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Tham khảo tài liệu 'kinematics and mechanisms 2008 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Consider a very small volume element of the lubricant moving in the direction of rotation of the journal in this case the x direction. The forces that act on this elemental volume and stabilize it are shown in Fig. 23.6. Here P is the pressure in the oil film at a distance x. It is independent of the thickness of the oil film or the y dimension. S is the shear stress in the oil film at a distance y above the bearing surface which is at y 0. The length L of the bearing is in the z direction. The equilibrium condition of this volume element gives us the following relationship Slaymaker 1955 Fuller 1984 P f dx dx dy dz S dx dz S Ẽ dy dy dx dz P dy dz 0 23.1 Therefore dp 23.2 dy J dx J Equation 23.2 represents a very important fundamental relationship. It clearly shows how the load-carrying pressure P is developed. It is the rate of change of the shear stress in the direction of the oil film thickness that generates the hydrostatic pressure P. As we shall see from Eq. 23.3 the shear stress is directly proportional to the shearing rate of the oil film dv dy as dv dy increases dS dy must increase. Since the thickness of the oil film decreases in the direction of rotation of the journal a progressive increase in the shearing rate of the oil film automatically occurs because the same flow rate of oil must be maintained through diminishing cross sections i.e. decreasing y dimension . This progressive increase in the shearing rate is capable of generating very high positive hydrostatic pressures to support very high loads. A profile of the pressure generated in the load-supporting segment of the oil film is shown in Fig. 23.5. By introducing the definition of the coefficient of viscosity we can relate the shear stress to a more measurable parameter such as the velocity v of the lubricant as S Ỉ 23.3 dy Figure 23.6 Schematic representation of the forces acting on a tiny volume element in the hydrodynamic lubricant film around a rotating journal. 1998 by CRC PRESS LLC .
