Bicycle model - vehicle dyanmics

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KPS
KPS
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Joined: Tue Oct 11, 2016 10:20 pm

Bicycle model - vehicle dyanmics

Hi people,

I'm new to this, but was looking for some advice. I started doing some Formula Student work, and currently am looking into some modelling (sim). I am trying to get a basic understanding of the vehicle through the use of a bicycle model.

I understand that I need to find the cornering stiffness but using some input data simulated. But in order to do this do I not need to know the Tire forces? And is this not something calculated through the magic formula (example) which requires the cornering stiffness in the first place...

I am currently trying to set up a bicycle model, just need to fill in the gaps on my knowledge.

Thanks!

Greg Locock
Greg Locock
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Joined: Fri Jun 29, 2012 11:48 pm

Re: Bicycle model - vehicle dyanmics

The cornering stiffness is a property of your tire model. It is the gradient of the lateral force vs slip angle line at your particular Fz (and speed if we are being snarky)

In the absence of any info use 1000N/deg as a plug-in figure. Or else use Fz/(5-10)/deg.

Obviously for a bicycle model the cornering stiffness is the sum of the two wheels on each axle.

KPS
KPS
0
Joined: Tue Oct 11, 2016 10:20 pm

Re: Bicycle model - vehicle dyanmics

Greg Locock wrote:The cornering stiffness is a property of your tire model. It is the gradient of the lateral force vs slip angle line at your particular Fz (and speed if we are being snarky)

In the absence of any info use 1000N/deg as a plug-in figure. Or else use Fz/(5-10)/deg.

Obviously for a bicycle model the cornering stiffness is the sum of the two wheels on each axle.
Are the tire lateral forces not what I should be finding within the bicycle model before ultimately getting the cornering stiffness? So it's the output?

Or is the tire lateral force the input for my bicycle model? So I have to use the magic formula (or similar) in order to find it and the plug it into my model.

Greg Locock
Greg Locock
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Joined: Fri Jun 29, 2012 11:48 pm

Re: Bicycle model - vehicle dyanmics

you need the tire's cornering stiffness to find the vehicle axle's cornering stiffness, I suppose.

Jersey Tom
Jersey Tom
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Joined: Mon May 29, 2006 7:49 pm
Location: Huntersville, NC

Re: Bicycle model - vehicle dyanmics

You do not need a vehicle model to figure out the cornering stiffness of a tire. If you have a tire model, and you know the vertical load on the tire, just exercise your tire model with some small perturbation in slip angle, e.g. +/- 0.1 degrees. (Delta Fy) / (Delta Slip Angle) = cornering stiffness. You can then use that in some linear range analysis in a bicycle model.

Tire lateral forces (and vehicle yaw, etc.) versus time are what you will be getting out of a bicycle model in some dynamic simulation. Cornering stiffness itself, for such a linearized model, is time-invariant.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

KPS
KPS
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Joined: Tue Oct 11, 2016 10:20 pm

Re: Bicycle model - vehicle dyanmics

Great, thank you very much all

Tim.Wright
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Joined: Fri Feb 13, 2009 5:29 am

Re: Bicycle model - vehicle dyanmics

Another thing I'd add is that the bicycle model can take take may forms depending on what you want to model, what information you have available and what you want to investigate.

At the base level is the classical linear, constant cornering stiffness model in Milliken (chapter 5) and Guiggiani. It's the fundamental tool to understand the 6 lateral and yaw derivative gains which are in turn the fundamentals of lateral vehicle handling dynamics. It's the simplest and therefore least precise model but if you don't understand it then you won't understand anything following. The job of a vehicle dynamics engineer is essentially the management of the front and rear cornering stiffness' in every situation and the linear bicycle model represents this in it's purest form.

The linear model can be solved statically without iterations, so you can use simple tools like excel to model it. Any input condition (velocity + steering angle) will only result in one response.

Many people would suggest that the linear bicycle model is useless for motorsport but this is not completely true. You just need to work with it differently. For example if you interrogate your tyre model (I assume you are part of the TTC?) to find the cornering stiffness at say 85% of max lat then you are able to construct a model representative of the vehicle operating at 85% of it's lateral capability (there's a bit more to it than that but the concept is correct).

The next step in complexity is a non linear tyre model. This doesn't necessarily mean a fully parameterised Pacejka model, there are simpler versions of Pacejka (4 parameters) then there is TM-Easy (polynomial based). These are more complicated and generally must be solved in the time domain using a dynamic solver (still feasible in excel though) because the problem is no longer statically determinate - there can be more than one solution to the response of the vehicle to a given input condition (velocity + steer angle).

The non linear models are interesting because they define the peak lateral acceleration capability (which you don't see in the linear model) but more importantly the stability condition of the vehicle in that condition can be calculated by using the instantaneous cornering stiffness of the model in any condition of cornering. At this point your are able to objectify the trade off between grip and stability at the limit.

From there, both the linear and non-linear models can have the front and rear 'tyre curve' modified to include kinematic, compliant and load transfer effects which work to introduce more or less slip on an axle for a certain lateral load which in-turn changes the cornering stiffness. This is also outlined in Milliken. For example roll steer has the effect of increasing (for compression toe-in) or decreasing (for compression toe-out) the cornering stiffness at any point.

One final thing I'd add, which seems to often be overlooked in Milliken, is that the cornering stiffness of an axle depends on the axle's vertical load (it's roughly proportional). So as you move mass or aero loading front and rear, you are changing the cornering stiffness of the axles. This is the reason why cornering stiffness numbers which are not related to a vertical load are useless. You need to find the cornering stiffness' of the FSAE tyres at the vertical load that roughly corresponds to your static weight force.
Not the engineer at Force India

browney
browney
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Joined: Sun Apr 15, 2012 9:13 am

Re: Bicycle model - vehicle dyanmics

Greg Locock wrote:
Wed Oct 12, 2016 3:27 am
The cornering stiffness is a property of your tire model. It is the gradient of the lateral force vs slip angle line at your particular Fz (and speed if we are being snarky)

In the absence of any info use 1000N/deg as a plug-in figure. Or else use Fz/(5-10)/deg.

Obviously for a bicycle model the cornering stiffness is the sum of the two wheels on each axle.

If you have a complex model (IE. An Adams model) can you just add the instantaneous FY/slip angle of the front tyres and rear tyres to calculate this? This would take into account both downforce and lateral load transfer so that the effect of the current tyre load sensitivity from both is taken into account.

I assume you add them arithmetically across the axle like springs in parallel (not springs in series).

joshuagore
joshuagore
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Joined: Fri Feb 12, 2010 3:01 am

Re: Bicycle model - vehicle dyanmics

Large carcass fat tires proved very helpful when I was trying to understand slip moments in the tire/front end of bikes. Fat and mid fat tires have relatively low inflation pressures and their deformation is dramatic so it can be photographed or video taped and analyzed. I was testing zero trail and zero self centering forces and then going extreme with lots of trail etc.. I learned a lot about transitioning from slip into a drift and how the tire springing out of slip can help kick that off like a Scandinavian flick. This was all for fun, but you can learn a lot from large volume bike tires, maybe it doesn't translate but its educational.

The most advanced work I've seen in this area is this work by Jim Papadopoulos, but it often assumes rigid tires. https://www.nature.com/articles/535338a

Greg Locock
Greg Locock
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Joined: Fri Jun 29, 2012 11:48 pm

Re: Bicycle model - vehicle dyanmics

Brownie, yes if you look at your Bundorf compliance budget, usually calculated in the constant radius event, the cornering compliances just add up for each axle.