(5) (5) (5) (5) The lubrication of bearings is a problem in fluid mechanics. The oil...

 

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(5) (5) (5) (5) The lubrication of bearings is a problem in fluid mechanics. The oil or lubricant between the bearing and the slider is a viscous fluid and most bearings operate in the laminar range with a very small Reynolds number. The spacing between the bearing and the slider (the flow gap) is much smaller than the length of the slider so that the flow becomes fully developed throughout most of the gap. Because the Reynolds number is so small, the inertia of the fluid is negligible compared with the pressure and viscous forces. Consider a step boaring moving at velocity U, as shown in Figure 3. The spacings h and h are much less than L and L and the width of the bearing in the z direction is assumed to be very large, so that leakage in the z direction can be neglected. To facilitate the analysis, we attach coordinate systems to the slider with the origins at the beginning of each bearing section and we invert the direction of y, such that the relative velocity is u=0 when y = 0, and u=-U when y = h in the respective sections. 4 42 Y+ slider bearing P=0 P=0 V Figure 3: The step bearing and its pressure distribution. (a) Assuming incompressible flow of a Newtonian fluid, simplify the equations of motion (the Navier-Stokes equations) in z and in y directions. (b) Find an expression for the total flow rate and for the pressure change between any two points in a single section of the bearing. (c) Find an expression for the relative pressure distribution in the step bearing, assuming a zero gauge pressure at the inlet and outlet, as shown in Figure 3. (d) Calculate the total load carrying capacity per unit length of z for a step bearing with the following conditions: U-0.5 m/s; oil-3.85 (N s)/m; Poil-900 kg/m h1 mm; L-30 mm h2 mm; L=100 mm (5) (5) (5) (5) The lubrication of bearings is a problem in fluid mechanics. The oil or lubricant between the bearing and the slider is a viscous fluid and most bearings operate in the laminar range with a very small Reynolds number. The spacing between the bearing and the slider (the flow gap) is much smaller than the length of the slider so that the flow becomes fully developed throughout most of the gap. Because the Reynolds number is so small, the inertia of the fluid is negligible compared with the pressure and viscous forces. Consider a step boaring moving at velocity U, as shown in Figure 3. The spacings h and h are much less than L and L and the width of the bearing in the z direction is assumed to be very large, so that leakage in the z direction can be neglected. To facilitate the analysis, we attach coordinate systems to the slider with the origins at the beginning of each bearing section and we invert the direction of y, such that the relative velocity is u=0 when y = 0, and u=-U when y = h in the respective sections. 4 42 Y+ slider bearing P=0 P=0 V Figure 3: The step bearing and its pressure distribution. (a) Assuming incompressible flow of a Newtonian fluid, simplify the equations of motion (the Navier-Stokes equations) in z and in y directions. (b) Find an expression for the total flow rate and for the pressure change between any two points in a single section of the bearing. (c) Find an expression for the relative pressure distribution in the step bearing, assuming a zero gauge pressure at the inlet and outlet, as shown in Figure 3. (d) Calculate the total load carrying capacity per unit length of z for a step bearing with the following conditions: U-0.5 m/s; oil-3.85 (N s)/m; Poil-900 kg/m h1 mm; L-30 mm h2 mm; L=100 mm

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Youve provided an image describing the problem of lubrication in bearings specifically a step bearing with a pressure distribution due to a slider moving at velocity U The problem asks for various ana... View the full answer