By A. Dorinson and K.C. Ludema (Eds.)

Even though it is widely known that friction, put on and lubrication are associated jointly in one interdisciplinary advanced of medical studying and technological perform, fragmented and really good methods nonetheless predominate. during this booklet, the authors research lubrication from an interdisciplinary point of view. They show that after the remedy of lubrication is published from the confines of the fluid movie thought, this interdisciplinary procedure comes into complete play. Tribological habit in terms of lubrication is then tested from significant issues of view: one is mechanical, not just with admire to the houses and behaviour of the lubricant but additionally of the surfaces being lubricated. the opposite is chemical and encompasses the chemistry of the lubricant, the surfaces and the ambient atmosphere. it truly is within the emphasis at the interplay of the elemental mechanical and chemical methods in lubrication that this publication differs from traditional remedies.

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**Example text**

The flow derivatives in the expressions for a , b , c , etc. can be regarded as displacements occurring in the time interval 6 t . Consider a point 0 (x,y,z) in the body of the fluid and a neighboring point 0' a distance h away, as shown in Fig. 3-2, such that 6x = Lh, 6y = mn, Figure 3-2. 6z = nh Orientation of the flow vectors in a fluid. 30 While 0 is being displaced by the flow components u , v , w in the time interval 6 t , 0‘ is being displaced by the components u + 6u, w + 6v, w + 6w. The net effect is elongation of the element: and if we define 5 as unit elongation, then au au 6X + - 6y + ( av 6g + + - av 6X + ax - 6z az ag - 6g a9 + - 62 az aw (3-4) 2Z After dividing through by n 2 and using its components, remembering that second order infinitesimal quantities such a s squares and cross-products can be neglected, we eventually arrive at By analogy with the treatments of strain as given in the texts on elasticity 1 2 1 , we define a radius vector to the point x , g , z such that k 9n substituting the appropriate equivalents into Eqn 3-5 we get k k2 = ax 2 + by2 + cz 2 + dlgz + d2xz + d3xg (3-6) The physical meaning of Eqn 3-6 is this: as the plane ABC (c6.

3. The flow is laminar; there anywhere within the film. 4. No external forces act on the film, so that X 5. Fluid inertia (acceleration forces, centrifugal forces in curved films, fluid gravity) i s negligible compared to viscous shear and hence UulUt = U w I D R = h l U t = 0. 6. There is no slip at the bearing surface. 7. all Compared with the two velocity gradients au/*dy and aw/’ay, other velocity gradients are negligible. This assumption would not be valid without assumption 3 . Derivatives of higher order of all velocity gradients other than ;lu/ay and a w / a y and with respect to variables other than y will drop out.

The geometrical coordinate x is measured from the center line in either direction. Each element of load p(n)dn along the entire line of the boundary from b , to b 2 acts at the location x to contribute to the normal displacement J, at that location as calculated by Eqn 3-52. II Figure 3-6. I . Elastic deformation of boundary and thickness of oil film. The elastohydrodynamic solution requires that Eqns 3-44, 3-45 and 3-46 be satisfied simultaneously. A full analytical solution has not yet been found, but numerical methods have been developed f o r use with the aid of high-speed digital computers.