Delay - yaw velocity to lateral acceleration 1

[GregLocock]

I haven't checked Gillespie yet.

In steady state circular cornering lateral acceleration is directly related to the yaw velocity:

LatAcc=tangential velocity * YawVelocity

However, in dynamic events, eg slow sinusoidal sweep of steering wheel angle, there is a phase delay between the two. I cannot wrap my head around this - is it due to Coriolis acceleration? That is given by radialvelocity*yawvelocity*2. typically we are looking at slip angles of say 0.25 degrees, so that would be tangential velocity*0.25/57.3*yawvelocity*2, which is in the right ballpark, but I don't like it.

Or is it the intuitively appealing argument that the yaw has to 'build up' before the lateral acceleration can increase?






Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[notnats]

Hmmm. Not my area so I hesitate to comment, but will the lateral acceleration not reach a maximum until the maximum slip angle is reached, so there will be a delay between yaw velocity and lateral accn? Will body roll play a part?

Is it analagous to a slalom skier? While the skis are unweighted they are experiencing a high yaw rate, but lateral acceleration is negligble until the edges are carving the turn.

What is the 1/57.3 factor in the slip angle equation?

Jeff

 

[NormPeterson]

If [YawVelocity] is a sine function over time with [TangentialVelocity] remaining constant, doesn't that also make [RadialVelocity] a function of time (that can be expressed somehow in terms of [YawVelocity]? The product of the two may not peak at the same time as either taken individually.

I'm thinking along the lines of acceleration being dv/dt, and if v is a sine function, acceleration would be some cosine function, (or a sine function with a phase angle).
Or maybe I'm all wet . . .

Norm

 

[shanba]

I would think its due to the elasticity of the system. If it were rigid, the delay would be much less.

 

[SusTestEng]

"I would think its due to the elasticity of the system. If it were rigid, the delay would be much less."

Shanba gets a star for that!

Greg, the reason for the delay is compliance related. In a steady-state corner the compliance of the suspension is already near it's designed elastic operating limit. But when the car is in a slalom type situation it has to travel through the compliance before it can reach it's lateral limit, causing a delay. In laymen's terms: the bushings have already "set" during a constant radius, while they need time to "set" during a transition. The car is not a rigid body in an ideal situation, so it doesn't act as math would suggest. As Shanba mentioned, if you would fun the same tests on say an F1 car, the results would be MUCH different, as they basically only have the compliance of the tire,and localized rigidity of the cabon tub to deal with.

 

[notnats]

I think we are all saying much the same thing, there is probably a time constant in the elasticity of the system. .... and after a night's sleep I realised that 57.3° is a radian

Jeff

 

[shanba]

Another factor I think is this. The front tires create the initial yaw moment on the sprung mass. Before the lat accel is present, the rear must react this change in direction request from the front. Once the rear starts to react this yaw moment, then the sprung mass accelerates at the given turn radius. Compliance just slows all these responses down.

 

[SusTestEng]

Then you have to ask, what is the result of 4-wheel steering in a similar situation? If the lateral acceleration response is much better, then shanba's assumption also holds some merit.

 

[Aday]

Shanba is correct, lateral acceleration can not occur until the vehicle has begun to assume a sideslip angle which creates rear tire slip angles and resultant force. One of the key motivations for active rear wheel steer is reducing the phase lag between yaw yelocity and lateral acceleration. Simulations and hardware testing on 4WS vehicles has verified this fact.

 

[shanba]

Rear steer effects are designed into pass car IRS suspension through bushing tuning to get a similar response. The range of tunability just isn't as great as the 4WS system, obviously.

 

[GregLocock]

OK, so here's the experiment. If I multiply all the compliances in the system, and the tyre cornering stiffness, by a factor of 4 then I should reduce the delay time by half.

Incidentally I'm a bit disappointed by statements like " it doesn't act as math would suggest"

I didn't make those equations up. Mr Newton did. If you measure the properties at a point, whether it is in the middle of a bowl of jelly, or a block of steel, they still apply.







Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[SusTestEng]

"Incidentally I'm a bit disappointed by statements like " it doesn't act as math would suggest"

I didn't make those equations up. Mr Newton did. If you measure the properties at a point, whether it is in the middle of a bowl of jelly, or a block of steel, they still apply."

I am saying that the system you are describing does not fit your mathmatical model you laid out. When the car is in a constant radius turn, it is basically at a steady state, therefor your model applies! BUT, when the car is in dynamic event, you have damping(from the compliance) that does not allow your model to hold true. So, factor in the yaw damping of the vehicle and it should then make more sense.

I can ask Gillespie if you really want a very direct answer, my friend works under his direction at Carsim.

 

[SusTestEng]

OK, I went back and read the original post and I think you are very close. I would have to think that Coriolis acceleration plays a factor. It must, because the radius is either increasing or decreasing during a slalom, therefor the center of the radius is moving and not constant like it would be during a constant raius turn. I still think compliance may be the slight part that is missing, either in the form of damping, or body roll. I say body roll, because your CG will be moving as the body rolls toward the outside of the radius, and not staying fixed like that of a block of steel or gokart or F1 car.

 

[notnats]

Isn't coriolus acceleration applicable to a frame of reference rotating about a fixed axis, such as the world, or a merry go round? So solving this as a coriolus problem with a constantly changing axis sounds like hard work.

Assuming that the contact patch is not slipping and is describing a sinusoidal motion, and that the phase shift is due to the elasticity of the tyres/suspension/driver's seat, is this not very similar to a vehicle driving over a series of sinusoidal humps?

Surely you suspension guys have got spreadsheets to cover this.

On the back wheels following the front wheels concept, if you drive a forklift, the initial lateral acceleration at the driver's seat is negative.

 

[Aday]

"OK, so here's the experiment. If I multiply all the compliances in the system, and the tyre cornering stiffness, by a factor of 4 then I should reduce the delay time by half."

I don't think this experiment would hold true. A vehicle's dynamic behavior can be simplified as classical 2nd order dynamic system with a spring, mass, and damping term. Milliken's book has a derivation of the equations. In any case the phase lag between yaw and lateral acceleration is not a simple linear relationship with compliance. These equations can easily be programed into Matlab if you want to play around with them.

 

[Tmoose]

Might be another complication here - In my moderately new copy of "Race Car Engineering & Mechanics" Paul Van Valkenburg devotes a few paragraphs to varying traction/slip angles phenomenon documented during cornering and braking. His suspicion/conclusion is it is related to tire tread temperature, and has a few charts showing race tire tread temps changing a lot in 2 seconds, and some eye witness commentary of the tread appearance varying while entering a corner, and being related to how ready-to-work the tread is.