Vehicle Dynamics Model

[Pedro]

Hi,

I´ve just developed a vehicle dynamics model using Simulink, but because it has 14 degrees of freedom (dof), I´ve found it hard to find other vehicle models so I can compare the results from mine to other with roughly the same number of dof. I´ve tried several articles, but the models I found were mostly with 2 or 3 dof.

So can anyone give me some suggestions on how to proceed with the model validation.

P.S: Please bare in mind that I´m quite new to vehicle dynamics modeling.

Thanks in advance.

Pedro Silva

[Pedro]

Hi,

I´ve just developed a vehicle dynamics model using Simulink, but because it has 14 degrees of freedom (dof), I´ve found it hard to find other vehicle models so I can compare the results from mine to other with roughly the same number of dof. I´ve tried several articles, but the models I found were mostly with 2 or 3 dof.

So can anyone give me some suggestions on how to proceed with the model validation.

P.S: Please bare in mind that I´m quite new to vehicle dynamics modeling.

Thanks in advance.

Pedro Silva

[HenningO]

I would recommend you to start your validation with hand calculations.

For instance steady state lateral/longitudinal acceleration, calculate load transfer and roll angle and compare it to your simulation results.

14 DOF in Simulink, that's got to be quite the model, I worked on a 7 DOF for my master thesis and I had a handful keeping track of all those lines and blocks!

[Pedro]

Thks for the advise HenningO.

Now I have another problem. While trying to compare my results with results from simpler models (2/3 dof), they all seem to use a simplified Pacejka model for the tires.

I'm using the LuGre model, whitch has different coeficients than those of the above model.
For example, the Pacejka model uses a cornering stiffness parameter, while the LuGre model doesn't have that parameter, it has parameters like the tire stiffness. Is there a relationship between the two models? How should I proceed to compare the two models?

Thks in advance.

Pedro Silva

[RHutch]

The tire model is the most important part of the simulation, most people that have worked on dynamic simulation engines for FSAE cars use the Pacejka model because extensive tire data is available. It doesn't matter how good your dynamic model is (or how many degrees of freedom it has) if your tire model doesn't accurately predict actual tire performance within the desired operating conditions. Checking the validity of the simulation model with simplified models (as mentioned before) is a good start and can be done without a lot of specific vehicle or tire data. Any real validation of the model requires matching, and more importantly predicting, actual vehicle performance. For this you really need access to a complete, well-sorted car with a pretty hefty data acquisition system. You also have to configure the model to match the car as closely as possible with the given set of modeling assumptions. For example, for a real 3d simulation you need the inertia tensor for all rigid-bodies you use in the model. Actually finding values for the tensor for the parts of an existing car is a significant amount of work (and usually involves a big swing and lots of time). In short, validating a complex model is not an easy task. I have been working on a pretty complete model for a couple of years as part of a PhD and am still amazed at the complexity of vehicle dynamics.

[BillCobb]

What Tire properties does your VD model require? Can you work with Spline Toolbox functions? [fnval] If so, I can help you with validation and then correlation. I can supply a 'perfect tire' and a perfect vehicle: one with installed axle sideslip gradients and steering gain. A model with no more than 5 non-zero parameters (speed, wheelbase, overall steering ratio, yaw radius of gyration (or Izz), WF and WR can be predefined such that the computed handling derivatives are specified quantities. Tests run by your simulation should deliver back the installed parameters. Simple Matlab scripts can be run to do frequency analysis of the resulting sim outputs. You will be giving it a chirp (frequency modulated) steer angle input. If your model won't run or produce the expected outputs, its NFG.

If you pass this test, I can show you how to roll your own tire model from the TTC data.

It is also possible to cook up a Pacejka model with the 'perfect' inputs, too, but the Spline functions will be easier to work with now, especially in Simulink.

How do you want to proceed?

[Pedro]

Hi BillCobb,

The parameters that my tire model require are:
-wheel radius;
-mass of the wheel;
-tire stiffness;
-Stribeck exponent;
-Stribeck velocity;
-Kinetic and static contact coeffient;
-moment of inertia about the wheel center;
-longitudinal/lateral rubber stiffness;
-longitudinal/lateral rubber damping;
-longitudinal/lateral rubber viscous relative damping.

