4569846498
Share Embed Flag
Download ePaper

4569846498

lollypop413
01.05.2017 Views

Tyre characteristics and modelling 273 Camber angle = 0 Aligning moment M z (Nm) F z = 8 kN F z = 6 kN F z = 4 kN φ Aligning moment stiffness = tan φ Slip angle (degrees) F z = 2 kN Fig. 5.25 Plotting aligning moment versus slip angle Spin axis {Y SAE } 1 Camber thrust F y {Z SAE } 1 Resultant force F R Tyre load F z Fig. 5.26 Generation of lateral force due to camber angle the camber thrust will always act in the direction that the tyre is inclined as shown in Figure 5.26. For the SAE system shown here a positive camber angle will produce a positive camber thrust for all tyres on the vehicle modelled in that system.

274 Multibody Systems Approach to Vehicle Dynamics Slip angle = 0 F z = 8 kN Lateral force F y (N) F z = 6 kN F z = 4 kN F z = 2 kN φ Camber stiffness C = tan φ Camber angle (degrees) Fig. 5.27 Plotting lateral force versus camber angle If the tyre is inclined at a camber angle , then deflection of the tyre and the associated radial stiffness will produce a resultant force, F R , acting towards the wheel centre. Resolving this into components will produce the tyre load and the camber thrust. An alternative explanation provided in Milliken and Milliken (1995) compares a stationary and rolling tyre. For the stationary tyre experimental observations of tread in the contact patch indicate a curved shape. As the tyre rolls the tread moving through the contact patch is constrained by the road to move along a straight line, the net reaction of these forces being the camber thrust. Figure 5.27 shows a typical plot of lateral force F y with camber angle for increasing tyre load with the slip angle set to zero. From the plot it can be seen that the camber stiffness C is the gradient of the curve measured at zero camber angle at a given tyre load. In order to understand why a cambered tyre rolling at zero slip angle produces an aligning moment, it is useful to consider the effect of the shape of the contact patch. Consider the situation shown in Figure 5.28 where the wheel and tyre are rolling at a camber angle with the slip angle equal to zero. The lower part of Figure 5.28 is a plan view on the tyre contact patch. The three points A, B and C, shown in Figure 5.28, are initially in line across the centre of the contact patch. If the tyre rolls so that point B moves to B at the rear of the contact patch then the rubber in the centre line is not subjected to any longitudinal stress. Due to the camber the tyre will corner and point A on the inside of the tyre will roll at a smaller radius of bend to point C on the outside of the tyre. If the tyre rubber was not subject to any longitudinal stress these points would move to A and C respectively. If it is assumed that the stiffness of the tyre restricts this and the points remain in line across the rear of the contact patch (A, B and C) then a longitudinal tensile stress acts on the inner A side and a compressive stress acts on the outer C side.

Tyre characteristics and modelling 273<br />

Camber angle = 0<br />

Aligning moment M z (Nm)<br />

F z = 8 kN<br />

F z = 6 kN<br />

F z = 4 kN<br />

φ<br />

Aligning moment stiffness = tan φ<br />

Slip angle (degrees)<br />

F z = 2 kN<br />

Fig. 5.25<br />

Plotting aligning moment versus slip angle<br />

<br />

Spin axis<br />

{Y SAE } 1<br />

Camber thrust F y<br />

{Z SAE } 1<br />

Resultant force F R<br />

Tyre load F z<br />

Fig. 5.26<br />

Generation of lateral force due to camber angle<br />

the camber thrust will always act in the direction that the tyre is inclined as<br />

shown in Figure 5.26. For the SAE system shown here a positive camber<br />

angle will produce a positive camber thrust for all tyres on the vehicle<br />

modelled in that system.

logo

products

Resources

Company

Terms of service
Privacy policy
Cookie policy
Cookie settings
Imprint
Change language
Made with love in Switzerland
© 2024 Yumpu.com all rights reserved

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!