Fluid Lubrication Theory of Roller Bearing—Part I: Fluid Lubrication Theory for Two Rotating Cylinders in Contact

Abstract

This paper which consists of Parts I and II presents a general and practical fluid lubrication theory of roller bearings lubricated by Newtonian and non-Newtonian lubricants with considerations to the effect of sliding of roller and the influence of unsteady load. In Part I, the fundamental theory for the lubrication between two rotating cylinders in contact has been investigated. The load capacity and friction of a non-Newtonian lubricant, supposed to be a Bingham plastic, coincide approximately at high speed with those of a Newtonian lubricant with viscosity equivalent to the plastic viscosity of the non-Newtonian lubricant. Under unsteady loads, the squeeze action works effectively so that the load capacity increases. The amount of friction is 4/3 and the load capacity is 2/3 in the case of two rotating cylinders in contact involving sliding, compared with that involving no sliding.

Gear rattle dynamics under non-stationary conditions: The lubricant role

“…The meshing forces (F EHL i ) are obtained from a previous quasi-static analysis, which calculation procedure has been extensively presented in scientific literature [9,12,13]. In order to obtain the hydrodynamic forces (F HDL i ), six formulations found in literature [29,30,31,32] were implemented in the model developed by the authors. These formulations are reorganised in equation-5-form, listing C W edge eq and C Squeeze eq expressions in Table 1 and naming them after their authors (Sasaki, Rahnejat and Wiegert).…”

“…Within this framework, the lubricant role is still to be understood, specifically under non-stationary conditions, since only few studies deal with this issue [1,6,7,26,27,28], being this the main goal of the present work, as well as the novelty with respect to the preliminary hydrodynamic force analysis under gear rattle conditions performed in [11]. In this regard, in previous analysis of the authors [11], six hydrodynamic formulations found in literature [29,30,31,32], which consider both squeeze and entraining fluid effects to model the fluid contact in HDL conditions, were implemented in the model developed by the authors [9,12,13] to simulate gear rattle under stationary conditions. Specifically, several mean input velocities were considered in that analysis, obtaining the dynamic response under several torque cases, concluding that, when constant input speed was considered, the wedge term overcomes the squeeze term effect on the dynamic response.…”

Squeeze Film Lubrication of Asymmetric Rollers by Bingham Plastic Fluid

“…where "p" and "  " are hydrodynamic pressure and shear stress of the fluid respectively. T he constitutive equation for Bingham plastic fluid is given by Sasaki et al (1962)…”

Gear rattle dynamics: Lubricant force formulation analysis on stationary conditions

“…Sasaki et al proposed an expression where wedge and squeeze terms were superposed. This means that each effect was calculated individually [26,28].…”