Krempel's friction ellipse
The Krempel friction ellipse , circumferential force-side force map , side force-traction map or frictional connection ellipse is a clear representation of the transmissible longitudinal and side forces of a tire with a combined slip angle and slip .
In contrast to Kamm's circle , the difference in the frictional connection potential can be illustrated in the transverse and longitudinal directions.
Explanation
To simplify matters, the Kamm circle is based on an isotropy of the transmissible lateral and longitudinal forces between tires and road surface. First of all, this means that a tire would achieve the same force level in the transverse direction as in the longitudinal direction. In fact, however, the forces that can be transmitted are direction-dependent. The reasons for the anisotropic behavior are mainly the geometry and the elastic behavior of the tire. These influence the compressive and shear stresses that arise in the contact area between the tire and the road, which in turn are decisive for the maximum transverse and longitudinal forces that can be transmitted. The profile of the tire surface also has an influence on the anisotropy.
The combination of slip angle and slip occurs z. B. when cornering, is braked or accelerated at the same time. The Krempel friction ellipse now shows that with higher lateral forces and the same longitudinal slip, a lower longitudinal force is generated. The same also applies vice versa, since the transmitted longitudinal force is reduced with a greater transverse force (and a greater slip angle) and constant longitudinal slip. In other words, the longitudinal force increases the slip angle requirement for the transmission of the same transverse force and the transverse force increases the longitudinal slip requirement for the same longitudinal force.
This only applies as long as the forces lie within the ellipse. This applies analogously to the Kamm circle, which for simplicity describes the same maximum force in terms of amount in the longitudinal direction as in the transverse direction. However, the Kamm circle does not provide any information on the transverse slip (slip angle) and longitudinal slip that is required for this.
A state in the area of drive slip is shown in red as an example. At around 1.7% slip (longitudinal) and a slip angle of 2 ° (transverse), the force labeled F y can be transmitted in the transverse direction and the force labeled F x in the longitudinal direction. F then represents the total force that can be transferred from the tire to the roadway in the xy plane . The diagram applies to a defined wheel load F z , i.e. H. a separate diagram would have to be created for a different wheel load. For real cornering, which is certainly subject to fluctuations in wheel load, a crumpled friction ellipse would not be sufficient. The internal tire pressure, like the temperature, is assumed to be constant.
The envelope (here with a slip angle of about 8 °) then represents the frictional connection limit for this tire, i.e. the limit of the force that can be horizontally transmitted to the road. Frictional connection means that a normal force (wheel load) can transmit a force in the road surface.
literature
- J. Reimpell, P. Sponagel: Chassis technology: tires and wheels. Vogel-Buchverlag, Würzburg 1986. ISBN 3-8023-0737-2
- Bert Breuer, Karlheinz H. Bill (ed.): Brake manual. Basics, components, systems, driving dynamics. Vieweg, Wiesbaden 2006. ISBN 3-8348-0064-3
- Günther Krempel: Experimental contribution to investigations on vehicle tires. Karlsruhe, 1965
- Hans B. Pacejka: Tire and Vehicle Dynamics. SAE Edition 2006, SAE ISBN 0-7680-1702-5
- Manfred Burckhardt: Chassis technology: wheel slip control systems. Vogel-Buchverlag, Würzburg 1993. ISBN 3-8023-0477-2