DYNAMIC RESPONSE OF GAS-LUBRICATED JOURNAL BEARING SYSTEMS

Abstract

The primary objective of the investigations of this thesis is the assessment of the linearized stability charts of the gas-lubricated journal bearing systems. Such investigations concerning the oil-lubricated as well as the gas-lubricated journal bearing systems, have been reported extensively in the published literature. The conventional approach toward such investigations has been based on the experimental and/or theoretical delineation of the motion of a uniformly rotating journal subjected to some prescribed disturbance in the transverse plane. In the present work, although the studies on the assessment of the linearized system stability are carried essentially by delineating the transverse motion of the journal center, the problem is attempted from an altogether different view point. The approach in this work involves the delineation of the motion of the journal center accelerated or decelerated from its steady state running position to certain prescribed speed levels and of the uniform motion thereafter. The thesis comprises of five chapters. Chapter 1 presents a detailed review of the gas bearing literature with emphasis on the dynamical aspects of the journal bearing systems. This chapter also details out the objective of the present investigations and the approach adopted for the assessment of the linearized system stability of the gas-lubricated journal bearings. It is explained that the assessment Investigations based on the accelerating or decelerating journal manifest from what may be naturally interpreted from the linearized system stability charts and, therefore, the present approach provides a more logical basis toward the assessment investigations. IV The delineation of the transverse motion of the center of a nonuniformly rotating journal is carried out by the numerical integration of the equations of the dynamical system of the gas-lubricated journal bearing system. The details of the analysis for this purpose are given in Chapter 2. The model of the journal bearing system being considered in this work is the classical rigid-rotor, rigid-pedestal, perfectly balanced, single-disc symmetrical system. The b,,, r+.+*+1 lnmAnn Priii t. l nnR of the translatory whirl of the journal center coupled with the nonlinear Reynolds' equation of the compressible lubrication, where the latter equation is modified to account for the nonuniform journal rotation. For the time-marching numerical integration, these equations are transformed into the first order state space equations, where the transformation of the Reynolds' equation is carried out by the Galerkin's finite element method. This solution scheme is new and has, hitherto, not been established by any other authors. Beginning with an equilibrium state, one needs the steady state pressure field as initial conditions for the time-marching solution. Further, investigations for the said objective need the 'linearized gas-lubricated journal bearing system stability charts. The analytical details of the solution of the Reynolds' equation for establishing the linearized system stability margin are also included in Chapter 2. Although not new, these latter analytical details are included for the completeness of the work and their presentation reflects the way these have been adopted by the author. The theoretical analysis of this chapter are general in respect of the journal bearing configurations. V The transient response analysis of the rotor bearing systems is a computationally expensive task. The computation cost increases many-fold with the gas-lubricated bearing systems due to the nonlinearity of the Reynolds' equation and its explicit time dependence. Further, since the present investigations address to the assessment of the linearized stability maps via the transient response analysis, - -the accuracy of the numerical calculations is also a matter of paramount importance. In fact the numerical implementation of the analysis of Chapter 2 toward the development of the computer softwares needed much ingenuity and involved considerable effort. The details of the computational schemes and the matters concerning the finite element discretization, the accuracy of numerical calculations, the computation time, and others are addressed in Chapter 3. The next two chapters of the thesis contain the results of the present investigations. The plane journal bearing is a general purpose bearing and the investigations related to this bearing are presented in Chapter 4. By their very nature, the gas bearings aptly find their application in very high speed machines. Consequently, the designers often look towards the bearing configurations of superior dynamic performance. The lobed bearings or the so-called noncircular bearings come in this category. The results of investigations on the noncircular bearings are presented In Chapter 5. The bearing configurations taken up in this chapter are the elliptical, offset-halves, three-lobe and four-lobe bearings. The results presented in these chapters are comprehensive in respect of the geometric and operational parameters. Ili Following the present nonlinear transient analysis the limiting orbital motions of the ,journal center are determined for the aforementioned configurations of the bearings. A Fast Fourier Transform (FFT) technique is used to obtain the frequency contents of these nonlinear orbits. For a bearing the nonlinear whirl frequency ratios obtained by the FFT analysis are compared with those predicted by the simplified linear theory. r M L... .. 4 s ..... ~ s .. c f the I L..... t .~ .. s .-....d in Chapter 6. The linearized stability maps are dependable in so far as these maps underestimate the margins of stable operation and hence lead to conservative designs. However, ever increasing speed and power and lighter weight requirement of the machinery demand optimal design solutions. The transient response analysis gives a more realistic estimate of the stability margins and as the present results indicate, the stability margins so obtained may be considerably higher than those based on the linearized system approach. It is believed that the results of the present investigations would provide useful information to the researchers as well as the designers involved in the area of gas bearing lubrication. The recommendations on the possible advancements in the present work are also included in Chapter 6. VII