Page 209 - Tribology in Machine Design

194 Tribology in machine design

integration must be made from zero to 2n, thus

The short bearing approximation assumes a linear velocity profile such that
(du/dy)y=o = (du/dy)y= H-Use of this approximation in eqn (5.53) will give
but one torque, contrary to the equilibrium condition of eqn (5.50). How-
ever, the result has been found to be not too different from the experi-
mentally determined values of the stationary member torque T s. Hence
we use eqn (5.53), with h from eqn (5.42), integrating and substituting
c = c d/2, r = d/2 and V v — U 2 = nd(n 2 — n\) where n 2 and n t are the rotation-
al velocities in r.p.s; the results are

Dimensionless torque ratios are obtained by dividing T s or T r by the no-
load torque T 0 given by the formula

and first setting n' = n 2— n\. Thus

5.5.3. Thermo-flow considerations
The amount of oil flowing out at the end of a journal bearing, i.e. the oil loss
at plane z=^orz= — ^ may be determined by integration of eqn (5.3b) over
the pressure region of the annular exit area, substituting rd0 for dx. Thus,
since W l = W 2=Q

To determine the flow Q H out of the two ends of the converging area or the
hydrodynamic film, dp/dz is obtained from eqn (5.48), h from eqn (5.42), and
Q» = 2Q from eqn (5.56). The limits of integration may be ©!=0 and
0 2 =TT, or the extent may be less in a partial bearing. However, Q H is more
easily found from the fluid rejected in circumferential flow. With the linear
velocity profiles of the short bearing approximation, shown in Fig. 5.16, and