Technical and Research Bulletin 3-51 - Amazon Web Services

or more concisely
R3 = RI,3 + Σδj·Iδj,R3 (j = 1 ... N). (6-2)
Likewise the moment in the shaft at station 24 is calculated using the equation
M24 = MI,24 + Σδj·Iδj,M24 (j = 1 ... N) (6-3)
Using a general notation, the reaction at any bearing or can be determined using an influence
equation of the form
Ri = RI,i + Σδj·Iδj,Ri (j = 1 ... N) (6-4)
where i is the bearing or shaft station at which the reaction Ri is calculated, j is the bearing
number (j = 1 ... N), and
RI,i = the straight-line or initial reaction at station i (from the static analysis results)
δj = the shaft offset at bearing j
Iδj,Ri = the influence of a unit offset of the shaft at bearing j on the reaction at station i
(from the static alignment analysis).
The number of influence equations can become quite large for a system with several bearings
and shaft stations. However, the matrix formulation of the influence equations is readily
adaptable to a spreadsheet format, which makes practicable an iterative approach for
determining an “optimum” bearing alignment.
6.6 DETERMINING THE DESIGN ALIGNMENT
After the analysis is completed, identify the maximum and minimum bearing reactions and
the maximum bending moments for the assumed alignment, and determine if any of the
design criteria are violated. An acceptable alignment satisfies all the criteria, although this is
not necessarily an optimal alignment. There is no one best alignment; theoretically there are
an infinite number of alignment configurations that would produce the same bearing load and
component stress values. Calculating the final design alignment settings can require trial and
error, particularly if the system has several bearings. The ability to achieve a satisfactory
alignment with a variety of configurations is the primary reason that shafting systems work
on ships.
The influence coefficients are useful for determining how much a bearing must be offset to
correct a problem. For example, consider a case where the load on a stern tube bearing
exceeds its allowable limit by 5000 lbf (22 kN) under the worst-case ship operating
condition. Repositioning the bearing lower with respect to the other bearings would reduce
its load. Assume that the static analysis shows that the influence coefficient of the stern tube
bearing on itself is 50 lbf/mil (9·10 -3 N/mm). Therefore, setting this bearing 0.100 inches
(2.5 mm) lower will reduce its load by 5000 lbf (22 kN), thus eliminating the overload
condition on this bearing. The same result could have been achieved by raising one or both
adjacent bearings. Unfortunately, the solution is rarely so simple since repositioning one or
more bearings may solve one problem and create another. Realigning a bearing changes the
load on that bearing and every other bearing in the system, (as seen from the influence
coefficient matrix), and it also changes the bending moments, stresses, deflections, and
slopes at every station along the shaft.
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