The inputs to the model are:
-steer angle;
-input torque.

I dont have a deep knowlegde of the Spline Toolbox, but I can give it a try.


Pedro Silva

[BillCobb]

See if you can turn this spewage into a Matlab file. Look up help for "Publish". Then 'publish' this script. Its a working Matlab routine.
___________________________________________
%% FSAE Primitive Vehicle Dynamics Model Parameters
%
% Bill Cobb

%% Concepts and SWAGS
% The goal is to produce adequate vehicle dynamics to check the test
% and data reduction procedures. I'm providing a 'primitive' vehicle suitable
% for performing the analysis which is a drivable construct.
%
% It is scaled to be on the order of a FSAE car.
% It has predefined front and rear axle sideslip compliances.
% It has 1.000 deg/g of understeer.
% It has a steering gain ('Steering Sensitivity') of 1.67 g/100 deg SWA
% at the test speed.
% It has a sideslip gain of 1.48 deg/g.
% It has a closed form solution for yaw velocity and lateral acceleration
% bandwidth (response time).
% There are no roll dynamics (yet).
% It is linear in all aspects of lateral dynamics.
% There are no tire aligning moments or rigid body aligning moments
% acting on it (Hold onto your shorts: that comes later).
%
% A frequency responce chirp input to the steering wheel for about 20.48
% seconds sampled at 0.01 seconds should give you enough content to
% reduce this model to Bode form. From this, you should be able to
% reproduce all the designated tire properties.
%
% Or else you vehicle model is NFG.

%% Vehicle Specifications
L=1374 % mm
SR=30 % Overall steering ratio
WF=310 % front axle weight (kg)
WR=290 % rear axle weight (kg)
DF=3 % Front axle sidelsip gain (deg/g)
DR=2 % Rear Axle sideslip gain (deg/g)
Speed=100 % kph
% For Yaw inertia, assume iut is a barbell (radius of gyration is 1.00

%% Tire Requirements
% Use Spline representation

slips = [ -10 0 10]
loads = [ -1519.92 -1421.87 ]
fy = [ 5066.743 7109.785; 0 0; -5066.743 -7109.785];

%% Fit Data to a Piecewise Polynomial
% Keep it simple at first.
% A much more complicated tire comes later...
LATE_SLIP_VERT = csaps({slips,loads},fy)

%% Surface Plot of Lateral Force
% Using the spline structure plotter:
fnplt(LATE_SLIP_VERT)

%% Check the Cornering Stiffness
% Compute Partial Dervative wrt slip
CS = fnder(LATE_SLIP_VERT,[1 0])
% Check to see that our required stiffnesses have been installed
cs = fnval(CS,{[-1 1],[-9.8*WF/2 -9.8*WR/2]})

%% Evaluating from Simulink
% All you need to do is use an Matlab Function Block call to get your tire
% data from Simulink with this Parameter:
% fnval(LATE_SLIP_VERT,{u(1),u(2)})
%
% Check it out using this statement from the Matlab Desktop:
plot([0:-.5:-10],fnval(LATE_SLIP_VERT,{[0:-.5:-10],-1520}),'o-')

%% Next Steps
% *Add tire aligning moments
%
% *Add roll dynamics
%
% *Add realistic slip and load dependent nonlinearities.
%
% *Add Camber to the list of independent variables in the tire model.
%
% *Substitute actual FSAE tire data representations for the primitives using
% the same tire model structure representation. (just more extra stuff).
% This can include the Piecewise Polynomial tire model or a Pacejka/MF5.2
% model.
%
%% Change the Input(s) as necessary.
% Run Step, Constant Radius, and Maximum Lateral Acceleration tests to explore
% the nonlinear control regimes.

%% Tire Selection Process
%Finally, use these proceedures to select front and rear tire
% constructions, rim widths and pressures to maximize your car's
% performance.

[Pedro]

Thks for the help. I'll give it a try.