Stability of a rigid rotor in turbulent hybrid porous journal bearings

Stability characteristics of hybrid porous journal bearings with a turbulent fluid film have been investigated theoretically following Constantinescu's turbulent lubrication theory. The stability curves have been drawn for different Re, eccentricity ratios, slenderness ratios and bearing speed parameters. In the absence of any experimental data, laminar flow results obtained by this analysis have been compared and found to be in excellent agreement with the previous results. It is observed that turbulence deteriorates the stability of the rotor and for better performance the value of the bearing feeding parameter, β, should be kept small.     

Stability analyses and experiments of spindle system using new type of slot-restricted gas journal bearings

A new type of slot-restricted gas journal bearing with non-uniform slot clearance in the circumferential direction is proposed in this paper. The stability characteristics of the new type of slot-restricted gas bearing are obtained by solving linear equations of motion of rotor with two degrees of freedom supported by one bearing to prove that the proposed new type of the slot-restricted gas journal bearing is much more stable than a conventional slot-restricted bearing. For comparisons with experimental results, the stability characteristics of four degrees of freedom rotor-bearing system are judged by the non-linear transition analyses. The instability threshold speed tests of the rotor-bearing system are performed. The instability threshold speed experimentally obtained is compared with theoretical results to confirm the validity of the numerical analyses. As a result of the analysis and experiment, it was shown that the proposed new type of slot-restricted gas journal bearing is much more stable than a conventional slot-restricted bearing due to non-uniform slot clearance.     

Metal woven wire cloth feeding system for gas bearings

The paper presents an experimental investigation of pneumatic resistances constructed using woven wire cloth. Tests were carried out on commercial Touraille stainless steel wire cloth featuring different mesh sizes.Two types of experiments were performed: (a) Mass flow rate through single resistances was measured with different upstream and downstream pressures and wire mesh sizes. (b) Pressure distribution and mass flow rate were measured on a pneumatic pad with a fine wire mesh feeding system. Two approaches of identification of the single resistances are discussed.Test results can be used as the basis for developing woven wire cloth pneumatic resistances whose conductance is equivalent to that of certain of the calibrated orifices normally used in gas bearings.     

Stability of multi orifice active tilting-pad journal bearings

The stability properties of actively lubricated tilting-pad journal bearings are investigated theoretically. The bearing preload factor and control system gains are varied, and stable and unstable regions are identified. It is seen, that the control system influences bearing stability, and that the nature and magnitude of this influence depends on the rotor mass, preload factor and rotational speed. Furthermore, it is shown that assuming the bearing pads to be rigid can produce a substantial error. A rigid pad model will overpredict the stable range of the bearing, thus it may lead to failure if trusted.     

Transient response of a journal supported on elastic bearings

By considering the inherent flexibility of the bearing liner, the non-linear dynamic response of a journal bearing system is determined in this study. The transient analysis is presented and the journal centre motion trajectories are plotted for rigid and flexible bearings. Effects of the different parameters such as the eccentricity ratio, and the deformation coefficient etc on non-linear trajectories are reported in this paper. The transient response of the system is also obtained for different values of the normalized journal mass which shows that a rotating system supported in a flexible bearing may have a better performance under dynamic conditions than one supported in rigid bearings.     

Dynamic performance of plain gas journal bearings

This paper presents dynamic performance characteristics of plain gas journal bearings. The perturbation formulation suggested by Lund has been modified to obtain stiffness and damping properties. Since rotor bearing axes are never perfectly parallel, the effect of skew has also been considered. Stability studies have been carried out for selected compressibility parameters     

A rig for testing lateral misalignment effects in a flexible rotor supported on three or more hydrodynamic journal bearings

The vibration behaviour of statically indeterminate rotor-bearing systems with hydrodynamic journal bearings is predicted to be significantly dependent on the relative lateral alignment of the bearing housings (i.e. system configurations). To validate this, a rig wherein the rotor is supported on four bearings is being designed. This paper describes the salient features of the rig which is shown to be capable of traversing several critical speeds over its operating range, to be capable of whirl instability, and to be capable of a wide range of lateral misalignment combinations which result in significant vibration amplitude changes. Appropriate instrumentation will enable bearing reaction forces and rotor motions to be measured for various speeds, unbalance and system configurations. Theoretical results suggest that the rig is well suited for misalignment identification experiments though the predicted ability of different system configurations to yield virtually identical vibration response emphasises the need for careful experimental design.     

