Tire longitudinal and lateral slip at low speed

[Anna Gul]

Greeting!
I am a research student and am working on vehicle modelling in matlab/simulink. Currently am studying behavior of standing car that how it settles it roll pitch and yaw angle.
While doing so i encountered a problem that how we would deal with longitudinal and slip velocities at low speed that are approaching zero.

longitudinal slip= (r*w- vx)./|vx| lateral slip= -arctan(vy./vx)

Should i ignore the velocities upto some value and let slip be zero. As tire forces are proportional to slip and when i include them the model becomes unstable. and specially the ratio becomes high.

I am stuck in this problem for months please help i found this forum really helpful.

[gruntguru]

Hi Anna. Greg Locock sometimes checks in here. I suggest you post at http://www.eng-tips.com/threadminder.cfm?pid=68

[Anna Gul]

Thankyou dear gruntguru

[rscsr]

Greeting!
I am a research student and am working on vehicle modelling in matlab/simulink. Currently am studying behavior of standing car that how it settles it roll pitch and yaw angle.
While doing so i encountered a problem that how we would deal with longitudinal and slip velocities at low speed that are approaching zero.

longitudinal slip= (r*w- vx)./|vx| lateral slip= -arctan(vy./vx)

Should i ignore the velocities upto some value and let slip be zero. As tire forces are proportional to slip and when i include them the model becomes unstable. and specially the ratio becomes high.

I am stuck in this problem for months please help i found this forum really helpful.

I assume that you are using the slip to calculate the forces on the car with curves like these:

That means once you are above a certain slip level the curve doesn't really change. So I would just use
longitudinal slip= max(200%, (r*w- vx)./|vx|))
And for the lateral slip I would use a small offset for vx to keep the vector generally pointed in the correct direction at small speeds. And atan2 should be way better anyway for this problem.

[Greg Locock]

Let's keep it here

longitudinal slip= (r*w- vx)./|vx|

so your problem is that as vx tends to zero r*w/vx is not a very stable calculation.

For a stationary car that seems to be irrelevant.

[Anna Gul]

Sir rscsr, yes i am calculating forces using slips....sir i agree that after a certain level longitudinal slip is constant and we need to use this formula. But sir what should i do for small velocities as the denominator factor makes it large an like wise we get large force. Should i ignore the slip in some range of velocities??


Respected greg, yes sir i am dealing with small velocities. Actually i wanted to see the settlement of the vehicle when it is at standstill and the small velocities appear because of the initial change of the orientation of the car having roll pitch and yaw angle rate.Sir in the transient phase when the rate of change of roll pitch and yaw angle isnt zero small velocities makes large forces and they are disturbing the response. Sir would you guide what should i do.

[Greg Locock]

Quick answer :if you are on a flat surface set your velocity dependent grip to 0.

Slower answer, so you are dropping the assembled car onto the ground and want to find out how it will 'sit', including the effects of tire grip to stop the wheels moving to their 'natural' position? Obviously they can roll, so use zero longitudinal grip, and just use friction laterally. if the brakes are on use friction longitudinally.

The 200% post above made no sense to me, I think the poster misunderstood the question.

[Anna Gul]

yes sir greg i want to observe that settlement ....sir do you mean that longitudinal slip should be set to zero so that forces in that direction for wheel should be zero?

[Anna Gul]

and sir i want to add the type of suspension is arm like so while settling i think that may change too..sir i want your suggestion and advice.

[DaveW]

I think that Greg is correct. The concept of slip angles requires vx to be non-zero.

One complication is that the tyre lateral stiffness is often neglected in vertical, pitch and roll response calculations. This is not (or should not be) the case when xv is zero (a rotating tyre will tend to reduce the lateral load carried by the tread, a static tyre will not). This has an effect on static rig tests, which show two "roll" modes, one with the centre of rotation below the ground plane (i.e. mostly translation), the other above (i.e. mostly roll).

[gruntguru]

My simplified view of this is, once rolling ceases the problem reverts to basic friction analysis - either dynamic friction if slip is occuring or static friction otherwise. In the static friction case the contact patch is fixed to the road surface and the rest of tyre becomes a 3 axis spring.

So during settling, the contact patch will initially be in static frictional contact with the road. Lateral (and perhaps longitudinal) displacements (due to track and wheelbase changes during suspension deflection) will load the tyre-carcass "spring" until (and if) the static coefficient is reached at which time the tyre will start to skid. Static friction will resume at some point and there will always be some residual lateral force once equilibrium is reached.

[Jersey Tom]

All of this is public domain information. You'll find low rolling speed effects covered under the topics of relaxation length and turnslip.

For a stationary vehicle I'd say just neglect lateral and longitudinal forces altogether and focus on calculation of Fz & Mx

[Anna Gul]

Thankyou respected jersay,gruntgru andDaveW!.... actually i am student fo electrical engg so have little knowledge in this field so thankyou for your concern.

Now all i understood is that the slips are for the vehicles that are already in motion and in stand still condition we need to consider friction and there is also an option to consider forces zero if want to ignore complexity. Even though the weight on the suspension arm is present we would only include vertical force. And this would be enough to settle the vehicle to equillibrium. : ))