Hydrodynamic lubrication of rough slider bearings with couple stress fluids

The combined effects of couple stresses and surface roughness on the performance characteristics of hydrodynamic lubrication of slider bearings with various film shapes, such as plane slider, exponential, secant and hyperbolic, are studied. A stochastic random variable with non-zero mean, variance and skewness is used to mathematically model the surface roughness of the slider bearing’s. The Stokes couple stress fluid model is used to characterize the rheological behavior of the lubricant with polymer additives. The modified expressions for the bearing characteristics, namely pressure, load carrying capacity, center of pressure, frictional force are obtained for the general lubrication film shape on the basis of Stokes microcontinuum theory for couple stress fluids. Results are computed numerically for various film shapes under consideration. It is observed that, for all the lubricant film shapes under consideration, the negatively skewed surface roughness increases the load carrying capacity, frictional force and temperature rise, while it reduces the coefficient of friction. On the contrary, the reverse trend is observed for positively skewed surface roughness. Further, these effects are more pronounced for the couple stress fluids.     

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 effects of surface irregularities on the performance characteristics of flexible finite journal bearings lubricated with couple stress fluids

A numerical solution for the elastohydrodynamic lubrication of finite journal bearings is presented. Couple stress effects resulting from blending the lubricant with various additives are considered. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearings, is implemented in the solution scheme. A simple elastic model is used to describe the elastic deformation of the bearing liner. Furthermore, the effects of surface waviness on the performance of the bearing are incorporated into the analysis. A comprehensive study illustrates the effects of couple stress, liner flexibility, and surface waviness on the steady‐state performance of finite‐width journal bearings. The results show that these effects should be considered at higher values of the eccentricity ratio.     

Transverse roughness in short journal bearing under dynamic loading

The stochastic theory developed by Christensen is applied to the analysis of dynamically loaded short rough bearings which have striations transverse to the direction of motion. An approximate polynomial is used, in place of a Gaussian function, to represent the roughness profile. To make the analysis applicable to real lubrication situations, it is assumed that the standard deviation of the roughness height and the minimum film thickness are of the same order. Attention is focussed on the cyclic squeeze films under sinusoidal loading. It is concluded that the transverse roughness results in an increase in the side leakage. The effect of roughness is more pronounced when the load direction is reversed.     

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.     

Stability of tri-taper journal bearings under dynamic load using a non-linear transient method

Stability of a tri-taper journal bearing which is subjected to steady, periodic and variable rotating loads is studied theoretically using a non-linear transient approach. The hydrodynamic forces are initially obtained by solving the Reynolds equation, satisfying the Reynolds boundary conditions. Further, the transient behavior of rotor bearing system is predicted by substituting these hydrodynamic forces in the equations of motion and then solving them by fourth order Runge Kutta method. Stability of the rotor bearing system is determined from the journal locus. Comparative studies predict that the dynamic performance is superior for a bearing with high ramp size and aspect ratio.     

Measurement of friction force and effects of oil fortifier in engine journal bearings under dynamic loading conditions

Commercial base oil and oil fortifier added to this oil are used to investigate the frictional behavior of the engine journal bearings using the theoretical Reynolds equation and experimental test rig. In the theoretical part of the study, the Reynolds equation that states the pressure distribution and friction force with finite width was solved by using the finite difference method. In the experimental part of the study, a new design test rig was conducted to measure the friction force, the lubricant film thickness of the engine journal bearing using base oil under dynamical loaded conditions. The effect of oil fortifier was detected measuring the friction force every three minutes in each 360 crank angle during 15 minutes of experiment. As the theoretical friction results showed similar variation with the experimental measurements of engine bearings, adding oil fortifier to the base oil presented a substantial reduction of friction force during the testing period.     

MHD steady and dynamic characteristics of wide tapered-land slider bearings

Based on the magneto-hydrodynamic (MHD) thin-film lubrication theory, steady load capacity and dynamic characteristics of wide tapered-land slider bearings lubricated with an electrically conducting fluid by the application of an external magnetic field are presented. Compared with the non-conducting lubricant (NLC) tapered-land bearing by Lin et al. (2006), the MHD bearing provides higher values of load capacity and dynamic coefficients. Compared with the MHD inclined-plane bearing by Lin et al. (2009), the MHD tapered-land bearing how an increase in load capacity and dynamic coefficients as well as a reduction in the steady friction parameter.     

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.     

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.     

Stability analysis of rough journal bearings under TEHL with non-Newtonian lubricants

The combined effects of surface roughness and lubricants rheology on stability of a rigid rotor supported on finite journal bearing under thermal elastohydrodynamic lubrication have been investigated using the transient method. The newly derived time dependent modified Reynolds and the adiabatic energy equations were formulated using a non-Newtonian Carreau viscosity model. The simultaneous systems of modified Reynolds equation, elasticity equation, energy equation, and the rotor motion equation with initial conditions were solved numerically using multigrid multi-level method with full approximation technique. From the characteristic equation, the instability threshold is then obtained with various surface roughness parameters and the elastic modulus of the bearing liner materials. The results show that stability of the bearing system deteriorates with decreasing both the power law exponent and the elastic modulus of bearing liner material. The rough surface journal bearing with transverse pattern under TEHL regime exhibits better stability when compared with the rough surface journal bearing with longitudinal pattern.     

