On mixed and fluid film lubrication the characteristics of hydrostatic bearings for hydraulic equipment are studied numerically. By applying a mixed lubrication model derived in a previous paper to the bearings, we clarify the effects of the surface roughness, eccentric or moment loads, supply pressure and speed of rotation on the friction, flow rate, and power losses. Introducing the concept of a ratio of hydrostatic balance, we show that the minimum power loss is given as the ratio becomes close to unity.

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Mixed lubrication characteristics of hydrostatic thrust bearings are examined experimentally. The effects of the surface roughness, supply pressure, loads, speed of rotation and size of restrictors on the frictional force, leakage-flow rate and power losses are clarified. Introducing the concept of mean pressure based on load-carrying capacity due to asperities, and the ratios of hydrostatic balance and leakage-flow rate, the experimental data can be normalized. Also good agreement is found between theoretical results based on a mixed lubrication model presented in a previous paper and the experiment.

A simulation of the rolling contact fatigue strength of a traction drive element was proposed. The simulation can account for both the distribution of sizes of inclusions in the element material and the influence of traction forces at the element surface. The shear strength of the matrix structure surrounding an inclusion was estimated with an equation. The hardness distribution and the Weibull distribution of inclusion dimensions, which were necessary parameters to calculate the rolling contact fatigue strength, were determined by observation of an actual test specimen. And the rolling contact fatigue strength was compared with the distribution of shear stresses in a roller affected by traction forces. A simulation assuming the same traction coefficient as that in the experiment predicted a rolling contact fatigue strength of 810 MPa with a standard deviation of 39.2 MPa, which differed from the experimental value by only 2.5%. Simulations of the rolling contact fatigue strength were then carried out while varying the traction coefficient. The contact force resulting in failure was observed to fall as the traction coefficient increased and the torque capacity increased. Thus, the torque capacity increases with the traction coefficient, regardless of changes in the rolling contact fatigue strength.

A thermohydrodynamic lubrication (THL) model of a hybrid (hydrostatic and hydrodynamic) thrust bearing is developed. It is applicable to a slipper of swashplate-type axial piston pumps and motors. The generalized Reynolds equation, three-dimensional energy equation, and the heat conduction equation are derived. Physical properties such as density, viscosity, specific heat at constant pressure, thermal conductivity, and thermal expansivity of a hydraulic oil are considered as functions of temperature and pressure. The effects of the operating conditions on the temperature rise, clearance shape, and the power loss are shown. The numerical parameters are specified for the fluid  a hydraulic oil with ISO VG 46  supply pressure 7 -21 MPa and rotational speed 15 -60 rps. The solutions between the slipper model and the circular hydrostatic thrust bearing as well as between the THL and isothermal (ISO) solutions are compared. Increases in the supply pressure, rotational speed, and the revolution-radius increase the maximum temperature and the power loss. Furthermore, the discrepancies between the THL and ISO solutions increase. The rotational speed affects characteristics more than the supply pressure.

The mixed and fluid film lubrication characteristics of plain journal bearings with shape changed by wear are numerically examined. A mixed lubrication model that employs both of the asperity-contact mechanism proposed by Greenwood and Williamson and the average flow model proposed by Patir and Cheng includes the effects of adsorbed film and elastic deformation is applied. Considering roughness interaction, the effects of the dent depth and operating conditions on the loci of the journal center, the asperity-contact and hydrodynamic fluid pressures, friction, and leakage are discussed. The following conclusions are drawn. In the mixed lubrication regime, the dent of the bearing noticeably influences the contact and fluid pressures. For smaller dents, the contact pressure and frictional coefficient reduce. In mixed and fluid film lubrication regimes, the pressure and coefficient increase for larger dents. Furthermore, as the dent increases and the Sommerfeld number decreases, the flow rate continuously increases.

The assumptions of a quadratic temperature profile and mean viscosity across the film, which are frequently used in the analysis of thermal elastohydrodynamic lubrication (EHL), are examined and discussed. Two different approaches for solving the thermal EHL problem are compared for line contact conditions, namely (a) a one-dimensional model based upon both the assumption of a quadratic temperature profile and the adoption of the mean physical properties across the film and (b) a twodimensional model which includes changes in temperature and physical properties of a lubricant across the film and which takes into account the conditions of reverse flow and heat convection across the film occurring at the inlet region. A multi-grid algorithm is implemented to solve these two conditions. The temperature profile and the general solutions in the conjunction obtained in both approaches are compared. For the one-dimensional model, results reveal that temperature peaks just prior to the inlet of the conjunction. This feature is not apparent in the two-dimensional model and results in lower values in film thickness and larger frictional coefficients than in the two-dimensional model. In the high-pressure region, both equations yield almost the same mean temperature.

This paper presents a time-dependent mathematical model of a hybrid (hydrostatic/hydrodynamic) thrust pad bearing as a slipper of swash-plate type axial piston pumps and motors for the use of tap water under mixed and fluid fihn lubrication condition. Effects are examined of the load eccentricity, time-lag of changes in the supply pressure and load, surface roughness, recess volume, and the revolution radius. The bearing's motion is simulated three-dimensionally, including roughness interaction and asperity contact. Solutions are obtained regarding the friction, flow rate, power loss, and stiffness. Calculations indicate that the eccentric load causes local contacts. The preceding change in the load poses a larger motion of the bearing. The hydrodynamic effect becomes marked as the revolution radius increases. As the recess volume increases, the bearing stiffness decreases.