Nonlinear behavior analysis of a rotor on two-lobe wave journal bearings

The dynamics of an unbalanced rigid rotor on two-lobe journal bearings with wave profile, symmetrically placed at its ends, is studied in numerical way. The radial dissymmetry of the shape given to the bearing bore makes the angular orientation of the same bearing one of the main parameters in the study of the system dynamics. Further parameters adopted in the investigations are the amplitude of the wave component which characterizes the profile of the bearing bore, the static unbalance and the speed of the rotor. Brute-force integration of system equations has been carried out in order to obtain qualitative portraits of the system dynamics in terms of bifurcation diagrams and trajectories of the journal centre. The study also illustrates the way numerical continuation method can highlight the dependence of the stable, synchronous response on the adopted parameters and allow a tracking of the same motion in a simulated run-up of the rotor.     

Theoretical analysis of the non-linear behavior of a flexible rotor supported by herringbone grooved gas journal bearings

This paper studies the behavior of a flexible rotor supported by a herringbone-grooved gas journal-bearing system. A hybrid method is employed to develop a time-dependent mathematical model of the bearing system. The finite difference method is employed with the successive over relaxation technique to solve the Reynolds equation. The system state trajectories, Poincaré maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor and the journal center in the horizontal and vertical directions under different operating conditions. The analysis reveals a complex dynamic behavior comprising periodic and quasi-periodic responses of the rotor and the journal center. The present numerical study illustrates the relationship between the dynamic behavior of this type of system and the rotor mass and bearing number. As such, the present results provide a deeper understanding of the non-linear dynamics of gas film rotor-bearing systems.     

On the non-linear stability of self-acting gas journal bearings

The non-linear stability of finite length self-acting gas journal bearings is studied by solving a time-dependent Reynolds equation using finite difference method. Two threshold values are discovered instead of one through which the self-acting gas journal bearings are changed from stable to unstable state. Keeping other parameters unchanged, when the mass of rotor exceeds the upper threshold value of mass, the system gets unstable; when the mass is less than the lower threshold value of mass, the system is stable; when the mass is between these two threshold values, the stability of bearings is determined by the amplitude of disturbance. Similar facts of two threshold values are also found when the stability parameter is chosen as external force or aspect ratio.     

Experimental investigations of precision spindles equipped with high stiffness gas journal bearings

The journal high stiffness bearings (HSBs) presented in this paper have been supplemented with special regulation systems that enable us to select optimal bearing characteristics by a slight circumferential turn of the journal bearing bush with respect to its fixed casing. The regulation system allows us to obtain the desired bearing characteristic compensating for the inaccuracy of its element production. Two different regulation systems are presented in this paper. The experimental investigations for static conditions of a single HSB with two above-mentioned regulation systems have been performed. Then, two spindles equipped with journal HSBs have been investigated. Each spindle was supported using two HSBs with the same regulation system. The results of these investigations for different rotational frequencies are reported. The effectiveness of the HSB regulation systems for practical optimization of the spindle characteristic have been shown. These bearings can be applied in precision grinding machines.     

High-speed stability of a rigid rotor supported by aerostatic journal bearings with compound restrictors

Demands for higher rotational speed and accuracy for effective manufacture of small holes on printed circuit boards and very small precise parts have been increasing remarkably. Aerostatic journal bearings with compound restrictors have greater stiffness than those with conventional inherently compensated restrictors and are one of the most effective candidates to satisfy these demands. In this work, the instability of a rigid rotor supported by aerostatic journal bearings with compound restrictors was investigated numerically and experimentally. It was found that this type of aerostatic bearings showed a much higher threshold speed for instability compared with bearings with inherently compensated restrictors.     

Stability analysis of externally-pressurized gas-lubricated porous bearings with journal rotation Part 1. Cylindrical whirl

Whirl stability (cylindrical) of externally-pressurized gas-lubricated porous journal bearings, considering one-dimensional flow through the porous matrix, is analysed by a first-order perturbation method. The effect of supply pressure, feeding parameter, porosity parameter and length-to-diameter ratio on the stability is also investigated.     

