Toroidal Vortex Flow

1. Toroidal Vortex Flow Conditions for vortex flow: Taylor Number: Reynolds Number: Figure 7.1 Toroidal vortex flow in a journal bearing.

2. Mass Flow Figure 7.1 Mass flow through rectangular-section control volume. (a) x-y plane; (b) y-z plane; (c) x-y plane. [From Hamrock and Dowson (1981).]

3. Reynolds Equation

4. Reynolds Equation Terms Figure 7.3 Density wedge. Figure 7.4 Stretch mechanism.

5. Reynolds Equation Terms Figure 7.5 Physical wedge mechanism. Figure 7.6 Normal squeeze mechanism.

6. Reynolds Equation Terms Figure 7.7 Translation squeeze mechanism. Figure 7.8 Local expansion mechanism.

7. Possible Motion in Bearings Figure 7.9 Normal squeeze and sliding velocities.

8. Possible Motion in Bearings Figure 7.9 Normal squeeze and sliding velocities.

9. Parallel-Surface Slider Bearing Figure 8.1 Velocity profiles in a parallel-surface slider bearing.

10. Flow in Inclined Slider Figure 8.2 Flow within a fixed-incline slider bearing (a) Couette flow; (b) Poiseuille flow; (c) resulting velocity profile.

11. Thrust Bearing Figure 8.3 Force components and oil film geometry in a hydrodynamically lubricated thrust sector. Figure 8.3 Thrust bearing geometry.

12. Parallel-Surface Bearing Figure 8.5 Parallel-surface slider bearing.

13. Fixed-Incline Slider Bearing Figure 8.6 Fixed-incline slider bearing. Figure 8.7 Pressure distributions of fixed-incline slider bearing.

14. Fixed-Incline Bearing Results Figure 8.8 Effect of film thickness ratio on normal load-carrying capacity. Figure 8.9 Effect of film thickness ratio on force components.

15. Fixed-Incline Bearing Results Figure 8.10 Effect of film thickness ratio on friction coefficient parameter. Figure 8.11 Effect of film thickness ratio on dimensionless volume flow rate.

16. Fixed-Incline Bearing Results Figure 8.12 Effect of film thickness ratio on dimensionless adiabatic temperature rise. Figure 8.13 Effect of film thickness ratio on dimensionless center of pressure.

17. Streamlines in Fixed-Incline Slider Bearing Figure 8.14 Streamlines in fixed-incline bearing at four film thickness ratios Ho. (a) Ho =2; (b) Ho =1 (critical value).

18. Streamlines in Fixed-Incline Slider Bearing (cont.) Figure 8.14 Concluded. (c) Ho = 0.5; (d) Ho = 0.25.

19. Parallel-Step Bearing Figure 8.15 Parallel-step slider bearing.

20. Parallel-Step Pad Slider Bearing Figure 9.1 Finite parallel-step-pad slider bearing.

21. Parallel-Step-Pad Bearing Results

22. Parallel-Step-Pad Bearing Results

23. Parallel-Step-Pad Bearing Results Figure 9.3 Shrouded-step slider bearings. (a) Semicircular step; (b) truncated triangular step.

24. Fixed-Incline-Pad Slider Bearing Figure 9.4 Side view of fixed-incline-pad bearing. [From Raimondi and Boyd (1955).] Figure 9.5 Configurations of multiple fixed-incline-pad thrust bearing. [From Raimondi and Boyd (1955).]

25. Film Thickness for Given Surface Finish

26. Fixed-Incline Slider Results Figure 9.6 Chart for determining minimum film thickness corresponding to maximum load or minimum power loss for various pad proportions - fixed-incline-pad bearings. [From Raimondi and Boyd (1955).]

27. Fixed-Incline Slider Results Figure 9.7 Chart for determining minimum film thickness for fixed-incline-pad thrust bearings. [From Raimondi and Boyd (1955).]

