Dynamic tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors

Aerostatic rectangular double-pad thrust bearings with compound restrictors have often been used in linear guideway systems of ultra-precision machine tools and precision measuring equipments, because high bearing stiffness is easily achieved in these bearings. However, in actual devices, various dynamic loads as well as static loads are imposed on these aerostatic bearings. Therefore, in this paper, the dynamic stiffness and damping coefficient of this type of bearing for tilt motion of a shaft are investigated, both theoretically and experimentally. It was consequently found that the dynamic tilt characteristics of the aerostatic thrust bearings considered in this paper are greatly influenced not only by design parameters such as the groove position and the groove depth but also by the squeeze effect.     

Numerical analysis of discharge coefficients in aerostatic bearings with orifice-type restrictors

Determining film pressure by solving the Reynolds equation is more effective than conducting bearing experiments or computational fluid dynamics simulations. The Reynolds equation can be solved easily in a numerical model; however, the accuracy of each model is dominated by the orifice discharge coefficient. This study compared two orifice flow models in inherent orifice restrictors and investigated the influences of geometry and flow parameters on the discharge coefficient. The results indicate that both orifice flow models can be used in inherent orifice restrictors, and the discharge coefficient of orifice-type restrictors is sensitive to the orifice diameter and film thickness.     

Static tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors

Aerostatic rectangular thrust bearings with compound restrictors have often been used in ultra-precision machine tools and precision measuring equipment because high bearing stiffness is easily achieved. Compound restrictors combine a feed-hole restrictor with a groove compensation restrictor. This paper investigates, theoretically and experimentally, the static tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors, when coupled loads or offset loads are applied. Furthermore, the usefulness of aerostatic thrust bearings with compound restrictors is clarified by comparison with the characteristics of conventional aerostatic thrust bearing with feedhole restrictors.     

Numerical and experimental analysis of aerostatic thrust bearings with porous restrictors

The finite element method is used to predict the performance of aerostatic thrust bearings with a complete porous surface. Results obtained by a 1D and 3D source flow model derived from D’Arcy’s law are compared for rectangular porous bearings having an infinite width. It turns out that the 1D source flow model is adequate for practical design parameters. For a circular aerostatic porous thrust bearing results calculated with several mathematical models for the source flow and slip flow are compared with experimental results. A relatively simple model incorporating unflatness and deformation of the bearing surface correlates well with the experimentally determined bearing performance.     

Discharge coefficient influence on the performance of aerostatic journal bearings

Aerostatic journal bearings need externally pressurized air. The discharge coefficient is usually assumed constant for sonic and subsonic flow conditions. However, some authors found that it is variable as a function of the pressure ratio, orifice throat discharge and supply pressures. The present study is a theoretical investigation of the discharge coefficient influence on the performance of aerostatic journal bearings. The Reynolds equation for compressible fluids is solved by the finite element method with triangular linear elements. For 0.5 eccentricity ratio, the bearing load carrying capacity difference is 0.5%, although the bearing total mass flow rate difference is 7.4%.     

Non-linear stability analysis of a rigid rotor on tilting pad journal bearings

This paper describes a method for conducting non-linear stability analysis on the synchronous motion of the journal axis and tilting pads in a system consisting of a symmetrical rigid rotor mounted on tilting pad journal bearings with two pads. The method makes it possible to obtain the limit curves separating the stable operating condition, characterized by the above motion, from the so-called unstable one characterized by motions of the pads and journal with a fundamental frequency equal to one half the rotor angular speed. A variational method is used to carry out stability analysis on the synchronous solution of the non-linear equations of motion, obtained in an approximated analytical form using a particularized harmonic balance method.     

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.     

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.     

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.     

The stability of a rigid rotor in ruptured finite journal bearings

The plane motion stability of a rigid rotor supported in fluid film journal bearings having a finite length and subjected to a steady external load and an unbalance load is theoretically analysed. Oil whirl is investigated for a ruptured film under separation boundary conditions. The non-linear equations of motion are solved by using numerical methods. Journal centre trajectories are obtained for different conditions of loading and speed. The stability threshold curve is plotted and compared with the curves of previous investigators obtained under other assumptions and boundary conditions.     

简单孔节流静压气体轴承优化设计的一种解析解法

静压气体轴承在工程中应用广泛,但其设计工作涉及的计算繁琐,工程中多采用图表法或数值计算法。为简化工程计算过程,也为研究气体轴承中各参数间的关系提供直观的分析依据,从解析角度研究了静压气体轴承的优化设计问题。以简单孔节流圆盘静压气体止推轴承为研究对象,以轴承刚度最大为优化准则,首先利用数值计算求出与供气压比对应的最佳节流压比,再利用最小二乘法拟合得到它们的解析关系式,以此为基础,进而求出最佳气膜厚度、最佳承载力、最大刚度和最佳气体流量的解析解,并与精确数值解进行了比较验证。得到的解析解,使气体轴承的工程设计简便、有效。     

Zero-load stability of a rigid rotor supported on pressurized porous gas bearings

A theoretical and experimental investigation of stability characteristics of a rigid rotor mounted on externally expressurized gas-lubricated porous bearings in made. The hydrodynamic fluid film forces of an unloaded journal which undergoes steady whirl are obtained to find limits of the stable region. The results are compared with experimental data and with a similar solution using Galerkin's method. The effect of a feeding parameter, supply pressure, thickness of porous bushing and porosity of bushing material on stability characteristics is also investigated.     

