Hi everybody,
I have a question about the circle of friction or Kamm circle. This circle is used in vehicle modelling, but I did not understand this well. I say my own opinion, please let me know if I am mistaken.
vehicle friction force at tire contact patch divided into two forces, lateral and longitudinal forces. As the coefficient of friction is u and the normal force is N, then the maximum of friction force is F_tot = uN. Now F_tot is the radius of the Kamm circle (?), then F_x and F_y are longitudinal and lateral forces, so ( F_x^2 + F_y^2 )^0.5 is lower or equal to F_tot.
If I was right, please tell me what is the use of Kamm circle?
Thanks in advance.
Hi Arash Marashian
F_tot is equal to tow thing. first one is uN and another one is ( F_x^2 + F_y^2 ) ^0.5. usually in dynamics you need to know friction diction, Kamm circle do this for you . in this case you don't know some force direction in DOF, as well as friction and motor force, but you know which path should be pass. in this case you know ratio of lateral and longitudinal force need to pass path. then with Kamm circle can compute forces.
Best Regards
i think there are two types of friction forces in two different directions and the total force is the resultant so read this article
https://arxiv.org/ftp/arxiv/papers/1008/1008.5041.pdf
Mohammad Hossein Rasti and Mohamed Elgohary
Thanks for your answers.
Friction circle (based on the assumption that a tire can develop equal limiting longitudinal and lateral forces) gives you:
- The maximum longitudinal force that the tire can develop while it is developing a specified lateral force, or
- The minimum lateral force that the tire can developed while it is developing a specified longitudinal force.
Consequently, the maximum longitudinal force in the absence of lateral force generation and the maximum lateral force in the absence of longitudinal force will both be equal to adhesion coefficient*normal tire load.
For tires developed for emphasized traction or cornering capability, "friction ellipse" may be more suitable.
Please note the correction in the previous answer:
Friction circle (based on the assumption that a tire can develop equal limiting longitudinal and lateral forces) gives you:
- The maximum longitudinal force that the tire can develop while it is developing a specified lateral force, or
- The maximum (not minimum as in the previous answer) lateral force that the tire can develop while it is developing a specified longitudinal force.
Consequently, the maximum longitudinal force in the absence of lateral force generation and the maximum lateral force in the absence of longitudinal force will both be equal to adhesion coefficient*normal tire load.
For tires developed for emphasized traction or cornering capability, "friction ellipse" may be more suitable.
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