Design and Stress Analysis of Extraterrestrial ... - The Black Vault

In the calculation of forces, we make the following assumption.
We shall assume that the flow of the working fluid in all elements
of the bearing is turbulent. This assumption is valid since lubrication
is accomplished by a liquid-metal heat carrier with low
viscosity. In addition, the high angular velocity contributes to the
turbulent flow of the lubricant. We shall assume that the motion
of the fluid in the bearing is quasi-stationary, i.e., the calculation
of nonstationary forces in bearings is performed according to
formulas of stationary flow. This is valid if the ratio of the
Reynolds numbers for the stationary and pulsating components of the
flow is Re nyAbc/RecTaH = 0-1.0 [nynbc = pulsation; CTaH = stationary].
Usually this relationship is maintained in the designs being studied.
It is further assumed that the working fluid is incompressible,
the viscosity of the fluid is constant, and there are no breaks in
the lubricating layer.
With these assumptions we shall set up an equation of the flow
rate for the i-th chamber of an N-chamber hydrostatic bearing with
diaphragm or capillary compensation (Fig. 3.85):
2Q ri+ Q j+1+ +, Q j, - 1 + Q3.l = 0, S-
(3.145)
where Qi is the flow rate through the nozzle, cm3/s;
QTi is the flow rate through the end connector of the chamber;
Qi i+l; Qi i-i are the flow rates along the connectors with
i + 1 and i - 1 chambers;
Q Bi is the flow rate of the liquid displaced from the i-th
chamber, caused by the forward speed of the pivot.
The first three terms in equation (3.145) can be represented
in the following form:
387