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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).
Notes concerning the design of valve springs as affected by spring coil vibrations.

Identifier  ExFiles\Box 56\2\  Scan095
Date  28th August 1930
  
NOTES CONCERNING THE DESIGN OF VALVE SPRINGS
AS AFFECTED BY SPRING COIL VIBRATIONS.

The following symbols are used :-

Diameter of wire = d (")
" " coil = D (")
Number of effective turns = k
Density of wires (lbs. per inch³) = w
Free length of spring = L (")
Set up length of spring = L₀
Fully compressed length of spring = L'
Modulus of shear of material of wire = C (lbw/sq.")
Load on spring = W (lbw)
Set up deflection of spring = δ₁
Fully compressed deflection of spring. = δ₂
Stress on material = f (lbs/sq.")

It can be shown that for the spring in the state of compressed rest

f = (Cdδ)/(πD²k)

W = (Cd⁴δ)/(8D³k)

It has further been shown that the fundamental natural frequency vibration of a spiral spring fixed at one end is

N = ¼ √(E/M)
  
  


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