting the special contribution of the inertial convection. Averaged inertia technique of was correspondingly described by Szeri et al [31] and is useful for the case of dampers with squeeze film where this effort protracted by San Andres and Vance [32]. In Ref.…”

Measurements of Pressure Distributions and Force Coefficients in a Squeeze Film Damper Part I: Fully Open Ended Configuration

“…Presented as a Soclety of Tribologlsts and Lubrlcatlon Englneem paper at the ASMEISTLE Trlbology Conference in Toronto, Ontario, Canada, October [8][9][10]1990 Final manuscript ~pproved May 25,1990 = SF11 radial clcar;~nce = p o~l i ' l~ t1;tmping coefficient conversion factor = ~LH''IC inertia coefficient conversion factor = p w H "~~~' force conversion factor = w o~'~~' pressure conversion factor = Cp . HP = po'R2 pressure conversion coefficient = diniensionless direct damping coeflicients = -j;l~, ~ior~nalizcd by ) L~9~/ @ = d;tniper .journal diameter = dimensionless direct inertia coefficients = /A€, iior11i;tlized by p~S~~~C S = dinicnsionless radial and tang.…”