Tire data for suspension design

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koushikatti
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Joined: 20 Nov 2013, 15:01

Tire data for suspension design

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hello,

I am a engineering graduate and have been a part of a formula student team for 2 consecutive years. My area of work in the team was vehicle dynamics. Currently i am trying to use tire data to optimise the suspension and the steering geometry that i designed for the last years car. I do not have any real time track data nor can i rely much on driver feedback , our drivers being pretty unexperienced. I have the tire data of AVON 13X6 tires. I have gone through quie a few articles related to tire data usage and have also gone through the relevant chapters in RCVD (Race Car Vehicle Dynamics by Milliken). Currently i already have a suspension geometry which i want to use as the starting point, the weight distribution, chasses stiffness and other relevent parameters of the car is known to me. For a given lateral accleration i know the vertical loads in eash tire through the lateral load transfer calculations. Now sice all the graphs in the tire data are related to the slip angles my primary concern is to find out a method (through some theoritical calculations) to know the slip angles of the tires for a given lateral acceleration. And this is where i am stuck. Can any one please guide me on how to progress with this?. And also how do i directly relate the slip angle of the front tires with the steering geometry?

Thanks!

Jersey Tom
166
Joined: 29 May 2006, 20:49
Location: Huntersville, NC

Re: Tire data for suspension design

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You the total vehicle mass, the front/rear distribution, and the lateral acceleration - yes? Then you can quite easily determine the lateral force sum of the front tires. The relationship between slip angle and steer angle as a function of wheelbase and yaw rate is in RCVD. From this, and knowing your steering setup, you can back-calculate what the front wheel slip angles should be.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

koushikatti
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Joined: 20 Nov 2013, 15:01

Re: Tire data for suspension design

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@jersey tom Thanks for the quick reply!

In RCVD the relationship beetween the slip angle, yaw rate and wheel base is given w.r.t. the bicycle model. To geometrically apply the same principle to a car model (with four wheel) i think the front and the rear track has to be considered to establish the proper geometrical relation. Also in this case the steering angle (delta) will be different for the left and the right wheel due to the steering geometry. i will start working on it now.

So if i consider a situation where the car is going through a corner of radius R with a constant velocity V. So the velocity of the center of mass of the car will be V, How do i get to know the yaw rate and the Yaw angle (side slip angle of the center of mass) at every instant?

Jersey Tom
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Joined: 29 May 2006, 20:49
Location: Huntersville, NC

Re: Tire data for suspension design

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If you're traveling around a constant radius at constant speed, the yaw rate is trivial to determine, no? It's a function of those two variables only.

You can determine the body slip angle by working out the solution for the rear tires first.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

gorich761
gorich761
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Re: Tire data for suspension design

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To geometrically apply the same principle to a car model (with four wheel) i think the front and the rear track has to be considered to establish the proper geometrical relation.

koushikatti
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Joined: 20 Nov 2013, 15:01

Re: Tire data for suspension design

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Let us say that the car has a lateral acceleration 'a' (steady state cornering) which is equal to V^2/R (V is the speed of the car and R is the radius of the car). So the inertia force at the CM of the car will be Ma (M is mass of the car). Now to balance these forces the tire would generate lateral forces. The front tires total lateral force and the rear tire total lateral force can be found out by the tourque and force balance. The tires would generate these forces due to the slip angle generated. Now considering the rear tire and neglecting the toe effects due to the geometry and chassis roll, the slip angle generated in both the tires would be same (static toe = 0) such that the total force generated by the two rear tires be equal to the rear tire lateral force found out by the torque and force balance previously. So the total force due to the rear tire would be Fr = Cro * alpha + Cri * alpha , where alpha is the rear tire slip angle and Cro and Cri are the tire lateral stiffness of the outside and the inside tires respectively , corresponding to the vertical load on the tires and the camber of the tires at that instant. Am i correct or am i going wrong somewhere? Please correct me. (Initial body slip angle has been considered to be zero )

Jersey Tom
166
Joined: 29 May 2006, 20:49
Location: Huntersville, NC

Re: Tire data for suspension design

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You are very close to correct. However, even with zero static toe and no kinematic effects the inside and outside rear tires will be operating at slightly different slip angles.

