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Bearing Design in Machinery Episode 1 Part 9

Tham khảo tài liệu 'bearing design in machinery episode 1 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The preceding equation is converted into dimensionless terms see Example Problem 6-1 - _ x 7 h h0 x ffi h hy and h0-Ĩ. dp 6pU 1 X x x2 dx h2 1 x2 3 Converting the pressure gradient to dimensionless form yields x2 x0 1 x2 3 ffi - dp 1 X ự2RÃ 6mU dx The left hand side of the equation is the dimensionless pressure X p 1 X dp 1 X X2 X0 1 X2 3 dx p0 hn _ 1 r ffiffi puj 0 Here p0 is a constant of integration which is atmospheric pressure far from the minimum clearance. In this equation p0 and x0 are two unknowns that can be solved for by the practical boundary conditions of the pressure wave compare to Eqs. 6-67 p p0 at x x1 dp -7- 0 at x x2 dx 2 p 0 at x x2 Atmospheric pressure is zero and the first boundary condition results in p0 0. The location of the end of the pressure wave x2 is solved by iterations. The solution is performed by guessing a value for x x2 then x0 is taken as x2 because at that point the pressure gradient is zero. The solution requires iterations in order to find x0 x2 which satisfies the boundary conditions. For each iteration integration is performed in the boundaries from 0 to x2 and the solution is obtained when the pressure at x2 is very close to zero. For numerical integration the boundary x1 where the pressure is zero is taken as a small value such as x 1 4. The solution is presented in Fig. 6-10. The curves indicate that the pressure wave is higher for higher rolling ratios. This means that the rolling plays a stronger role in hydrodynamic pressure generation in comparison to sliding. Copyright 2003 by Marcel Dekker Inc. All Rights Reserved. 6-2 A flat plate slides on a lubricated cylinder as shown in Fig. 4-7. The cylinder radius is R the lubricant viscosity is m and the minimum clearance between the stationary cylinder and plate is hn. The elastic deformation of the cylinder and plate is negligible. 1. Apply numerical iterations and plot the dimensionless pressure wave. Assume practical boundary conditions of the pressure according to Eq.