Stability analysis of externally-pressurized gas-lubricated porous bearings with journal rotation Part 2. Conical whirl

The stability analysis of externally pressurized gas journal bearings under conical mode of vibration has been obtained using a first-order perturbation method. The effect of journal speed, feeding parameter, supply pressure, porosity parameter and length-to-diameter ratio on the conical whirl and whirl ratio has been investigated.     

Static characteristics of externally pressurized gas journal bearings with circular slot restrictors

The static characteristics of an externally pressurized gas journal bearing with a circular slot restrictor are described. The slot configuration is circumferentially continuous and is simpler than that of the journal bearing with discrete slots proposed by Dee and Shires¹. Here, the optimum design conditions for the load capacity are theoretically determined and it is shown that gas journal bearings with a circular slot restrictor possess a load capacity comparable to designs which have discrete slots.     

Hybrid journal bearings with particular reference to hole-entry configurations

There is a spectrum of pressure-fed journal bearings ranging from the purely hydrostatic bearing characteristics, ie zero speed operation, to the purely hydrodynamic bearing characteristics which depend completely on speed. Between these two extremes, hybrid bearing characteristics rely on mixed modes of external pressurisation and speed-dependent pressurisation. Large high speed hydrodynamic bearings require the lubricant to be pumped under pressure for temperature control. It is therefore attractive to use this external source of pressure to enhance the start-up performance by reducing wear and improving stability. Hybrid bearings offer the possibility of improving on both the zero-speed characteristics of hydrostatic bearings and on the whole range of speed characteristics of hydrodynamic bearings. It is concluded that hole-entry bearings may be particularly effective when compared with other bearing configurations for good load support and low energy consumption, when used in any of the four modes of operation including: zero-speed hydrostatic mode; high-speed hydrodynamic mode; zero and high-speed hybrid mode; and jacking mode where areas are pressurised for start-up. A modification to the procedure for solving the Reynolds equation is introduced to cope with cavitated regions. The technique presented for solving the bearing pressures and cavitation boundaries is efficient and has relevance to any type of liquid film bearing     

Steady state and dynamic characteristics of axial grooved journal bearings

The steady state and dynamic characteristics including whirl instability of oil journal bearings with single axial groove located at the top of the bearing and then at some angular interval from the top from which oil is supplied at constant pressure are obtained theoretically. The Reynolds equation is solved numerically by finite difference method satisfying the appropriate boundary conditions. The dynamic behaviour in terms of stiffness and damping coefficients of fluid film and stability are found using a first-order perturbation method for each location of the groove. It has been shown that both load capacity, end flow is maximum when the feeding groove is at 12° location and thereafter the load capacity falls, stability improves for smaller groove angle and groove length at higher value of eccentricity ratio and speed. The stiffness and damping coefficient magnitude is found to be higher for the bearing with smaller groove angle and groove length, the difference between the hydrodynamic and hydrostatic load increases at 12° groove location.     

Non-linear dynamic analysis of rub-impact rotor supported by turbulent journal bearings with non-linear suspension

This study presents a dynamic analysis of a rub-impact rotor supported by two turbulent model journal bearings with non-linear suspension. The dynamics of the rotor center and bearing center are studied. The analysis of the rotor-bearing system is investigated under the assumptions of turbulent lubricant flow and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios and dimensionless unbalance parameter. The numerical results show that the stability of the system varies with the non-dimensional speed ratios and the non-dimensional unbalance parameters. The contribution of this study is to provide a further understanding of the characteristics and dynamic behaviors of the rotor-bearing system.     

Experimental study of journal bearings with undulating journal surface

A journal bearing test rig was designed and constructed to test the behaviour of journals with wavy surfaces, the circumferential undulations being varied both in amplitude and in number. Results show that wavy journal surfaces may well enhance the load carrying capacity of a bearing. Moreover, surface undulations are shown to move the journal centre locus closer to the load line, ie cause a lower attitude angle. These effects are found to be more pronounced with larger wave amplitudes, and with higher numbers of waves around the journal circumference. In general, friction is found to be reduced with increase in surface wave amplitude.Good agreement is shown to exist between test results and a computer aided analysis conducted by the authors to predict wavy journals performance¹. It has been established that a wavy journal surface may, under certain conditions, display higher load capacity, lower friction and permit safer running of journal than bearings with perfectly smooth surfaces.