Transient Response of Externally Pressurized Fluid Film Bearings©

Abstract

The transient response of a point-mass rotor supported i n turbulent and hydrostatic bearings under a variety of external loadc are preflow, externally pressurized fluid film bearings is presented. The equasented. Transient responses based on a n approximate model which lions of motion are solved numerically with local linearization at uses constant rotordynamic f m e coeflicienls are also included and each integration time step. The bearing reaction f m e s are calculated shown to compare well with the full nonlinear responses. The nonporn the numerical solution of unsteady bulk-flow equations includlinear model needs small time steps with large execution times, while ing fluid inertia, turbulence, variable fluid properlies and thermal the simple linear model provides reliable resulh i n a minute fraction energy transport. Examples fbr the transient response of damper seals of time. A x , AY = rotor accelerations [m/s2] C = radial clearance function [m] c~ = fluid specific heat u/kg 'K] Cxx, CXY. CYX, CYY = damping force (linear) coefficients [Ns/ml c d = orifice discharge coefficient D = 2 R; bearing diameter [m] Dx(r) 9 D Y (~) =journal (rotor) center displacements in inertial coordinates [m] do = orifice diameter [m] = turbulent flow friction factors at journal and bearing surfaces 1,. 1 = bearing axial leng~h, recess axial length [ml M = point rotor mass [kg] Mxx, MXY, M Y X , MYY = bearing (linear) inertia force coefficients [kg] p, p, = fluid pressure, recess pressure [~/ m~] 9, = external supply pressure [~/ m~) Re = (RC/p)*; nominal circumferential flow Reynolds number RJ3 RB = flow Reynolds numbers relative to journal and bearing surfaces ' j 7 rt J a,+j = 0.001375 bM = 500,000 , CM = lo4. x. Y eM = 3.0 Fx, I.; = bearing fluid film forces along {X,Y} axes 1, 1, [Nl 7; 7; H = C + D x ( t ) cos0 + D y ( t ) sine; film u thickness [m] ' -J.xP uY H, = recess depth [m] Kxx, KXY. KYX. Kw = bearing (linear) force stiffness coefficients "x. "Y [N/ml W X ( I ) , W Y ( I ) 147 = roughness depths atjournal and bearing surfaces [m] = (Re, %) circumferential and axial flow coordinates = time coordinate [s], initial time [s] = temperature, supply temperature [OK] = rotor imbalance displacement [m] = bulk-flow velocities in circumferential ( x ) and axial (y) directions [m/s] =journal (rotor) velocity components [m/s] = external loads applied on rotor [N] Downloaded by [Ryerson University Library] at 02:01 06 June 2016 I 3 7.

Dynamic analysis of a 2-lobe geometrically imperfect journal bearing system

“…Linearized dynamic coefficients are obtained by small perturbations in displacement and velocity about the equilibrium journal position. The linearized equation of motion of the journal in the non-dimensional form is expressed as 29,31,32…”

“…They used the nonlinear time transient method to compute the journal center trajectory. San Andres 32 compared the transient response analysis of a five pocket circular journal bearing operating in the turbulent regime obtained by using approximate model and nonlinear model. He observed that the nonlinear model gives accurate results on the expense of large computational time with small time step, whereas linear model needs less time step.…”

Dynamic modeling of hydrostatic guideway considering compressibility and inertia effect

“…Tichy [14] demonstrated that fluid inertia force had an effect on the dynamic characteristic of rotor systems through some experiments. Besides, the linear model of fluid film force was investigated by Andres [15]. He investigated the transient response of externally pressurized fluid film bearing and proposed an approximate linear model of fluid film force.…”

A Quasi 2D Method for the Rotordynamic Analysis of Centered Labyrinth Liquid Seals

“…The alternate way would be a non linear time integration of the whole system (rotor, bearings, seals, etc.) but it seems that forces and moments deduced by using this simplified model are accurate enough for rotordynamic simulation purposes (San Andres, 1997). At this stage, the problem could be described as the solution of an unsteady (but harmonically varying), turbulent, three-dimensional (3D) flow field.…”