tailieunhanh - Engineering Tribology 2E Episode 4

Tham khảo tài liệu 'engineering tribology 2e episode 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Hydrodynamic Lubrication 111 Figure Pressure distribution in the long bearing approximation. Now a boundary condition is needed to solve this equation and it is assumed that at some point along the film pressure is at a maximum. At this point the pressure gradient is zero . dp dx 0 and the corresponding film thickness is denoted as h . Thus the boundary condition is dP 0 at h h dx Substituting to gives C -6Unh and the final form of the one-dimensional Reynolds equation for the long bearing approximation is 1 1 F dp h - h dx L which is particularly useful in the analysis of linear pad bearings. Note that the velocity U in the convention assumed is negative as shown in Figure . Narrow Bearing Approximation Finally it is assumed that the pressure gradient acting along the x axis is very much smaller than along the y axis . dp dx dp dy as shown in Figure . This is known in the literature as a narrow bearing approximation or Ocvirk s approximation 3 . Actually this particular approach was introduced for the first time by an Australian . Michell in 1905. It was applied to the approximate analysis of load capacity in a journal bearing 10 . A similar method was also presented by cardullo 62 . Michell observed that the flow in a bearing of finite length was influenced more by pressure gradients perpendicular to the sides 112 Engineering Tribology of the bearing than pressure gradients parallel to the direction of sliding. A formula for the hydrodynamic pressure field was derived based on the assumption that dp dx dp dy. This work was severely criticized by other workers for neglecting the effect of pressure variation in the x direction when equating for flow in the axial or y direction and the work was ignored for about 25 years as a result of this initial unenthusiastic reception. Ocvirk and Dubois later developed the idea extensively in a series of excellent papers and Michell s approximation has since gained general acceptance. The utility