Thermo-hydrodynamic analysis of herringbone grooved journal bearings

Steady-state and stability characteristics of herringbone grooved journal bearings (HGJBs) are found considering thermal effect. The temperature of the fluid film rises significantly due to the frictional heat, thereby the viscosity of the fluid and the load carrying capacity decrease. A thermodynamic analysis requires the simultaneous solution of Reynolds equation along with energy equation of the fluid and heat conduction equations in the bush and the shaft. The linearized first-order perturbation technique is employed for the prediction of stiffness and damping coefficients of the oil film. Thereafter mass parameter and whirl ratio are found from the stability analysis. It is difficult to obtain the solution due to the numerical instability when the bearing is operated at high eccentricity ratios.     

Dynamic analysis of a rigid rotor supported by three-pad hydrostatic squeeze film damper lubricated with ferrofluid

This work describes an analytical study on the dynamic behaviour of a three-pad hydrostatic journal bearing lubricated with ferrofluids. Each pad is fed with an external pressure through a capillary restrictor-type hydraulic resistance. Ferrofluid or magnetic fluid is a colloidal dispersion of magnetic nano-particles in a carrier liquid. In this study, a non-linear method was performed using Jenkins model in order to investigate the effect of ferrofluids lubrication on the vibrations amplitude and the transmitted forces of hydrostatic squeeze film dampers. The results presented in this paper showed that the ferrofluid lubrication is useful in controlling the bearing vibrations and transmitted forces. The results illustrated in this work are expected to be quite useful to the bearing designers.     

Performance analysis of a multirecess capillary compensated conical hydrostatic journal bearing

The present paper is aimed to study theoretically the performance of a 4-pocket hydrostatic conical journal bearing system. The Reynolds equation governing the flow of lubricant in the clearance space of bearing has been solved using FEM. The bearing static and dynamic performance characteristics have been presented for the values of external load W¯_r=0.1-1.0 and for the semi cone angles (γ=10°, 20°, 30° and 40°). The numerically simulated results indicate that the lubricant flow rate is significantly reduced in case of conical journal bearing vis a vis the corresponding similar circular hydrostatic journal bearing.     

Chaos of rub-impact rotor supported by bearings with nonlinear suspension

The nonlinear dynamic analysis of the rotor-bearing system is studied in this paper and is supported by oil-film short bearings with nonlinear suspension. An observation of a nonlinearly supported model and the rub-impact between rotor and stator is needed. Therefore for more precise analysis of rotor-bearing systems, the rub-impact between rotor and stator is also proposed in this paper. The displacements in the horizontal and the vertical directions charactering the theoretical model of the system are considered with non-dimensional speed ratio. Inclusive of the analysis methods of the dynamic trajectory, the power spectrum, the Poincaré maps and the bifurcation diagrams are used to analyze the behavior of the rotor centre and bearing centre in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent analysis is also used in this study to identify the chaotic motion. It is concluded that the trajectory of rotor centre and bearing centre have undesirable vibrations. Especially at s=5.6, the rotor centre is at chaotic motion but the bearing centre is still at quasi-periodic motion. With the analysis of the dynamic behavior of these operating conditions, the theoretical and practical idea for controlling rotor-bearing systems and optimizing their operation can be more precise.     

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.     

Rapid performance evaluation of journal bearings

This paper describes a rapid method for evaluating the significant design parameters such as load capacity, maximum pressure, flow, power loss, and maximum temperature in the oil film. The proposed analytical pressure expression is a modification of that given by Reason and Narang. An analytical expression for maximum pressure is presented. The accuracy of the proposed modification is validated up to an eccentricity ratio of 0.99. The effective temperature rise, which depends on the fraction of heat generation carried away by lubricant, is chosen to be a function of the eccentricity ratio. An expression for maximum temperature, based on existing experimental findings, is given. A journal bearing design table is provided to help the designer without the involvement of numerical and mathematical complexities.     

Numerical investigation of static and dynamic characteristics of aerostatic thrust bearings with small feed holes

Recently, laser beam machining and micro drills have made it easier to manufacture small feed holes of less than 0.1 mm diameter. Accordingly, aerostatic bearings with these small feed holes have become commercially available for improving bearing performance. In this work, an aerostatic annular thrust bearing with small feed holes of less than 0.05 mm diameter was treated and the static and the dynamic characteristics of this type of bearing were investigated numerically. In numerical calculations, computational fluid dynamics (CFD) was used to determine discharge coefficients for a small feed hole and the finite difference method (FDM) was used to obtain the bearing characteristics. In addition, the characteristics of this type of bearing were compared with those of aerostatic thrust bearings with typical compound restrictors to show clearly the features of this type of bearing.     

Linear stability of short journal bearings with consideration of flow rheology and surface roughness

The combined effects of surface roughness and flow rheology on the linear stability of a rigid rotor supported on short-length journal bearings are analyzed. The modified Reynolds equation and the rotor motion equation are linearized about the equilibrium position and the fluid film is modeled as spring and damping elements. From the characteristic equation, the instability threshold is then obtained with various surface roughness parameters (standard derivation, σ, and Peklenik number, γ), flow rheology (power-law index, n) and eccentricity ratios (). The results show that the size of the stability regions of different roughness patterns has the following characteristics: longitudinal (γ>1)>isotropic (γ=1)>smooth>transverse (γ<1). The stability of the bearing system deteriorates with decreasing power-law index. Moreover, there are crossing points in the vicinity of =0.45 among the curves of dimensionless speed parameter ( ) associated with various power-law indices and surface roughness parameters.