Modeling of Wheel Rolling Resistance

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I person been moving connected longitudinal tyre exemplary for a while and perpetually brushwood problems pinch nan formulation of rolling resistance. Consider 1 instrumentality exemplary coming down from a damp. It is simply a 2DOF strategy (V and omega). The FBD of nan problem is arsenic such:Free Body Diagram

Defining +x on down nan damp leads to Newton's equation: m * g * sin(beta)-F_c=m*V_dot.

Defining +omega on down nan damp leads to equation: F_c * R=J * omega_dot.

Define F_c: m * g * mu_k * cos(beta).

Above equations create specified a situation: The wide starts rolling and ever accelerates, which is not physically meaningful. After a while it should spell astatine changeless speed.

To do so, I adhd rolling guidance arsenic Pajeska's suggestion:

F_r = (q_0 + q_1*abs(V/Vc) + q_2(V/Vc)^4) * N

Adding rolling guidance arsenic above, I get this situation: The wide starts rolling pinch mini gaffe arsenic expected, past it reaches its maximum linear speed; however, it starts spinning! For, I selected application constituent of rolling guidance arsenic interaction point, which is again Pajeska's suggestion.

So my questions are:

  1. what should beryllium nan exertion constituent of rolling guidance and why?
  2. does angular velocity (omega) impact rolling resistance?
  3. what will beryllium guidance of rolling resistance, inverse of V aliases omega?
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