Slip angle can be defined as the arctan of lateral velocity over longitudinal velocity. With non-zero yaw rate and track width, there will be some influence on the longitudinal velocity of inside vs. outside tire.

For such a simple case as this you can perhaps neglect it, but worth thinking about for completeness.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

koushikatti
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Joined: 20 Nov 2013, 15:01

Re: Tire data for suspension design

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@Jersey... Thanks for the reply.
So now taking into account static toe and the rool steer (the toe introduced in the rear tires due to the chassis roll). if i consider the toe angle of the outer tire to be TAo and the toe angle of the inner tire as TAi (taking the toe angle sign according to the vehicle axis system) , then the slip angle introduced in the inner tire would be (alpha + TAi) and that of the outer tire woould be (alpha+TAo), where alpha is the slip angle that would have been developed had there been no rool steer and no static to in ot toe out.
In a similar case for the front tires if the toe intorduced in the inner tire be DELTAi and that of the inner tire be DELTAo, then the slip angle introduced in the inner tire would be alpha+DELTAi and that of the outer tire would be alpha+DELTAo (alpha being the abgle that would have been introduced had there been no steering input and the geometrical effects of roll steer being neglected).
The assumption made is that the vehicle side slip angle is zero ( the vehicle enters the corner tangent to the radius of the turn)

Is this what has to be considered in trying to predict the vehicle performance in skid pad test at constant throttle? or am i missing out on something?

Greg Locock
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Joined: 30 Jun 2012, 00:48

Re: Tire data for suspension design

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That sounds roughly right but I am a little nervous about "The assumption made is that the vehicle side slip angle is zero" as the vehicel side slip and that of the rear axle are very closely connected. Which vehicle dynamics book are you using? Reichell and Stompf, and RCVD, go through this in some detail.

koushikatti
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Joined: 20 Nov 2013, 15:01

Re: Tire data for suspension design

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@Greg.. I am following RCVD. I have gonr through the revelent chapters of it but could not find much on deteriming the slip angle of the front and rear tires given the steering input, lateral acceleration and vehicle side slip angle(more preciesly the direction of approach of the vehicle relative to the radius of curvature of the corner).Here is what i am trying to do:
1. Find the lateral accn from the vehicle velocity and the radius of the turn
2. Find the total front axle and the rear axle force to generate the required lateral accn (found out by force and torque balance about the CM of the car.
3. Determine lateral load transfer due to the lateral acceleration by considering roll stiffness distribution, roll axis height etc, and hence the vertical load in each tire.
4.The required front and rear axle force would be generated by the inner and the outer tires of the front and the rear axle
5. Slip angles would be induced in the tires in such a way that in each axle the sum of inner and outer tire force due to slip angle would be equal to the axle force found out in STEP 2.
6.So given the vertical load , the camber angle and the toe-angle (steering angle + the toe induced due to body roll and static toe) for each tire the task is to find the slip angle that each tire generates to satisfy STEP 5 (And this is where i am getting stuck)
7.After determining the lateral forces and slip angle of each tires the vehicle understeer/oversteer , maximum speed in the turn etc can be found out.
About the vehicle side slip angle to be zero , i have considered that the direction of vehicle approach in the turn is tangential to the corner, and hence vehicle side slip angle will be zero
If you know any particular chapter / article in RCVD or any other link that addresses this issue please let me know.

Thank you!

