Mechanics of Solids

, Volume 53, Issue 3, pp 249–255 | Cite as

Three Models of Shimmy in Rolling Tasks of a Towed Pneumatic Wheel

  • B. M. ShifrinEmail author


Rolling without sliding of the pneumowheel, towed by means of a rigid device of length L, is considered. The angles of rotation of this device during vibrations are studied. Cases LL* and L > L* are distinguished, where L* is the length at which the system is located at the boundary of stability. To describe the interaction of the running surface of the tire with the supporting plane, three well-known linear rolling models are used — the nonholonomic one, as well as the string and slip models. The case L > L* is studied with the help of reduced mathematical models — modeling oscillators. The main results of the study: all three models indicate the same length L*D/2 (D is the outer diameter of the free tire), in the parameter range studied the first two models actually coincide, with an imbalance of the pneumatic wheel and LL*–which is often found in practice–parametric resonances occur if the Clarke–Dodge–Naibekken numbers DΩ/VA (VA is the speed of the hinge-hitch, Ω is the natural frequency of oscillations when the pneumatic wheel does not roll) belong to the natural series. In addition, the effect of the speed VA on the natural frequency of oscillation is quantitatively described, and comments are made on the verification of shimming models and the relationship of mechanical permanent tires.


shimmy towed pneumatic wheel tire stability limit oscillation 


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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Flight Academy of the National Aviation UniversityKropivnitskiiUkraine

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