NNR IN RAPIDLY ROTATED METALS By - Nottingham eTheses ...

4.2.3 STRESSES
- 45 -
The rotor has to withstand the large internal stresses gener-
ated by rapid rotation. Considering the simplified case of an
infinitely long hollow tube (and hence ignoring axial stresses)
the radial and tangential stresses are given by(5l)
a
r=r8l
23+u [a2+b2-r2-a2b2-
Q= pw2 3+u ra2 3u
+ b2 -1- r2 + a2b2
tr8L 3+ 11
r2
where Wr is the angular velocity, p is the Poisson ratio and p is
the density of the rotor material; a and b are the internal and
external radii respectively. Therefore the maximum tangential
stress acts at the inner edge of the tube. The radial stress is
zero at the surfaces and has a maximum value at a radius given
by ab.
For the case of a solid rod a is zero and the maximum stresses
act at the centre where
at =a =pb2w2 3 8u
These stresses are proportional to the squares of both the external
radius and the spinning frequency.
4.2.4 THE PROBLEM OF WHIRL AND ROTOR BALANCE(52)
Probably the simplest rotor system would take the form of a
cylinder supported by one or more journal bearings, but most journal
r2
(4.1)
(4.2)