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Bearing Design in Machinery Episode 1 Part 7

Tham khảo tài liệu 'bearing design in machinery episode 1 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | However if the x coordinate is in the direction of a diverging clearance the clearance increases with x as shown in Fig. 1-2 Eq. 5-15 changes its sign and takes the following form 6U m dx h0 - h for initial 0 positive slope in Fig. 4-5 5-15 5.4 FLUID FILM BETWEEN A FLAT PLATE AND A CYLINDER A fluid film between a plate and a cylinder is shown in Fig. 5-4. In Chapter 4 the pressure wave for relative sliding is derived where the cylinder is stationary and a flat plate has a constant velocity in the x direction. In the following example the previous problem is extended to a combination of rolling and sliding. In this case the flat plate has a velocity U in the x direction and the cylinder rotates at an angular velocity o around its stationary center. The coordinate system x y is stationary. In Sec. 4.8 it is mentioned that there is a significant pressure wave only in the region close to the minimum film thickness. In this region the slope between the two surfaces the fluid film boundaries as well as between the two surface velocities is of a very small angle a. For a small a we can approximate that cos a 1. Fig. 5-4 Fluid film between a moving plate and a rotating cylinder. Copyright 2003 by Marcel Dekker Inc. All Rights Reserved. In Fig. 5-4 the surface velocity of the cylinder is not parallel to the x direction and it has a normal component V2. The surface velocities on the rotating cylinder surface are _ _dh __ U2 oR cos a oR V2 o R 5-16 dx At the same time on the lower plate there is only velocity U in the x direction and the boundary velocity is U1 U V1 0 5-17 Substituting Eqs. 5-16 and 5-17 into the right side of Eq. 5-11 yields . dh dh dh 6 U1 - U2 12 V2 - V1 6 U - oR 12oR d- dx dx dx .dh . . 6 U oR 5-18 dx The Reynolds equation for a fluid film between a plate and a cylinder becomes d h3 ap d h3 dp dh T ãz 6 U oR 5-19 dx m dx dz m dz dx For a long bearing the pressure gradient in the axial direction is negligible dp dz ffi 0. Integration of Eq. 5-19 yields