I Motorcycle model and tire force

AI Thread Summary
The discussion revolves around challenges in applying tire forces in a multi-body motorcycle model using Lagrange's equations. The user notes that while the kinematic model is validated, the generalized force from the longitudinal tire force appears to act at the wheel hub rather than the contact point, leading to discrepancies in torque calculations. This issue arises because there are no generalized coordinates linking the wheel hub to the tire contact point, resulting in a loss of torque contribution. Suggestions include incorporating the rotational mass and angular velocity of the wheel to correct the equations. The conversation highlights the need for accurate modeling to account for forces during motorcycle dynamics, especially in different riding conditions.
LucaCaiaffa
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I'm having issues in the application of tire forces while deriving a multi-body model of a motorcycle via Lagrange.

Immagine.png

In particular, I considered several bodies that are: swingarm, main frame,
front upper fork, front lower fork and wheels.

I suppose the wheels to have zero slippage, then knowing the wheel rear torque
as ##T## and the rear radius as ##R_r## we have that ##F_x=T/R_r##

The kinematic model is correct and also forces from suspensions (the model
have been validated).The problem arises from the application point of ##F_x##.
While calculating the generalized force from ##F_x## the rear radius disappear,
meaning that the applied force acts like if it is applied in the center of the rear wheel instead of the contact point of the tire.

This results in same vehicle acceleration but different applied torques, but i don't know how to handle this issue.

I saw that many models found the same problem, but i don't get the point why this appears.

Thank you for your support
 
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The represented force points in the wrong direction.
The pavement-tire contact patch is the fulcrum of a lever.
The chain applied force is at top of the rear sprocket, the reaction force is applied to the axis of the tire, which moves forward, pushing the chassis via swingarm.
 
Last edited:
LucaCaiaffa said:
While calculating the generalized force from ##F_x## the rear radius disappear
What do you mean by "it disappears"?

Lnewqban said:
The represented force points in the wrong direction.
No, it's not if it is the reaction force from the ground acting on the motorcycle.
 
jack action said:
What do you mean by "it disappears"?
I mean that there is no difference in applying the longitudinal tire force in the contact point or in the wheel hub.

This happens because no generalized coordinates relates the wheel hub and the tire contact point, and their jacobians for computing the generalized forces result the same.

For this reason I think I am "losing" a torque contribution in doing this.

Simplifying the problem, if i consider the motorcycle as a unique rigid body, I should have a torque contribution from the longitudinal force as ##T=F_xh## where ##h## is the height of the center of mass.

My model instead seems to lose the radius from the height of center of mass.
 
We will need to see your equation to help you further.

LucaCaiaffa said:
This happens because no generalized coordinates relates the wheel hub and the tire contact point,
I don't have real experience with the Lagrange equation, but can't you include the rotational wheel mass and angular velocity? The wheel angular displacement ##\theta## does relate to the motorcycle displacement ##x## with ##x= \theta R_r##.
 

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