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I'm trying to wrap my head around the question: "what is the optimal slip ratio and how do I go about controlling it?". I'm working on a control strategy for an electrical vehicle. The issue I'm facing is that of maximizing traction. The way I can measure slip ratio is by measuring difference between wheel velocity and vehicle velocity (both of which let's assume are measured separately).

Now, what I need to do (I think) is to figure out a way to maximize traction by always keeping the slip ratio at some specific value. But what value? Also it seems wrong to always try to keep wheel speeds at an offset from vehicle speed. I suppose I only should be doing this during acceleration/deceleration? How can I do this in a generic way without having to implement different strategies for accel/decel?

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  • $\begingroup$ Will it depend on the purpose? max accel may be at slip=0, but max delivered power may be at slip =10% $\endgroup$
    – Solar Mike
    Oct 23 '18 at 10:35
  • $\begingroup$ "Optimal" according to what metric? In most general applications optimal slip will be 0 as it minimizes the wear of the tire by a huge margin, while still providing excellent traction, acceleration and power delivered. The little gains achievable by increasing it (anywhere) above 0 as per Chris John's answer, are almost never worth reducing the lifetime of the tire by a couple orders of magnitude. Exception may be motor sports, $\endgroup$
    – SF.
    Nov 23 '18 at 11:54
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Ultimately it is empirical.

For absolution maximum traction rubber tyres tend to deliver maximum grip in a fairly narrow window in the transition between purely static friction and full sliding friction.

This is very contextual and will depend on tyre construction and chemistry as well as tyre temperature and the nature and surface properties of the pavement.

F1 teams expend vast resources in understanding this and need to do it again form scratch for each track they go to and it can all go out of the window if the weather changes even slightly.

So for a road car you need to be fairly conservative. It is certainly possible that some sort of machine learning approach could provide adaptive control based on the conditions but in terms of traction the conservative approach is to aim to have zero slip. If noting else this will be safer for normal driving.

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  • $\begingroup$ I'm trying to solve the problem of traction loss - ie when a tire experiences high acceleration rate I want to design a controller that would keep the tire from spinning out yet still keep acceleration at maximum and also to do so with decent precision. I want to maximize traction taking into account weight transfer and while being adaptive enough to deal with varying grip. $\endgroup$
    – Martin
    Oct 24 '18 at 11:09
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If you want to design a performance tire just for best traction, just before slippage and are not at the moment concerned with endurance, heat control, and many other factors, first you need to select quality material rubber which is soft and will leave a sacrificial black track under high acceleration when it heats up. Fusing the tire to the road.

like the revving drag cars do to turn the surface of tire to a highly sticky goo.

Also you tires structure has to be layered in concentric rings and build gradually from the first adhesive layer designed for ultimate grip, to more and more tougher layers to have both strength and elasticity to transmit the power of drive shaft to the skin layer while providing adequate play to give the skin time to adjust gently to power jerks of the engine and the road.

Also the walls of the tire have to be designed not to wrinkle or yaw at power step ups or sharp turns.

Experienced drivers know the trick of driving on icy road without skidding, easy does it, no sudden accelerations or breaks! A good tire does this naturally, while maintaining a tight grip, it allows the engine to power up and down and the car take turns without losing grip, by letting the sanwitched layers take the impact.

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  • $\begingroup$ I'm trying to create the most efficient control of the tire (ie I'm working on electric motor control and what I want to do is maximize the traction with existing tire such that acceleraiton can be maximized to the point just before loss of traction due to too much torque being applied). $\endgroup$
    – Martin
    Oct 24 '18 at 11:07
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Ended up not worrying about slip and instead just making sure the tires don't spin out by synchronizing their velocity but without forcing them to spin at the same velocity (ie I implemented coupling). Now slip is held at optimal value by the very nature of this control strategy.

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  • $\begingroup$ This does not answer your question. It needs to be added to your question as an edit & marked as such. $\endgroup$
    – Fred
    Nov 29 '18 at 12:26
  • $\begingroup$ It does actually because if you synchronize velocities by correcting wheels that have lost traction against wheels that have traction then you automatically optimize slip. This solution indirectly keeps slip at a value that generates optimal traction. $\endgroup$
    – Martin
    Dec 11 '18 at 20:31

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