Jersey Tom
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Joined: 29 May 2006, 20:49
Location: Huntersville, NC

Re: Tire data for suspension design

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koushikatti wrote:1. Find the lateral accn from the vehicle velocity and the radius of the turn
2. Find the total front axle and the rear axle force to generate the required lateral accn (found out by force and torque balance about the CM of the car.
3. Determine lateral load transfer due to the lateral acceleration by considering roll stiffness distribution, roll axis height etc, and hence the vertical load in each tire.
4.The required front and rear axle force would be generated by the inner and the outer tires of the front and the rear axle
5. Slip angles would be induced in the tires in such a way that in each axle the sum of inner and outer tire force due to slip angle would be equal to the axle force found out in STEP 2.
6.So given the vertical load , the camber angle and the toe-angle (steering angle + the toe induced due to body roll and static toe) for each tire the task is to find the slip angle that each tire generates to satisfy STEP 5 (And this is where i am getting stuck)
Solve for the rear axle slip angle first, by itself. That should be easy enough. Once you know the rear slip angle and knowing the yaw rate, you can solve for the body slip angle. Once you know the body slip angle, solve for the front axle slip, and you can determine the front steer angle.

Really all of this is contingent on the assumption that the front steer angle is important to know. Maybe it is, maybe it isn't - that's up to you. But if all you want to know are steady state tire/wheel slip angles... front steer isn't really important (other than for Ackermann effects and weight jacking / camber change with steer... but that's getting into secondary stuff).
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

koushikatti
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Joined: 20 Nov 2013, 15:01

Re: Tire data for suspension design

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@jersey are the front tires slip angle (the inner and the outer tire) a function of the steer angle as well ?I think so it is but i am not sure.

koushikatti wrote:@Jersey... Thanks for the reply.
So now taking into account static toe and the rool steer (the toe introduced in the rear tires due to the chassis roll). if i consider the toe angle of the outer tire to be TAo and the toe angle of the inner tire as TAi (taking the toe angle sign according to the vehicle axis system) , then the slip angle introduced in the inner tire would be (alpha + TAi) and that of the outer tire woould be (alpha+TAo), where alpha is the slip angle that would have been developed had there been no rool steer and no static to in ot toe out.
In a similar case for the front tires if the toe intorduced in the inner tire be DELTAi and that of the inner tire be DELTAo, then the slip angle introduced in the inner tire would be alpha+DELTAi and that of the outer tire would be alpha+DELTAo (alpha being the abgle that would have been introduced had there been no steering input and the geometrical effects of roll steer being neglected).
The assumption made is that the vehicle side slip angle is zero ( the vehicle enters the corner tangent to the radius of the turn)

Is this what has to be considered in trying to predict the vehicle performance in skid pad test at constant throttle? or am i missing out on something?

Jersey Tom
166
Joined: 29 May 2006, 20:49
Location: Huntersville, NC

Re: Tire data for suspension design

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koushikatti wrote:@jersey are the front tires slip angle (the inner and the outer tire) a function of the steer angle as well ?I think so it is but i am not sure.
Yes and no. It may be more useful in this case to think of it as.. the steer angle is a function of the front tires slip angle, rather than the other way around.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

koushikatti
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Joined: 20 Nov 2013, 15:01

Re: Tire data for suspension design

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Jersey Tom wrote:
koushikatti wrote:@jersey are the front tires slip angle (the inner and the outer tire) a function of the steer angle as well ?I think so it is but i am not sure.
Yes and no. It may be more useful in this case to think of it as.. the steer angle is a function of the front tires slip angle, rather than the other way around.
So you mean to say that first the slip angle of the front tires have to be determined (so that it generates the required force for force and moment balance for uniform circular motion) , and after determing that the slip angle, the steer angle has to be determined to generate that slip angle and simultanously to maintain the uniform circular motion. Is it so?

Jersey Tom
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Joined: 29 May 2006, 20:49
Location: Huntersville, NC

Re: Tire data for suspension design

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koushikatti wrote:and after determing that the slip angle, the steer angle has to be determined to generate that slip angle?
That is a choice you have to make. What do you need the steer angle for? If you are working out steering ratios etc. then yes you could do that as your final step. But if you just want to know what your tire states are, then you might be able to skip that.

There are several ways of doing this. As an engineer you need to have some creativity and get used to choosing or making your own approach. In the working world you will not be handed a step-by-step list of how to solve a problem.

Another option you could have here would be to write out a math function which returns the lateral force and yaw moment at any given combination of steer and body slip angle.. then use a solver to vary those two variables until you converge on a solution which hits your target lateral and reduces yaw moment to zero.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

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