p.8 a wheel with tire is barely a wheel;
p.11 there are two distinct contributions to the spin velocity of the rim;
p.11 in a wheel, longitudinal velocities are expected to be much higher than lateral ones;
p.15 the name “self-aligning torque” is meaningless and even misleading;
p.21 rim kinematics depends on six variables, but often (not always) only five may be relevant for the tire;
p.22 a reasonable definition of pure rolling for a wheel with tire is that the grip actions t have no global effect;
p.20 pure rolling and free rolling are different concepts;
p.27 tire slips measure the distance from pure rolling;
p.30 tire slips do not provide any direct information on the amount of sliding at any point of the contact patch;
p.32 tire forces and moments depend on both the camber angleγ and the spin slipϕ.
References
1. Bastow D, Howard G, Whitehead JP (2004) Car suspension and handling, 4th edn. SAE In- ternational, Warrendale
2. Bergman W (1977) Critical review of the state-of-the-art in the tire and force measurements.
SAE Preprint (770331)
3. Clark SK (ed) (2008) The pneumatic tire. NHTSA–DOT HS 810 561
4. Dixon JC (1991) Tyres, suspension and handling. Cambridge University Press, Cambridge 5. Font Mezquita J, Dols Ruiz JF (2006) La Dinámica del Automóvil. Editorial de la UPV, Va-
lencia
6. Gillespie TD (1992) Fundamentals of vehicle dynamics. SAE International, Warrendale 7. Meirovitch L (1970) Methods of analytical dynamics. McGraw-Hill, New York
8. Michelin (2001) The tyre encyclopaedia. Part 1: grip. Société de Technologie Michelin, Clermont–Ferrand [CD-ROM]
9. Michelin (2002) The tyre encyclopaedia. Part 2: comfort. Société de Technologie Michelin, Clermont–Ferrand [CD-ROM]
10. Michelin (2003) The tyre encyclopaedia. Part 3: rolling resistance. Société de Technologie Michelin, Clermont–Ferrand [CD-ROM]
11. Milliken WF, Milliken DL (1995) Race car vehicle dynamics. SAE International, Warrendale 12. Murray RM, Li Z, Sastry SS (1994) A mathematical introduction to robot manipulation. CRC
Press, Boca Raton
13. Pacejka HB (1996) The tyre as a vehicle component. In: 26th FISITA congress ’96: engineer- ing challenge human friendly vehicles, Prague, June 17–21, pp 1–19
References 45 14. Pacejka HB (2002) Tyre and vehicle dynamics. Butterworth–Heinemann, Oxford
15. Pacejka HB (2005) Slip: camber and turning. Veh Syst Dyn 43(Supplement):3–17
16. Pacejka HB, Sharp RS (1991) Shear force development by pneumatic tyres in steady state conditions: a review of modelling aspects. Veh Syst Dyn 20:121–176
17. Popov VL (2010) Contact mechanics and friction. Springer, Berlin
18. Pytel A, Kiusalaas J (1999) Engineering mechanics—statics. Brooks/Cole, Pacific Grove 19. Wong JY (2001) Theory of ground vehicles. Wiley, New York
Vehicle Model for Handling and Performance
In Chap.1vehicle modeling has been approached in general terms. To get quantita- tive information there is the need to be more specific.
As already stated, in the study of handling and performance the road is assumed to be perfectly flat (no bumps) and with uniform features. Typically a good paved road, either dry or wet [1,5].
The vehicle model fulfills all the assumptions listed at p.4, with the addition of:
(1) negligible suspension deflections;
(2) negligible tire vertical deformations;
(3) small steering angles (otherwise, steering axes passing through the center of the corresponding wheel and perpendicular to the road);
(4) perfectly rigid steering system.
Mathematically these additional assumptions amount to having the vehicle always in its reference configuration, as shown in Fig.1.4, with the exception of the steering anglesδij of each wheel (δ11being front-left,δ12front-right, etc.). More precisely, a1,a2,l,t1,t2andhare all constant during the vehicle motion. This is fairly rea- sonable if the motion is not too harsh, that is if accelerations are not too big and do not change abruptly.
Typically, the steering axis (pivot line) is something like in Fig.3.1, with a caster angle and a kingpin inclination angle. Therefore, there are a trail and a scrub radius.
They are key quantities in the design of the steering system. However, their effects on the dynamics of the whole vehicle may be neglected in some cases, particularly with small steering angles and perfectly rigid steering systems (as assumed here).
The net effect of all these hypotheses is that the vehicle body has a planar mo- tion parallel to the road. This is quite a remarkable fact since it greatly simplifies the analysis. Moreover, the wheel centers have a fixed position with respect to the vehicle body. This also helps a lot.
Notwithstanding its (apparent) simplicity, this vehicle model still shows a very rich and interesting dynamic behavior, and has proven to be a valuable tool to cap- ture and understand many aspects of the dynamics of real vehicles. Of course, the M. Guiggiani, The Science of Vehicle Dynamics, DOI10.1007/978-94-017-8533-4_3,
© Springer Science+Business Media Dordrecht 2014
47
48 3 Vehicle Model for Handling and Performance
Fig. 3.1 Steering axis
underlying hypotheses impose some restrictions on its applicability, which a vehicle engineer should be well aware of.