Summary
As a step towards formation of design rules for ball and socket joints, a solution of the lubrication equations for an “ideal” joint (in which the socket completely surrounds the ball) under steady loading and rotation is presented. The results are compared with those for an infinitely wide plain bearing. The friction for the ball is found to be higher, and the load capacity lower, than that of the plain bearing under similar conditions.
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Abbreviations
- h :
-
lubricant film thickness
- p :
-
pressure
- μ :
-
absolute viscosity
- \(\bar v, \bar w\) :
-
average of v, w, over film thickness h
- v, w :
-
components of fluid velocity in θ, φ directions
- U θ , U φ :
-
components of relative velocity of surfaces in θ, φ directions
- R :
-
mean radius of spheres
- H :
-
difference between ball and socket radii
- c :
-
eccentricity ratio
- Ω :
-
angular speed of ball
- B :
-
=pH 2/6μcΩR 2
- P :
-
load component along Oy
- N :
-
load component along Oz
- M :
-
driving moment to spin around Ox
- λ :
-
moment coefficient
- λ p , P p :
-
suffix p refers to unit width of plain bearing
Reference
Sommerfeld, A., The Mechanics of Deformable Bodies, Academic Press Inc., New York, 1950, pages 253–263.
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Tanner, R.I. Hydrodynamic lubrication of ball and socket joints. Appl. sci. Res. 8, 45–51 (1959). https://doi.org/10.1007/BF00411737
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DOI: https://doi.org/10.1007/BF00411737