The effects of angle of convergence on the shape and thickness of the core are analyzed theoretically by considering variable film thickness in an externally pressurized circular thrust bearing. Using the assumptions of the lubrication theory, modified Reynold’s equation and the governing equations are obtained. Using the boundary conditions of the problem in the constitutive equations we get the velocity of the core region as well as flow region. By considering the equilibrium of an element in the yield surface, an algebraic equation to determine the thickness of the yield surface is derived. Numerical solutions are obtained for the thickness of yield surface and velocities for various values of Bingham Numbers and the angle of convergence.
In the present theoretical investigation, the combined effects of fluid inertia forces and sinusoidal injection of the Bingham lubricant, on the performance of an externally pressurized thrust bearing with circular geometry are studied. Using the conventional two-constant Bingham model and by adopting the method of averaging inertia terms, the reduced Navier-Stokes equations are modified and numerical solutions have been obtained for the bearing performances such as the pressure distribution and the load carrying capacity for different values of Bingham number, Reynolds number, time and amplitude. The effects of fluid inertia forces and the non-Newtonian characteristics of the Bingham lubricant on the bearing performances for different sinusoidal conditions are discussed.
Lubricants with variable viscosity are assuming greater importance for its application in polymer industry, thermal reactors and in biomechanics. With the bearing operations in machines being subject to high speeds, loads, increasing mechanical shearing forces and continually increasing pressure, there has been an increasing interest to use non-Newtonian fluids characterized by a yield value. Some of them, which fit into this class, are Bingham, Casson and Herchel-Bulkley models. In the present work, the problem of an externally pressurized thrust bearing lubricated with Herschel-Bulkley fluid under the sinusoidal flow rate has been investigated. Herschel-Bulkley fluids are characterized by a yield value, which leads to the formation of rigid core in the flow region. The shape and extent of the core has been determined numerically for various values of the Herschel-Bulkley number, power-law index, amplitude of sinusoidal fluid film and time. Numerical solutions have been obtained for the bearing performances such as pressure distribution and load capacity for different values of the Herschel-Bulkley number, power-law index, amplitude of sinusoidal fluid film and time. The effects of sinusoidal injection of the lubricant and the non-Newtonian characteristics on the bearing performances have been discussed.
Thrust bearing are innately developed to withstand axial load. When the bearing is subjected to high speed operations, heavy load, high stiffness etc., suggesting a change in the design of the bearing plays a vital role in its performance. Friction is developed between the circular plates while the bearing operates. To reduce this friction, the bearing is lubricated with lubricants such as mineral oil, greases etc., Generally, lubricants are classified into two types that is Newtonian and non-Newtonian. However, non-Newtonian fluids characterized by an yield value such as Bingham, Casson and Herschel Bulkley, are attracting the tribologists, at present. And also, the study of fluid inertia on thrust bearing is required to optimize the performance of the bearings. In this investigation, we have ventured to analyze the performance of the bearing by considering the combined effects of fluid inertia forces and non-Newtonian characteristic with Bingham fluid as lubricant in an externally pressurized converging circular thrust bearing. Such studies will be useful in the design of the bearing for the optimum performance using the appropriate lubricant in various machineries operating in an extreme condition in the industries. Averaging the inertia terms over film thickness and defining a modified pressure gradient, the rheodynamic lubrication equation containing inertia terms has been analyzed. Using the appropriate boundary conditions and considering externally pressurized flow in narrow clearance between two converging discs is symmetric w.r.t r and z axis, the velocity distributions, the modified pressure gradient and thereby the film pressure and the load capacity of the bearing have been obtained numerically for different values of Bingham number, Reynolds number and angle of convergence. In addition to that, the effects of the inertia forces, non-Newtonian characteristics and angle of convergence on the bearing performances have been discussed.
The combined effects of fluid inertia and viscous forces of a Herschel-Bulkley lubricant in an externally pressurized thrust bearing with circular geometry have been analyzed theoretically. Although the researchers of the past, laid out a foundation for the hydrodynamic lubrication, modern researchers intend to use non-Newtonian fluids characterized by a yield-value, such as Bingham, Casson and Herschel-Bulkley fluids as lubricants. More over, Tribologists emphasize a fact that in order to analyze the performance of the bearings adequately, it is necessary to consider the combined effects of fluid inertia and viscous forces of non-Newtonian lubricants. Therefore, in this research article, the combined effects of fluid inertia and viscous forces have been investigated theoretically in an externally pressurized thrust bearing with circular geometry using Herschel-Bulkley fluid as lubricant. The shape and extent of the core, along the radius, have been determined numerically for various values of the Herschel-Bulkley number and the power-law index. Using the appropriate boundary conditions, the velocity distributions in the flow and the core regions have been obtained. By considering the equilibrium of an element of the core in the fluid, the modified pressure gradient has been evaluated and thereby the film pressure and the load capacity of the bearing have been obtained numerically for different values of Reynolds number, Herschel-Bulkley number and power-law index. The effects of the inertia forces and the non-Newtonian characteristics of the lubricant, on the bearing performances have also been discussed.
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