At limit tire treatment for chassis design

[CHagen]

Most equations for chassis design involve the tires cornering stiffness which is zero at its peak lateral force for a given condition. Just looking in Miliken this zeros out a lot of values if you were designing a neutral car that in theory all tires reached the limit at the same time or if you were analysing a car simply at the lateral force limits at each tire in the conditions being analyzed. This seems unrealistic, partly because it is, but I was curious if there was another type of analysis of design approach for when the tire is not in the neutral region...?

 

[WolfHR]

I don't think the tyre cornering stiffness can be zero at all- it is a constant value for a given tyre and is defined as the initial slope of lateral force vs slip angle graph... It is used for analysis in linear region where Fy can be roughly represented as cornering stiffness times slip angle. In your example, one could say that if cornering stiffness was used that it should be replaced by lateral force over slip angle, but one would/could miss a lot of omitted even if implied simplifications that were used (or may be even that it was somewhere used as derive).

As for limit behaviour, more knowledgeable members than myself should point you in right direction... Substituting this or that in linear range equations would IMHO be a big no-no, because there are simplifications (not often visible at a first glance) involved in linear range equations.

 

[GregLocock]

At the peak of the lat force vs slip graph the cornering stiffness is zero, that is, additional slip angle causes no additional cornering force, and then as you go further the lat force drops.

Milliken's method of moments is a great way of looking at steady state limit handling, and it based on equations.

For limit handling I don't use equations much, mainly simulations. If equations were used all I'd really do is check that the front saturates first, ie that we have limit understeer, but more typically I look at brake in turn, double lane change, throttle on/off in turn, and some other tests. I don't run a simple skidpan test typically, oddly enough.

Cheers

Greg Locock


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[cibachrome]

Try to keep in mind that each axle has a PAIR of tires on it AND has a second axle, also with a pair of tires on it AND that your 'neutral' conditon is more realistically a state of mind and NOT an operational target. There is too much which can disrupt the vehicle's stability, control gain and driver 'pleasability' if you achieved a 'neutral' trim. Plus, the transient response of a 'neutral' car becomes first order: it's sluggish, has low bandwidth and can be knocked off this knife edge by wear, track temperature and proximity to other vehicles. If operated in closed loop control (with 'feeling'), your driver will be worn out almost as fast as trying to drive an oversteering setup. Stop reading books and write and validate a simulation. Old School vs. New School.

 

[CHagen]

Pardon the ignorance, but write a simulation? What exactly do you mean by that?

 

[GregLocock]

He said validate, not write.

However most people seriously interested in vehicle dynamics have written simulators of some form, whether a bicycle model or a 4 wheeled bike, or a full blown multi body dynamics simulator. Since the weakpoint is almost invariably the tire model or data the complexity of the vehicle model on top of it makes surprisingly little difference to the utility of the model.

Milliken's moment method is actually a full vehicle simulation, it's just there are no pretty pictures to keep the managers happy, just one big scary graph.

Cheers

Greg Locock


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