Hydrodynamic Lubrication of Finite Slider Bearings: Effect of One Dimensional Film Shape, and Their Computer Aided Optimum Designs

Abstract

The effect of the film shape on the load carrying capacity of a hydrodynamically lubricated bearing has not been considered an important factor in the past. Flat-faced tapered bearing and the Raileigh’s step bearing of constant film thickness have been the primary forms of film shapes for slider bearing studies and design data developments. This article, by the computer aided numerical solution of the Reynolds equation for two dimensional incompressible lubricant flow, investigates hydrodynamically lubricated slider bearings having different film shapes and studies the effect of the film shape on the performance characteristics of finite bearings; and it shows that optimized bearing with film shapes having descending slope toward the trailing edge of the bearing has considerably higher load carrying capacity than the optimized flat-faced tapered bearing of the same properties. For example the truncated cycloidal film shape yields 26.3 percent higher load carrying capacity for Lz/Lx = 1 size ratio, and 44 percent higher for Lz/Lx = 1/2. The article then presents charts for the optimum designs of finite slider bearings having tapered, exponential, catenoidal, polynomial, and truncated-cycloidal film shapes, and illustrates their use in numerical bearing design examples. These charts also furnish information on flow rate, side leakage, temperature rise, coefficient of friction, and friction power loss in optimum bearings. Appended to the article are analytical solutions for infinitely wide bearings with optimum bearing characteristics. The computer aided numerical solution of the Reynolds equation in most general form is presented by which finite or infinitely wide hydrodynamically or hydrostatically lubricated bearings, externally pressurized or not, can be studied. A digital computer program is made available.

Numerical Investigation of Pressure Profile in Hydrodynamic Lubrication Thrust Bearing

“…Various 3D meshes of nondimensional pressure distribution are shown from Figures 3 , 4 , 5 , 6 , and 7 . The results generated by the researchers [ 17 , 18 ] are closely matching the path with grid size of 4 × 4, 8 × 8 and so forth. The results computed by [ 12 ], with the limited grid size of 9 × 9, are also showing good agreement with the present higher order grid size.…”

“…The authors have reported that the increase in pressure is more for the exponential and hyperbolic sliders [ 16 ]. Moreover, investigators [ 17 , 18 ] have studied the THD behavior of a slider bearing having a pocket and reported that the maximum pressure is higher for the pocketed bearing in comparison to plane slider bearing. [ 19 , 20 ] studied the influence of film shape on the performance of longitudinally rough, infinitely wide slider bearing for isothermal conditions and reported better load carrying capacity with exponential, secant, and hyperbolic film shapes in comparison to the inclined plane film shape.…”

Computational Fluid Dynamics Performance Prediction for the Hydrodynamic Bearings of the VentrAssist Rotary Blood Pump

“…The problem of finite bearing width is an old one, first analyzed by Michell (6). With the addition of rotary geometry as here, the problem was addressed numerically by Gregory and Maday (7), and a representative review of the literature is given by Bagci and Singh (8). Their results show that a taper bearing of width 2 L (the situation of 1 of the 1.3 bearings, if the rotation is ignored) achieves some 72 to 74% of its infinite‐width load capacity in the range d 1 / d 2 = 1.6 to 3.0, which corresponds to d 2 = 83.3 to 25 μm here.…”

Two-dimensional lubrication analysis and design optimization of a Scotch Yoke engine linear bearing

“…By integrating equation (6) twice and considering equation (2) as well as the boundary conditions, at…”