Reynolds equation reduced to ordinary differential equations by separation of variables. Two resulting equations integrated directly. Third equation and boundary conditions interpreted and solved as an isoperimetric problem.
Get full access to this article
View all access options for this article.
References
1.
SzeriA.PowersD. ‘Full journal bearings in turbulent and laminar regimes’, J. mech. Engng Sci.19679 (No. 3), 167.
2.
SzeriA.PowersD. ‘Pivoted plane pad bearings; a variational solution’, J. lubric. Technol., Trans. Am. Soc. mech. Engrs197092 (Series F), 466.
3.
PinkusO.SternlichtB.Theory of hydrodynamic lubrication1960 (McGraw-Hill Inc., New York).
4.
McCutchenC. W. ‘The frictional properties of animal joints’, Wear19625, 1.
5.
LinnF. C. ‘Lubrication of animal joints: 1. The arthrotripsometer’, J. Bone Jt Surg.196749A, 1079.
6.
McCutchenC. W. ‘Physiological lubrication’, Proc. Instn mech. Engrs1967181 (Pt 3J), 55.
7.
LinnF. C. ‘Lubrication of animal joints: II. The mechanism’, J. biomech.19681, 193.
8.
WilkinsJ. F. ‘Proteolytic destruction of synovial boundary lubrication’, Nature, Land.1968219, 1050.
9.
LinnF. C.RadinE. L. ‘Lubrication of animal joints: III. The effect of certain chemical alterations of the cartilage and lubricant’, Arthritis Rheum.196811, 674.
10.
RadinE. L.SwannD. A.WeisserP. A. ‘Separation of a hyaluronate-free lubricating fraction from synovial fluid’, Nature, Lond.1970228, 377.
11.
McCutchenC. W. ‘Boundary lubrication by synovial fluid: Demonstration and possible osmotic explanation’, Fedn Proc. Fedn Am. Socs exp. Biol.196625, 1061.
12.
LongfieldM. D.DowsonD.WalkerP. S.WrightV. ‘Boosted lubrication of human joints by fluid enrichment and entrapment’, Biomed. Eng.19694 (No. 11), 517.
13.
MorrisonJ. B. ‘Bio-engineering analysis of force actions transmitted by the knee joint’, Bio-medical Engng19683 (No. 4), 164.
14.
The following communication relates to the paper ‘Dimensional analysis of wear by particle impact in fluid flows’, by J. C. GIBBINGS, published in 1971, vol. 13, No. 4, p. 234.
15.
FinnieI.WolakJ.KabilY. ‘Erosion of metals by solid particles’, J. Mater.19672 (No. 3), 682.
16.
SheldonG. L. ‘Similarities and differences in the erosion behaviour of materials’, Trans. Am. Soc. mech. Engrs197092 (Series D), 619.
17.
BitterJ. G. A. ‘A study of erosion phenomena: Parts I and II’, Wear19636, 5 and 169.
18.
GoodwinJ. E.SageW.TillyG. P. ‘Study of erosion by solid particles’, Proc. Instn mech. Engrs1969–70184 (Pt 1), 279.
19.
TillyG. P.SageW. ‘The interaction of particle and material behaviour in erosion processes’, Wear197016, 447.
20.
LangmuirI.BlodgettK. ‘Mathematical investigation of water droplet trajectories’, U. S. Army Air Force Tech. Kept 5418, 1946.
21.
TillyG. P. ‘Erosion caused by airborne particles’, Wear196914, 63.
22.
WoodC. D.EspenschadeP. W. ‘Mechanisms of dust erosion’, S. A. E. Summer Meeting Pre-print 880A, 1964.
23.
SageW.TillyG. P. ‘The significance of particle size in sand erosion of small gas turbines’, Jl R. aeronaut. Soc.196973 (No. 701), 427.
24.
SchonG.MasudaS. ‘Expansion of a space-charge cloud’, J. appl. Phys.19692 (Series 2), 115.