28. Fixed-Incline Slider Results Figure 9.8 Chart for determining dimensionless temperature rise due to viscous shear heating of lubricant in fixed-incline-pad thrust bearings. [From Raimondi and Boyd (1955)]

29. Fixed-Incline Slider Results Figure 9.9 Chart for determining performance parameters of fixed-incline-pad thrust bearings. (a) Friction coefficient; (b) power loss. [From Raimondi and Boyd (1955)].

30. Fixed-Incline Slider Results Figure 9.9 Concluded. (c) Lubricant flow; (d) lubricant side flow.

31. Pivoted-Pad Slider Bearing Figure 9.10 Side view of pivoted-pad thrust bearing. [From Raimondi and Boyd (1955).] Figure 9.11 Configuration of multiple pivoted-pad thrust bearing. [From Raimondi and Boyd (1955).]

32. Pivoted-Pad Slider Results Figure 9.12 Chart for determining pivot location corresponding to maximum load or minimum power loss for various pad proportions - pivoted-pad bearings. [From Raimondi and Boyd (1955).]

33. Pivoted-Pad Slider Results Figure 9.14 Chart for determining dimensionless temperature rise due to viscous shear heating of lubricant for pivoted-pad thrust bearing. [From Raimondi and Boyd (1955).] Figure 9.13 Chart for determining outlet film thickness for pivoted-pad thrust bearings. [From Raimondi and Boyd (1955).]

34. Pivoted-Pad Slider Results Figure 9.15 Chart for determining performance parameters for pivoted-pad thrust bearings. (a) Dimensionless load; (b) friction coefficient. [From Raimondi and Boyd (1955).]

35. Pivoted-Pad Slider Results Figure 9.15 Concluded. (c) Lubricant flow; (d) lubricant side flow; (e) power loss.

36. Journal Bearing Figure 10.2 Unwrapped film shape in a journal bearing. Figure 10.1 Hydrodynamic journal bearing geometry.

37. Sommerfeld Angle

38. Full Sommerfeld Solution Sommerfeld substitution: Pressure distribution: Maximum pressure: Figure 10.3 Pressure distribution for full Sommerfeld solution.

39. Forces for Sommerfeld Solution Figure 10.4 Coordinate system and force components in a journal bearing. Figure 10.5 Vector forces acting on a journal.

40. Reynolds Boundary Condition Figure 10.7 Pressure profile for a journal bearing using Reynolds boundary condition. Figure 10.6 Location of shaft center for full and half Sommerfeld journal bearing solutions.

41. Hydrodynamic Journal Bearings Sommerfeld number: Diameter-to-width ratio: Figure 11.1 Pressure distribution around a journal bearing.

42. Film Thickness and Eccentricity Figure 11.2 Effect of bearing number on minimum film thickness for four diameter-to-width ratios. [From Raimondi and Boyd (1958)].

43. Attitude Angle Figure 11.3 Effect of bearing number on attitude angle for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]

44. Friction Coefficient Figure 11.4 Effect of bearing number on friction coefficient for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]

45. Fluid Flow Figure 11.5 Effect of bearing number on dimensionless flow rate for four diameter-to-width ratios. [From Raimondi and Boyd (1958).] Figure 11.6 Effect of bearing number on volume side flow ratio for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]

46. Maximum Pressure & Location Figure 11.7 Effect of bearing number on dimensionless maximum film pressure for four diameter-to-width ratios. [From Raimondi and Boyd (1958).] Figure 11.8 Effect of bearing number on location of terminating and maximum pressures for four diameter-to-width ratios. [From Raimondi and Boyd (1958).]

47. Effect of Radial Clearance Figure 11.9 Effect of radial clearance on some performance parameters for a particular case.

48. Fixed-Incline Pad Journal Bearings

49. Effect of Preload Figure 11.11 Effect of preload factor mp on two-lobe bearings. (a) Largest shaft that fits in bearing. (b) mp =0; largest shaft, ra; bearing clearance cb = c. (c) mp =1.0; largest shaft, rb; bearing clearance cb =0. [From Allaire and Flack (1980).]

50. Hydrodynamic Squeeze Film Bearings Figure 12.2 Journal bearing with normal squeeze film action. Rotational velocities are all zero. Figure 12.1 Parallel-surface squeeze film bearing.