 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| B.M. Shifrin, "Three Models of Shimmy in Rolling Tasks of a Towed Pneumatic Wheel," Mech. Solids. 53 (3), 249-255 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
3 |
Pages |
249-255 |
| DOI |
10.3103/S0025654418070026 |
| Title |
Three Models of Shimmy in Rolling Tasks of a Towed Pneumatic Wheel |
| Author(s) |
B.M. Shifrin (Flight Academy of the National Aviation University, ul. Dobrovol'skogo 1, Kropivnitskii, 25005 Ukraine, b_shifrin@mail.ru) |
| Abstract |
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 L≈L* 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 L≈L* - 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. |
| Keywords |
shimmy, towed pneumatic wheel, tire, stability limit, oscillation |
| References |
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|
| Received |
20 September 2016 |
| Link to Fulltext |
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