Page 206 - Tribology in Machine Design

Sliding-element bearings 191

to-diameter ratio is often less than 1.0. This makes the flow in the Z
direction and the end leakage a much larger portion of the whole. Michell in
1929 and Cardullo in 1930 proposed that the dp/dz term of eqn (5.43) be
retained and the dp/dx term be dropped. Ocvirk in 1952, by neglecting the
parabolic, pressure-induced flow portion of the U velocity, obtained the
Reynolds equation in the same form as proposed by Michell and Cardullo,
but with greater justification. This form is

Unlike eqn (5.44), eqn (5.46) is easily integrated, and it leads to the load
number, a non-dimensional group of parameters, including length, which is
useful in design and in plotting experimental results. It will be used here in
the remaining derivations and discussion of the principles involved. It is
known as the Ocvirk solution or the short-bearing approximation. If there
is no misalignment of the shaft and bearing, then h and dh/dx are
independent of z and eqn (5.46) may be integrated twice to give

From the boundary conditions dp/dz=Q at z =0 and p =0 at z = ± j. This is
shown in Fig. 5.14. Thus

Figure 5.14