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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).
Page from a report analyzing the causes and potential cures for vehicle wheel wobble or shimmy.

Identifier  ExFiles\Box 170\3\  img046
Date  14th July 1933 guessed
  
-14-

2. By increasing the inertia about the kingpin by adjustable weights and thus getting an increase of 20% or more in the total inertia, and then by jacking up the centre of the rear axle, we have produced wobbles as slow as 70 cycles per minute. Further increase in moment of inertia about the kingpins appears to remove all wobble from the system.

In every case the general cycle of events in the relation between wobble and the sinusoidal path of the wheels appears to be the same. However in really violent wobble of type (1) above, the loop of the wheel spindle is inclined at nearly 45° and has the general form of the initial loop of the shimmy cycle.

Frequency.

In every case the controlling frequency appears to be the frequency of car snake. For example in the normal 350 a minute low speed wobble with steering gear connected, considerable changes can be made in wheel inertia or in stiffness of the remaining means used to control the wheels (such as springs on the tie rod butting against the frame) without any very great change in the wobble frequency. When one attempts to make the wobble frequency exceed 400 a minute, or drop below 350 a minute, it disappears entirely.

Consequently slack or flexibility in the steering system, which must lower the natural wobble frequency considerably, changes the actual frequency of self-induced wobble very little, and only makes the resulting wobble more violent. Increasing caster which also must raise the natural frequency about the kingpins, does not result in a cure, but through increasing the excitation, makes the wobble much worse.

The chief cures (besides damping friction in the steering mechanism) appear to be :-

reducing caster as much as possible, to reduce excitation.

stiffening the steering mechanism to raise the natural frequency of wobble.

Other chances.

Changing the natural rocking frequency of the car, or greatly increasing the moment of inertia about the
  
  


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