Static and dynamic characteristics of externally pressurized circular step thrust bearings lubricated with couple stress fluids

The combined effects of couple stresses, fluid inertia and recess volume fluid compressibility on the steady-state performance and the dynamic stiffness and damping characteristics of hydrostatic circular step thrust bearings are presented theoretically. Based on the micro-continuum theory, the modified Reynolds equation and the recess flow continuity equation are derived by using the Stokes constitutive equations to account for the couple stress effect resulting from a lubricant blended with various additives. Using a perturbation technique, results in terms of steady-state load-carrying capacity, oil flow rate, stiffness and damping coefficients are presented. A design example is also illustrated for engineering and industrial applications.     

Analysis of damping characteristics of squeeze films under dynamic (cyclic) loading

This paper presents an analytical study of the damping characteristics of circular discs subjected to dynamic loads. Assuming a circular hydrostatic thrust bearing describing different geometrical configurations and surface texture irregularities (on both the macro- and micro-scales) and subjected to sinusoidal harmonic excitations, an analytical formulation to identify the oil film thickness variation as a function of damping loads is proposed. The Reynolds equation in the discretized form has been solved numerically using the tdma (Thomas Algorithm). Such a direct technique has proved to be reliable in solving similar problems and minimizing computational time compared with conventional iterative procedures. Compared to the performance of a flat and smooth circular disc, results indicated that the micro- and macro-surface undulations play a major role in dictating the squeeze action damping characteristics     

Investigation of sintered bronze bearings under high-speed conditions

An experimental study has been made of sintered bronze bearings under high speed and light load conditions. The temperature rise, friction coefficient, oil loss rate and wear of the bearings were all measured during the tests at a speed of 69 000 r/min with or without oil supplement and under different loads. Contrary to the theory, the results showed that sintered bronze bearings could operate under hydrodynamic conditions for long periods (more than 4000 hours). The effects of different oils on the performance of the bearings were studied for speeds in the range 5000–50 000 r/min and with a load of 2.34 kgf/cm². The results indicated that the correct selection of oil for porous bearings is very important.     

Non-Newtonian effects on the dynamic characteristics of one-dimensional slider bearings: Rabinowitsch fluid model

The non-Newtonian effects of an isothermal incompressibe laminar-flow lubricant on the dynamic stiffness and damping characteristics of one-dimensional slider bearings are theoretically examined. On the basis of Rabinowitsch fluid (cubic equation) model, the modified Reynolds equation considering bearing-squeeze action is derived to take into account the transient motion of the slider, and the non-Newtonian properties of lubricants. Applying a small perturbation technique, both the steady-state performance and the dynamic characteristics are evaluated. According to the results, the steady film pressure, load-carrying capacity, and the dynamic stiffness and damping behaviors are significantly affected by the values of the dimensionless nonlinear factor accounting for non-Newtonian effects, the wedge parameter of a slider profile and the squeeze number of bearing-squeeze action.     

精密多油楔动压轴系的楔形间隙参数与油膜运动稳定特性

针对精密仪器轴系的研制和精度分析,研究了立式三油楔动压轴系的结构、轴承轮廓结构,建立数学模型、分析模型,对轴系动压油膜的动力特性做了分析.对于主轴在动压油膜反力与外载荷作用下处于某一平衡位置(e,θb)运转时,能否经得起任意微扰动的干扰而失稳,建立了油膜运动稳定性的判据.应用数值模拟和计算机编程,深入研究了关键设计参数楔形间隙bm、cm相应的油膜运动稳定特性,揭示了楔形间隙值与轴系失稳的对应关系,给出了油膜稳定性因数Log(Sp)与偏心率ε(ε=e/c)之间的变化曲线图,并指出了楔形间隙参数最佳的取值范围.研究结果指出:楔形间隙是轴系设计和制造的重要敏感参数;最大楔形间隙bm和最小间隙cm值之间应保持一定的比例,否则油膜运动发散,轴系平衡失稳,导致主轴转动中产生较大的晃动.对于低速立式三油楔动压轴系,则bm-cm≥0.8 μm.比较研究结果与成功轴系实例,表明实例中bm、cm取得符合轴系的油膜稳定条件.证明研究结果对该类轴系的设计具有实用性.     

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.     

路面不平度作用下汽车动载分析

建立了二自由度汽车动力学模型,运用虚拟激励法和精细逐步积分法计算了车辆在路面不平度作用下对路面的动载荷,并通过对算例的分析,考察了车速和路面不平度对车辆动载荷变化的影响,及汽车悬架减振器阻尼和动载系数之间的关系.结果表明该方法可行.     

Thermal characteristics of misaligned finite journal bearings

Adiabatic analysis of a journal bearing is presented for maximum allowable misalignment with a length: diameter ratio of one. The direction of journal misalignment is allowed to vary up to the axial plane containing the load vector. Reynolds and energy equations are solved simultaneously using finite differences, considering both axial and spiral oil inlet conditions. The results show that bearing behaviour is significantly affected by journal misalignment. It is also noted that thermal effects are more pronounced for bearings with axial rather than spiral oil inlet grooves.     

The combined effects of the centripetal inertia and the surface roughness on the hydrostatic thrust spherical bearings performance

This paper deals with the surface roughness and the predominant centripetal inertia terms due to the shaft rotation of the externally pressurized thrust spherical bearings. The solutions are presented for the fitted type of bearings, un-recessed and recessed hemispherical and partial hemispherical seats, with capillary tube and orifice restrictors. On the basis of the stochastic theory, Reynolds equation is developed. The bearing surfaces are assumed to have randomly distributed roughness. Expressions for the pressure distribution, load carrying capacity, volume flow rate, frictional torque, friction factor, power factor, power losses and stiffness factor are obtained. The paper shows the combined effects of the centripetal inertia and the surface roughness on the bearing performance. An optimum design based on the minimum power losses, minimum flow rate and optimal restrictor dimensions is theoretically examined.