Page 255 - Tribology in Machine Design

240 Tribology in machine design

the streamers and is influenced by surface tension forces. However it has
been found that it can be located with reasonable accuracy by imposing the
condition

at that point. When this condition, together with p=0 at x= — oo is
imposed on eqn (6.21) it is found that ^ =0.443, whence x x =0.475(2/?/i 0)*.
The pressure distribution is shown by the solid line curve in Fig. 6.4. In this
case the total load supported by the film is given by

In most practical situations it is the load which is specified. Then, eqn (6.23)
can be used to calculate the minimum film thickness h 0. To secure effective
lubrication, h 0 must be greater than the surface irregularities. It is seen from
eqn (6.23) that the load carrying capacity of the film is generated by a rolling
action expressed by (V^ + V 2). If the cylinders rotate at the same peripheral
velocity in opposite directions, then (V^ + V 2] is zero, and no pressure is
developed in the film.

Cose (ii) - Elastic cylinders
Under all engineering loads the cylinders deform elastically in the pressure
zone so that the expression for the film profile becomes

where u zl and u z2 are the normal elastic displacements of the two surfaces
and are given by the Hertz theory. Thus

This equation and the Reynolds eqn (6.18) constitute a pair of simultaneous
equations for the film shape h(x) and the pressure p(x). They can be
combined into a single integral equation for h(x) which can be solved
numerically. The film shape obtained in that way is then substituted into
the Reynolds equation to find the pressure distribution p(x).
An important parameter from the point of view of the designer is the
minimum film thickness h min. In all cases h min&Q.8hi. The lubrication
process in which elastic deformation of the solid surface plays a significant
role is known as elastohydrodynamic lubrication.

Case (Hi) - Variable viscosity of the lubricant
It is well known that the viscosity of most practical lubricants is very
sensitive to changes in pressure and temperature. In contacts characteristic
of higher kinematic pairs, the pressures tend to be high so that it is not