A new shimmy model

• Published in: Proceedings of the Steklov Institute of Mathematics Vol. 281; no. 1; pp. 27 - 36
• Main Authors: Zhuravlev, V. Ph, Klimov, D. M., Plotnikov, P. K.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-07-2013
• Subjects: Mathematics; Mathematics and Statistics; STEKLOV Institute; Ball Bearing; Torsional Vibration; Slip Velocity; Front Wheel
• ISSN: 0081-5438; 1531-8605
• DOI: 10.1134/S0081543813040044

Shimmy is a phenomenon of intense angular self-excited vibrations of the wheels of a carriage. Such self-excited vibrations present a serious threat to traffic safety, which accounts for the great interest of researchers in this phenomenon. The problem is of highest importance for the front wheels of aircraft. Usually, the deformation of pneumatic tires is considered to be the main factor responsible for shimmy. Without challenging this thesis, we nevertheless note that this is not the only factor. The shimmy phenomenon can be observed in everyday life in the case of various carriages that often have nothing to do with pneumatics if the wheels are rigid. Below we will show that the theory of polycomponent dry friction fully explains the shimmy phenomenon for absolutely rigid wheels and, hence, is at least one of the factors responsible for shimmy in the general case. The reason why researchers have not taken dry friction into account when explaining shimmy is that the theory of this kind of friction has not been well developed; at the same time one has failed to explain shimmy in the framework of other existing theories.