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Bearing Design in Machinery Episode 1 Part 8

Tham khảo tài liệu 'bearing design in machinery episode 1 part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The journal surface velocity is U ROj and the sleeve surface velocity is the product XU where X is the rolling-to-sliding ratio. The common journal bearing has a pure sliding and X 0 while in pure rolling X 1. For all other combinations 0 X 1. The tangential velocities in the x direction of the fluid-film boundaries of the two surfaces are U1 R1 ữh XRo _ 1 t 6-18 U2 ROj cos a ROj The normal components in the y direction of the velocity of the fluid film boundaries journal and sleeve surfaces are V1 0 @h V2 Ro 1 j @x 6-19 For the general case of a combined rolling and sliding the expression on the right-hand side of Reynolds equation is obtained by substituting the preceding components of the surface velocity . @h @h . @h 6 U1 - U2 -h 12 V2 - V1 6 XU - U @h 12 U-h - 0 @x @x @x @h 6U 1 X -h 6-20 @x Here U ROj is the journal surface velocity. Finally the Reynolds equation for a combined rolling and sliding of a journal bearing is as follows d ih3 @p d ih3 dp @h -7- I 7- I 6Ro - 1 XH-@x m iixj @z m @z - óx 6-21a For X 0 and X 1 the right-hand-side of the Reynolds equation is in agreement with the previous derivations for pure sliding and pure rolling respectively The right-hand side of Eq. 6-21a indicates that pure rolling action doubles the pressure wave in comparison to a pure sliding. Equation 6-21a is often written in the basic form d ih3 dp d ih3 dp @h 771 7777 I 77Ã7 6R oj ob 77 -x m -x -z m -z -x 6-21b In journal bearings the difference between the journal radius and the bearing radius is small and we can assume that R1 R. Copyright 2003 by Marcel Dekker Inc. All Rights Reserved. 6.5 PRESSURE WAVE IN A LONG JOURNAL BEARING For a common long journal bearing with a stationary sleeve the pressure wave is derived by a double integration of Eq. 6.12 . After the first integration the following explicit expression for the pressure gradient is obtained d 6U m dx h C1 h3 6-22 Here C1 is a constant of integration. In this equation a regular derivative replaces the partial