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2023 | OriginalPaper | Chapter

2. Mechanics of the Wheel with Tire

Author : Massimo Guiggiani

Published in: The Science of Vehicle Dynamics

Publisher: Springer International Publishing

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Abstract

All road vehicles have wheels and almost all of them have wheels with pneumatic tires. Wheels have been around for many centuries, but only with the invention, and enhancement, of the pneumatic tire it has been possible to conceive fast and comfortable road vehicles [5].

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previous chapter Introduction
next chapter Vehicle Model for Handling and Performance
Footnotes
1
Only in competitions it is worthwhile to employ special (and secret) gas mixtures instead of air. The use of nitrogen, as often recommended, is in fact almost equivalent to air [18], except for the cost.
 
2
As pointed out by Jon W. Mooney in his review, in Noise Control Engineering Journal, Vol. 62, 2014, the explanation and the figure provided in the first edition of this book were not correct. A similar (incorrect) explanation has appeared in [9, Fig. 1.19], published in 2017.
 
3
A rigid wheel is essentially an axisymmetric convex rigid surface. The typical rigid wheel is a toroid.
 
4
\({\textsf{S}}_w\) is the system recommended by ISO (see, e.g., [20, Appendix 1])
 
5
In the SAE terminology, it is \(\omega _c \,\textbf{j}_c\) that is called spin velocity [6, 16].
 
6
The two symbols \(\mathbf {V\!\!\,}_o\) and \(\mathbf {V\!\!\,}_O\) are equivalent. Using \(\mathbf {V\!\!\,}_o\) is just a matter of taste.
 
7
What is relevant in vehicle dynamics is the moment of \((\textbf{F}\!,\textbf{M}_O)\) with respect to the steering axisof the wheel. But this is another story (Fig. 3.​1).
 
8
More precisely, it is necessary to have a mathematical description of the shape of the road surface in the contact patch. The plane just happens to be the simplest.
 
9
We remark that, as discussed in Chap. 11, steady-state kinematics of the rim does not necessarily implies steady-state behavior of the tire.
 
10
We have basically a steady-state behavior even if the operating conditions do not change “too fast”.
 
11
As a general rule, a subscript or a superscript r means “pure rolling”.
 
12
However, in the brush model, and precisely on Sect. 11.​1.​5, the effect on C of the elastic compliance of the carcass is taken into account.
 
13
All other angles are positive angles if measured counterclockwise, as usually done in mathematical writing.
 
14
Once again, we called tire slips what should be called rim slips.
 
15
In a step steer the steering wheel of a car may reach \(\omega _z={20}^{\circ }\)/s=0.35 rad/s. At a forward speed of 20 m/s, the same wheels have about \(\omega _c=\) 80 rad/s. The contribution of \(\omega _z\) to \(\varphi \) is therefore like a camber angle \(\gamma \simeq {0,5}^{\circ }\).
 
16
\(\sin (C\uppi /2)=\sin ((2-C)\uppi /2)\), since \(1<C<2\).
 
Literature
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2.
Bakker E, Pacejka H, Lidner L (1989) A new tire model with an application in vehicle dynamics studies. SAE Trans 98:101–113
3.
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4.
Bergman W (1977) Critical review of the state-of-the-art in the tire and force measurements. SAE Trans 86:1436–1450
5.
Clark SK (2008) The pneumatic tire. NHTSA-DOT HS 810 561
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Michelin (2002) The tyre encyclopaedia. Part 2: comfort. Société de Technologie Michelin, Clermont–Ferrand, [CD-ROM]
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NHTSA (2009) The effects of varying the levels of nitrogen in the inflation gas of tires on laboratory test performance. Report DOT HS 811 094, National Highway Traffic Safety Administration, Washington
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Pacejka HB (1996) The tyre as a vehicle component. In: 26th FISITA congress ’96: engineering challenge human friendly vehicles, Prague, June 17–21, pp 1–19
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Pacejka HB (2002) Tyre and vehicle dynamics. Butterworth-Heinemann, Oxford
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Pacejka HB (2005) Slip: camber and turning. Veh Syst Dyn 43(Supplement):3–17CrossRef
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Pacejka HB (2012) Tire and vehicle dynamics, 3rd edn. Butterworth-Heinemann, Oxford
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Pacejka HB, Sharp RS (1991) Shear force development by pneumatic tyres in steady state conditions: a review of modelling aspects. Veh Syst Dyn 20:121–176CrossRef
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Purdy JF (1963) Mathematics underlying the design of pneumatic tires. Edwards Brothers, Ann Arbor
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Pytel A, Kiusalaas J (1999) Engineering mechanics-statics. Brooks/Cole, Pacific Grove
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Zegelaar P (1998) The dynamic response of tyres to brake torque variations and road unevenesses. Delft University of Technology, Delft
Metadata
Title
Mechanics of the Wheel with Tire
Author
Massimo Guiggiani
Copyright Year
2023
Book
The Science of Vehicle Dynamics

Print ISBN: 978-3-031-06460-9

Electronic ISBN: 978-3-031-06461-6

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-3-031-06461-6_2

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