Modelling the tyre as a spring in a quarter car model (Part 2)

[NickTheFill]

TL;DR Summary

Quarter Car Model

Hi all,
I'd like to resurrect an old thread in which the original question is still yet unresolved in my mind.
Simply put, in a simple quarter car model, the tyre can never leave the ground as it is modelled as a spring attached to the ground surface.
In reality however, subject to input, the tyre is free to leave the ground as it is only acting as a compression spring.
I am specifically interested in tyre chatter and would like to develop my modelling skills to further help my understanding. I have only ever developed quarter car models in MatLab and that was five years ago as an undergaduate.
What do you all recommend??
Thanks in advance...

 

[Baluncore]

The tyre material is distorted by road contact, when on the road.
The area of the contact patch changes in proportion to load.
The sidewalls flex, where the belt of the tread contacts the road.
The belt has a constant length, independent of tread wear depth.
The height of the axle above the ground changes with patch area and load.
The axle, hub, and rim, are suspended by sidewall tension from above.
All the above is static geometric analysis.
There are also dynamic effects.
Will you model tyre internal air pressure as being constant?
The speed of sound, in the belt, is dependent on internal air pressure, tension.
At high road speed, low air pressure, standing waves form in the belt.
When the tread contacts the road, at the speed of sound in the belt, the tyre delaminates.

 

[NickTheFill]

The tyre material is distorted by road contact, when on the road.
The area of the contact patch changes in proportion to load.
The sidewalls flex, where the belt of the tread contacts the road.
The belt has a constant length, independent of tread wear depth.
The height of the axle above the ground changes with patch area and load.
The axle, hub, and rim, are suspended by sidewall tension from above.
All the above is static geometric analysis.
There are also dynamic effects.
Will you model tyre internal air pressure as being constant?
The speed of sound, in the belt, is dependent on internal air pressure, tension.
At high road speed, low air pressure, standing waves form in the belt.
When the tread contacts the road, at the speed of sound in the belt, the tyre delaminates.

Thanks, what do you think about my query regarding the tyre being unable to leave the ground (glued to the ground) in a conventional quarter car model?

 

[Baluncore]

The transfer function between the height of the axle above the road, and the axle load, mediated by the contact patch, should allow the tyre to leave the ground.

How else can you study tyre chatter or suspension oscillation?

The problem with leaving the ground, is that the model then becomes non-linear, and you will need to simulate the transient response over time.

 

[NickTheFill]

Ok thanks. The way I see it is that the tyre spring element of the model actually never produces a restoring force pulling the wheel back to ground. This is in contrast to the 2DoF 1/4 car models I’ve worked on in Matlab at undergraduate level.

 

[NickTheFill]

Can this type of non linear analysis be completed using Matlab?

 

[sophiecentaur]

The problem with leaving the ground, is that the model then becomes non-linear, and you will need to simulate the transient response over time.

I would think that any valid model of a tyre in operation should include the characteristics of the dampers. The wheel can leave the road for several wheel rotations when a damper is shot. (I've seen it happen on the Motorway.) Even the tyre itself won't have a linear load / displacement law.