Kamm circle
The Kamm circle or Kamm friction circle (named after Wunibald Kamm ) is a graphic representation of the division of the possible total force on the wheel into the cornering force in the transverse direction and the braking force or drive force in the longitudinal direction of the wheel until the maximum frictional force is reached .
Explanation
The Kamm circle represents the idealized relationship between the longitudinal and lateral guidance force on the wheel of a vehicle. The radius corresponds to the maximum total force available in each case that the wheel can transfer to the road. The maximum frictional force depends on the maximum coefficient of adhesion - influenced by the condition of the road surface and the rolling speed - and the normal force on the wheel. For example, if the coefficient of friction between the wheel and the roadway decreases due to moisture, the total force available is reduced.
If the utilized (= actual) total wheel force approaches the limit value shown in the Kamm circle, the slip initially increases until finally all the tread particles slide in the tire contact area . The slip or the sliding movement basically occurs in the direction of the total force, i.e. H. proportionally also transversely to the rolling direction; If there is no lane guidance, this effect leads to the vehicle breaking out due to understeering or oversteering .
The most important statement of the Kamm circle is therefore that the longitudinal force and the cornering force depend on one another and that the total force resulting from these forces cannot exceed the maximum available frictional force. This follows from the Pythagorean theorem and the parallelogram of forces . In general, when the longitudinal force is increased, less cornering force is available, i.e. the need for cornering force may not be met. Conversely, it is true that maximum acceleration or deceleration in non-lane-guided vehicles is therefore only possible when driving straight ahead.
Although the Kamm circle represents an idealized simplification, it is well suited to explain the basis of the dynamic driving relationships. An extended model, which includes the dependence on the direction of force, is provided by the Krempel friction ellipse . Here u. a. tries to consider circumstances where the maximum circumferential force is greater than the maximum side force, such as B. in cars.
Vehicle technical measures
With mechatronic systems it is possible to largely avoid exceeding the frictional connection limit. With traction control (ASR) and anti-lock braking systems (ABS), the slip on the tire is limited in such a way that the wheels cannot lock or spin. Ideally, this preserves the maneuverability of the vehicle, because attention is paid to a sufficiently high cornering potential.
This state is u. a. not always reached when braking or accelerating in curves. Electronic stability programs (ESP / ESC) have been developed since the 1990s to optimize the longitudinal and lateral forces on the wheel . As an extension of ABS, usually with ASR through ESP / ESC, attempts are made to prevent both oversteering and understeering of a vehicle through targeted (automatic) braking of one or more wheels. In addition to the force distribution between the longitudinal and cornering forces on individual wheels, ESP / ESC also specifically influences the entire yaw moment on the vehicle resulting from these wheel forces .
In (multi-lane) vehicles with all-wheel drive , the acceleration force is distributed over four or more wheels, which improves the overall force distribution. When braking, however, the distributed drag torque of the engine can affect the ABS.
literature
- Horst Bauer (Hrsg.): Kraftfahrtechnisches Taschenbuch. Robert Bosch GMBH. Vieweg-Verlag, Wiesbaden 2003. ISBN 3-528-23876-3
- Hans-Hermann Braess, Ulrich Seiffert: Vieweg manual automotive technology. Vieweg, Wiesbaden 2005. ISBN 3528331143
- Bert Breuer, Karlheinz H. Bill (ed.): Brake manual. Basics, components, systems, driving dynamics. Vieweg, Wiesbaden 2003. ISBN 3-528-03952-3