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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).
Technical analysis of wheel shimmy and tramp, including diagrams of wheel movement.

Identifier  ExFiles\Box 170\3\  img033
Date  14th July 1933 guessed
  
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At A when the wheel meets the ground, it is toed in and produces a side thrust F in the direction of the arrow. This has a moment arm h about the roll axis of the axle. The couple F x h is such as to push the right front wheel down. At E as the wheel starts to leave the ground, the condition is reversed.

These couples lead the corresponding displacements of the axle by a phase angle of about 90° and so feed energy into the tramp.

[DIAGRAM]
C SHIMMY STARTING
E END OF SHIMMY
A
B
D
F
G

If the sketch represents a right wheel and A is a spot at the centre of the wheel hub, it is observed that during the shimmy this spot moves in a loop as shown, the rotation of the spot round the loop being the same direction as the rotation of the wheel.

When the shimmy is at a maximum, the loop is vertical as shown at B. On drums it has been observed as large as 3 inches high and 1-1/2 inches wide. This indicates a tramp of 3" either side of centre and a wobble of 5° either side of centre. When this occurs at a frequency of 600 cycles a minute and a speed of 50 to 60 miles per hour, it is easy to show that the forces involved are very high.
  
  


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