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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Theoretical analysis of spring stresses, frequency, and deflection, including mathematical formulas.

Identifier  ExFiles\Box 56\2\  Scan099
Date  28th August 1930 guessed
  
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d/kD^2 however, has been put up which means that 1/kD^5/3
has been put up. This can be done either by reducing k or
reducing D.{John DeLooze - Company Secretary} Other circumstances could be brought into
account to determine whether the change should be made
by altering k on the one hand or D on the other.
It will be clear that in any case the rate of the
spring would have been increased because the set up load
remaining the same the initial deflection is less. The
stress on the material may suffer no change in the set up
position or may be increased, but in the fully compressed
position it will be increased in either case, still, as
mentioned before, the reduction in dynamic stress due to
increased frequency number of the spring may more than
counteract this. Beyond the general lines of change
indicated in the above, no definite rule for the change can
be laid down because it is difficult to estimate the
relative magnitude of the stresses due to the natural periods
in the spring and those due to the statical conditions.
From the fact that the frequency and the material
static stress for a given deflection vary as the same
quantity d/kD^2 it will readily be seen that there is no
optimum set of quantities which can be arrived at to give
the maximum frequency for a given stress per unit deflection.
The whole problem/therefore somewhat indefinite and can
  
  


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